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. 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.
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 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?
(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 processed 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…
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. 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 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.