Two women are sitting across my table and in the midst of an intense discussion. I don't know the exact content of their conversation as I can't understand Swiss German. But from the looks of it, it appears they are fighting... against numbers! Several papers and books of Elementary Algebra litter their table - a common scene at the Einestine cafe of the ETH, during high study hours. And that got me thinking about numbers...
Through the glass wall, I could see old and new buildings seamlessly standing next to one another, covering the visible landscape of Zurich. No doubt that an intense amount of numbers and mathematical principles were invested in their design and construction... if not for their elegance, at least owing to their proximity to the reputed ETH campus. :) What is most intriguing is that these buildings, as well as pretty much every thing around me, are very static, very rigid, very predictable. But then again, they are products of very static, very rigid, very predictable (once you know the rules) entities called Numbers! Mathematics!
Through the glass wall, I could see old and new buildings seamlessly standing next to one another, covering the visible landscape of Zurich. No doubt that an intense amount of numbers and mathematical principles were invested in their design and construction... if not for their elegance, at least owing to their proximity to the reputed ETH campus. :) What is most intriguing is that these buildings, as well as pretty much every thing around me, are very static, very rigid, very predictable. But then again, they are products of very static, very rigid, very predictable (once you know the rules) entities called Numbers! Mathematics!
What are these mighty Numbers though? Are they real? I am sure mathematicians posses very highly elaborated perspectives about this concept. From my highly simplistic perspectives though, numbers, and mathematics at large, are as real as we want them to be. They represent the most effective way, to date, for us to collectively understand and manipulate Nature. But are they really the scripts of Nature? Can we envision knowledge and creation without the kind of numeric framework known to mankind at present?
I think the necessity for numeric representation of nature is closely tied to the cognitive capacity of the human brain and efficiency of interpersonal communications. Bluntly speaking, the brain functions under the principle of experiencing its environment (learning), storing some pattern of the experience (memory), and responding to the environment based on these two (adaptation). For this process to succeed, it is very essential that the brain has a certain framework, a scaffold, a reference. It can't simply learn and form memories anew every time. Or it probably does not wish to, as that would involve a tremendous amount of resources. So, in time, it would settle to simpler options that build upon its past experiences, things it can easily cross reference to expand an already existing pool of knowledge. Indeed, this is a very efficient working strategy for an entity very much constrained in space, time, and resources... but, alas, all the lost new-learning opportunities! The brain must be quite a stubborn creation, and some people take this trait to the extreme :).
I think urge of the brain for a fixed framework also sticks out to some personal and societal traits. We learn about things and easily take it as a universal truth; it is just easier! - This is a computer. I wish to have a computer. So my future computer should be something like this. It would be extremely implausible for me if someone sells me some liquid in a jar as a computer, although it may be zillions of times faster than a modern supercomputer. - So probably the way our brains function predisposes us to a rather rigid behavioral framework.
It seems there is a job opening for mathematics right here. Numbers are fixed (more or less) and can be arranged to represent our experiences in an extremely rigid manner. That saves our brains from confusion, provides a rule/reference which simplifies future learning/adaptation. At a behavioral level, this creates, propagates, and sustains consensus. That way we don't have to reinvent the wheel in every generation. We only improve upon it. Essentially the wheel in ancient Egypt and modern spacecrafts have pretty much similar design concepts. Is it possible that something very different - not circular, not rotating, not linked to a gear - could have been discovered had our ancestors' brains not got stuck in one design that they decided to keep and improve upon?
It seems there is a job opening for mathematics right here. Numbers are fixed (more or less) and can be arranged to represent our experiences in an extremely rigid manner. That saves our brains from confusion, provides a rule/reference which simplifies future learning/adaptation. At a behavioral level, this creates, propagates, and sustains consensus. That way we don't have to reinvent the wheel in every generation. We only improve upon it. Essentially the wheel in ancient Egypt and modern spacecrafts have pretty much similar design concepts. Is it possible that something very different - not circular, not rotating, not linked to a gear - could have been discovered had our ancestors' brains not got stuck in one design that they decided to keep and improve upon?
Besides its highly adaptive way of thinking, the brain also tends not to remember everything it experiences with 100% accuracy. It needs a codified representation of some of the important things it wishes to retrieve later. Even more crucial than this, brains can not communicate amongst each other with 100% efficiency... far from it actually. These factors further instigate the need for a fixed, highly reproducible, means of storing and sharing information outside of the brain.
I believe numbers are a result, at least partly, of these factors, or rather limitations. And for the purpose they were created, they have indeed scored astonishing accomplishments. They literally have built a world of civilizations, means of concurring nature for the benefit of mankind. But I think we also came to take them too seriously. We believe that they are almost real. We believe whatever can not be represented, understood, reproduced within a codified numeric framework is unreal, an artifact. Any progress in our understanding of nature seems possible only within the realm of numbers and goes as far as numbers can push themselves. We made them the official, and sole, language of Science. I think it is good to have an official language, but multilingualism may have more advantages.
I think, if something happens in this universe, it is part of the reality of this universe despite what we think of it. Its codification in some elegant equations only makes it reproducibly understood by our consensual brains, which for all we know could be collectively wrong. We need to understand that the thinking strategy that our brains opted out for has been essential for our evolution; but it is neither the best strategy, not the sole means of comprehending the universe. We need to be open to the possibility of a reality beyond numbers, but perhaps at the tip of our noses.
The women sitting across the table are now gone. I guess they won the battle for today, but the war continues. Looking through the glass walls, I still see the buildings. After all, where would they go? But what if they actually could go somewhere? What if they are more dynamic, responsive, alive? Perhaps that is my biological dream. Yet life may have a lot to each us, to be less rigid and more adaptive. Perhaps someday, when science learns to think in other languages, perhaps learn from life itself, we may live in dynamic, alive buildings, and a more open and inclusive world. Perhaps then, we might see the huge ocean surrounding our tiny numeric empire.
