Why not? The point is to be able to distinguish the cases.
505 karma · joined November 28, 2011
This is true, but only because BGP announcements don't involve DNS, and so all the DNS security in the world won't help. Agreed that there is a lot of scope for doing better on BGP security, though - and indeed DNS security.
Well, OK, that's unfair, because Buddhism and formal logic are both human endeavours, and have to deal with the same facts. But this disconnect is even true with parts of Greek philosophy. "Atoms" as we understand them are very different from "atoms" as Aristotle thought of them, even though there is a historical connection. Today's chemists would do badly if they relied on Aristotle for anything other than historical curiosity.
A related problem, which speaks to the leaky abstraction issue, is "proof irrelevance". Typically, if I've proved something, it shouldn't matter exactly how I did it. But it turns out to be tricky to make sure that the proof objects in the system don't accidentally carry too much information about where they came from. Sure, you can define a way to erase the details, but you still have to prove that erasing doesn't mess up the deductive system.
None of this is insurmountable, but it's a glimpse into the reasons why encoding mathematics computationally is not trivial.
In the classical approach of "compiling" everything into sets/logic/etc., you end up with just the assembly language problem that's being discussed, where all the high-level structure vanishes. In order to do your bottom-up approach instead, one of the things that needs to happen is to make the theory really compositional, so that once you've defined some abstraction or higher-level concept, you can use it in constructions and proofs without having to break the abstraction. You don't need to know - and in fact you shouldn't be able to find out - just how the natural numbers were constructed, as long as they work by the right rules. This motivates the use of type theory to describe mathematical objects, and say which operations are allowed. We want to be able to add two numbers and get another number, but we don't want to be able to intersect two numbers as if they were sets, even if they happen to have been built out of sets.
So I think you are right - or at least, there are plenty of people who agree with you that this is a good idea. It is difficult to actually do, of course, but that's life.
Otherwise, perhaps it is possible for the provenance to be deliberately marked in some way that is resistant to forgery. For example, the adult cells used could be provided by some independent source who is generally trusted not to "leak" the corresponding embryonic cells. Then, if you produce ESCs with the right genome (which is easy to test), you must have done it using adult cells alone. If a clever and unscrupulous biologist could forge that - say by taking a normal ESC and injecting foreign genetic material, or by cloning the mouse and harvesting the new embryo - then perhaps some alternative marker could be devised. It would have to be something that could be introduced into the adult mouse cells, but couldn't be easily extracted, swamped by a new marker, or transferred in the cloning process. Or we could cross-check against other signs that those methods might have been used - some biological equivalent of tamper-evidence, maybe?
"A certain well known mathematican, we'll call him Professor P.T. (these are not his initials...), upon his arrival at Harvard University, was scheduled to teach Math 1a (the first semester of freshman calculus.) He asked his fellow faculty members what he was supposed to teach in this course, and they told him: limits, continuity, differentiability, and a little bit of indefinite integration.
The next day he came back and asked: What am I supposed to cover in the second lecture?"
(from Spiro Karigiannis at http://mathoverflow.net/a/53238 - comments below refer to a version of the story where the professor is from the USSR specifically)
Alas, in this scenario we don't even have the ability to count, since we have a limited number of internal states to use to store numbers. So the really clever part is to encode additional information in the flow of additional messages. For example, to find the middle soldier, we can send out two pings, one three times faster than the other. They meet when the slower ping has gone through half the soldiers, and the faster one has gone all the way down the line, and back through half the soldiers (it's three times faster). Additional pings of different speeds can bounce back and forth in order to divide the interval still further - effectively, recursing into narrower sub-lines. Everything is set up so that all of the sub-lines reach their minimal size - one soldier - at the same time, at which point they know it's time to fire. The "recursion" means that the number of states can be bounded, as there are only a few different "modes" for the soldiers to operate in, regardless of the length of the sub-line involved.
Recursion is probably the same way. For Colbert purposes you could certainly come up with some glib explanation. When I, or you, or anyone else, have learned recursion we've probably started with that, but then proceeded to build connections with induction, PL semantics, computer architecture, compiler/runtime implementations, and all the other allied topics.
But I do think the earliest, most informal, explanation has its place too, because you have to start somewhere. The learning process is (at least for me) more like proceeding through lots of explanations of the same thing, at greater levels of detail and with different metaphors and external references, than it is like a linear progression from topic to topic.
It's actually quite hard to determine who is the intended target of a word like "he", since experience presents us with all kinds of difficult cases; appeal to appearance or behaviour or even chromosomes doesn't work universally. At some point, we either have to let people decide for themselves what they want, or impose our own arbitrary classification on them. Someone is making a judgement and I'd rather it be "I feel I am male" than "I feel you look male".
Sure, it might be nice if there were a simple flowchart, based on only objectively observable data, that we could follow to end up with either "he" or "she" in the end. But no such flowchart exists. I propose to drop the "objective" criterion and just ask the person what they prefer - especially given that the only reasons for having a he/she pronoun system are historical and social. If you want to talk about what's going on biologically, in great detail, then feel free, but the pronoun system doesn't have to correspond to that.
Still, calling somebody by their preferred name and pronouns does not grant them admission to the women's locker room, or anything else like that. It is a matter of courtesy.
The other thing is that often, in order to have a gender change legally recognized, or to access surgery and so on, one has to prove that one has already been living as a member of the appropriate gender. What this means is highly contested, but stuff like "people know me as Alice, not Bob" is part of it. It's difficult enough without people setting themselves up as linguistic gatekeepers, and deciding that they know better than Alice.