Suppose we start with two sexes that have none of the particular attributes of males and females. Call them by their neutral names A and B. All we need specify is that every mating has to be between an A and a B. Now, any animal, whether an A or a B, faces a trade-off. Time and effort devoted to fighting with rivals cannot be spent on rearing existing offspring, and vice versa. Any animal can be expected to balance its effort between these two rival claims. The point I am about to come to is that the As may settle at a different balance from the Bs and that, once they do, there is likely to be an escalating disparity between them.
To see this, suppose that the two sexes, the As and the Bs, differ from one another, right from the start, in whether they can most influence their success by investing in children or by investing in fighting (I’ll use fighting to stand for all kinds of direct competition within one sex). Initially the difference between the sexes can be very slight, since my point will be that there is an inherent tendency for it to grow. Say the As start out with fighting making a greater contribution to their reproductive success than parental behaviour does; the Bs, on the other hand, start out with parental behaviour contributing slightly more than fighting to variation in their reproductive success. This means, for example, that although an A of course benefits from parental care, the difference between a successful carer and an unsuccessful carer among the As is smaller than the difference between a successful fighter and an unsuccessful fighter among the As. Among the Bs, just the reverse is true. So, for a given amount of effort, an A can do itself good by fighting, whereas a B is more likely to do itself good by shifting its effort away from fighting and towards parental care.
In subsequent generations, therefore, the As will fight a bit more than their parents, the Bs will fight a bit less and care a bit more than their parents. Now, the difference between the best A and the worst A with respect to fighting will be even greater, the difference between the best A and the worst A will be even less. Therefore an A has even more to gain by putting its effort into fighting, even less to gain by putting its effort into caring. Exactly the opposite will be true of the Bs as the generations go by. The key idea here is that a small initial difference between the sexes can be self-enhancing: selection can start with an initial, slight difference and make it grow larger and larger, until the As become what we now call males, the Bs what we now call females. The initial difference can be small enough to arise at random. After all, the starting conditions of the two sexes are unlikely to be exactly identical.
From The Selfish Gene. A fantastic explanation of the fundamental difference between the sexes, and why you would expect the asymmetry to arise1. This explains the evolution of the male and female gametes; which in turn explains the disparate strategies adopted by male and female members of a species when it comes to mating.
Evolution is amazing.
1. The only problem with arguments without numbers, such as this one, is I can never be sure if I’m missing a flaw well ensconced in the smooth, convincing wording. I’ve fallen for them too many times!
“You know, when I was a young man, hypocrisy was deemed the worst of vices,” Finkle-McGraw said. “It was all because of moral relativism. You see, in that sort of a climate, you are not allowed to criticize others—after all, if there is no absolute right and wrong, then what grounds is there for criticism?”
“Now, this led to a good deal of general frustration, for people are naturally censorious and love nothing better than to criticise others’ shortcomings. And so it was that they seized on hypocrisy and elevated it from a ubiquitous peccadillo into the monarch of all vices. For, you see, even if there is no right and wrong, you can find grounds to criticise another person by contrasting what he has espoused with what he has actually done. In this case, you are not making any judgment whatsoever as to the correctness of his views or the morality of his behavior—you are merely pointing out that he has said one thing and done another. Virtually all political discourse in the days of my youth was devoted to the ferreting out of hypocrisy.
“You wouldn’t believe the things they said about the original Victorians. Calling someone a Victorian in those days was almost like calling them a fascist or a Nazi.”
Both Hackworth and Major Napier were dumbfounded. “Your Grace!” Napier exclaimed. “I was naturally aware that their moral stance was radically different from ours—but I am astonished to be informed that they actually condemned the first Victorians.”
“Of course they did,” Finkle-McGraw said.
“Because the first Victorians were hypocrites,” Hackworth said, getting it.
Finkle-McGraw beamed upon Hackworth like a master upon his favoured pupil. “As you can see, Major Napier, my estimate of Mr. Hackworth’s mental acuity was not ill-founded.”
“While I would never have supposed otherwise, Your Grace,” Major Napier said, “it is nonetheless gratifying to have seen a demonstration.” Napier raised his glass in Hackworth’s direction.
“Because they were hypocrites,” Finkle-McGraw said, after igniting his calabash and shooting a few tremendous fountains of smoke into the air, “the Victorians were despised in the late twentieth century. Many of the persons who held such opinions were, of course, guilty of the most nefandous conduct themselves, and yet saw no paradox in holding such views because they were not hypocrites themselves—they took no moral stances and lived by none.”
“So they were morally superior to the Victorians—” Major Napier said, still a bit snowed under.
“—even though—in fact, because—they had no morals at all.”
There was a moment of silent, bewildered head-shaking around the copper table.
“We take a somewhat different view of hypocrisy,” Finkle-McGraw continued. “In the late-twentieth-century Weltanschauung, a hypocrite was someone who espoused high moral views as part of a planned campaign of deception—he never held these beliefs sincerely and routinely violated them in privacy. Of course, most hypocrites are not like that. Most of the time, it’s a spirit-is-willing, flesh-is-weak sort of thing.”
“That we occasionally violate our own stated moral code,” Major Napier said, working it through, “does not imply that we are insincere in espousing that code.”
“Of course not,” Finkle-McGraw said. “It’s perfectly obvious, really. No one ever said that it was easy to hew to a strict code of conduct. Really, the difficulties involved—the missteps we make along the way—are what make it interesting. The internal, and eternal, struggle, between our base impulses and the rigorous demands of our own moral system is quintessentially human. It is how we conduct ourselves in that struggle that determines how we may in time be judged by a higher power.”
From “The Diamond Age” by Neal Stephenson.
The notion that it is a moral failing to say one thing and do another is bizarre.
It might be less than ideal (whatever that means), but it certainly beats preaching nothing and lacking morality altogether.
Hypocrisy is overrated.
Two short excerpts from “The Value of Science” by Richard Feynman:
Another value of science is the fun called intellectual enjoyment which some people get from reading and learning and thinking about it, and which others get from working in it. This is a very real and important point and one which is not considered enough by those who tell us it is our social responsibility to reflect on the impact of science on society.
Is this mere personal enjoyment of value to society as a whole? No! But it is also a responsibility to consider the value of society itself. Is it, in the last analysis, to arrange things so that people can enjoy things? If so, the enjoyment of science is as important as anything else.
Not a point of view you hear often. (As a side-note, I am reminded of the science power-dream alluded to in Fred Hoyle’s “The Black Cloud” [spoiler alert]. One of the reasons you don’t hear this point of view being expressed often is perhaps because the ones in charge of allocating resources towards science are often ignoramuses who lack the capability to comprehend this argument.)
When we read about this in the newspaper, it says, “The scientist says that this discovery may have importance in the cure of cancer.” The paper is only interested in the use of the idea, not the idea itself. Hardly anyone can understand the importance of the idea, it is so remarkable. Except that, possibly, some children catch on. And when a child catches on to an idea like that, we have a scientist. These ideas do filter down (in spite of all the conversation about TV replacing thinking), and lots of kids get the spirit — and when they have the spirit you have a scientist. It’s too late for them to get the spirit when they are in our universities, so we must attempt to explain these ideas to children.
An interesting thing about R.P.F’s essays* is that they convey the profundity of their ideas in the simplest of language. Try as I might, I cannot think of anything relevant to add to the excerpt.
R.P.F says it all.
A while ago, it was thought that the trick to making a machine play chess well was to extend how far down the branching network of possible moves it could examine. Irrespective of how far they can look ahead, though, skilled human chess players can confidently confound (or at least match) most chess programs of today.
I found a fascinating account of this puzzler involving AI and human thinking in (where else?) GEB. Apparently, the reason for this was known from the 1940s; If you’ve ever played chess- or play regularly but with skill befitting a two year old, you’ll come to appreciate the reason immensely.
Chess novices and chess masters perceive a chess situation in completely different terms. The results of the Dutch psychologist Adriaan de Groot’s study (from the 1940’s) imply that chess masters perceive the distribution of pieces in chunks.
There is a higher-level description of the board than the straightforward “white pawn on K5, black rook on Q6” type of description, and the master somehow produces such a mental image of the board. This was proven by the high speed with which a master could reproduce an actual position taken from a game, compared with the novice’s plodding reconstruction of the position, after both of them had five second glances at the board. Highly revealing was the fact that masters’ mistakes involved placing whole groups of pieces in the wrong place, which left the game strategically almost the same, but to a novice’s eyes, not at all the same. The clincher was to do the same experiment but with pieces randomly assigned to the squares on the board, instead of copied from actual games. The masters were found to be simply no better than the novices in reconstructing such random boards.
The conclusion is that in normal chess play, certain types of situation recur- certain patterns- and it is on these high-level patterns that the master is sensitive. He thinks on a different level from the novice; his set of concepts is different. Nearly everyone is surprised to find out that in actual play, a master rarely looks ahead any further than a novice does- and moreover, a master usually examines only a handful of possible moves! The trick is that his mode of perceiving the board is like a filter: he literally does not see bad moves when he looks at a chess situation- no more than chess amateurs see illegal moves when they look at a chess situation. Anyone who has played even a little chess has organized his perception so that diagonal rook-moves, forward capture by pawns, and so forth, are never brought to mind. Similarly, master-level players have built up higher levels of organization in the way they see the board; consequently, to them, bad moves are as unlikely as illegal moves are, to most people. This might be called implicit pruning of the giant branching tree of possibilities. By contrast, explicit pruning would involve thinking of a move, and after superficial examination, deciding not to pursue examining it any further.
If you pause to think about this, it comes across as an utterly spellbinding revelation. Like the proverbial frog in the well, mental models and levels of perception above what we are used to are very hard to digest- but they’re there, as the excerpt explains.
The “chunking into levels” is a predominant theme in all complex systems we see*, at least in the way we seek to understand and analyze them- from computer systems (Hardwired-code->machine language->Assembly language->Interpreters and Compilers) to DNA (Specifying each nucleotide atom-by-atom->Describing codons with symbols for nucleotides->Macromolecules->Cells), and even human thinking.
The last bit requires a little exposition, but first, we note the analogy between the nightmare of writing complex useful computer code in machine language and the terror of reading a virus DNA atom by atom. In both cases, we would miss out on the higher level structures that embody computer programs and virus DNA with their attributes- complex systems possess meaning on multiple levels.
The multi-level description extends to virtually every complex phenomenon. Weather systems, for instance, possess “hardware” (the earth’s atmosphere) which has certain properties hardwired into it (hardwired code) in the form of the laws that flitting air molecules obey, and “software”, which is the weather itself. Looking at the motions of individual molecules is akin to reading a huge, complicated program on the machine language level. We chunk higher level patterns into storms and clouds, pressures and winds- large scale coherent trends that emerge from the motion of astronomical number of molecules.
As for multi-level human thinking, it is illuminating to first appreciate that a higher level perception of a system does not necessarily mean an understanding of the lower levels too. One does not need to know machine language to write complex computer programs, nor is one required to be aware of individual molecule trajectories to describe or predict the weather.** In fact, a higher level of a system may itself not be “aware” of the levels it is composed of, such as AI programs that are ignorant of the operating system they are running on. The higher level descriptions are “sealed off” from the levels below them, although there is some “leakage” between the hierarchical levels of science. (This is necessarily a good thing- or people could not obtain an approximate understanding of other people without first figuring out how quarks interact.)
The title of the post is another excerpt from GEB, derived as a somewhat whimsical analogy:
The idea that “you” know all about “yourself” is so familiar from interaction with people that it is natural to extend it to the computer- after all, AI programs are intelligent enough that they can “talk” to you in English! Asking an AI program (which is compiled code) about the underlying operating system is not unlike asking a person “Why are you producing so few red blood cells today?” People do not know about that level- the “operating system level”- of their bodies.
This post owes its existence in entirety to GEB, the Big Book of Big Ideas.
It’s not often that I find subtle math lessons hidden in works of fiction; much less blatant, straightforward, undisguised ones. They’re always welcome- especially when they reinforce something I’m already aware of.
An excerpt from Cory Doctorow’s Little Brother:
If you ever decide to do something as stupid as build an automatic
terrorism detector, here’s a math lesson you need to learn first. It’s
called “the paradox of the false positive,” and it’s a doozy.
Say you have a new disease, called Super-AIDS. Only one in a million
people gets Super-AIDS. You develop a test for Super-AIDS that’s 99
percent accurate. I mean, 99 percent of the time, it gives the correct
result — true if the subject is infected, and false if the subject is
healthy. You give the test to a million people.
One in a million people have Super-AIDS. One in a hundred people that
you test will generate a “false positive” — the test will say he has
Super-AIDS even though he doesn’t. That’s what “99 percent accurate”
means: one percent wrong.
What’s one percent of one million?
1,000,000/100 = 10,000
One in a million people has Super-AIDS. If you test a million random
people, you’ll probably only find one case of real Super-AIDS. But
your test won’t identify *one* person as having Super-AIDS. It will
identify *10,000* people as having it.
Your 99 percent accurate test will perform with 99.99 percent *inaccuracy*.
That’s the paradox of the false positive. When you try to find
something really rare, your test’s accuracy has to match the rarity of
the thing you’re looking for. If you’re trying to point at a single
pixel on your screen, a sharp pencil is a good pointer: the pencil-tip
is a lot smaller (more accurate) than the pixels. But a pencil-tip is
no good at pointing at a single *atom* in your screen. For that, you
need a pointer — a test — that’s one atom wide or less at the tip.
The “false positive cautionary” rears its head all too often; I’ve seen it on TED, in textbooks on probability, and even in a puzzle column in The Times of India- which is the last place you expect to find common sense.
‘Little Brother’ itself was very… didactic. This isn’t a review, so I’ll let a few more (spoiler-free) excerpts do the talking.
The law didn’t care if you were actually doing anything bad; they were
willing to put you under the microscope just for being statistically
I wasn’t the only one who got screwed up by
the histograms. There are lots of people who have abnormal traffic
patterns, abnormal usage patterns. Abnormal is so common, it’s
And finally, a few lines that really struck a chord, primarily because they’re intimately representative of a teenager’s awe.
If you’ve never programmed a computer, you
should. There’s nothing like it in the whole world. When you program a
computer, it does *exactly* what you tell it to do. It’s like
designing a machine — any machine, like a car, like a faucet, like a
gas-hinge for a door — using math and instructions. It’s awesome in
the truest sense: it can fill you with awe.
(Side note: Little brother is licenced under the Creative Commons licence and can be downloaded for free off the Internet.)