In a two-way barter trade, two people (1 and 2) exchange two objects (A and B). From the voluntary nature of the transaction, we conclude that both people value their new possessions more than their old; to one person A > B while to the other B > A. These two statements contradict each other, but that's okay because they apply to different people; Person 1 prefers A to B while Person 2 prefers B to A. In fact, this contradiction is what makes trade possible. At this point, there is little temptation to label either person as being wrong.

Now imagine that prior to the trade, the two people had in fact just walked out of the same store, having bought the objects of the trade in the store. At best, if both objects cost the same, the trade seems pointless. In all other cases, one of the people could have done better by just paying less for his post-trade object in the store. This untaken better option prompts us to label the choice as irrational.

In the first case, we had no problem believing that people could have differing preferences for objects. In the second case, however, once the objects acquired price tags, it seemed stupid to trade something with a higher price for one with a smaller price. The way I presented it, the objects were actually cash in the recent past, and trading any two amounts of cash for each other is clearly irrational because the numerically larger amount can always do more.

I wrote this essay to clear up some confusion regarding the zero-sumness of the stock market. In that case, the object A is a stock certificate while object B is money. The question is basically whether stock has an objective price independent of the buyer. If such a thing existed, then every successful stock sales means either the buyer or the seller has made a pricing mistake.

Conclusion? I don't know. I've distilled it as far as I can.

Haven't written in a while. I have been busy with redoing the ROCSA website, the Career Fair, learning about Fixed-Point Combinators using DrScheme.

In other news, it worries me that learning from people with different viewpoints is so difficult. The specific ones I am thinking about are really violent in their modes of persuasion and invoke all manners of unproven authority at the slightest provocation. They are also quick to issue absolute statements, constantly reasserting whatever authority they choose as the sole source of knowledge, issuing ultamatums at every turn. This is shallow discourse, distasteful shallow arrogant noisemaking. I feel the joys of intellectual discourse being drained from me everytime I talk to brutes like this. How they mistake data for knowledge, and rote memorization for thought!

Yes I do want to talk to people significantly different from myself, but clearly I have overreached the optimal distance here. So just how much variety can I take? I think one thing is for sure, that there must be a shared interest in philosophy. In my book, this amounts to an interest in exploring hierarchies of fundamentality in one's concepts about the world, and more likely than not two people both reaching for the depths would tend to reach the same few places. The hope is that having such places to start from would greatly lessen the conversational burden of being mortally different.

Ah, the strange dreams that keep me going.

Professor Chakraborty described some work identifying what is essentially an analog-to-digital circuit in the immune system. One thing he mentioned was the future use of renormalization group theory to study these systems.

My impression of renormalization group theory is that it is essentially a study of the fixed points of rescaling iterations. At its core, RG is essentially a type of wipeout process. Another wipeout process, the Central Limit Theorem discards everything but the first and second moments of the PDE; likewise, RG discards all but a few details about the Hamiltonian, and by doing so allows many different Hamiltonians to behave in very similar ways near the fixed point. This is exciting because for a given group of similar behaving Hamiltonians (the Universality Classes), one is allowed to pick the easiest one to study.

Now imagine you are a bacteria. You control the characteristics of your membrane by controlling the structure of the proteins and lipids in it. If your membrane structure were in the regime described by RG, would it not also imply that its nature changes rather abruptly with changes in genetics? As in, most of the time the membrane manages to stay in one universality class or another, but then abruptly changes when you cross over. I can't imagine that such a mapping would be very conducive to natural selection.

Alternatively, the smooth modification of bulk characteristic with respect to small changes in molecular detail could be some kind of scaling within each universality class. Hmm.