∀∃∞

In the New year, I have generally been busy reading and browsing on a wide range of topics. In the process, I keep encountering interesting facets of thoughts and ideas, ranging from very old books to recent developments in research. In the weeks to follow, I intend to post about some of these, that seem worthy of sharing and discussion.. which shall hopefully resurrect this place. Let there be blog!

At some point, I got curious about understanding the ‘big’ economic picture mathematically. That is when I first began learning of problems in the very nature of some basic ideas in macroeconomics. For example, the mechanics of money creation, which largely happens today on the basis of “Fractional Reserve Banking“, seems rather bewildering. The ‘system’ went beyond my tangible perception somewhere, so let us leave that. Beginning to critically go through the arguments presented in a microeconomics book, I encountered something very strange being done there.

In the introductory chapter, the book said that the [presented] economic theory is based on the assumption that firms try to maximize their own profits; and though this may be inaccurate at times, there is sufficient reason to generally use the theory since it largely explains a broad range of phenomena regarding the behaviour of firms.
Well, this is where I perceive a flaw in the cause-effect dependence. To justify the assumption of self-maximizing firms, we observe the ‘phenomenal’ behaviour of existing firms; which makes you wonder.. don’t the policies and decisions made based on economic theories shape the behaviour of firms? And in that case, how are these theories and policies made for the ‘first’ time, if that is to be?

Escher 'outdraws'.. himself, I'd say. Twice.
Do you see what we do? To ourself?

Let us turn to a parallel in mathematics: Euclid’s fifth postulate was based on the observation of the ‘existing’ lines, i.e. the straight lines drawn on flat paper as seen and imagined by Euclid and others; and hence the Parallel Postulate seemed to be a reasonable property to assume.

It goes without saying that Euclid and others have tried to derive the property from other axioms, but in vain. Possibilities of creating “non-Euclidean geometries” that work without using that axiom began to be pursued over time; but they fully bore fruit much later. For instance, hyperbolic geometry and Riemannian geometry came about in the 19th century.

There are several lessons to learn here, I feel. Think about it.. the mental energies of people across several thousand years were put to work on a seemingly small point! And yet, we abandoned a radical idea such as Google Wave so easily. (There are still a couple days left for you to try Wave, before it shuts down.) There were initial issues with providing a glitch-free experience; and there was the question of the learning curve; rather, of our readily considering such a radical mental transformation. Why are we so short-sighted that we acted the way we collectively did? As I see it, the power of Wave API together with the open-source development model could have transformed that service.. only if it were given a chance.

The consequences of our actions become even more a topic of introspection, when one realizes that Riemannian geometry, a result of an age-old pursuit for the seemingly trivial, is one of the key concepts used by 20th century Einstein to base his theory of General Relativity! If those hundreds of mathematicians had not worked towards their unseen future, the occurrence of relativity (and hence, many modern technologies such as GPS and flight/space navigation) might have been offset by years.. maybe decades.. maybe eternity? Scary thought. I am only glad that Wave would reappear as Apache Wave, so nothing would be lost.. probably.

Besides this, there is another lesson to learn through the above example.. when mathematics was faced with a dilemma, it willingly split into multiple possibilities; it did not ‘choose’ one and kill the other. In a very similar fashion, when the study of economics is made on such a one-sided self-recurring basis as the profit-maximization assumption, I feel the possibility of there being another economical model that is created to work without such an assumption. Current economic theories are based on a marginally softer notion of self-maximization than the extreme end; yet, the entire spectrum is not represented. (Ideas such as communism and socialism are not directly relevant here; they are elaborate socio-economic models and do not relate to any fundamental mathematical assumptions in micro/macroeconomic analysis.)

The final lesson: One has to make the mental leap of considering a hyperbola to be a line, to get to a whole new geometry. When will we all evolve?

Escher's reptiles
Transcend pattern.. think better

Escher all the way..

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