Updated: Mathematical models and reality – A peek at the opening of Plato’s Cave

In a previous post I very briefly expressed some thoughts about how close are mathematical models to actual reality, using the examples of a bird flock and a school of fish.   I did not mention it at the time, but my thoughts about such models came to mind by thinking about the several projects on the works that aim to simulate a human brain.  It is important to confess that I am kind of skeptical of the short term success of such projects; what is somewhat unclear to me is why am I skeptical. I take that back; I think I am skeptical from a fundamental neurobiology point of view. My skepticism is particularly acute when I think about the various versions of “connectome” projects, although in all honesty, at least part of my attitude comes from my general dislike of “-omics”.

Besides neurobiology and my grumpiness about -omics, this post is an initial attempt to organize my thoughts on the matter.  I apologize in advance; I feel that I am rambling a little…

Maybe I am in a philosophical mood, little grasshoppers… For the record, i think I like philosophy. I say “I think” because I have never taken any course on it besides the most rudimentary basic in my humanities course as a college Freshman in 19-noneofyourfingbusiness… (:-D)…

I think that the first time that I explicitly thought about these things was when I read one of Richard Dawkins’ books; I think is was Climbing Mount Improbable.  As all of Dawkins’ science books, it is a delight to read.  One of the chapters included a description of how relatively simple is to write a computer program to simulate, with eerie efficiency, the flying behavior of a flock of birds.

I remember thinking at the time that this was ok, but that reality must be something more to it than the reduction of the behavior of a dot in a computer screen to a few (actually very few) mathematical rules.  That can’t be all there is; what about what is actually going on in an individual brain of a given bird? Everything the bird sees from far above? What is something itches?

(Ok, go ahead, feel free to insert your favorite “bird brain” joke here…)

Anyway, I thought about the millions of neuronal connections in that little bird brain, I thought about the thousands of complex calculations that it processes in mere thousands of a second, the kind of calculations that made it flap its wings a little faster or a little slower or the ones that made it veer to the right or to the left, up or down… its left wing still itching like crazy …

Am I making sense?

Now, what I think that I am thinking is that we can model flock behavior all we want; we’ll inevitably fall into the proverbial asymptote, getting closer and closer to reality but never, ever quite there.  The same applies to a human brain, at an even bigger scale. The best simulation is no simulation at all!  However, if this is true, we are forever trapped within our own minds.  We can never know the true nature of reality.  We can imagine and model reality, but we could never, ever experience it directly.  Somehow these thoughts reminded me of the idea articulated in the 1970s by the philosopher Thomas Nagel in his essay “What is it like to be a bat?“, essentially about the nature of consciousness.

On the other hand, somehow I started thinking (and do not ask me why,  I don’t even know why I think the things I think about) about how we model the motions of astronomical objects.  We can do this with a high degree of precision.  Moreover, this is not even modern knowledge; people have been able to predict and model these types of things for thousands of years now.

Now, if you think about this (and you knew this was coming), a model of how the planet Mars moves through the Solar System is, as accurate as it is, just another approximation of reality.  The mathematical equations used to trace the movements of the planet treat the planet essentially as a point in space.  These equations are not explicitly concerned with every speck of dust, every stone or even every mountain in the planet.  In strict terms, every little movement, every minor “marsquake” changes the planet’s actual position ever so slightly, but is does not matter, since it does not significantly affect our ability to determine how to get a space probe there.

In other words, all the trillions of little points in space that correspond to every little rock, that correspond to every spec of Martian dust are implicitly accounted for within the single point that the Newtonian model of gravitation works with.

And still, this is strictly just an approximation of reality.

Plato’s Cave Allegory states that we are like prisoners chained to the wall of a cave, forever unable to look at the cave’s entrance, which would take us to the actual reality.  According to this analogy, our only hope of ever catching a glimpse of true reality is by looking at the shadows cast by the objects that happen to pass by the cave’s opening.

Although I still cannot say that I am a fan of a human brain simulation, it seems that mathematical modeling at least allows us to take a barely “corner of our eyes” view of the entrance of the cave.  Nothing more, nothing less, but it is a little better than mere shadows.  There is hope to know ourselves a little better. Is there a plane of existence with a more complete understanding of reality? I truly hope so…

In the meantime, I think I finally truly understand Plato’s Cave Analogy.

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  1. This will sound strange, but I think video and photography are wonderful aids to thinking about how we understand reality. Think of those videos which simulate moving through space and approaching the earth at a very high speed moving in close and closer until you reach ground level and perhaps focusing in on a field and then one ant in the field, one cell in the ant and one atom in that cell, etc. Things look different depending on where in the sequence you are.

    If you are above the earth, you don’t see the field. if you are above the field, you don’t see the ant, if you are above the ant you don’t see the cell and so forth. It’s all there the whole time, but what you see depends on what you are focusing on. Which level you are at in the range between space and atom, if you will.

    When it comes to computer simulations of the sort you are talking about here. we can get to a certain level of detail. We can simulate the effect of what is going on in the levels beneath the level we are examining, but ultimately it is not as revealing as we might think.

    An alien mapping out the trajectory of the earth’s movements knows nothing of the awe of a man watching the sunrise. And which reality is more real, more engaging – knowing that the earth has wobbbled a bit from one day to the next or knowing that the sun rise has given a man at the end of his rope hope to go on that day?


    1. Not strange at all, it is a great comparison! Video photography, etc., are extensions of our senses, just like a microscope or a telescope. Also, You reminded me of many movie scenes (like in the “Men in Black” movies or in “Contact”) when they zoom in or out, revealing different levels of reality. Then there is of course, what you said our mental realities…. Lots of things to think about indeed… (:-)


  2. Yes, for some aspects of our reality do not needs extreme accuracy of measure. Such as dots (planets) in universe. Is possible know reality and I think that say “all we see are representations, nothing more” is a irresponsable posture.


    1. Hi! I did not say that we are all representations, there is an undeniable level of reality. Our perceptions of reality, now those are representations, no question about it. We are very limited when we want to figure out reality… Thanks for your comment!


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