Sunday, June 17, 2007

A little reductionism goes a long way

Back in freshman year of college, I took a course called Relativism, Reason, and Reality. I had been exposed to a little existentialism in high school, and I was sufficiently intrigued to consider a philosophy minor. Until I took R, R, and more R. Academic philosophy seems like nothing so much as the dumping ground for failed theoretical mathematicians. Rather than proving well-defined theorems with precise logic, most of the works we read aspired to rigor, but were ultimately undone by their dependence upon metaphor, allusion, and the inherent vagueness of colloquial language. If you can't completely define the assumptions and terms with which you are working, it is impossible to construct an irrefutable argument. There is no room for dissent in proper mathematics. While philosophers may argue about the nature of truth, and the most complex theorems may require years of consideration before they are finally accepted or rejected, mathematics is as close as the human mind can come to absolute certainty. So far as I can see, the greatest potential weakness in mathematics is the distinct possibility that all humans are inherently and consistently irrational, in which case true rational thought is forever beyond our grasp. Short of the mass failure of the human mind, however, mathematics seems beyond challenge.

Despite my dissatisfaction with the presentation of the material, we did discuss some interesting ideas in R, R, & R. Consider the following: surely, were a single atom of your body replaced by an equivalent atom, you would agree that your identity would remain uncompromised. The new atom and the old atom are indistinguishable, so even though the particles composing your body would be slightly altered, the pattern would remain entirely unchanged. Similarly, if you believe that you are nothing more than your body, then if 1%, or 10%, or 100% of the atoms in your body were instantaneously switched with identical atoms, the exchange should go entirely entirely unnoticed and your identity should remain intact.

Now consider the case where your body is reconstructed somewhere other than its original location; say, ten feet away. The pattern of your body is the same. Your location hasn't changed much. I would hope that you would be willing to accept that the resulting person would still be you.

But what if your original body were not destroyed in the process? What if an exact, perfect duplicate were created ten feet away, but you were left standing exactly where you were before. Would you then allow yourself to be killed, knowing that a perfect duplicate would immediately take your place? Would this stranger standing next to you actually be you?

This may sound suspiciously like the sort of philosophical nonsense I was railing against a few paragraphs above, but consider the following: are you not effectively being replaced with an exact copy of yourself every instant? Does continuity in space and time really affect the core of the argument? To what extent can you legitimately claim that the you-of-right-now is the same as the you-of-five-minutes-ago? If death is just the cessation of this succession of you's, why should the you-of-right-now care that the you-of-50-years-from-now (or 5-minutes-from-now) will not exist? Why bother planning for the future or defining yourself in terms of past actions? In what sense can you be said exist, if your existence is inextricably bound to a single instant?

Consider in this light Descartes' claim that "I think, therefore I am." Certainly, there are thoughts, but the thinker need not be consistent. At any given moment, you have access to memories of past thoughts, but such memories are but imperfect afterimages of the original thought, and you are bound to this previous thinker only by these echoes. Where then is the "I" that is doing the thinking?


mim said...

I took the same course, only it was spring of my senior year. I needed one last HASD to graduate, and yet I found it quite enjoyable. Looks like there weren't any staggering breakthroughs in the philosophy of mind in those 5 years, but the questions are fun to think about. It also served its function as an introduction to the field of philosophy, which I give more credit than you do. It seemed to me to be logical reasoning applied to things that weren't numbers. The history of mathematics and philosophy have been intertwined for millennia.

Maybe it was the logic itself that was interesting, the papers that seemed to be most highly acclaimed by the professional philosophers explored the consequences of some particular assumption, whether true or not. "Say there was a teleporter, would the copy be you or would the original?" But then also, "Say there was a teleporter and the copy was you." And just as interesting, "say there was a teleporter and the original was you."

Eric said...

Statistical physics provides, I think, an interesting perspective on thsi problem. In stat physics we talk about an ensemble -- a thought experiment in which we have an infinite number of identically prepared and isolated gases. Each gas does something different, some singular behavior. By averaging this behavior together, we get an approximation of teh behavior of a single real gas.

The reason this is at all justified is that within the gas, we actually find each of the copies represented in both space and time. Let's say that a cluster of atoms has some two different ways to behave. Now we observe under a microscope that in soem small region of the gas they behave one way and only that way. The hand writes, and having written, moves on, etc. And yet elsewhere in the gas, both forward in time, and elsewhere in space, we see that another bunch of atoms behave the *other* way.

This is called ergodicity -- it justifies using ensembles, because here the ensemble approach (which is sort of bayesian) and the traditional frequentist approach to probability both agree -- time averages can be replaced with ensemble averages, because no part of phase space is unreachable from any other. Basically the trick works because there's 10^23 of everything -- everything not prohibited becomes compulsory, in that it will be done by at least some part of the system.

Now ensembles can be extended somewhat to deal with non-equilibrium phenomena. Gavin Crooks has done some meta-ensemble work which is weird but probably useful. But anyway, I wiill be using ensemble here as a bit of a metaphor.

You and your twin would probably belong to the same Mean Monkey Ensemble. Anything he says you might say sometime in teh future. If you are offered a chocolate frog, you may refuse, and he might accept. But the actions could easily be reveresed later on, and no one woudl be surprised.

Yet this isn't how we view identity. We seem to view identity as though the actions I have taken are solely mine and that they are justified based on the essense of who I am etc. Or maybe they are mistakes, but those actions are still mine and mine alone, and *that* instantiation of what I *could* have done, might have done, etc. is me. We speak of someone's "potential" as the envelope of what their ensemble of people might do. We feel bad if a particular copy (us) has failed to take chocolate frogs, have sex, do well in school, etc. Because in reality, in frequentist probability, there is no ensemble of Mean Monkeys to observe, and we cannot always replace the averaged behavior fo what you might do with the averaged behavior of what you end up actually doing. Maybe we can while you are at work -- we can average every day you spend in lab and use that as an ensemble. But for isolated singular actions such as deciding whether or not to attend MIT or get married ot a particular person or not, etc. there is not usually a second-chance.

Thus it may be useful to distinguish events in which we can model the Mean Monkey of this particular reality as an ensemble of Mean Monkeys, and events in which we cannot. Because the importance of your identity as distinct from a similarly prepared twin is meaningful in one distinction (instead of going to ETH he leaves academia and lives in a hut in the woods getting nominally to be a forest ranger, which causes him to have a very bifurcated experience to you) and not so much in the other distinction (he jacked off and read web comics today, while you worked, but tomorrow the activities will be reversed.) This places identity on somewhat of a more empirical (and therefore less philosophical/worthless) grounds, similar to Alan Turing's definition of intelligence.