The Mind as a Mathematical Function

The Mind as a Mathematical Function: How our perceptions are image representations of what truly is and how we can never have any knowledge of the thing in itself.


Hang with me, this is going to be great!

In mathematics, a function is defined as a mapping from one set of elements, to another, where every element of the first set is mapped to a single distinct element of the second set.

Here is a little figure to visually represent what a function is. (For now, forget what a bijection is)

Fig 1


Above in Fig. 1 we have two ‘sets’, as depicted by the circles, and each set contains ‘elements’ (i.e. things). The first set contains five elements, each being a distinct shape. The second set contains five numbers, each being distinct. The figure satisfies the definition of a function because EVERY element (shape) from the first set is mapped (i.e. “used”), and there does NOT exist an element in the first set (i.e. a shape) that is mapped (as depicted by the arrow) to more than one element in the second set (i.e. there doesn’t exist any shape that has two or more arrows coming from it).

So, again, a mathematical function is a mapping of ALL the elements from one set, to the elements of a second set, where only one distinct mapping occurs for each element from the first set.

Fig. 2

In Figure 2 we see that this is NOT a function. Do you see why? It is because one of the elements from the first set (‘0’ from input) is mapped to more than one element in the second set(‘-2’ and ‘1’ in the output).

Mathematics, and any field of study, is filled with jargon, language and definitions. I would like to provide some terminology before continuing. The “first set” from which the function does the mapping, is called the “domain”. The elements within the domain are called the “pre-images”. The second set, to which the function does the mapping to, is called the “co-domain”, and the elements within it are called the “images”.

Using our new found vocabulary, we can see from Figure 1 that the domain of the function is a set of shapes, and the co-domain is a set of numbers. We can also say that, for example, the image of the star, with respect to the function, is the number 1. As well, we can say that the pre-image of the number 1 is the star shape (with respect to the function).


Now, most of us, when we think of functions in terms of math, think of something like this:

Fig. 3



Figure 3 depicts a graph of a function y= x (squared). The domain is the set of real numbers, and the co-domain is also the set of real numbers. For any given element in the domain (i.e. any given pre-image), there exists one and only one element in the co-domain (i.e. image) that it is mapped to. An example would be mapping x = 0, to y = 0 (since y = 0 (squared), and 0 squared = 0, therefore y = 0). So in this function, 0 maps to 0, and 1 maps to 1, and 2 maps to 4, etc, etc, as depicted by the graph.

Now, when we draw graphs and figures, as presented above, we can see what elements exist in the domain (the first set) and what elements exist in the co-domain (the second set). We see the pre-images and the images. But in real life not all functions work like this.

Fig. 4



A function that we can DEFINE is perhaps not always common in real life. Figure 4 shows another function. Here, we have inputs, and the function (“function machine”) acts like a black box, and just gives us the outputs, though we may not know how the function did so. Perhaps the person that engineered the function machine knows (if such a person exists), but we often do not.

We surround ourselves with machines that are functions. For example, a tv remote. One function on the remote is the volume up button. If I press the volume up button, it maps to a distinct event, that being the audio output of the tv increases by a single interval. If, for example, sometimes when I clicked on the volume up button the volume went up by 5 intervals, or down by one, or it caused the tv to change channels, or all together, this would not be a function, as the single input (pre-image/element “up button press”) would map to different things (image/element tv channel change, etc, etc). Now, for most of the population, the tv remote is a black box function. We don’t know how this mapping works, we only know that it does it. But somewhere, someone out there does know.

In both the mathematical graph examples and the tv remote examples we were aware and had knowledge of both the inputs (pre-images) and the outputs (images) of the functions. Is there not instances of when we are ONLY aware of the outputs (images) of a given function?

Let’s say I had a graph, or a table containing the coordinates of a graph available to me. And suppose I was with someone who didn’t have access to such a graph or table. Perhaps I am with you, and you are that person. Suppose I were to read to you all the images of a given function, such as the one from Figure 3. Suppose I skipped out the decimal numbers and only listed the integers (whole numbers) starting from 0, that were images (y values) of the function y = x (squared). Suppose I read them in increasing order. I would say “zero, one, four, nine, sixteen, twenty five…”. Now, reading them in order, and only having information of the images of the function you MAY be able to deduce what the actual function is, and in doing so, what the pre-images might be. “AHA! Each number you mention is the square of a number… so the pre-images are zero, one, two, three, four, …. “.

But what about the function from the Figure 1? Listing to you the images “one, two, three, four, five”, you might infer any number of functions, and thus any number of pre-images. It would be highly doubtful, though possible, that you may be correct in hypothesizing that the pre-images were distinct geometric shapes. But that would simply be a lucky guess, and not an expression of true knowledge.

Likewise, what if I were to return to my original function from Fig. 3, and instead listed the images in random order, “one hundred forty-four, four, eighty one, ten thousand…” etc? It would be possible, though not likely, to correctly state what the pre-images were, and what the function was. For all you know the function is simply a mapping of any number to itself (i.e. y = x), or again, from shapes to numbers, or people to numbers (as we do for identification cards), etc.

Now, this is very important. When we have only perceptual knowledge of the images of a function, it is impossible to infer any knowledge as to the pre-images (the input) to the function. The images are perceived, and the function remains a black box, with the inputs, the pre-images, unknowable. We are left with only the inference that whatever it is that they are, they do exist. Nothing more can be known about them.

The Mind as a Function

I am going to make an assumption. That the universe/reality is not solipsistic in nature. Solipsism is the belief that only YOU (i.e. me) exist, and nothing else is real. There exists only one single mind, and everything else only exists inside that mind.

Let’s assume that the universe does not follow that structure, and that there actually are things that populate the universe other than myself. Mathematically speaking, the number of elements in the input set, the domain (the number of pre-images) is greater than one.

Now that you also exist in this universe, I am capable of using the word ‘we’. Since we are conscious beings, we are conscious of something. To be conscious is to be conscious of something. In this moment I am conscious of my typing, my laptop, I have a slight need to pee beginning to build, I can hear some buzzing from the walls, and I am conscious that I am about to end this sentence. The objects that we are conscious of include our perceptions (vision, smells, tastes, sounds, tactile sensations) and our thoughts.

I am led to believe that the mind is a function. If, in fact, the mind is a function, then the objects of our consciousness, the things we are aware of, all the things that you can possibly experience, are images that are mapped onto (the outputs), via the mind, from a given input (pre-image).

First, I will have to argue that there exists a distinct mapping from every pre-image to each image. Secondly, that means that whatever exists in the domain (i.e. the universe) is “mappable”.

I believe that it is intrinsic in our existing in the world that we operate with the logical structure that every pre-image produces a single distinct image. This, I believe, is nothing more than the mathematical description of causality. Cause and effect. I argue that to deny this is equivalent to an admission of insanity.

There are many definitions to insanity, but a popular colloquial definition is ‘someone who repeats the same process, expecting a different result.’ Is this not nothing more than to deny causality? Implicit in this definition is an individual in the world, acting in one way, and expecting a different effect to occur. We call such a person insane. We implicitly recognize that in order to effect a change, a different causal force must be applied to a given circumstance. In order for a unique effect to happen, one that differs from when we apply input x, we must apply a different input (i.e. try anything BUT x) if we are to have any hopes of observing a new unique effect to occur.

To operate in the world is to implicitly, if not explicitly, be ruled by causality. When we experience hunger we are moved to eat. This is causality. Not only this, the mere idea that IF we eat THEN the hunger will be taken care of, is a logical inference that abides by causality. Why else would anyone ACT in the world, if they did not implicitly believe that the act would effect a change? When someone is upset, we ask “what happened?” Why? Because implicitly we operate under the structure of causality, we make the inference “Person x wasn’t upset before. Person x is upset now. An event must have happened to cause person x to being upset.” Causality.

Since we operate under the structure of causality, it is normal for us to infer that when we “see” or “hear” or “smell” or perceive something, that the perception itself was caused by something. That when I see a book on the table next to me, that the event, the phenomenological experience of perceiving a visual of a “book”, is caused because there ACTUALLY IS a book on the table, or at a minimum, that there is something that inflicts onto me a perception of the book. The perception of the book is a representation of something that, external to me, has an ACTUAL objective existence. That is to say, the perception of the book is an image, and what that image (perception) represents is an actual book (the pre-image).

So, we have the pre-image, the thing that has external existence from myself. That being an objectively existing object in the universe, a book. The mind, a function, maps that book and produces an image (quite an appropriate term, I would add) that is my perceptual phenomenological experience.

Causality is important because, when I turn around and return back again to the book, the book still looks the same. It hasn’t changed. It isn’t a book one moment, and then a tissue box another. It isn’t a book one moment, and a blanket the next. If the pre-image of what is mapped, via my mind, to “the book” were to change to something else, I would have evidence that the mapping is not to one distinct image, and so the mind would not be a function. Also, it is a book and only a book. It is not both a book and a basket. It is simply a book. Because I operate under causality, I infer that the thing from which my vision of “the book” emanates from (i.e. the physical matter), is a constant thing, and it is a single thing, and thus, it maps to only one image. Because my phenomenological experience is consistent, I can only infer that the mapping is distinct. With that, the things we perceive are images of a mapping, via the mind (a function), from objects that exist in the world, external to us.

To argue that all things in the universe are mappable, I will save for another day. It is sufficient for my purposes here in this post to deal with the distinct mappings of the mind from objects/pre-images in the universe to perceptual phenomena/images.


Can we know about the “objective” universe?

Remember that function y = x (squared)? Remember the thought experiment of only being aware of the images, and not being able to deduce, to know, what the function was? What the pre-images were? What the objects were which caused the existence of the images, via the function?

Most humans believe in objective truth and that objects in the universe have an objective existence. That if all humans were removed from the universe this very instant, the book on the table would still exist, as I had always perceived it. I ask myself the question: What does such an assertion even mean?

Our perceptions are the only things we are capable of experiencing. Every sight, every smell and every thought is a perception that “exists” in the mind. If the mind is a function, and our perceptions are images that are mapped from external inputs, then, again, I ask: What does it mean to say that ‘if all humans were to cease to exist that the book on the table will still exist as it does now’? This is the same as asking what does it mean to say that ‘if all functions were to cease to exist, the images of the functions would still exist’? My answer: it means nothing. The question is a meaningless one.

We perceive the world through the mind. The world, the universe, is mapped to our perceptions via a function, the mind. We ONLY ever experience and have knowledge of the output, of the images of the function. To make the inference, the belief, that what we perceive is actually what exists is to say that the images of the function are equal to the pre-images. Meaning, the function maps every element to itself (i.e. y = x). “Of course the book that you see REALLY IS the book! Of course it is!” That would be the reply of most, I believe. But we have nothing but empirical evidence to the contrary.

We have so much diversity in perception among living organisms. Some species can perceive greater or lesser ranges of the electromagnetic spectrum (black and white vs. color vs. ultraviolet), of sound frequencies, of scent. We have color blindness. We have synesthesia. We have people who taste colour, and people who see sound. We have people that can see objects, like the book on my table, except those objects are numbers. When asked to compute 239487239847239 * 293472938472983 + 2347 divided by 12322, there are people, human beings, that see structures, objects, representative of those numbers in front of them, and they don’t do ‘math’ to calculate the answer, they just look at the resulting structure and see it, the way I see the book on the table.

With such empirical evidence for diversity of perception, who (or what organism) can say which one is “objectively true”?! It is meaningless. The mere fact that perceptions can be different simply shows that different living things capable of perception have different functions. The images of those functions are different because the functions (minds) are different. To say any one set of images (perceptions) are the objective truth is nothing more than bias and sheer egoism and adoption of convention.

What does have “objective” existence are the pre-images. The set of ‘things’, external to us in the universe, that the mind maps to our perceptions. The thing is, we cannot have any knowledge of them, as they actually are. It is a pure impossibility. We can only come to know them through the mind, through a function, through mappings to our perceptions, through images.

If tomorrow all conscious beings were removed from the universe the book would not continue to exist. What would exist, would be something, and that something would be the pre-image that maps to what I call the book. Any meaningful description of that pre-image is unknowable, other than the inference I make of its necessary existence.


Finding a scientific explanation for consciousness

What is consciousness?

It is a seemingly tough thing to get your mind around. We all experience consciousness, or at least I have faith that other people experience consciousness and aren’t just unaware zombies.

Consciousness is different than mind, that is for sure. There can be processes of the mind that you are not conscious of. Computations and cognitive events that occur in the mind but you are not aware of, not conscious of all the same. Rather, you are conscious of your mind (or contents/objects of your mind). Consciousness is awareness. The consciousness is aware of things, it is aware of objects. To be conscious is to be conscious of something. Of what you are reading, of tastes, visual field, smells, tactile sensations, thoughts, emotions, memories, etc. Your mind is capable of constructing/presenting to the consciousness all sorts of sensations, all sorts of thoughts, all sorts of memories and emotions. We each have a vast range of memories at our disposal, but we are only conscious of the ones that we are conscious of, the ones we are made aware of.

So consciousness is an awareness.

This awareness is of whatever it is you perceive through the senses as it is constructed and presented by the mind. Meaning, consciousness is an awareness of the objects of the mind. It is like a light being shone onto something, and that something is an activity of the mind.

Consciousness is unified. I don’t experience a consciousness of my visual field of my laptop right now that is separate from my tactile sensations as I press on the keyboard. Rather, the two occur in one single unified experience. They occur together. It isn’t one consciousness experience one set of perceptions and a different consciousness that is aware of another set. Everything – my thoughts, emotions, sense perceptions, memories, all occur together in a single unified field. One consciousness.

Consciousness is non-reducible. In science we like to reduce things. A human body is reduced to systems (skeletal system, central nervous system, reproductive system, etc). These systems are reduced to organs, tissues, etc. These are reduced to cells. Cells are reduced to macromolecules. Macromolecules are reduced to atoms. Atoms are reduced to subatomic particles. Subatomic particles are reduced to probabilistic quantum events that have no real physical existence. But consciousness, consciousness isn’t reducible beyond itself. It simply is. It is awareness. It is awareness of objects, and you can’t reduce the awareness beyond what it is.

Consciousness is one of, if not, THE big ticket areas of study today. It is found to play a role in our modern day physics (quantum mechanics), it is one of the hottest topics of study in philosophy (philosophy of mind), it is at the core of the yoga, meditative, new age and mindfulness movement, and it is the final frontier of psychology, computer science (artificial intelligence), neuroscience and cognitive science.

Each domain has its own approach and tool kit to use in attempting to tackle the problem of explaining consciousness, but how will science attempt such a feat?

Science claims to be objective. Science is also a methodology that has limited scope and range.

The current leading model in science is that the mind and consciousness are caused by biological processes in the brain. This is to say, that the mind and consciousness arise from molecules and atoms interacting with each other according to the laws of physics. To not believe this to be the case is to pretty much commit academic suicide.

I won’t discuss the problems associated with this view, or why I might have a problem with it (though I will ask what it means for molecules to have knowledge of molecules, and how can molecules be aware of molecules, if awareness and mind are just properties of molecules). Rather, I will ask what science would need to do to look for consciousness via experiment.

A proper experiment controls all the variables except one. If that one variable is altered and it has no effect on the thing being measured, it is inferred that the variable has no causal relationship with the effect being studied. If, on the other hand, the variable is altered and it is found to have an effect on the thing being measured, it can be stated that there is a correlation between the two, and from there further investigations can be made to see if this is just a correlation, or if the relation is a causal one.

An example can help.

You enter into a new home and you want to determine which light switches on the walls control which light bulbs on the ceilings. Let’s say there are 10 switches and 10 light bulbs in this house. It would be unscientific and not helpful to turn on 5 switches then walk and around and see which light bulbs went on. You controlled 5 variables, but changed the other 5, and now you can’t really tell which light bulbs correlate with which switches. The best way to go about determining these relations is to leave 9 of the switches in the off position, turn one switch on, and then see which light bulb changes. Hopefully you see a 1-to-1 correlation. You can switch it on, and off, on and off. See that they always correlate, and if you are so confident in this relation, you can infer that the light switch has a causal relationship with the light bulb, in that the switch being turned on causes the light bulb to go on. And you can continue this process for the other 9 switches.

Now, what if the exact same scenario was repeated, except in this scenario you enter a new home and there is a dog there. What you don’t know is that this dog is scared of illuminated light bulbs. You repeat the experiment above, and what you find is everytime you turn on a light switch two things occur: a light bulb illuminates, and the dog barks. Now, if you have never turned on a light switch before, you have never seen a light bulb before, and you have no previous concepts of electricity, it is just as likely in the above scenario that you would correlate the dog barking with the light switch, and the light switch to the light bulb illumination, and the light bulb illumination to the dog barking. You might even infer that this is more of a correlation, but that the light switch being turned on causes the dog to bark and the dog barking causes the light bulb to illuminate. It sounds silly, but it would be perfectly plausible for someone who had no previous concepts of light switches, light bulbs, dogs, and electricity.

The example might seem silly, but it isn’t. It isn’t silly because the pursuit of science is a pursuit from a state of ignorance (no knowledge of the universe) to a state of facts and truths. Meaning, at some point along the way during the pursuit of science electricity was not known, light switches were not known, light bulbs were not known, nor the reason for dogs barking nor their effects. At some point, none of these concepts were known. And in all truth, any field of scientific study is a field of unknown. No correlation or causal relation is obvious. When you don’t know anything about dogs, light switches, light bulbs or electricity, the model that light switches cause dogs to bark which cause light bulbs to go on is perfectly plausible.

Back to consciousness.

How are we to study consciousness through science under the model that consciousness and mind exist through a causal relationship from atoms and molecules that comprise the brain?

Let’s go back to the house with the light bulbs. If you had a light switch and turned it on and off and not a single light changed, what conclusion could you arrive at? Well, let’s say you changed all the light bulbs making sure they were all working. Light switch on, and nothing. No light bulbs illuminated. Well, you could have to conclude that the light switch has no causal relation to any of the light bulbs. The light switch’s on/off position has no bearing on any of the other light switches functionality. The light switch would have no effect on the lights. It has no relation to them. Maybe to something else, maybe an outlet, maybe it isn’t even connected to any wires/electricity. Who knows! But, you would conclude that it has no causal relation to the light bulbs.

Ok. Now, in the house with light switches and light bulbs we had a model to test: there are light switches and light bulbs and the light bulbs are causally controlled by the light switches. In the study of consciousness/mind we have a model to test: there are atoms/molecules/cells and mind/consciousness and the mind/consciousness is causally controlled by the atoms/molecules/cells.

Now, atoms/molecules/cells are in constant motion, and they are constantly in flux. Being in flux means they are coming and going, never being, always becoming. An atom spends some time comprising this molecule, then is transferred in a chemical reaction and comprises that molecule, then finds its way into the blood stream or spinal fluid, and eventually makes its way out of the body. Likewise, an atom that was once a part of a seed on the earths surface is now in your belly, and then finds its way into the brain and is part of a neuron and part of a dopamine molecule, etc, etc. All these atoms are moving, all of these molecules are moving, all of these cells are moving. Nothing is static, nothing is fixed, all is flux.

And yet, we experience a single unified non-reducible consciousness. All this change, and yet only one single consciousness. Yes, it is true that the objects of consciousness (objects of our mind) are constantly changing, but consciousness itself never changes. It always is. 

So, if we keep changing the light switches and the light bulbs don’t change and we conclude that the light switches have no causal role in producing or affecting the light bulbs, then if the atoms are constantly moving, constantly differing, constantly changing their relations, their states, their levels, their activities and consciousness is still this single unified non-reducible thing from moment to moment remaining unchanged, then we must also conclude that these atoms, these molecules, these cells have no causal influence/affect/role in determining consciousness.

If there does exist a causal relationship between something physical (atoms/molecules/cells/etc) and the existence of consciousness, then there must exist a light switch. There must exist something, whether it is an atom, a molecule, a cell, a set of atoms, a set of molecules, a set of cells, a relation between members of these sets…etc…something that when present or absent consciousness exists, and oppositely when absent or present consciousness does not exist.

I am not saying such a thing exists, in fact I believe the exact opposite, but that is just a hypothesis/conjecture.

But if there did exist a physical causal relationship for consciousness, first it must be shown that there exists a certain distinct and discrete physical state (atoms/molecules/cells/relations between these, etc) that correlates with consciousness, and the perturbation of this physical state would have to correlate with the absence of consciousness.

We don’t know of one, and finding one would require quite complex relations/modelling to be done as it is known that all physical systems, the brain included, are constantly in flux. How can a state of flux produce a constant stream of consciousness, a singular, unified non-reducible consciousness? The analogy with our house of light bulbs would be a house where light switches are constantly in flux, turning themselves on and off continuously, and yet we think that one light bulb stays on constantly, and we want to figure out what the causal relationship between these dancing in-flux light switches have on that single continuously lit light bulb. Seems illogical and impossible, doesn’t it? I am not saying it is impossible, but it seems unlikely.

Of course, there is a difference between the two analogies that leaves it hard to even talk scientifically about producing consciousness. The light bulbs are either on or off, that is not really open for debate. Consciousness, though, is. Consciousness is always of something. Conscious of my hunger, conscious of my dog wanting to go for a walk, conscious of how tired I am. Conscious of how long this blog post is getting. Consciousness is always of an object. Now, the question remains: What happens when you are conscious of no-thing? Commonly this is referred to as unconscious or not conscious, like deep sleep without a dream. But how can we distinguish that state from being conscious, but conscious of no-thing, no object? What criteria do we have to make that judgement?

So even if we found that light switch, that physical state in the brain, we still couldn’t distinguish between the two interpretations of the physical state causally affecting:

  1. No consciousness (off light switch position); or
  2. Consciousness of no object (off light switch position)

And so the pursuit of science to find such a causal explanation for consciousness seems deeply troubled. It is interesting though, that is for sure.

With that, I walk my dog and then sleep.

Hypotheses, parent hypotheses and instrumentation

The pursuit of knowledge begins with a hypothesis.

Whether or not it is explicitly known or made conscious of, the act of posing a hypothesis itself rests on a hypothesis (or assumption) that the truth value of a hypothesis can be ascertained (that the hypothesis can be verified or refuted). This must be assumed otherwise posing the hypothesis itself would be a vain pursuit. One asks a question with the implicit assumption that an answer exists. I do not ask, “Why is the garbage can sprinkler farm house?”, because I do not believe that to be a question, I do not believe it to be a question because there exists no answer, and there is a specific logical structure to questions and answers, being that questions have answers. If a question has no answer, then it isn’t really a question, it is just a string of words I can utter but has no meaning.

I also do not believe, “Why does the farm house cook?”, to be a question because though I can create a concept of what this sentence means, it still is a meaningless question. Questions, in order to be questions, must make sense, be meaningful, and be categorized as having an answer.

No hypothesis can be posed without another hypothesis being integral, inclusive, contained within itself. For example, when I pose the hypothesis that expressing a certain protein in liver cells will have causal influences on the levels (and thus function (note: protein levels correlate to function is itself a hypothesis)) of the other proteins expressed in that cell, this hypothesis poses within itself a vast multitude of preceding and necessary hypotheses. Hypotheses such as: that proteins exist, that proteins carry out functions, that proteins interact, that our model of the cell is true, that our instrumentation works the way it does (from the accuracy of a pipette that draws our chemical solutions, to the mechanical integrity of a centrifuge, to the accuracy of our electronic thermostats, to the software we use, etc, etc), and many other hypotheses. Essentially every currently held to be “true” model within science is a hypothesis that has yet to be refuted. It can never be proven to be true (as this would be inductive and not deductive), so it is still a hypothesis yet to be refuted. And so for any hypothesis, H, stated at time, t(n), then that hypothesis statement would rest on all other non-refuted hypotheses at time t(n-1), t(n-2)…until it finally rests on the axioms that provided the very logical structure (rules, assumptions, postulates, definitions) of the field of knowing that the hypothesis exists in.

Now, I am curious about the logical structure behind an explanation/interpretation behind instrumentation in quantum mechanical experiments. Actually, about instrumentation in general.

A couple of months ago I was watching a scientific documentary on netflix and there was “imaging” of the surface of materials such as metals. Images were something like this:

And so we are told a story, an interpretation of this image that we are viewing (note: the image itself is represented via atoms that form a screen printout from the computer this was used to create and in our case represented via atoms composing our laptop screens) is that atoms really are physically extended things in space, we can kind of visualize them. The amazing thing about this image is the interpretation/meaning conveyed that atoms really are physical geometric things that exist. It is interpreted as a confirmation that beneath what we can see are these smaller, real, physical things that we can’t see, and those things make up the things we can see. Atoms. Matter.

But here is the problem with an experiment like this. What you get from this image is that atoms have these three dimensional shapes. There are parts of an atom that are closer to one point in space (i.e. you, or something one namometer away from a certain gps location) and then there are some parts of that very same atom that are further away from that very same point. That is to say, a single atom is not a dimensionless point, it has a physical geometry and has regions that differ over space. The atoms on the surface of the substance depicted above clearly have dimension. There are parts of the atoms that appear closer to the perspective of the observer than other regions of the very same atom. Meaning, pick any object in the room you are in. Comprising that object are atoms, let’s pick one of them. Now, if we were to measure the distance from let’s say your nose, or any other single point in space, to that atom, we could get multiple measurements. We could get multiple measurements because we could be measuring from that point (your nose) to different areas/regions/parts of the same single atom. Just like measuring your distance from a ball, that distance depends on what point you are measuring on the ball, the front, the side, the back, the top, bottom, etc.

Ok. This might seem obvious. Why am I taking such great attention to this? Because if this is true, then we have to see what causal effects, what logical relations this new truth has for all the preceding hypotheses that this hypothesis is founded upon. In this case, what struck out to me was instrumentation. Now, the instrument that do these imaging techniques, which tell us that atoms have geometry, involves measuring. It has to be able to measure distances and thus geometries. There is a source, which exists in space, and thus has a (hypothesized) very real space it occupies, with a very real distance separating itself from the sample it is to measure. The method to measure is to send, from the source, a laser (electromagnetic radiation) which moves at a constant and known (Maxwellian/Einsteinian) speed (the speed of light), and it will hit the surface of the object, and bounce back to a detector. We can measure the time it takes for the laser beam to be emitted from the source and then detected by the detector. Since we know the time it took for the laser to travel, and we know how fast it is travelling, we can tell how far (the distance) it traveled. If we can be incredibly precise with this distance we can compute the geometry of the surface the light is reflecting from. Just think if you were blind folded and you were given a device, say a cannon or gun, that you knew shot something at a constant and defined speed. You shot the cannon/gun in a direction, and all you knew was the length of time it took to hit something. You could move yourself left and right slowly shooting over and over, collecting data points and deduce the shape of the thing you were shooting at. You could do this in the very room you are in now. Closer things to you would get hit earlier, further things would get hit later.

Now, returning to the experiment itself, the entire instrument itself is made up of atoms, including the detector. Now, if we were to visualize what the surface of the detector would look like, it should (by hypothesis) look like the surface of the material in the image above (since it too is made up of atoms). Now, if this is the case, that means that the detector itself has a geometrical shape, with regions of a given atom that are closer or farther away than any given point in space.

This is important. This is important because the detector detects once the laser reaches (excites) the detector. The laser is assumed to be so precise (small in physical size in terms of the wave traversing over space which would include concepts such as frequency, amplitude, wave length) that it will contact a point on the material (collection of atoms) the size smaller than an atom. I find this hard to get across. What I mean is this, if you use your right index finger to touch your leg, the thing we would call the point of contact isn’t really much of a point. It probably occupies an area of several millimeters. When you try to be precise with your big clunky finger tip, well, it touches an area of your leg. Now, our laser, like our finger tip, is going to touch the surface of that material. In order for it to produce the resolution of an atom in an image the laser (finger tip) has to have an area of contact that is smaller than the area of an atom. It must be smaller than an atom. That is a pre-requisite to be able to tell that one point on an atom is further or closer away than another, which after all is the entire pursuit of this imaging.

So, this laser is so precise that it can touch one part of an atom while still not touching another part of that very same atom. Ok. Now, let us try to visualize with our imagination this experiment occurring. Shrink yourself down to the size of the atoms. The light source is emitted (laser), it travels across space and hits on an area of an atom that makes up the “surface” of the material object, then the light reflects and moves towards the detector, where there again the laser will touch another area on the surface of another geometrically three dimensional atom. Is this not a problem? The reason why this would be a problem stems from the fact that we take this image to be a truth statement. It is a visual statement, and can be verbalized by stating that it is true and representative of reality that atoms are three dimensionally extended things. We make this statement because we assume that our hypothesis that our instrumentation functions “properly” is true. Our concept of our instrumentation functioning properly is that it is representative of reality, that it functions as we think it does.

But now, if we come to recognize that a physical detector made up of physical atoms which all have a three dimensional geometry, and that the laser can hit those atoms at any various part and still be touching that same atom (this is to say, that the laser can touch the same atom at different areas), and that each of these parts/areas of the atom can be physically closer or farther away from the path in which the laser has been travelling, then we can not know if the laser hit a region/area/part of the atoms of the detector that were closer or further from the point that the laser hit on the atoms of the material.

Maybe something like this:


In this image you can see that the light hits a specific point on the atom of the material, then moves towards the detector and hits a specific point on the detector. Now, the detector can tell when it was excited (when the ‘detection’ occurred). It cannot tell, by default, which area of a single atom was activated, since it is the very same atom and just one thing. It is binary, either activated or not, there is no more information that can be contained within the activation. The activation/excitation/detection within the detector would be the exact same whether it occurred at one point of the atom or another. It is still the same atom.  And so the light source could hit a single point on the material, but the path the laser follows, as it is a wave and thus moving and spreading over an area as it travels, it could hit different areas/points/regions of the very same atom. Why does this matter? Because different areas of the same atom necessarily occupy different regions in three dimensional space, relative to each other these areas of the atom will be closer/further in relation to a straight line from the point of contact of the laser on the surface of the material. Meaning, one laser will travel a bit further and one a bit less than the other. Moving at a constant and equivalent speed, this means that what is detected will be in one scenario, a wave having a shorter time span, and in another scenario a wave will have traveled over a longer time span.

Why does this matter? In these scenarios we have a source that emits at the same time point, time = 0, and both hit the same point on the atom of the surface material being imaged, then the laser reflects and moves towards the detector. In both instances the laser strikes the same identical atom (in non-simultaneous events of course!). In one instance the atom is contacted at a point closer, and in one instance the atom is contacted at a point further from the point of the surface material. This means that the time recorded for one instance will be longer than the other. Most importantly, they will be different! Yet for both scenarios the same point on the surface being imaged is being measured by the laser. It is the same point of contact, and thus, our hopes, our hypothesis for the instrument we are using is that when the laser hits a specific point on the surface, it will reliably be detected as an accurate and truthful representation of what the actual surface material is like in reality. But this cannot be.

This cannot be the case because we can have two very separate pieces of data for a single measurement. Is that point in space, the thing we are trying to image closer or farther? Did it take the laser 0.0000000000000000000000000000000000000000000000001 or 0.00000000000000000000000000000000000000000000000011 seconds to travel to the detector? It might seem like a small difference, but in all reality that is a 10% difference, highly significant. If you look at any object relative to you that you can see right now and you could not tell if it was where it actually is, relative to you, or 10% closer or further away, well, then the print on my wall is either 8 feet away, or it is close to 7 or close to 9 feet away. I don’t mean seemingly, I mean truthfully, in reality. Because we take that image to be a truth statement, and I think that the print on my wall is truthfully a specific distance away from me.

So we cannot truly, from the data, tell what could be the true image, the true three dimensional geometry of the material. We can’t because we start with the hypothesis that the image produced is true. If it is true, then we must take that new piece of data and see how it affects all the preceding hypotheses which that hypothesis (that the image is true). In doing so, we find that the hypothesis that the image is true becomes an impossible contradiction: it cannot be true since it refutes itself as argued above. The result of the hypothesis implies a direct refutation of a hypothesis from which the parent hypothesis relies upon. So the imaging is meaningless. Yet we take it to be true.

I am also interested in this line of reasoning and looking at preceding hypotheses when it comes to instrumentation for experiments in quantum mechanics. But I am tired and this thought will have to wait for another time.

Encryption of Information and Allegory

We all live in a digital world. We communicate via phone, text, e-mail, skype and various social media platforms. We share pictures, private information, private documents, both personally, professionally and institutionally over this digital world. This data is sensitive and often proprietary. It can be sensitive and so we want to keep it discrete and secret. It is important that when people communicate by e-mail or text on their smart phone that the information being shared is kept solely between the parties involved.

With this need in mind we have the concept of encryption. From war strategies to confidential corporate data to sharing a personal story, we want to maintain privacy and we do this, digitally, through encryption. Encryption involves altering information (which comes in the form of symbols (syntax/language/etc)) in such a way that the information is not obvious. The person intended to receive the information is made aware of this relation between the true information and the encryption of it. There are obviously many ways of encoding/encrypting a message.

I am faced with a question. Methods of encryption are made, and they are decoded/cracked/solved. From this, new methods of encryption are developed. With this in mind, I am curious if it is possible for there to exist a method of encryption such that it would be necessarily impossible to crack/decode without knowledge of the encryption method? Is there a proof that would claim that it is impossible for such a method of encryption to exist?

If such a proof exists, one that would show that it is impossible to create an uncrackable code, and thus there is no possibility for the existence of a perfect method of encryption, then that would mean, necessarily, that all information in existence can be made aware of, can be known. It would mean that it is possible to know the meaning of all information in existence.

This would necessarily follow since there would be no possible way for information that is “out there” in the world/universe to be encoded in such a way that it could not be perceived, no matter how convoluted and complex that information might be encoded. That is, if there does in fact exist information in the universe, it cannot be encrypted perfectly, and so necessarily, it is possible to be made aware of that information.

If this is true then there are very meaningful consequences to be considered.

There are views and interpretations that put information as the structure of the universe, of reality. Information is the word or concept for what is conveyed by something. Information is meaning in that sense, since meaning is what is conveyed by something. This something could be symbols, objects, events, series of events, relations, physical objects, phenomena, sense data, etc, etc… essentially, experience of the phenomenal world. Everything is information.

An atom is information. You cannot know an atom and not know that it is an atom of something. You cannot know an atom and not know that it is composed of subatomic particles. If you do not know those things about the atom then you cannot truly say you know the atom, since those concepts are contained within the concept of ‘atom’. You might know that there exists a word ‘atom’, and you might have a rough idea of what an atom is, but that isn’t truly knowing an atom. To know what an atom is, is to know the concepts contained within ‘atom’.

Likewise, you cannot know what is happening in a sporting event without knowing the sport and rules and relations they all play to one another. You cannot know what is happening in a chess game without knowing the rules of chess, the pieces, how they relate to each other, the structure of a game, the possible moves, etc. So a move in chess is information. It contains and conveys something: meaning. The same is true of a kiss, of seeing the sun rise, of seeing a brand image, of a smell, of a visual field, of the sense data one would call ‘heat’, of a certain sound, etc. Everything is information.

What is interesting about lots of our information is that they are social constructs. Seeing a man with a football run across a painted line on a grass field allows me to perceive a “touchdown”. “Touchdown” was the information conveyed to me when certain events, objects and phenomena were perceived. But a “touchdown” is a social construct. It isn’t something that can be measured using physical methods of science. There is nothing in crossing a line on grass with a football that intrinsically, out there in the universe, constitutes a “touchdown”. If it did then all cultures, all humans would naturally know what a touchdown was when they saw it. It wouldn’t need to be explained. Rather, we see certain events and under certain circumstances we impose onto reality the concept of “touchdown”, which is something we learn that is associated with a specific set of criteria (man + football + crossing a painted line +…..). The same is true of so many concepts, (in fact, all) from marriage, gender roles, what constitutes a date or friendship, what a proper meal is, what is healthy, what the function of biological processes are, what is an economy, money, social norms… the list goes on and on. We agree, and disagree, on what constitutes life (is a bacteria alive? is a virus? is a 2 month fetus? is the planet? is the universe? is a protein?). We even have to agree what constitutes a mountain. That is a concept upheld by our own definitions. The same is true with what an ocean vs sea is. Where does the mountain end? Can a line of demarcation be drawn at an exact set of atoms, objectively, of where any given mountain begins and ends? Of course not. The same is true for where an ocean ends and a sea begins. That distinction doesn’t exist “out there”, objectively, in nature, rather it is a convention we hold and impose on reality, and our thinking so makes it “true”.

A touchdown is a touchdown by convention, yes, but it in order for the information/meaning “touchdown” to be conveyed a certain logical structure has to be satisfied. The elements that make a touchdown a touchdown have to be present, and have to be consistent with what constitutes a touchdown. A logical structure still has to be satisfied, even if that logical structure is also held in convention. For example, it would be hard to imagine the meaning/information conveyed in a man from a football team carrying a football into an end zone as a marriage. Perhaps it is possible, but I cannot see it being the case where even if people all agreed that set of criteria constitutes a wedding, that it would make it so. I think this way because the concept of “wedding” has a different logical structure than a man carrying a football into an end zone. We also couldn’t say that the football player “died”. Essentially, what I am trying to communicate is that we can’t impose just any belief/concept/truth to any (set of) syntax/symbols/objects/relationships/etc. It must still fit a logical structure in order to be satisfied, because that logical structure is also a convention and is involved in holding the conventional concepts as true.

This is related to information and information encryption because anything, any syntax, any object, any symbol, literally anything at all (even the relationships between syntax/objects/symbols, and the relationships between those relationships, ad infinitum) can be and is given meaning, can and does convey a meaning. This can be done because any mind, any culture, any person, any conscious being can impose onto that object/syntax/symbol/relation/etc any meaning whatsoever, as long as it follows a consistent, coherent and cogent logical structure (which itself is information/meaning that is held in convention). In doing so, that object/syntax/symbol/relation/etc will now carry that meaning and information in the future. If this is true, that any symbol/syntax/object/relation/etc (i.e. anything at all) can carry any possible form of meaning/information (as long as it follows a coherent, consistent, cogent logical structure), and if it is true that any and all information in existence can possibly be observed (no matter how complex the form the information is encoded/encrypted), I contend, with these two truth statements together, that any and every logically coherent/cogent/consistently structured word view will have the ability at arriving at any and all information/meaning that can and does exist. Essentially, what this means and can be interpreted as, is that any logically consistent/cogent/coherently structured system/world view can arrive at all the same information/meaning (i.e. truth statements) as any other logically consistent/cogent/coherently structured system/world view. As long as there are no contradictions in a world view, it will arrive at the same truths, just in different ways, from other non-self-contradicting systems/world views. More plainly, all non-self-contradicting world views are allegories/metaphors/analogies of the each others, since they all arrive at the same truth. Whether it is a religious, mystical, logical, scientific, personal world view, as long as it is consistent within itself, any and all world views will come to the same information, the same meanings, the same self-imposed truths.

All is allegory.

In a different light, if we are to assume that there does in fact exist a truly objective reality/universe, then that universe/reality can be knowable, as it is information that makes it objective, since “objective” is a predicate that describes something (i.e. something that is  being described as objective), and the thing that it describes is a truth statement, which is information/meaning. So, if there does exist an objective universe, then it should be possible to come to determine the information that makes it objective (this being considered the laws of physics and the pursuit of science). Though, as I have written previously, I have doubts and think that the objective/subjective dichotomy of events/reality/universe/nature is a problematic duality that is either incomplete, false or meaningless. But this warrants more attention.

But all of this rests on the possibility/impossibility to perfectly encode information such that it would be impossible to be cracked. This will require more investigation!

(Note: Of course, it is possible for someone to think that a man carrying a football to an end zone is in fact a marriage, but that would be logically inconsistent, assuming all other world views/concepts were the same. The importance of the non-contradictory world view is something akin to working 95% done through a sudoku puzzle and realizing you have two 8’s in a row. Somewhere you made a deduction that was wrong (i.e. not necessarily true).The entire system, the entire puzzle is wrong(it contradicts itself), and can only be corrected if all the false assertions can be traced back to the first wrong deduction. But, this isn’t always possible in sudoku, as also it is for real life. In such a case we might call such a person with a contradictory world view to be wrong, crazy, insane, odd, etc. No matter the label we apply to that person, their world view can’t be taken seriously if it is not coherent/cogent/consistent within itself.)

All Novembers Come to an End

I set for myself the goal that for the month of November I would write a blog post every day on the topic of science. From there, I made a list of all of the things I wanted to cover and write about.

Though the total blog post count is around 15 or 16, I still covered all the material that I was hoping to. Many of my blog posts were in the range of 10+ pages, so I think that is fine that I didn’t actually hit 30 blog posts. Many of those posts could have been split up into multiple posts. In the end, the content I wanted to cover was delivered.

Science and the scientific revolution was born from curiosity and the inability to accept the status quo in terms of explanatory theories and models of how the universe/world/nature/reality operated. In that same sense, I believe that it is healthy to question science, and to fully grasp what are the fundamental underlying foundational assumptions and beliefs from which the entire pursuit of science rests.

Science provides meaning to our lives, in the sense that it provides a framework, a model, a story line in which we place ourselves within. This framework/model/story line/paradigm/world view gives an explanation for how this does that, and how we relate to the universe we are a part of (whether or not that universe is nothing more than dead, lifeless, inert atoms and forces).

I contend that the mind needs a model, a world view, a paradigm for the sense data that it acquires, for the raw phenomenal experience that it produces and is experienced by the consciousness. The experience of awareness is always of something, and the mind functions in attributing meaning to all of those somethings. A bundle of certain phenomenal experience is classified as the concept of apple, a bundle of another set of phenomenal experiences are classified as the concept of rock, and so on. The concepts we create and impose on the construction of reality, concepts such as home, brother, breakfast, money, marriage, couch, pet, organic food, all must fit together into a cohesive and cogent story line. This story line, this narrative, is to include the set of ALL phenomenal experiences. The instant a new experience comes into existence for you, me, or anyone, the mind experiencing it must place that experience somewhere in the already adopted framework/model/story line/world view/narrative. It must mesh in perfectly, not create any contradictions, and not disturb any of the other concepts set in place.

What I mean is, imagine you were to undergo a brand new phenomenal experience tomorrow. Let’s say you saw something (a thing, an event, who knows) that you have never experienced whatsoever before. This new experience was so novel that you can’t relate it to anything whatsoever you have ever experienced before. You must find a way to relate it to something from which you can derive meaning from it. If it is a visual experience, you can classify it as a physical thing, perhaps a natural organic thing, a living thing, or a synthetic thing; you can classify it by color, by size, geometric shape. If it has an emotional tie to it, you can relate that emotion to one you have experienced before, and make the appropriate associations. If the emotion that occurs in the novel experience is one that you recognize to be similar as a previous emotion from past life experiences, then you can label and categorize that emotion as _____ (happy, sad, good, bad, depressed, etc). In doing so, we derive meaning to the experience, bit by bit.

But if you experience something brand new, one that cannot be classified by any previous experience, one that cannot be explained through any body of knowledge, any previous emotional experience, any previous visual experience, then what then?

This experience will pose a difficulty, a challenge, and will have consequences. The mind, though, will do its best and force a connection, it will force meaning to apply to that experience, as long as one is possible.

Deriving meaning is the strength of any form of ‘knowledge’. Any narrative, any story line that we subscribe to places the events that occur within that narrative/story line (i.e. life) and in doing so provides them with structure, relations and meaning. This is the function of any world view. A world view and any systems of epistemology provides a narrative, a structure, a framework in which all experiences can be given meaning. World views take many forms. World views can be formed and expressed through mythology, through folk lore, through allegory, through religion, through culture and through science. Any explanatory narrative/story line provides this function. In doing so, in providing a narrative/story line what the world view does is provides a script for the mind. A very simple example of script, narrative, and meanings can be seen in food.

Food is a concept. Surely we are capable of putting any object, as long as it is sufficiently small enough, into our mouths and swallowing. But not every object in the world is classified as food. In order for something to be classified as food it is necessary for it to be something that you can put in your mouth and swallow, but it is not sufficient. There must be something else about that object in order for us to call it food. Whatever that is, is a social construct. It could be that it has certain nutritional content, or that it doesn’t kill us. But that is hard to define since even the consumption of too much water can kill anyone, or any food for that matter. And even a rock will have nutritional content, as our body does require metals and minerals. But some things we classify as food, and others not. And so, when we construct a set of all things that we label as “food”, we have created a concept. And any object in the world (which is to say a bundle of phenomena which we give a label and thus meaning to) which we consider to be food, we have now given meaning to that object that was not previously there. A young child that sees an apple for the first time has no idea what that is. It could be anything. It has no meaning for the child yet. But once told that it is food, and given the apple to eat, now the child has ‘knowledge’, but really meaning as to what that object is and how it relates to himself. That object (the apple) has meaning as it relates to himself – it is something edible, it is food. From that point on every other member of the class of ‘apples’ that the child (and in the future as an adult) will see will now be given meaning. That meaning is something edible, with certain benefits, certain flavors, etc, etc. Not just that, but we have a concept of what constitutes a meal. There is nothing objective about “mealness” that is “out there” in nature, in the universe. But we have concepts in our mind as to what a meal is, and what isn’t a meal. A combination of certain foods with the lack of other foods constitutes a meal. This concept of ‘meal’ is another level of meaning that we derive from literally the simultaneous presence of certain foods, which are nothing more than objects that we classify as food, which are nothing more than phenomenal experiences that we classify as objects.

In addition to this, we have concepts of the order in which food is eaten within a meal, as well as what foods belong to which meals. If anyone went to a restaurant and ordered a meal that included appetizers, main dish and desert, one would be completely confused and perhaps even upset if the order of the food presented was: desert, appetizer, main dish. Why? Because we have concepts of what order food is eaten in, and this very order gives us meaning. Not just meaning, but the meanings are organized within schemas/story lines/narratives that provide us with scripts. The idea of eating cake first at a restaurant for a fancy dinner, or even soup for breakfast is not really even on the radar. It is not part of a script on what is the norm for eating a meal. To do that would have a completely different meaning: poor decision making, bad nutrition, weird tastes, etc. Funny how that is. The meaning that we get from an out of order meal is one of irregularity, oddness, lack of social etiquette, and perhaps even improper health. If someone told you they ate popcorn for breakfast and eggs and toast at night to watch a movie, this would be perceived as strange. Popcorn is not really conceptualized as a breakfast food, nor is eggs and toast a movie food. These are not typical of our scripts, of our narratives, of our norms, of our concepts.

In this way, we bundle concepts together into schemas, into narratives, into story lines, and these all provide scripts for us in how to behave, how to relate certain experiences, events, people, places, things, emotions, etc. In its totality, all of this acts to provide meaning for the human experience.

Science, religion, mythology and folklore are all belief systems. They all require assumptions, they all require faith. They all appeal to withhold certain aesthetic preferences and they all are subject to maintaining themselves via convention.

My critique and view of science might seem critical, and it is, but it is not dismissive. Science simply isn’t what we think it is. Science is a system of providing meaning. But it is a system of providing meaning in the exact same way that religion, mythology or folklore is. It is simply providing a framework and model to describe nature/reality/the world/the universe, in much the same way that religion/mythology/folklore is. It provides a structure for explanation, for deriving meaning. Is science and the assertions made within science true? Yes and no. The statements made are just as true and just as false as the statements made by any religion one holds to be true, just as true and just as false as the statements made by any mythology or folklore one holds to be true, just as true and just as false as the statements made by any culture one holds. Viewed from within the given system, the statements made by it are true, whereas viewed from a different distinct system, a differing systems statements are seen as false. The two systems have different criteria for the judgement of truth, and the two are incommensurable. They cannot be compared meaningfully.

Does this mean that science is not worth pursuing? No, it gives meaning to so many people. I think the problem is our relationship to science. To hold it as objective truth and that all other world views (religion/mythology/folklore/etc) are wrong, and only science is right, well, is as meaningless and meaningful as saying that only a certain mythology is true and all other religions/sciences/folklores are wrong. Whichever one you hold to be true is true for you, because that will be how you view your world, view your experience, structure your reality and derive meaning from all your experiences.

You can’t use logic to show that one should be logical. This is illogical and circular. You can’t use science to show that one should accept science. You can’t use the bible to argue that one should follow the bible. For any given system of epistemology, for any given system of knowledge, the criteria of judging whether one should adopt and acquire and use that system of knowledge always rests outside of the system in question. It is always a question of aesthetics (does this system appeal to you, do you enjoy it, does it resonate with you), faith/belief (do you think that it will provide what you seek from it, i.e. meaning, structure and answers/explanations) and the continual adherence to that system of knowledge, no matter what it is, can only be held if it is coherent (the story/narrative it provides is without any major contradictions/plot holes/things that are not explained properly) and agreed upon by convention.

This is a necessary truth. And if it is in fact the case, then it is important then to pick a system that resonates with you, and in realizing that it is just a belief and that each other person is simply doing the same, that a little bit of respect for others and their beliefs might be best.

On the Impossibility of Objective Scientific Truth

I can imagine the title of this blog post to be polarizing. I can understand and appreciate why. There are many reasons, and I feel that I can address each of them accordingly, however the scope of each fall far beyond what I am willing to communicate in a given blog post.

It was Aristotle who said it was the sign of an intelligent man who can entertain an idea that he doesn’t hold to be true. With that said, let’s entertain an idea and see what comes from it.

As someone who has been so closely tied to science, sometimes I cannot get a good picture of what the general public’s view of it is. Likewise, people would ask me about the general public’s view of MMA. It was hard for me to answer. I thought I had an idea, but because I was so entrenched, it was hard for me to really get an idea what the lay persons view was. I had to make an effort to get an idea of what people think of science, and what scientists think of science and what the general view of what science is held to be.

Though science, as a concept, (in the same way that capitalism or democracy as concepts) could take on various forms and have different meanings, generally, I believe it is held to be a mechanism/process/methodology of acquiring objective truthThis objective truth is always of something, meaning truth is a predicate of something which we ascribe to. This objective truth is of nature, the universe, reality, the world, etc. It is of what is. Now, in order for there to be even a possibility of an objective truth of nature, the universe, reality, the world, etc, then there would have to be an objective truth. There is an objective truth to reality, the world, the universe, nature, etc. That is what is postulated by science and the scientific pursuit. The entire pursuit rests on this postulate, this belief, this hypothesis, this assumption. If there did not exist any objective truth to the universe, reality, the world, nature, etc, then this would be an untenable pursuit/methodology/ideology. 

(Though, I am not sure it would be a pointless pursuit, as the experience of scientific pursuit, though it might be an endless chase, it provides focus, meaning, structure, and clarity. It provides pursuit and aspiration, and this is an exercise of one of our greatest valued traits and qualities.)

We do not believe that science is without purpose, that it is not a vain pursuit, and that it brings truth into our body of knowledge, knowledge that guides our world views, our actions in the world and our beliefs on what is possible or not possible. We don’t believe this to be the case because we think that it can accomplish its task, and that it is accomplishing its task. We then must also accept, intrinsically, that the universe operates in an objectively knowable way. That must be a necessary belief in order to accept scientific knowledge to be possible.

I am lead to believe that whether intrinsically believed, or explicitly stated, most people would agree that science is about the pursuit of objective truth. Now, since this truth can only be communicated, it must be represented and communicated through language. No body of objective scientific knowledge can be known or knowable from introspection, from intuition or any personal, subjective manner, such as through a personal experience. Though the knowledge gained through personal experience might also match the truth of a unit of scientific knowledge, to say that it must be true (based solely on the personal experience without any previous knowledge, scientific or otherwise) would be wrong. I might have a personal experience that I feel is “objectively true” of something, and perhaps 10 or 100 years from now science will demonstrate it to be “true”, but this does not mean I can say I objectively knew, or that I truly knew about that “truth”.

The only way to personally arrive at and experience an objective scientific truth is to be the person performing, witnessing and interpreting the scientific experiment. All other members of the populace (of the entire world, and all throughout the future history of the world) who acquire that knowledge take it as an accepted truth of the universe, nature, reality, the world, and do so through learning. This learning is done through communication, and this communication can only be done through language.

So every piece of scientific truth is communicated through a truth statement. Grammatically, a truth statement (though the structure may differ depending on the language and form of language) is a sentence.

All scientific truth statements are communicated as/in sentences.

I will return to this later.

Now, we in our scientific pursuit of finding truth or coming to determine something to be true, we must have a means of doing so. We must have at our disposal a criteria from which we can judge something to be true or not true. Otherwise, we can never make the proper judgement of what is a scientific truth. So, there must be an objectively agreed upon definition/concept of what truth is. It must be objective, because if it was not, then the entire enterprise of arriving at an objective truth would not be possible. So, our criteria for judging whether a statement is true or not must be objectively true. But how can we do that? Would this not be a circular process? How do you get an objectively true criteria for judgement for what is objectively true?

But, in any case, we do have to decide on a criteria. Science as a methodology is not the criteria, rather, it produces data for the criteria. The criteria we use is based off of empirical data. The criteria, aside from convention, belief and aesthetics, is logical. It is either inductively reasoned to be true, or deductively reasoned to be true. Now, only one of these reasoning methods is necessarily true, while the other we induce it to be true, we say that it is true based on a finite number of past experiences which we infer to be representative for all the future. Deductive inferences are necessarily true (the 9 in the row of sudoku must be in that spot) while inductive inferences are not (I studied the effects of pesticide use on crops on mice for 8 weeks and since I see them to be “healthy” (what is my criteria again?) then I state that forever in the future, definitively, that the pesticides are safe).

Now, I will argue that in order for scientific knowledge to be true, then our scientific deductions, our scientific discoveries, our scientific statements must have then been arrived at through deduction. Inductive reasoning does not necessitate truth, so it is not a valid criterion for judging truth value. That is simply convention and belief (in a certain aesthetic preference).

In order to meaningfully say that we have a body of scientific knowledge that is true then these truth statements must have been arrived at through deductive means. In order for something to be deductively true, it must be necessarily true. Now, aside from a deductive argument in the case of mathematics and geometry, most of our scientific knowledge comes from the observation and interpretation of events/occurrences/phenomena in the world via experiments. How are we to deduce that the interpretation of the results, that the explanation given, that the results obtained are necessarily true, objectively, of nature? It seems to me that in order to arrive at necessary truth via empirical evidence and experimentation, one must arrive at every possible experiment, every possible empirical evidence and do this by testing every possible hypothesis. Once all competing possible hypotheses have been tested and refuted, the one left standing can be deduced to be true. If there is another hypothesis that has yet to have been tested, how can we say, necessarily, that the one that is held to be “true” is in fact true? And so all hypotheses, no matter how seemingly improbably or far-fetched, must necessarily be tested in order to validly state that any given scientific statement (knowledge) is necessarily true. 

So, in order for a hypothesis to at some point be removed of hypothetical status and be acquired as a true statement of the objective nature of the universe, of valid scientific knowledge, then all other possible hypotheses must be tested first and all are discredited/shown to be false.

If this is the case (and it appears that it is) then is it possible to arrive at a true empirical and objective scientific statement (i.e. model, explanation, paradigm, etc)? This seems like it might be an impossible task. There need not necessarily be an infinite number of hypotheses in order for this to be impossible, rather, there only needs to be just one more possible hypothesis. Always, just one more. As long as there is just one more hypothesis that requires our testing, then there can be no deduced true scientific truth statement.

At first glance it might seem intuitive that we could always pose another hypothesis, no matter how far-fetched it is. There could always be another possible means of explaining a process or empirical phenomenal experience. But can this be shown necessarily? 

In order to address this question, it can be approached from how science progresses.

The entire body of the pursuit scientific knowledge can be visualized and modeled as a tree (infinitely?) growing.

science tree

The trunk of the tree could be viewed as the set of all axioms, definitions, postulates, etc, that science is based off of. Some underlying assumptions of scientific knowledge have already been covered, such as that the universe is objectively knowable, and that we can arrive at that knowledge. Other assumptions would be cause-effect relations, mathematics and geometry, that nature is regular such that once we see a pattern in nature we can infer that the pattern will continue into the future, etc.

From these axioms springs forth our body of knowledge. Each unit of knowledge could be seen as a growth of the tree branch, a line in the diagram, or a sentence in the truth statement. Each unit of knowledge represents a hypothesis. A hypothesis might not be tested yet, and so no growth past that part of the tree, no extension of that scientific theory, can be made, until the hypothesis withstands verificationism/disprovability(I.e. the hypothesis stands up to scientific rigor). Some branches on the tree, some models and theories, will grow and then come to a stop. Some models can only go so far, and then they die, forcing a growth from a more initial part of the tree, a more basic and fundamental scientific truth statement. Sometimes scientific models and theories take wrong turns, and once determined to be wrong, the scientific community responsible for those models and theories have to take a few steps back and take a new direction.

Now, every hypothesis is a hypothetical truth statement. That is to say, it is a statement of hypothetical truth. The statement, in order to no longer be classified as a hypothetical statement and be considered a member of the class/set of all truth statements must be judged to be true, and as we have seen that can only be done through deduction (which is to say, by testing all other hypothetical truth statements first, i.e. testing all possible hypotheses).When the tree grows, it rests on the previous parts of that branch that it has extended from connecting it to the trunk (axioms) which provide it with nutrients (validity/means for being true). Just in that way, any hypothesis to be tested also takes all previously non-refuted hypotheses (i.e. currently accepted models/theories) into account in order for that given hypothesis to be possibly/plausibly true.

An example might be good. Let’s say for example any and all currently investigated hypotheses based on dark matter and dark energy. The truth value of any and all such hypotheses rest on the truth value of the hypothesis that there exists dark matter and dark energy. That is a hypothesis, as it has not been proven to be true. It has not been proven to be true because it has not been held up to deduction. It has not been held up to deduction because not every possible hypothesis to explain why mathematical predictions for the masses and energy in the universe (which rests on other hypotheses such as the universe being a closed system, the accuracy and truth value of our proposed laws, concepts of forces and geometry of the universe) do not match what has been observed empirically. Every hypothesis made rests on another hypothesis. It rests on it because it grows from the hypotheses that precedes it. Like a tree branch, the newest growth proceeds from the older branch. The older branch must remain alive in order for the newest segment to remain alive. A current hypothesis rests on an older hypothesis that has not been refuted. At any time a hypothesis is refuted, like a point along a tree branch, any further growth from that hypothesis (or tree branch) will also be refuted (die).

And so as more and more experiments are done, more and more hypotheses will be refuted (branches die off or stop growing). If we were to follow our visual model for the growth of scientific knowledge, then ultimately, a deductively arrived at empirical scientifically objective truth would look like a tree with a single branch on it. As all other branches would act as competing hypotheses, and they would all be refuted, necessarily, in order for there to be a single objective truth.

Now, each growth along the tree occurs in bursts. In the same way that a model or theory or knowledge in science extends by units. These units are single hypotheses. Each hypothesis is a statement of hypothetical truth, and thus, is a statement communicated in language. So, we can say that each hypothesis is a sentence.

So, if we model each hypothesis (aka potential truth statement within the body of scientific knowledge) as a sentence, then we can view each successive growth along that tree branch, along that hypothesis, as another sentence. Therefore, once the single branch is arrived at and modeled in language, it would represent to us a series of sentences about the truth of all scientific knowledge, which is to say, a complete theory/model/explanation of the universe/nature/reality/the world/etc. This series of sentences could be turned into a single sentence. Each sentence could be connected to the other in order to form a single sentence simply by ligating the two sentences via the use of the conjunction word “and”. So instead of having the following sentences: A. B. There would be the single sentence: A and B. Where A/B represent sentences of hypothetical truth value (hypotheses/scientific truth statements). This process could be continued such that the entire body of scientific knowledge was contained within a single sentence which contained within it each and every truth statement, conjoined together via the use of the conjunctive “and”.

If this is the case, then we must then consider the simple a priori truth that any and every sentence can be extended indefinitely. Each and every sentence can be extended by the addition of another “and”. This is exactly the same as saying that another hypotheses can always be posed. There is always one more hypothesis that someone can pose. In the same way, given any sentence, no matter how long or what the content is, it can always be extended with the use of “and”.

This sentence can be extended and it will continue and then it will get longer and it will end up being a run on sentence but it won’t matter because in the end it will still be one single sentence and that sentence can either be true or false and the truth or falsity of that entire sentence can be judged and so if it is found to be false then the entire sentence is false and if it is found to be true then the entire sentence will be true and if that is the case then that sentence will be true but if we extend from that true sentence another segment by adding and to it then that will form a new sentence altogether which has its very own truth value and then we will have to judge that new sentence for its truth value and and and and…

If that is case, then that sentence can increase indefinitely, as it can always be increased once more. Since every increase of the sentence represents a new hypotheses to be tested, then the extension of the sentence directly means an extension to the number of experiments that must be done (test of hypothesis). This necessarily means that there can always be one more experiment needed to be done in order to come to a deductive statement regarding the truth value of a scientific statement. If this is the case, then no deductive empirically scientific truth statements can be made. This means that science can never produce a single true sentence. This means that science cannot produce a single truth statement. This means that not a single scientific truth can be arrived at via deduction, through scientific experimentation (this does not necessarily dismiss mathematics and geometry, though that is a separate topic).

So. What does that mean? What meaning can we derive from this?

We started with the belief/assumption/postulate that science was in the business of arriving at objective truth statements. The experiments and results themselves are not the criteria for judging whether those results are true or not. Rather, we produce results and we must judge whether those results are true or not. The criteria of that judgement must be objective in order to maintain that science and scientific knowledge is objective. As Kuhn argued and as can be seen and experienced in the world, science progresses under convention, belief, aesthetics and some application of logic, logic being the sole basis for making scientific statements objectively true. The logic applied can be deductive or inductive. Since we are in the domain of truth, and not the domain of confidence or probable or anything short of necessarily the case, then inductive reasoning cannot grant us valid scientific knowledge. It is not necessarily true. Rather, we must use deductive reasoning.

A deductively arrived at explanation/model/theory must be necessarily true. In order for a single theory or model be necessarily true over every other theory or model, each and every possible model/theory must be tested, and all are found to be refuted except one. That single non-refuted theory/model can only then be accepted as true.

So in order to arrive at a deductively true scientific truth statement we must test all hypotheses (all theories and models of explanation). Every hypothesis rests on other hypotheses. No single hypothesis can be determined, by deduction, to be true, until all others are refuted. But since another hypothesis can always be posed, then there will always be another hypothesis to refute. Therefore it is impossible to truly arrive at an objectively true scientific statement. This is true only given all the definitions and assumptions and postulates that were put forward earlier. This truth statement is no different than a truth statement from science. The validity of its truthfulness must be judged based on a criteria, and must meet judgement.

I would be happy to see where the errors might be, but as of yet I am not yet aware of any. If we were to settle at any given scientific theory and decide to stop testing, we would necessarily have to stop hypothesizing as well. This would have to be something agreed upon, by convention. It would have to be an acceptance and perhaps an enjoyment and appeal to the aesthetic of the model/theory that science provides for the universe/reality/nature/the world/etc. But, logically speaking, it is always possible to pose one more hypothesis. So, science can arrive at something, but that is only based on non-objectively arrived at criteria such as aesthetics, belief and convention. Thus, the only “knowledge:” that could ever be arrived at via science would be belief/allegory/myth/folk lore, or a set of false beliefs (erroneous world views).

If you are satisfied with that argument you do not need to read any further. I will now approach this argument from a different method, one related to sets and set theory.

Let K be the set of all Knowledge. All the elements contained within K are all the knowledge in existence.

set k

Every single thing that we can determine/label as knowledge belongs to the set K. Knowledge of what I did yesterday for lunch belongs in K, knowledge of how I felt my bathroom renovations were finished is contained in K, and knowledge that for a triangle on a flat planar surface, the sum of the interior angles are equal to 180 degrees, while those of  a triangle on the surface of a sphere are greater than 180 degrees.

Now, we can group together some of those elements(units of knowledge) into separate sub-sets. We can call one sub-set, P, be the set of all personal/subjective knowledge (i.e. I have knowledge that I am hungry, that I need to brush my teeth, that I am going to do renovations today, etc). Let S be the set of all scientific and objective knowledge.

set s and p

Now, all of the knowledge, all of the elements within the subset P and the subset S are all contained within the greater parent set K. Some knowledge from P (personal/subjective) can overlap with that from S (scientific objective knowledge). This is visually represented by the area of overlap between the circles S and P.

Our current concern is science and scientific knowledge, and so we are only concerned with the elements contained within subset S. All elements within S are truth statements that convey scientifically derived objective truths. So, all elements within S are statements, and thus are sentences.

In order for a sentence to become a member of the set S, it must be found to be necessarily true via the methodology of science. This is to say, in order for a sentence to become a member of the set S, it must be necessarily true via experimentation. Again, as we mentioned above, in order for a scientific truth to be necessarily true (such as an interpretation, a model, a theory of science, an explanation) it must stand up to deduction. That is to say, that sentence can only be necessarily true if all other sentences (scientific explanations/hypotheses) have been refuted.

Let HS represent the set of all Hypothetical Scientific Truth Statements. All the elements/members of this set are all the possible hypotheses that can be posed. This set contains all possible hypotheses. Therefore, early on in scientific pursuit, it will contain many members (many possible hypotheses), but as experiments are carried out, and hypotheses are refuted and found to be untrue (not possible), then the set will have less and less members. This is the case because after a hypothetical truth statement is determined to be false, it is no longer a hypothetical truth statement and we can now classify it as a false statement.

Visually, we could represent this as such:

set e

We now have an even greater/fundamental set, E, the set of all sentences. Within E, the set of all sentences, some sentences belong to the set of all knowledge, K, (meaning true sentences) some sentences are hypothetical truth statements, HS, and other sentences are false and thus belong to the set of all false sentences, F.

It is clear that in order for there to be a member of the set S (scientific objective truth statements), this can only occur when there is only a single member/element in the set HS (hypothetical scientific truth statements). This must be the case because deductively, a scientific hypothesis/statement can only be necessarily true if all other possible hypotheses have been refuted and discarded. So, the inclusion of sentence (member) within S rests on the membership of elements (sentences) within the subset HS. If there are at any point more than one member (sentences) within HS, then there can not be any members (true sentences) within S. Once HS has only a single member (which is to say there exists only a single hypotheses (or sentence of hypothetical truth value) that has not been refuted) we can deduce that it must necessarily be true (again, assuming there is an objective truth to be found). Then, and only then, can we then re-classify that hypothetical truth statement (sentence) as a sentence that belongs to the set/class of scientific truth statements.

So, the existence of ANY elements/members within S, which is to say the existence of any scientific truth statements whatsoever, rests on there being only a single member within the set HS.

However, since HS represents the set of all hypothetical truth statements, and since truth statements are sentences we run into two reasons why this set will never be reduced to a single member. First, we can always produce one more sentence. We can always produce one more hypothesis. The existence of just one more hypothesis will leave the set HS perpetually with more than one member/element. Secondly,a priori we know that any sentence can be extended by the use of the conjunctive “and”, then every sentence can be extended indefinitely, and thus this new extension of the sentence must be tested as a new and unique hypothesis of its own. This requires one more experiment. Since we can indefinitely extend any and every sentence by the use of the conjunctive “and” then we will always have at least one more experiment to perform. Thus, deductively arriving at a single truth statement is untenable.

So, HS can never have a single member, and this being the case, S, the set of all scientific objective knowledge can never have any members. This means that there can be no objective scientific knowledge.

The only time HS can have a single member is if we consciously decide not to pose any further hypotheses. Since, logically speaking, there can always be more hypotheses to be put forward, it is always possible to pose one more hypothesis. However, it is not necessary. There is nothing forcing anyone from posing a new hypothesis. Therefore, the fate of the set HS arriving at a single hypothesis rests solely on the decision to pose a new hypothesis. This being the case, then the criteria in which HS is found to have a single member (and thus S has a member) comes when, via convention, belief and aesthetics, it is found that the single member of HS and thus S are satisfactory and no further hypotheses are warranted or wanted. Convention – because it must be agreed upon, whether implicitly or explicitly, not to pose a new hypothesis. This would occur when the current hypothesis/explanation/truth statement/sentence is deemed acceptable and no other is necessary. Belief – because though it is not known necessarily, the hypothesis/explanation/truth statement/sentence that is deemed acceptable is done so under the belief that it is true and will be true in perpetuity, and it explains the objective truth of all phenomena. Aesthetics – because we have to accept the hypothesis/explanation/truth statement/sentence as something that fits. It is something that we think makes sense of the world. Logic alone can not be enough for someone to accept something as true. In the face of a logically sound argument whose conclusion is unpleasant and unwanted (aesthetically unpleasing) people will try to find a way to disprove it or find a way to circumvent the logic. To accept the logical argument is to agree with the aesthetic of it.

Now, though there can always be more hypotheses to be posed, one can simply be happy/content with not asking any more. This, under the axioms, assumptions and definitions agreed upon within this system, is the only means for arriving at an objective scientific truth. Which is to say, the only way that objective scientific truth is to be arrived at is through convention, belief and aesthetics. Something that most people would agree is not science itself.

And so, for there to be any membership within S, necessarily, logically speaking, the member of S would not actually be an objective truth statement, rather, it would be one agreed upon by convention, taken on belief/faith, and found to be agreeable in its aesthetics. It is for this reason, as well as others(such as how paradigm shifts occur and how science progresses) that I contend that science is no different than any world view that we would classify as allegory/myth/folk lore.

But what do I know. If there are errors in my reasoning, I would welcome being shown them. But at this point, I am pressed to find them.













Geometry Matters!

[I apologize. I am publishing my rough draft. I edited it and cleaned it up, but when I tried to save it everything got lost. I cannot be bothered to repeat those efforts.]

The stage is set. It is the 4th century BCE. It is ancient Greece. People are thinking about ideas. Possible explanations for how the world works, how nature operates, are being entertained. A Greek mathematician, Euclid, decides to essentially compile all known geometric and mathematical knowledge known in the world at that point. His work, the elements, is the foundation for much of the mathematics and geometry to move throughout history in human thought.

Now imagine. Place yourself in this time. This is the beginning of creating a system of math and geometry, of putting it to language in written form and to have the ability to send out to the world for people to consume and acquire. It is a hypothetical truth statement, it is not a book of false statements. They assert their own validity and truth value. Nothing of this sort had existed up until then (at least that we have empirical evidence of, and of such vastness). Now, what reason might a person who picks up this book ever decide to accept it as truth at all? Imagine, the very first argument for mathematics or geometry. The first time someone ever said “the sum of all angles within a triangle is 180 degrees” or that “the area of a triangle = 1/2 the length of the base multiplied by the length of the height of the triangle. What criteria would someone who has never heard that before have to accept it as truth?

This question can be answered for both how any child consumes and acquires mathematics, and for how the people of the day, grown men and women, who had lived their entire lives without knowledge of geometric and mathematical proofs and methods, are to accept mathematics…

The child does so simply by accepting it as true by convention. They are told this is the way things are, this is the truth, you memorize it, and you will be tested on it later to make sure that you still remember, you have acquired these truth statements. Perhaps this is why many kids do not do well with mathematics. They are not taught the first principals of which they are based off of. Instead, they are asked simply to believe, on faith, via convention, via authority, that what is being told of them is true. Others acquire it easier because they find it aesthetically pleasing. It makes sense to them. They see how it fits together. It is an aesthetic event and phenomena. They see something and conceive of something that someone else cannot. They see connections and relations where the other person cannot. Perhaps this is why memorization is not optimal.

But imagine a grown man, in the 4th or 3rd century BCE. Or whatever century copies of this book, The Elements, finds its way to you, to your country, and translated in your language (which requires someone who knows both languages, and is in contact with a scribe of sorts, and the means to produce the book). There was no internet, no data transfer, no email, no planes. Animals, carts, people, and testimony (gossip/news).Now, you receive this copy of the book, and you are now told all these things. What is your criteria for accepting it? Do you simply accept all foreign and different truth statements.

Geometry is not quite the same as farming or making cloths. Though farming could very well be an aesthetic and phenomenal model of geometry. Geometry could be intuited from farming, once one saw land, related sizes of one plot with the size of the plants growing, inferred that double that size would double the size of crop production. Found some system of denoting the size/shape/geometry/area of the crop (number of steps, lengths of cow, whatever), then made the inference that if that same area is repeated a similar crop would be produced. There is a correlation made. A connection between two things that would not have normally been there before. A new concept. And that concept is that of identity or relation. If this = that, and you make another this, then you should get another that.

It is not necessarily true, but it is an inference, a hypothesis, an assumption, a guess, an axiom.

And then we do that. Then once successful, or a relation is made, then desire can come into play. If I know I can manipulate nature, I can make an action in the world and a causal effect would come about that I wanted to, then now the only question I should ask is, what is it that I want?

And so a food quota could be produced. If I reason that we need a certain amount of food, and there are this many of us, we will need to produce this much. Now that I know how much I want, I can solve for x, x being the size of the plot of land necessary to produce the amount of food that I desire. I need this amount of land.

I am on a tangent.

So, what reason would that person have to accept it as true? So mathematics has to give you a reason to accept it. Geometry has to provide a reason to accept it. Mathematics/geometry come up to you and say “I am the truth”, you would want to ask “why?” or “how can I know that you are the truth?”. Mathematics would say “Here are my assumptions, the starting point from which I necessarily arrive at these truths. I call these assumptions axioms. I assume them, I take them to be the case because they are self-evident and do not require any proof of their own. In fact, they cannot be proven. That is just the way it is.

So, let’s make believe. Let’s pretend you are that person from over 2300 years ago. You open the book,first you see a list of definitions.

  • A point is that which has no part
  • A line is a breadthless length
  • A straight line is a line which lies evenly with the points on itself
  • A surface is that which has length and breadth only
  • A plane surface is a surface which lies evenly with the straight lines on itself
  • A figure is that which is contained by any boundary or boundaries
  • A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another

And more. Now, it is you, the reader, to decide whether or not you choose to accept this as true. What does it mean for a point to have no part? Can something with no parts exist? A straight line is made up of points. And so on. All resting on a point is that which has no part. A point (something with existence) is that which has no part (is not made up of anything).

Now to the the assumptions, the axioms you see are:

  1. Things which are equal to the same thing are also equal to one another.
  2. If equals be added to equals, the wholes are equal.
  3. If equals be subtracted from equals, the remainders are equal.
  4. Things which coincide with one another are equal to one another.
  5. the whole is greater than the part.

So, we have if A=B, and B=C, then A=C, x + y = x + y, x – y = x – y, if A=B then B=A, and if A and B are both things (not zero, not non-existing), then A + B > (is greater than) A, and A + B > B.

Those are up to you to decide if you accept them as true or not. This is a book you just got and have nobody in the world to talk to about if you accept or not. You have never read this book yet, though perhaps have heard the ideas (or not).

From these axioms Euclid moves to his 5 postulates. Let it be postulated that:

  1. A line can be drawn from two points.
  2. Any line can be extended along that straight line indefinitely.
  3. For any straight line, a circle can be drawn having the line as the radius and one end point the center of the circle.
  4. All right angles are congruent.
  5. If two lines that intersect a third line such that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

The first seems fairly straight forward. Pick any two points and a straight line can be drawn. We have the definition of what points and a straight line are above. This seems fine. The second also seems fine. You have a line, you can just keep making it longer, and it will still be that same straight line. You can make a circle by taking a line, keeping one end constant, and rotating it around in any direction along the other end of that line. All lines that form at 90 degrees/perpendicular are the same. But the last one… what does that look like?

There are two lines (one ones going more horizontally) and they intersect a third, any third line, in any orientation. If the two internal angles (alpha and beta) are less than two right angles, then if you extend those lines, eventually they will meet on that same side. we can use the opposite side, (the left side of the picture where the lines are moving away) and choose to see if those are smaller than two 90 degrees either, it doesn’t matter. But when we DO find these angles to be less than two 90 degrees, the lines will necessarily touch if those lines are extended, eventually.

And so, from just this hundreds of pages of proofs for propositions were deduced, using 100% only what was stated above, and no other influence or knowledge. Just those definitions, those axioms and those propositions (and any deductions that came along the way).

From that a form of geometry, a single form, came into existence. This form of geometry stayed in existence as the only form for roughly 2000 years. There was only Euclidean geometry. From acquiring this geometry we could now see things using these concepts, see relations using these concepts. We used geometry to model our reality, our technologies, our understanding of the world. We used these geometries to describe forces, to describe physics, the laws that physics and the sciences are based from.

Historically, the 5th postulate of Euclid has always been the one that stands out. It simply has. It is a longer postulate, yes. But there was something about it that caused it to stick out from since day one. In the middle ages Islamic philosophers attempted to disprove the 5th postulate.

Then in the 19th century non-Euclidean geometries came into acceptance as valid concepts.

For any given system, as long as the same starting definitions and assumptions are held to be true, no matter what logical deduction and interpretation that can be arrived at is valid. So, if it is possible to start from the same basic statements (definitions and axioms) and only necessarily true (deductive) statements are made from that logical system with the same set of rules, then whatever is deduced, however it is interpreted, will be true. There can be no means to say one interpretation is more true or valid than the other.

Euclidean geometry is true when the lines drawn are on a flat planar surface, but surfaces are not defined such that they have to be flat. They are just two dimensional figures. In fact, there is no reason why we should even infer that a plane SHOULD be flat. But that was just how Euclid saw things, and that is just how everyone else saw things. And that was what was accepted, by convention, as geometry.

But almost no surface is flat. Surfaces are curved. When you zoom in enough, there actually is no such thing as a flat surface. Flat surfaces can only exist in a universe where lines are made of points and points are made of nothing (no parts), which is to say, no dimensions. But in a physical universe of stuff, of matter, everything has a part, everything takes up space, has volume, has three dimensions. So a mathematically, geometrically flat surface is not even possible.

We see more often in the world curved surfaces. Such as the entire surface of your body, the surface of a tree, of a leaf, of the earth.

And so if we look at the geometry, as defined by Euclid, on the surface of a sphere (such as the Earth), we get straight lines forming a grid such as our longitude, and our latitude. The unique thing is that any given straight line on the surface makes a complete circle around it along the longest possible route (the circumference). Each line of longitude pass through two points, the poles. Now, if we take a look at the 5th postulate using this spherical surface:

We will see the example again of the 5th postulate. Take any two lines and a third that intersects them both. Like these 3 lines:


You will see that any two straight lines that can be drawn parallel from the equator of a sphere (or any longitudinal line), will eventually meet at a single point (the pole of the sphere). Euclids 5th postulate states that that occurs when the sum of the two interior angles are LESS THAN the sum of two right angles. Yet, in the spherical geometry we see that the sum of the two internal angles are equal to two right angles, because they both are right angles, and all right angles are the same (congruent).

So the 5th postulate is not true under this spherical geometry (non-flat planar surface).

and interesting thing to see is that under this spherical geometry the sum of the angles of a triangle necessarily must be GREATER than 180 degrees. This is very different than any geometry we normally believe to be true. And yet, empirically it is true for our planet.

If you were to go buy a piece of land and the gps coordinates of that land were such that along a given line of latitude (ie. the equator), and you were to draw two straight lines heading to a single point (meaning the shape of the land was a triangle), you could literally get out your ruler and protractor and measure it out, and the sum total of the angles on the inside of that triangle would add up to more than 180 degrees. It is the geometry of our planet. It is empirically observable. It is true.

Yet we don’t see geometry that way. We see it as flat and in a plane.

We could do the same thing for other surfaces. For hyperbolic geometries, geometries of any shape.

So what? What does this matter to me? How does geometry matter?

Geometry matters because it is directly related to how we perceive in the universe, how we perform science, how science and math is used to explain the universe, and our entire body of scientific “knowledge”.

Here is why:

Because both sets of geometry are both 100% true, both 100% equally possible, either can be adopted. Now, science operates under the belief that the truth of the universe, the true way the universe is and can be explained and modeled, is objective. Meaning there is one single truth to be discovered and elucidated.

That means that there can only be one geometric shape of the universe. Is the universe a sphere? Is it planar? Is it hyperbolic? Is it _____ (insert any possible geometric surface curvature here)?

So science and scientific knowledge depends on there being only one single true geometric shape of the universe.

Now, science is a study of empirical data. To determine something scientifically it must be testable. You must be able to refute the claim made by science, the theory.

An experiment could be made. You could take the surface of whatever it is you want test to determine its curvature. And you can draw along that surface grids that pertain to all the different geometries. Euclidean or non-Euclidean (spherical, hyperbolic, etc) grids on the same one single surface (ie. the floor of the room you are in now). And the experiment could be done that you will roll a ball on that surface along a straight line, and you could then watch the path of that ball and see which grid it traverses. Then you would know the answer to the surface curvature (the geometry of it).

You can do this experiment because it rests on the belief/assumption/axiom/Newtonian “law” that all of physics is based off, of inertia. That something when put in motion will stay in motion along a straight line until some external force prevents this. This is your basic law of inertia. Self evident. It needs no proof. It is an axiom of science.

So, keeping this in mind you do the experiment. The ball traverses the floor and you can see and plot out its path empirically. Now, it will follow a straight line in SOME grid system used (and each grid system used represents a distinct possible geometry that follows Euclids rules of geometry). Now, here is the thing. From the results of this experiment it is impossible to judge which geometry the surface actually is (objectively). You cannot determine an “absolute” geometry.

The reason for this is because you can interpret the results in any way, and none are necessarily true. If the path of the ball followed along the grid of straight lines that represented a flat surface geometry, and not of a curved surface, you could say one of two things, all based on the law inertia:

  1. The surface is flat, and no forces were acting on the ball.
  2. The surface is curved, and a force was acting on it such that it moved off the straight line of the curved surface and so it appeared to move on a flat surface.

Likewise, if the ball followed along the grad of lines that represented a curved (ie. spherical or hyperbolic geometry) surface, you could say one of the two things, all based on the law of inertia:

  1. The surface is curved, and no forces were acting on the ball.
  2. The surface is flat, and a force was acting on the ball such that it moved off the straight line and so it appeared to move on a curve.

No matter what the outcome, a necessarily true interpretation cannot be found. All interpretations are valid.

The inference of forces stems from objects moving out of an inertial frame (a straight line given that accepted geometry). So the two are co-dependent. With that said, depending on which geometry you decide to accept, this will change the existence of forces. Some disappear and new ones appear under different geometries of space, of the universe.

So when we hold a “scientific fact” to be the absolute and objective truth of the way things are, we should keep things like this in mind. That we cannot truly know for certain, as an objective truth. Even our very fundamental concept of the geometry of things comes into question. An alien from another part of the universe that evolved such that their ancient mathematicians and philosophers first devised a mathematics and geometry which was conceptually spherical will have deduced different laws to explain the same universe. They could create the same technologies and everything. The only difference is the model, the aesthetic of the universe, the allegory for truth changes. What is being represented by the model will still be accurate in the way an analogy is accurate.

And so meeting that alien we might have different laws of physics, different equations and conceptual schemas of what exists, what is in the universe, what laws govern it, etc. But both will be capable of the exact same things.



A(n aesthetic) theory of everything

Science is the pursuit of the theory of everything. It has the motivation and goal to explain all that can be explained (via science). It looks to explain all of nature, all of the universe through equations. It is seeking a grand unified theory of everything. The truth that science seeks to encapsulate is the objective truth of the universe.

Let’s just assume this is possible. Let’s just assume that this occurs. Suppose that today or tomorrow or next year scientific explanations have come to a conclusion. EVERYTHING can now be explained. Everything. There is no more mystery that science cannot explain, cannot model, cannot predict. This is what the scientific pursuit aims for. It is its purpose.

Now, we should ask ourselves some questions.

First, is this what we want? Is life better when we know absolutely everything about everything, where all things can be explained and all predictions knowable? It is an important question to ask.

Second, how will this knowledge be consumed? Do we believe or expect every single person on the planet to now memorize or come to know all of the science that explains everything? I can hardly expect this to be the case, since today there is LESS scientific knowledge (I assume) than there would be come the day when science has explained everything. And if generally people are not educated in all of the current science, then why should/would they be in the future when even more (all) scientific knowledge is made known?

There are also those people who do not have scientific minds. They don’t process information in that way. They don’t conceptualize atoms and cellular pathways and molecular mechanisms and physical laws. What use will be a scientific model for those people?

Once (again, I am assuming this is even possible) all things are known through science, this knowledge, if it is to be useful, will need to be consumable. In order for it to be consumable it must be understandable and easy to relate to and to conceptualize. It must be simple enough to grasp for all. These become issues of aesthetics. Not just that, it should be enjoyable and fun to consume. This is also an issue of aesthetics.

Once science has finalized all the knowledge of the universe, there will be few interested in the jargon and mechanical technicalities involved in understanding. What good is knowledge if it is too complicated or unpleasant to consume and acquire? What will become necessary (for most, and preferred by all) will be a conceptual schema of that knowledge that can be enjoyable and easy to communicate and represent. Aesthetics.

This is what allegory brings to the table, it is its strength. This is what metaphor and story make possible. I do not foresee a culture of people, upon knowing all of the objective truths of the universe, being capable of communicating all of these truths through complicated mechanisms and equations. What I see as much more likely is an allegorical representation of those equations, of those mechanisms, of those physical laws. I see this as a necessary process if the scientific pursuit ever succeeds in achieving its goal. Culturally, socially and qualitatively, it will allow all people to make use and maintain the knowledge gained.

We do this to degrees today. Watch any PBS/Discovery channel scientific show and the explanations (which is meant to reach a general audience of a wide range of cognitive abilities) given are often soaked in analogy, metaphor and allegory. A concept that is already ready at hand for the viewer is taken into account and used in an analogy so that they can consume and derive meaning from the scientific model. When I am asked for a scientific explanation for a given thing I am forced to do this as well. I cannot use the language and jargon of the scientific world. That would be a horrible explanation as it doesn’t take into account the person who is looking for the explanation.

And in this same way the general public will want to reap the knowledge that comes when science has come to ‘know everything’. And in this same way, it must be consumable and aesthetically pleasing. Scientific knowledge via allegory, via metaphor, via myth and story.

I find it curious. Science was born from not accepting the current stories of the time, the current, you may say, myths. In its own pursuit it may very well end in a myth, a story, an allegory of its own.

A physical/scientific rationale for skepticism?

All conscious beings are conscious of something. We perceive. Right now, reading this post, you are perceiving the screen, the words, and the meaning that you derive from those words.

We trust that what we perceive is precisely what is actually “out there” in the “real world” (i.e. reality). We trust our senses and our perceptions to be a correct portrayal of “reality”. We do this, despite having full knowledge of a wide range of variance in how we and other people perceive “reality”. We can have differing views from others on what is hot, cold, blue, red, grey. We can even have variance in our own views. When we are sick our sense of taste is different. Try drinking orange juice after brushing your teeth. It tastes metallic! When you are in a different mood, things appear differently. When you are starving, food tastes better.

So what does that mean? Is the taste of orange juice “in” the orange juice? Is the taste of orange juice a property of the orange juice? Most people would probably say so. But how can that be? The orange juice didn’t change between when I was thirsty, when I was sick, or after I brushed my teeth. Why is the perceived taste not constant?

We inherently know that our own states can alter how we perceive things through our senses. And so, with a scientific world view of atoms and mechanisms, we can say that each state is different in some causal way. The toothpaste on my tongue altered how I taste the orange juice. But really, truly, the REAL taste of the orange juice is still there. I just didn’t accurately experience it. That is probably a common interpretation.

There are other examples of differing perception. Color blindness. Synesthesia (where people mix up senses, i.e. they smell colors, taste sound, etc). Now, with all this variance, whether it is color blindness, synesthesia or the difference between orange juice with or without brushed teeth, under what criteria are we to judge is the “actual”, the “true”, the “normal” the “REAL” taste of orange juice, the real phenomena in question? Aside from convention, I am not so sure.

And so, if that is the case, is reality just something we agree upon?

We believe that our everyday normal waking experience of the objects we perceive is the true reality of things. And those other examples, color blindness, synesthesia, brushed teeth, etc, all of those states are abnormal. Those are the special cases. But really, truly, our “normal” waking state is the truth of reality. I won’t comment on this view point, but needless to stay it is not a good argument.

A scientific hypothesis could be made that under the assumption of evolution the organisms that are best able to perceive nature/reality as it truly is will be better at surviving. This is a valid hypothesis. But it opens the door to a counter hypothesis along the same lines. It is perfectly conceivable as well that perceiving things truly as they are might be a detriment to the survival of an organism. Why else could denial come into existence? It is better to deny the existence of something, some experience or some truth, for ones mental sake (which is important for survival and success) than to address it as a reality. There certainly are scenarios where ignorance is much more important to survival and success than absolute knowledge.

In addition to this counter hypothesis there is a possible scientific rationale for skepticism, for being skeptical that what we perceive is actually fully true of how things really are.

We model ourselves through science and scientific theories. Under this model the body is made up of cells, cells are simply molecules, molecules are just atoms. These atoms, molecules and all the operations that occur in the body operate under forces (electrochemical, etc) and are governed by the laws of physics. Now, we also operate under the view that our perception is a physical process. The orange juice hits my tongue. It physically touches it. This physical interaction is nothing more than atoms touching other atoms. The taste buds (physical receptors on my tongue that bind molecules in the orange juice, that is, molecules OF orange juice) once activated play a game of dominoes with other atoms, a cellular process called a signalling cascade. The orange juice touches the taste bud, that taste bud (molecules) interact with another molecule, and that with another, and another, and another until molecules in your nerves reach molecules in your brain, and somehow, the experience of taste is perceived.

Now, someone who might have a “defective” taste bud (i.e. a genetic mutation that causes the tongue cells to express a different orange juice receptor) such that there sense of taste might differ from what everyone else tastes. For that person, they might always taste orange juice as if they brushed their teeth. Or maybe they taste something completely different. We believe that the reason why people differ in their perceptions have a physical causal reason.

Here is the thought experiment: It is perfectly plausible that there might actually be a single objective truth to what orange juice tastes like. Let’s just assume this. If this were the case, then in order to perceive it, there must be a perfectly tuned machine (the human body and all the machinery, i.e. molecules) capable of tasting the orange juice as it is. But, it is perfectly plausible that in order for the orange juice to be perceived EXACTLY as it truly is in reality, the machinery involved (the molecules and biochemical structures of the cell) are not stable or possible under the laws of physics. It is quite possible that yes, there is a single true objective taste to how orange juice actually is, but if there is, it can only be experienced as such under specific physical conditions. And it is perfectly plausible that those physical conditions are simply not stable under our laws of physics, or via the machinery of the human body (carbon based organic chemistry), etc.

If this is the case, there is a scientific rationale for skepticism. It would be impossible to know if it was the case or not.

So what does that mean? You tell me.

Bag of Chemicals Thought Experiment

With dualism it is hard to conceptualize how consciousness could arise from matter. If there are two separate categories of things (i.e. substances), how could they ever interact?

In order for two things to be able to interact in any manner, they must have something in common in which to interact. Imagine two people with lots in common, they have many means to interact. Imagine two people with polarizing personalities/interests/traits, they would have less things in common in which to interact, but at the end of the day, they still have quite a lot in common being that they are both humans, both on earth, both have physical bodies, etc.

Oil and water have minimal interactions. If you combine the two in a container you will find all the oil stays together on the surface of the water. Water is hydrophilic (obviously), while oil is hydrophobic. It doesn’t like to interact with water. Now, despite this, it still does interact with water because they both, categorically, have something in common: they both are made up of physical matter (i.e. atoms).

Now, mind/experience/consciousness is a non-physical thing (substance). While physical matter is, well, a physical thing (substance). How is it that one could possibly produce the other?

Let’s address the possibility that matter produces mind, as is commonly held in various schools of thought (scientific, psychological, etc). This is the underlying assumption behind views that depression is just the result of chemistry of the brain. What this view holds is that the presence or absence of more or less or different atoms touching other atoms (physical) results in a different state of consciousness (non-physical).

How can this be?

Some take this to be the case, as it stands. It is that way. I would like to bring a thought experiment into view which might challenge such a view. It addresses the ontology of consciousness, how consciousness, this non-physical thing, comes into existence, into being.

Let’s assume that a single atom (or sub-atomic particle such as an electron, a quark, etc) has no consciousness. It is dead. Lifeless. Inert.

Imagine someone has a bag of chemicals (atoms). The bag might be really big. It could even be the size of the universe. But for all intents and purposes, it is a bag of chemicals of a certain size, with a certain amount of chemicals in it. The chemicals have no means of escaping the bag, and no chemicals can enter the bag. Essentially, it is a closed system (just like the universe).

Now, the chemicals at first are just elementary elements to start with. Just your basic building blocks of matter. Hydrogen atoms, helium atoms, etc.

You shake the bag of atoms, and you do so over time (perhaps over 14 billion years; you are quite old and quite determined to perform this experiment). The atoms will, according to the laws of physics, move around, collide into each other, be attracted, be repulsed, bind to one another, dissociate, etc, etc.

Now, remember, initially we started with a bag with just physical stuff. Only one category of thing, physical matter. There is no consciousness, no non-physical thing in the bag yet. Now, today, in this moment, we can agree that there is consciousness in the universe, this non-physical thing. So, in order to go from a universe made up of ONLY one category of things (physical stuff) to a universe in which there are two categories of things (physical and non-physical stuff), there must be a precise moment where that one new category of things (non-physical stuff) comes into existence.

So, the bag of chemicals is being shaken around. Atoms are combining, doing their thing. At some point a star is formed, and at some point a star explodes, heavier atoms like metals are formed, some come together under certain forces and form structures we might call planets. Atoms keep atoming. Physical matter keeps doing its physical matter stuff (motion and collision).

Now, whether or not it is human consciousness, animal consciousness, a plant consciousness, a rock, a worm, a bacteria, a whatever, it is of no concern. What matters is that at some point the bag of chemicals (the universe) goes from a state of only atoms (physical stuff) to atoms and consciousness (physical and non-physical stuff). Now, at this current moment there is still only physical stuff (atoms), and as we approach the moment where consciousness comes into being, what do we have? We have dead, lifeless, non-conscious atoms in motion, in space, colliding and interacting according to physical laws. In theory each atom could be known by simply its location in space (if we could apply a gps location to it over the bag (universe), and it has motion. That is ALL THAT THERE IS in the bag (universe) at this point. Atoms. Moving. Some atoms are grouped together, and some form structures, but still, it is just dead, lifeless, non-conscious bits of physical stuff of certain amounts in certain arrangements. Like lego pieces arranged in a certain way over here, and arranged in a certain way over there.

Now, if our starting assumptions are correct, them being:

  1. There exists two different things in the universe: physical stuff (matter) and non-physical stuff (mind/consciousness/etc).
  2. Matter causes consciousness (physical stuff causes non-physical stuff to exist).
  3. Fundamental physical stuff (atoms, sub-atomic particles, etc) do not, in themselves, have consciousness.

So, if these assumptions are to be correct, and our system, our bag of chemicals (the universe) is to make a transition from a system that has only matter (physical stuff) in existence to a system that has both matter and mind (physical and non-physical stuff) in existence, and this transition occurs at a definite moment in time, t, then we should bring our attention to this moment in time, t.

Just moments before this moment in time, t, let’s say t minus 1 minute, maybe t minus 1 second, maybe t minus 1 nanosecond, maybe t mins 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 seconds. Whatever. As you approach time point t, what you will have are physical atoms in specific locations in space (three dimensional space coordinates, i.e. gps locations). Then, at time t, what has changed? If we are to accept that in one moment the system has no consciousness, and then the next it does, what has changed? Imagine a system of dead, lifeless atoms, and they all have their locations in space, and are moving on their paths (as they have for all of time), colliding, attracting, repulsing, etc, based on the laws of physics. Then, all of a sudden, the different just before time t and the actual moment of time t, what has changed? Atoms just moved a bit more into different spatial coordinates (gps locations), just as they have for all eternity before this moment in time, t.

Why is consciousness, this non-physical thing supposed to exist now? What is special about THIS spatial coordination of atoms, of matter? Literally, just a nano-second earlier there was no consciousness in the system. Remember, we are holding that the system goes from non-consciousness to consciousness. So there must a an exact time, t, where the transition occurs. So, just a nano-second earlier there was no consciousness in the system. You could give every single atom in the system, the bag, the universe, a specific gps location. And then a nano-second later at the moment of time ‘t’, the moment where consciousness comes into existence, what has changed? In a nano-second each of those atoms, those non-conscious things, have moved a little bit, based on their individual velocities given to them by forces from the physical laws of the universe/bag/system/nature. Where is the cause of consciousness? How could it arrive? And even if it were to somehow be formed from such a system, “where” does it exist? “What” is being conscious? Is it a property of the atoms? Is it a property of something other than the atoms? But there are only atoms. Is it something separate from the atoms? If so, how could the atoms, the only things in existence, create something from which they had no starting materials? What does that even mean?!?!

It seems logically inconsistent. A contradiction. Impossible, or at least, conceptually inconceivable.

Perhaps our starting assumptions are not correct. Let us start with the third.

Fundamental physical stuff (atoms, sub-atomic particles, etc) do not, in themselves, have consciousness

Is this a self-evident truth? For what reason do we have to hold this to be true? Well, assuming the first assumption is true, in that there is a dualistic universe of matter and mind, two distinct and mutually exclusive categories of stuff, I am forced to look at my own experience as a human. I have a body, and that body is made up of large number of cells. Each of these cells is made up of a large number of molecules. Each molecule is made up of a large number of atoms. Each atom is made up of a large number of protons, neutrons, electrons. We could keep going. Essentially, the thing I call ‘my body’, is a collection of an insane number of constituent building blocks of physical matter. Now, I only experience a single consciousness. Consciousness is irreducible, in that it is single, continuous, contiguous and it unites all my experience and perceptions into one single field. It is single, and it must be single, because if it was fragmented I could never have the possibility of memory. If each perception, each moment, was a different/separate consciousness, then information from one could never be made available to another. Memory, and so much more, would not be possible. I don’t experience my laptop as a separate experience to the temperature I am feeling now, as a separate experience to my dog snoring on the couch. Consciousness is all unified, singular, into one experience.

Now, I experience this singular, continuous, unified field of consciousness (thought the objects of my consciousness change, it is always “I” who experiences them). But the body is made up of a ridiculously unfathomable number of physical things. If each of these physical things had their own consciousness, how could I arrive at a single unified experience of consciousness? Especially if I am in perfect fluidity with the greater system, my environment. At every moment atoms, dead, lifeless, inert, non-conscious atoms from my environment are flowing and assembling “into” my body, and at that same moment atoms, dead, lifeless, inert, non-conscious atoms from “my body” are flowing and “leaving” and going off into the environment. I breath. Dead, non-conscious physical atoms come from my environment, enter my blood stream by binding hemoglobin, get shuttled to cells, form chemical reactions, and now, as opposed to just moments ago, are now structurally a constituent of the body. Did I gain consciousness? Does that even mean anything? When I eat, when I defecate, when I spit, when I scratch my head and thousands upon thousands of skin cells are removed from my body, when I bleed, I am losing these atoms. Is my consciousness being lost or affected?

We don’t believe so, do we? Because we have one unified consciousness. So we hold this assumption that atoms do not have consciousness. Otherwise, why wouldn’t I experience multiple consciousnesses. The consciousness from that atom, or that, or that, and that, and that one over there too. That is not our experience.

We also do not accept that atoms have consciousness, otherwise that would raise ethical issues as to how to treat every single atom in the universe.

Assumption two:

Matter causes consciousness (physical stuff causes non-physical stuff to exist).

Perhaps this assumption is not warranted. It is a generally held belief by modern scientific thinkers. Why are we becoming such a medicated culture? Why do we give our children drugs that we infer will have a causal effect on how they behave, how they perceive and experience existence? Someone that is depressed believes that the drug, which is just a collection of dead, lifeless atoms, will lead to a causal path where those dead, lifeless atoms will, following the laws of chemistry (which is nothing other than physics), interact with other dead, lifeless atoms, and somehow, in some way, that will lead to a change in the quality of the conscious experience (from depressed to not depressed).

I am not sure that this assumption is true, but it is not wrong to say that this is a standing assumption that the western, scientifically minded world holds to be true. Whether conscious or not, it is an underlying philosophical assumption and world view in which our behavior and decision relies upon.

Assumption one:

There exists two different things in the universe: physical stuff (matter) and non-physical stuff (mind/consciousness/etc).

This the biggest assumption of the three. The other two rely completely on the truth value of this assumption. This assumption is actually an inference that we make, as I mentioned in the materialism vs. immaterialism post, here. Essentially, we infer that there are these two things because we have a conscious experience. This conscious experience is of things. That is, consciousness has objects. When we are conscious, we are conscious of things. The only criteria that you have that you are conscious right now is that you are conscious of something. Properly put, in Descartes cogito ergo sum, what he is saying is that for as long as he is thinking (conscious), he is. For as long as we have an object of which we are conscious of, then we the thing that is doing the consciousness, the thing that is aware (the Self, consciousness itself), then we know that we are conscious. This is the case in waking life and dream states. But in deep sleep, there is no object of consciousness. The object of consciousness is no-thing. It isn’t that consciousness does not exist, rather, with the lack of an object of consciousness, there is no ego, no self, no criteria, no “I-am-ness” to make an inference of experience.

Now, we definitely know that consciousness exists. This is the single most truthful axiom, the single most self-evident truth that cannot be denied. More so than any other assumption or axiom, such as the axiom of non-contradiction (i.e. If P then not P is not true as it would imply a contradiction, i.e. my dog is sitting on the couch, by the principle of non-contradiction I cannot logically structure the thought that she is also not sitting on the couch (though this is quite possible and quite common in dreams, i.e. it was my house but also not my house, that person was my family member but also not my family member)))))))

So, we are conscious. And we are conscious of objects. Dualism comes into play when we infer that the things we are conscious of (which, in itself, consciousness is a non-physical thing, it is an experience, and nobody can touch my experience, though they can touch me and the things I am experiencing) have a physical true existence outside of our minds. We quite literally through this inference bring the objects of consciousness into a physical real existence. Just think, if a new born was put into a coma, and like the matrix movies, was kept alive for the span of a regular human life via feeding tubes, heart pumps, etc, etc, and that baby were to dream its entire life. For that baby (or adult or anyone in this thought experiment), all of the objects of its consciousness (the content of its dream) would be given ontology. It would be given existence. Reality. It would be real. The objects of the consciousness would be inferred to have real existence, out there, external to the mind.

When we are in dreams, in the moment, while we are conscious of those objects of consciousness (the content of the dreams), we are experiencing them as real. They ARE real. The mind, the consciousness, makes them real. We are experiencing them. There was a dream that changed my life and compelled me to investigate consciousness. I was in nature, some sort of forest type setting. I came to a narrow stream, it was about 3 feet wide. I decided I wanted to jump over the stream, I was heading to the other side. As I jumped over the stream a snake sprang out from the water and was looking to bite me. I was so scared, so startled, I woke in one of those cliche tv/movie panics. I was terrified, even still in waking life.

How could this be so?

If I think of a snake jumping at me now I am not scared. It is not real. There is no reality to it. I “know” it is just in my mind and not something that is actually “out there”, with a real physical existence.

But in the dream, the dream IS the object of my consciousness. It is the ONLY object of my consciousness. It is the only thing that IS. What is the object of my consciousness is brought into a real existence, it is inferred to be real, to be true, to be out there. The conscious experience of the object BRINGS it into existence, in relation to the thing that experiencing it, me.

Anyway. I have gone way off track and I am hungry.

Though I cannot prove any of the three assumptions to be true, and in fact I do not necessarily hold all or any of them to be true, my purpose of the thought experiment is to see logical impossibility of consciousness coming into existence from such a system.

Though it is worth addressing, quickly, the concept of emergent properties. Emergent properties are only concepts and conceptual. They exist only in the mind, and are analytic, which is to say necessarily definitional. When someone says hydrogen and oxygen combine to form water, and water has completely different properties that did not exist in hydrogen nor in oxygen, and so H2O, water, is more than the sum of its parts. It has emergent properties. And that this is what consciousness is. Something that emerges from atoms.

I have only a few things to say. First, this on the surface seems an intelligible argument, but it isn’t. It isn’t because what has emerged is still a physical thing. No new non-physical thing has emerged. Water is still physical. Show me how hydrogen and oxygen can combine to form a conscious experience.

More importantly, hydrogen + oxygen = water is a definition. It is like all bachelors are unmarried men. When I say the word bachelor, “unmarried men” is not an emergent property. It is just a definition. We first started with something, water, and we gave it a definition, H2O. H2O is given an analytic definition of being two hydrogen atoms and one oxygen. We made that definition, that rule, that concept in order to explain what “water” is.

To say water is an emergent property of hydrogen and oxygen is sillyness. We start with a phenomenal experience and we give it a symbol, syntax, a name, a word “water”. Then years go by, and eventually we want to explain just exactly what water is. So we create concepts of atoms, and we say water is H2O. In order to do that, we first instate what H is and what O is. We make up a system based on definitions. Now to turn around after all that and say “we have hydrogen as the real stuff, we have oxygen as the real stuff, and if we combine them something new comes into being, separate from the two, water. Water is an emergent property” is circular and non-sense. It is like starting off with forming a language, and before the written word existed we might have had the word “goat”. It is an utterance, a sound we make. Then, once someone decided it would be a good idea to take the sounds we make in our language and produce a written language so that we could write things down, an alphabet must be created. “Goat”, the sound and word, existed. Then, by definitions and convention, a certain symbol (letter) would represent the “guh” sound of “goat”, the letter g. And the “teh” sound of “goat” would be represented by the letter “t”, and so on.

Now, to develop the alphabet which is to represent the language and sounds, then to turn around and say “hey, ‘goatness’ is not contained in g, o, a or t alphabet symbols. Yet, when I combine them together into g-o-a-t, something new comes into existence that wasn’t there before, therefore goat is an emergent property” IS JUST PLAIN WRONG! It is not true. We created a definition of what the word goat is to be (g+o+a+t connected into one sound), in the same way that we define a bachelor to be unmarried man. It is purely analytic (definition). The predicate (description) is contained in the concept of the subject. It is contained via a definition. H2O is contained in the concept of water, as are H and O. There is no emergent property.

I have written for too long. I will count this as two blog posts towards my monthly goal of a blog post each day, as I could easily have divided it up.

All this to say, consciousness is not an emergent property. It is the fundamental foundation of our existence, the single strongest assumption/axiom we can rely on, and the thought experiment above shows that it is logically inconsistent and conceptually difficult (to say the least) to conceive of how dead lifeless atoms in one geo spatial position at a moment in time could have no consciousness, but if some of those atoms moved a fraction of a nanometer in one direction, at a new time point, t, consciousness would now exist. It does not seem plausible.