A singularly technogeeky plot bunny

[legerdemer]

... But here's Phil:

"In the event that I am reincarnated, I would like to return as a deadly virus, to contribute something to solving overpopulation (1988)"

Oh dear. I hadn't heard him comment on that particular topic before, but the general level of tact sounds like Phil.

In addition to On Death, which AH quoted, the following are jaw-dropping "good": On Age, Arriving to open a youth centre in Brighton, Meeting Nigeria's president, who was in robes, To the General Dental Council, Told by president Obama of meetings already that day with the Chinese, Russians, Brown and Cameron.

It's a favorite theme for him. I think he has been quoted three different times, using essentially that same formulation. He and Prince Bernard of the Netherlands co-founded the WWF (not the wrestling federation), not so much because they are fond of critters, but because they dislike humans. And they had some other, more pecuniary motives as well.

I heard an NPR report about some (the?) hunters' association which raises money for animal conservation so that they "have animals left to shoot" or some such thing. It makes sense for these people to pay to limit their fetishes for killing endangered animals. I keep hoping they'll themselves become rare enough to be endangered - no such luck yet.

 

[AlwaysHungry]

The WWF was all about setting up wildlife refuges on top of important deposits of raw materials, basically squirreling them away for exploitation later on after a more compliant colonial government was in place. In one instance, they created a refuge for rhinoceroses where there were none, and then brought the rhinos in from elsewhere to make it legit.

 

[AlwaysHungry]

From the Wired article on Alphago vs Sedol, emphasis added:

“It’s not a human move. I’ve never seen a human play this move,” he says. “So beautiful.”... just about everyone was shocked.

It has been suggested that there are different kinds of intelligence. There is some dude named Howard Gardner who has a lot fans on the web, and he theorizes that there are as many as 9 different types, although I think he is being overly fussy. It is clear that one of his types, "Logical-Mathematical", is the forte of computers, and they will generally kick a human's ass in that department. However, that's a pretty crude type of intelligence in my book. Gardner has other categories, such as "musical" and "spatial", which I would be inclined to lump into a broader category which I would call "aesthetic" intelligence, an area where computers will tend to be utterly paralyzed. I don't know whether someone out there is attempting it, but my intuition tells me that it may take forever to program computers for aesthetic reasoning.

And I think this is significant, because aesthetic thinking is closely bound to progress in science. Einstein described how, whenever he was stymied by a problem, he would play the violin or the piano and it would unblock his scientific imagination. Friedrich Schiller, who understood aesthetics better than anyone else I know, wrote an essay called "On the aesthetic estimation of magnitude", which touches upon aesthetics and the natural sciences.

So when the gentleman is quoted saying that the computer's go strategy is "beautiful," he is thinking like a human. That is his reaction to a move that he did not foresee, because as a trained go player, he has an unconscious prejudice toward strategies that are either familiar, or which are defined by the way in which they deviate from familiar strategies. It is a sort of tunnel vision. The computer doesn't operate that way (although it may be programmed to anticipate familiar strategies by an opponent.) The computer doesn't see its move as "beautiful." If it did, perhaps if would become a far more formidable opponent.

 

[Handley_Page]

Does anyone else remember a film from 1970 called "The Forbin Project" ?

 

[AlwaysHungry]

It occurred to me this morning, while driving across town, that when a computer can effectively ad lib a joke, with the requisite affect and timing, that will be the vaunted "singularity".

 

[Bramblethorn]

It has been suggested that there are different kinds of intelligence. There is some dude named Howard Gardner who has a lot fans on the web, and he theorizes that there are as many as 9 different types, although I think he is being overly fussy.

Intelligence certainly isn't a single-dimensional quality, although I'm sceptical of any theory that claims to have a nice simple breakdown to it. There's more than one way to approach any given problem; I find mathematical ideas are sometimes useful for understanding interpersonal relationships, and aesthetic intuition is very useful for mathematical work.

It is clear that one of his types, "Logical-Mathematical", is the forte of computers, and they will generally kick a human's ass in that department. However, that's a pretty crude type of intelligence in my book.

Ooh, now, them's fighting words!

I see a fair bit of mathematics teaching and it depresses me, because I can absolutely understand why people come out of the school thinking that maths is just tedious memorisation and learning to do slight variations of the same thing over and over. It's as if you taught students "painting" for an hour a day for twelve years, but the only thing you taught was the technical side, drawing cylinders and spheres, learning how to use a grid for perspective and how to wash your brushes, without ever so much as visiting an art gallery let alone studying what paintings mean to the artists.

These days, a computer can solve most high-school maths problems. I can ask Mathworld to calculate the volume of the solid of revolution formed by rotating y=4-x^2 around the x-axis and it will give me the answer before I can scratch myself.

But the deeper stuff... I don't think it's impossible for a computer, but training a computer to the level of being able to produce results like Cantor's diagonal argument or Euclid's proof that there are infinitely primes, I suspect that's at least as hard as programming one that can write meaningful novels or moving music.

Something that might surprise most people is that mathematics is a very intuitive pursuit. Sure, you need the technical skills, in the same way that a painter needs to know how to mix paints and achieve certain effects. But very often it's intuition that provides the direction for those skills. Being able to look at a problem and immediately know "the answer's going to look something like THIS", that's tremendously important. Ramanujan used to get unexpected mathematical results in dreams.

So when the gentleman is quoted saying that the computer's go strategy is "beautiful," he is thinking like a human. That is his reaction to a move that he did not foresee, because as a trained go player, he has an unconscious prejudice toward strategies that are either familiar, or which are defined by the way in which they deviate from familiar strategies. It is a sort of tunnel vision. The computer doesn't operate that way (although it may be programmed to anticipate familiar strategies by an opponent.) The computer doesn't see its move as "beautiful." If it did, perhaps if would become a far more formidable opponent.

I caught an interesting presentation about AlphaGo a couple of weeks back, from somebody with interests in both go and programming. He mentioned that unlike chess, go is played and taught very intuitively; players learn that certain shapes work better than others, and there's a lot of "I don't know exactly why this works well but it does". So for humans, a big part of go is absorbing and internalising other players' intuitions. (Not the only part, mind; logic is also important.)

Part of the learning process for AlphaGo was to train it on a big database of human games, teach it to recognise patterns that recur, and so train it to predict what a human player would do in any given situation (even for games outside the training database) with very good accuracy. As far as I can tell, that has a lot in common with how a human learns go.

(One of the really nifty parts is that they then used that combined with some brute-force tricks to have AlphaGo play millions of games against itself, then retrained it on that database: "can I learn to predict what choice my brute-force calculation will pick, without having to actually run the brute-force calculation?" They then repeated that several times, getting better with each iteration.)

Does it see a move as "beautiful"? I'm not sure that's an answerable question. It can see that some moves are better than others, it can assess that this is the move a human would probably play in this situation... and even for humans, an awful lot of "beauty" boils down to assimilating other humans' aesthetics.

 

[AlwaysHungry]

Ooh, now, them's fighting words!

I didn't intend to denigrate math per se. I never ascended beyond calculus in high school, but I enjoyed it. Later, when I read an article about Cantor's Aleph numbers, I was very much intrigued. However (and I'm not sure just how to articulate this,) it seems to me that the "mathematical/logical" category of intelligence, in Gardner's system, must be the most rudimentary type. It aims for internal consistency. Computers like internal consistency. I think that the cognitive activity involved in constructing an effective joke or metaphor would be far more difficult to program into a computer, because jokes and metaphors involve an intentional violation of rudimentary logic, in order to transport the mind to a higher cognitive level where the paradox can be resolved, an activity which gives joy to humans. I'm not convinced that a computer is capable of that.

Does it see a move as "beautiful"? I'm not sure that's an answerable question. It can see that some moves are better than others, it can assess that this is the move a human would probably play in this situation... and even for humans, an awful lot of "beauty" boils down to assimilating other humans' aesthetics.

I think it works like language. Words and phrases have meaning for us because of traditions which have accumulated socially over time. Music is a type of language. It is based on "assimilating other humans' aesthetics", and then commenting on them ironically, using the "meaning" that has arisen through social consensus and creating new meaning through metaphor.

 

[Bramblethorn]

I didn't intend to denigrate math per se. I never ascended beyond calculus in high school, but I enjoyed it. Later, when I read an article about Cantor's Aleph numbers, I was very much intrigued. However (and I'm not sure just how to articulate this,) it seems to me that the "mathematical/logical" category of intelligence, in Gardner's system, must be the most rudimentary type. It aims for internal consistency. Computers like internal consistency. I think that the cognitive activity involved in constructing an effective joke or metaphor would be far more difficult to program into a computer, because jokes and metaphors involve an intentional violation of rudimentary logic, in order to transport the mind to a higher cognitive level where the paradox can be resolved, an activity which gives joy to humans. I'm not convinced that a computer is capable of that.

Internal consistency is vital in mathematics, but it's only part of the puzzle. It's like an author learning the rules of spelling and grammar, or a painter having to know which paints will fade or flake off the canvas and which ones will last, and how to get the parallax right. You need to know that stuff, otherwise you'll waste a lot of time creating something that falls apart in a pile of crap. But on its own, it won't take you very far - like having a boat with oars but no map or compass.

A couple of examples:

#1 - I encountered this question in a trivia contest a while back: "A Grand Slam tennis tournament has 128 players in a single draw. In each round, the remaining players are paired up and the winner of each match goes through to the next round. How many matches does it take to determine the winner?"

(Before reading on, stop to work out the answer, and take note of how you work it out.)

I had the answer before the host had finished saying "winner". Somebody asked me if I already knew it; it's not that it's a terribly difficult question, but they were surprised that I was able to answer instantly.

Now, there are several ways you can approach a question like that. The most obvious way is to work it through: round 1 has 128/2 = 64 matches, round 2 has 32 matches, and so on to the final, which gives 64+32+16+8+4+2+1 = 127 matches. I think most people would approach it that way. It's okay for this particular question, but it takes about fifteen mental-arithmetic operations to get the answer. If we'd started with a bigger number, say 8192 players, it would be a very slow method.

Somebody who's been working hard at high-school maths might be able to recall an answer for this: 64+32+...+1... hey, I recognise all these as powers of two and I remember a formula for this particular series: double the starting term and subtract one, so that's 64 x 2 - 1 = 127. That's faster, especially for big starting numbers, but it's also a bit limited in that it only works if you start with a power of two.

My thought process was: each match creates one loser, and to narrow it down to a single winner we need to create (128-1) = 127 losers, so that's 127 matches. Done.

I didn't need to remember a formula and I didn't need to be quick at mental calculation; I was able to answer instantly because reframing the question in terms of losers rather than winners meant I didn't have to do anything harder than subtracting 1 from 128.

In that particular case, grinding the numbers will get you there in the end. But for harder problems you pretty much NEED to be able to make mental shifts like that, examine the problem from several different angles and identify one that's going to work. Otherwise even with the best computer assistance you can spend a lifetime grinding away without getting close.

#2: suppose we have a chessboard, but somebody's painted all the squares white. You can pick any 3x1 rectangle on the board and reverse the colour of ALL the squares in that rectangle, and you can keep doing that as often as you like. Is it possible to get to an all-black board?

For example, if we start out by selecting the rectangle marked in red, we change those three squares to black:

http://forum.literotica.com/attachment.php?attachmentid=1850352&stc=1&d=1460781303

If we now select the rectangle marked in blue, two more squares become black, but one that had been changed to black now changes back to white:

http://forum.literotica.com/attachment.php?attachmentid=1850356&stc=1&d=1460781303

If you play around with it for a while, you'll probably find that it's tantalisingly easy to get CLOSE to an all-black board, but that last square is elusive. Is it really impossible, or is there a winning method that we just haven't found yet?

Answering that by brute force is hard, but a little creativity makes it easy. Let's mark all the squares on the board with numbers 1, 2, and 3, running down the diagonals like so:

http://forum.literotica.com/attachment.php?attachmentid=1850360&stc=1&d=1460781303

If you count them up, you'll find there are 22 squares of type 1 and 21 squares of type 2. So we start out an even number of white Type 1s, and an odd number of white Type 2s.

It's easy to see that any 3x1 rectangle will cover exactly one square of each type. So every time we pick a rectangle and reverse its colours, we're changing the count of white Type 1 squares by 1 (might be an increase, might be a decrease), and likewise for Type 2. Every time, odds become evens and evens become odd.

This means that whenever the count of white Type 1s is even, the count of white Type 2s is odd, and vice versa. In particular, if there are no white Type 1s left on the board, the count of white type 2s must be odd (hence non-zero) so we can never have all the Type 1 and Type 2 squares black at the same time, making it impossible to turn the whole board black.

Again, by finding a new way to look at the problem, we make it easy. I had never seen this particular problem before I came up with that solution, but I'd seen similar ideas applied elsewhere.

The general idea I used here is to look for an "invariant" - some property of the system that never changes under the operations we're allowed to perform - and then show that it MUST change to get the end result we're seeking, hence proving it's impossible. There are many proofs of this type, but I think training a computer to generalise that approach would be difficult.

Getting back to that "learning the rules" thing... as in the other arts, a lot of what's interesting in maths comes from people who learned the rules, saw their limitations, then challenged them in search of deeper truths. Numbers started out simply as things you could count on your fingers. Then the framework got extended to rational numbers. The extensions to irrational numbers, zero and negatives, transcendental and complex numbers, calculus, hyperbolic geometry - all of those were revolutionary in their time, all of them required setting aside long-held assumptions about how mathematics worked and finding new ways to think about it.

 

[curl4ever]

VERY fun puzzles!

Thanks, Bramblethorn!

- curl