Wednesday, November 30, 2005
Dying to talk to someone
I was imagining having an Uncle Joe across the galaxy: being able to talk to him over the radio, but unable ever to see him. Then I realized that scenario does not make sense. The incongruity between my intuition and my understanding of physics was delightful.
Radio waves are light, and hence subject to the speed of light, so a single conversation at interstellar ranges could take lifetimes. Moreover, since visible light and infrared light are both light, my inability to see Uncle Joe is practically identical to my inability to exchange radio messages with him.
One difference is that radio signals are serial, whereas visual signals are series-parallel. If we needed to transmit radio messages in parallel, though, we could do it by using more than one frequency (“channel”).
A stranger difference between radio and visual is the potential for broadcasting at different volumes. To broadcast a visual image of Joe more “loudly”, Joe’s engineers would have to shine more light on him, and to distinguish him from background radiation I would require more light than his body could reflect without combusting. Still, intergalactic radio and intergalactic semaphore are essentially the same process.
My Earth-formed concept of distance does not predict well what happens at interstellar ranges. That tickles me. The Earth-formed concepts of number, or Euclidean geometry, those seem to hold at any range in the universe. (Non-Euclidean geometries have been sought by astronomers, but none found.) However, other intuitions just don’t scale.
Calculatedly subconscious generosity
Part I: Conditions under which altruism is inevitable
A rationally self-interested person will, if he understands enough psychology and has enough stuff (and satisfies some plausible assumptions) choose to be altruistic. Check it:
Consider a hypothetical person, Dude With Stuff. Dude will give away some of his stuff, or some of his time (not that there’s much difference), because he’ll recognize that it is optimal for his own happiness. Dude recognizes the positive but diminishing marginal returns to “consumption” (which I’ll define here as enjoyment on his own of his stuff), just as Dude recognizes the positive but diminishing returns to altruism. Some of the return to altruism comes in the form of reciprocation – friendship, political back-scratching, etc. Some comes in the form of recognition by third parties. Hopefully, some of the return to altruism is the selfless joy of giving, without thought of future material gain.
A rational Dude will engage in altruism whenever the value of an additional unit of altruism is above that of an additional unit of consumption. Dude can only continue to be totally selfish for as long as the value of additional consumption is above the value of the first unit of altruism. If consumption gets arbitrarily small (which is conceivable although not unavoidable) and if altruism is everywhere positive (which seems likely for the average person but is again not unavoidable), then there exists a threshold of wealth beyond which altruism is better for Dude than additional consumption.
Part II: Maximizing the psychological effectiveness of altruism
So far I have left out something which for many people may to be a big factor in altruistic behavior: they dislike the calculation. Therefore, one might rationally decide to foster some subconscious behavior pattern in oneself such that the likelihood of choosing high-yield benefiters to one’s altruism is high, and the cost of consciously making that calculation is small. Even if the subconscious algorithm were subject to error, that error might be more than compensated for by the benefit to one’s sense of well-being by not having to witness one’s own pecuniary scheming.
I believe this sublimation occurs in everyone, to some degree. Sure, gift-giving is often consciously rational, but a lot of it is unconsciously rational.
Consider an example: When someone on the street stops you to ask the time, you might think to yourself, “What costs and benefits do I incur from revealing the information this person has asked? I am slowed; that’s a cost. Maybe I feel like a better person if I answer truthfully than if I ignore; that’s a benefit. And there’s a chance word could get around that I’m a jerk; avoiding that is a benefit. On net, I guess the slowing down is outweighed by those two benefits, so I’ll respond.”
But you don’t do that, right? You probably don’t even make a conscious decision to answer – you just do it. Somehow, the cost-benefit analysis you’ve avoided has been sublimated.
That may seem like a trivial example, but more “substantial” decisions operate in the same way: A mother deciding whether to feed her son’s friend; a drug user deciding whether to share with his neighbor; a woman deciding whether to give her boyfriend a ride to work; etc. Sometimes altruistic decisions are conscious, but many, perhaps most of them, are not ... and maybe that's optimal. We make faster decisions, the decisions are on net pretty good, and we feel better about ourselves in making them.
Sunday, November 13, 2005
We really ought to have three ears.
The brain calculates the origin of a sound in part by measuring the time elapsed between the sound’s arrival at one ear and its arrival at the other. Other procedures accompany that one, such as spectral analysis. (For instance, your brain knows that distant sounds lose treble, even if you don’t.) However, the elapsed-time calculation is a fundamental one.
The brain’s calculations of the origins of sound work astonishingly well; however, they IS prone to error. For instance, a sound reaching your skull from directly behind you can sometimes sound as if it comes from somewhere else. It’s an unsettling illusion, because it persists even after you’ve recognized it, as long as you don’t move your head.
If we had three noncollinear ears, we could triangulate, and such ambiguities would vanish.
(Sticklers for the geometric truth might gripe that, were the elapsed-time calculation the brain’s only method for determining the origin of a sound, then every sound not originating from the plane spanned by the three ears could be interpreted as having one of two distinct origins. We would need four ears in general position to truly make no mistakes. However, choosing from among two choices is so much easier than choosing from a continuous circular array that I think our brains could adequately handle the task using spectral analysis or other tricks. That is, I don't think a fourth ear would be worth the trouble.)
The argument that we need more than two receivers to adequately determine the spatial origin of signals applies only to ears, not eyes. If we were content with knowing the direction of a signal, then a single eye would be enough; we use two of them so that we can determine how far something is from the receiver. (Astonishingly, we manage the same task with our ears. I don't think an extra ear would help with the distance calculation at all.)