PATRICK WINSTON: I have
extremely bad news. Halloween falls this
year on a Sunday. But we in 6.034 refuse to suffer
the slings and arrows of outrageous fortune. So we've decided that Halloween
is today, as far 6.034 is concerned. Kenny, could you give
me a hand, please? If you could take that and
put it over there. STUDENT: [INAUDIBLE]? PATRICK WINSTON: Mm hm. Just give it to them. You can take as much of
this as you like. The rest will be given to that
herd of stampeding freshman that comes in after. It's a cornucopia
of legal drugs. Chocolate does produce a kind of
mild high, and I recommend it before quizzes and
giving lectures. I have a friend of mine, one
of the Nobel laureates in biology, always eats chocolate
before he lectures. Gives him a little edge. Otherwise, he'll be flat. So I recommend it. It will take, I suppose, a
little while to digest that neural net stuff. A little richer than usual
in mathematics. So today, we're going to talk
about another effort at mimicking biology. This is easy stuff. It's just conceptual. And you won't see this
on the next quiz. But you will see it
on the final. It's one of those quiz five type
problems, where I ask you questions to see if you
were here and awake. So a typical question might
be, Professor Winston is a creationist, or something
like that. Not too hard to answer. In any event, if it's been
hard to develop a real understanding of intelligence,
occasionally the hope is that by mimicking biology or
mimicking evolution, you can circumnavigate all
the problems. And one of those kinds
of efforts is ever to imitate evolution. So we're going to talk today
about so-called genetic algorithms, which are
naive attempts to mimic naive evolution. Now, I realize that most MIT
students have a basic grasp of sexual reproduction. But I've found in talking with
students that many times, they're a little fuzzy on
some of the details. So let's start off by reflecting
a little bit about how that works. So let's see, we need
pink and blue. And here's our cell, and here
is its nucleus, and here are mommy and daddy's chromosomes. We'll just pretend
there's one pair. Now ordinarily, in
ordinary cell division, you get two cells. Both have a nucleus, and the
process of producing them involves the duplication
of those chromosomes. And then one pair ends up in
each of the child cells, and that's all there is to that. That's mitosis. But then, when we talk about
reproduction, it's more complicated because those
chromosomes get all twisted up, and they break, and
they recombine. So when we talk about the cells
that split off from one of these germ cells, it's no
longer appropriate to talk about the pink one and the blue
one, because the pink one and the blue one are
all mixed up. So you get two chromosomes
here and two here. But through some miracle of
nature, which has always amazed me, these two cells
split, in turn, into four cells altogether. And each of those four cells at
the bottom gets one of the chromosomes that was produced by
the twisting up of the rope and recombination. Then, along comes a
special occasion. And now we can think of this as
being a blue one and this as being a pink one. And they come together, and you
get a new person, like so. Note that your mother and
father's chromosomes are never, never recombined. It's your grandparents
chromosomes that recombine. So that's what it's like. And the main thing to
note about this is-- well, a couple things. If you happen to be female,
this part of the process-- this part over here-- took place before
you were born. If you happen to be male, it's
going on right now as we speak, which probably
explains something. But in any event, it's
going on right now. But whenever it goes on, there
are lots of opportunities for throwing dice. So God threw all the dice before
you were born, if you happen to be a female, in this
part of the process over here. Then, of course, more dice got
thrown here when the decision was made about which particular
cells got to fuse to form a new individual. So I want to beat on this
idea of lots of choice. When we talk about genetic
algorithms, and we talk about nature, there are lots
of choices in there. And that means there are lots
of choices to intervene, to screw around, to make things
work out the way you want. But in any event,
there we are. That's the basic idea, and it
all starts with chromosomes. So we could think of
implementing something that imitates that with the ACTG
stuff that you learned all about in Seminar 1. But we're computer scientists. We don't like Base 4. We like Base 2. So I'm going to just suggest
that our chromosomes are binary in this system that
we're going to build. So that might be a chromosome. And it doesn't have
to be binary. It can be symbolic
for fall I care. But it's just some string of
things that determine how the ultimate system behaves. So it all starts out, then,
with some of these chromosomes, some of these
simulated chromosomes, simulated, simplified,
and naive. And there's a population
of chromosomes. The population of chromosomes--
it might be subject to a little
bit of mutation. That is to say, a zero
becomes a one, or a one becomes a zero. That happens a lot. That mutation stuff happens
over here when things get twisted up and recombined. There are copying errors
and stuff. Cosmic rays hit it
all the time. All sorts of reasons why
there might be a single point of change. That produces the
mutation effect. So here, we have a population
that starts off over here. And some of those things are
subject to mutation. And you'll note, here's a whole
bunch of choice already. How many of these mutations
do you allow per chromosome, for example? How many of the chromosomes
just slip through without any mutation? Those are choices
you can make. Once you've made those choices,
then we have the crossover phenomenon. Let's identify one of these guys
as the pink one and one of these guys as the blue one. And so now we have the pink one
cruised along as well as the blue one. The pink one and the blue one
cross and produce a new chromosome, just
like in nature. So we take the front part of
one, back part of the other, and we fuse them together. And some may slip by without
any of that, like so. Well, these things are meant to
be combined in pairs, like so, but they may not have
any crossover in them. So you have another
set of choices. How many crossovers do you
allow per recombination? You get another set
of choices. So now we've got a population
of modified chromosomes through mutation
and crossover. So the next thing to do is we
have the genotype to phenotype transition. That is to say the chromosome
determines the individual. It may be a person. It may be a cow. It may be a computer program. I don't care what. But that code down
there has to be interpreted to be a something. So it is the genotype, and it
has to be interpreted to be something which is the
phenotype, the thing that the stuff down there is
encoding for. So here, we have a bunch
of individuals. Now, each of those individuals,
because they have varying chromosomal composition,
will have a different fitness. So these fitnesses might be-- well, who knows how they
might be scored. But we're computer scientists. We might as well use numbers. So maybe this guy's fitness is
88, and this guy's fitness is 77, and so on. So now that we've
got fitness-- by the way, notice all the
choices involved there-- choice of how you interpret the
genotype, choice about how the phenotype produces
the fitness. And now we have a choice about
how the fitness produces a probability, like 0.8 and 0.1,
or something like that-- probability of survival into
the next generation. So now, once we've got those
probabilities, we actually have selection. And those phenotypes out there
produce genotypes, a new set of chromosomes, and that
completes our loop that goes back in there. And so that's the
new generation. Sounds simple. So if you're going to make this
work, of course, you have a million choices, as I'm going
to emphasize over and over again. And one of your choices is,
for example, how do you compute the probability of
survival to the next generation given the fitness? So we have to go, somehow, from
numbers like these to probabilities like those. So I'm going to talk about
several ways of doing it. None of them are magic. None of them was specified
and stipulated by God as the right way. But they have increasingly good
properties with respect to this kind of processing. So the simplest thing
you can do-- idea number one for
computing the-- see, what you do is you get this
whole bag of individuals, and you have to decide who's
going to survive to the next generation. So at each step, everything in
the bank has a probability of being the one you pick out and
put in the next generation. So at any step, the sum of the
probabilities for each of those guys is 1, because
that's how high probability works. The probability of a complete
set, added all up, is probability of 1. So one thing you can do is you
can say that the probability that you're going to draw
individual i is equal to, or maybe is proportional to, the
fitness of that individual. I haven't completed the
expression, so it's not a probability yet, because some
piece of it won't add up to 1. How can I ensure that
it will add up to 1? That's easy. Right. All I have to do is divide
by the sum of the fitnesses over i. So there's a probability measure
that's produced from the fitnesses. Yeah. STUDENT: You need to
make sure that the fitnesses aren't negative. PATRICK WINSTON: Have to make
sure the fitnesses are what? STUDENT: Aren't negative. PATRICK WINSTON: He says
I have to make sure the fitnesses aren't negative. Yeah, it would be embarrassing
if they were. So we'll just [? strike ?]
anything like that as 0. You've got a lot of choice how
you can calculate the fitness. And maybe you will produce
negative numbers, in which case you have to think a little
bit more about it. So now, what about an example? Well, I'm going to show
you an example. Why don't I show you
the example. What we're going to do is we're
going to have a genetic algorithm that looks for an
optimal value in a space. And there's the space. Now, you'll notice it's a bunch
of contour lines, a bunch of hills in that space. Let me show you how that
space was produced. The fitness is a function of x
and y, and it's equal to the sine of some constant times x,
quantity squared, times the sine of some constant y,
quantity squared, e to the plus x plus y divided
by some constant. So sigma and omega there are
just in there so that it kind of makes a nice picture
for demonstration. So there's a space. And clearly, where you want to
be in this space is in the upper right-hand corner. That's the optimal value. But we have a genetic
algorithm that doesn't know anything. All it knows how to do is
mutate and cross over. So it's going to start off
with a population of 1. It's a little red dot down
in the lower left. So here's how it's
going to evolve. There's going to be s chromosome
consisting of two numbers, an x number and
a y number, like, say, 0.3 and 0.7. Here's another one, which
might be 0.6 and 0.2. So the mutation operator is
going to take one of those values and change
it a little bit. So it might say, well, we'll
take 3, and we'll make it 0.2. And the crossover operation is
going to exchange the x and y values of pairs. So if we have a crossover here,
then what we're going to get out from this one-- well, we're going to get out
a combination of these two. And it's going to
look like this. Because what we're going to do
is we're going to take the x value of 1 and combine it with
the y value of the other one. So this is going to be 0.2-- my mutated value and 0.2-- and this is going to
be 0.6 and 0.7. So that's how my little genetic
algorithm heck is going to work. So having coded this up, we
can now see how it flows. Let's run it 10 generations. So the population is rapidly
expanded to some fixed limit. I forgot what it is-- 30 or so. And we can run that
100 generations. And so this seems to be getting
stuck, kind of, right? So what's the problem? The problem is local maxima. This is fundamentally a
hill-climbing mechanism. Note that I have not included
any crossover so far. So if I do have crossover,
then if I've got a good x value and a good y value, I can
cross them over and get them both in the
same situation. But nevertheless, this thing
doesn't seem to be working very well. STUDENT: Professor,
I have a question. PATRICK WINSTON: Yeah. STUDENT: That picture
is just the contour lines of that function. PATRICK WINSTON: The contour
lines of that function. So the reason you see a lot of
contour lines in the upper right is because it gets much
higher because there's that exponential term that
increases as you go up to the right. So I don't know, it looks-- let's put some crossover in
and repeat the experience. We'll run 100 generations. I don't know. It just doesn't seem to
be going anywhere. Sometimes, it'll go right
to the global maximum. Sometimes it takes
a long time. It's got a random number
generator in there, so I have no control over it. So it's going to get there. I couldn't tell whether
the crossover was doing any good or not. Oh, well, here's one. Let's make this a little
bit more complicated. Suppose that's the space. Now it's going to be in real
trouble, because it'll never get across that moat. You know, you would think that
it would climb up to the x maximum or to the y maximum,
but it's not going to do very well. Even with crossover, it's just
not going to do very well, because it's climbing up
those local hills. Anybody got an idea about one
simple thing we could do to make it work better? Yeah, you could increase
step size, right? Let me you see if
that will help. You know, even that doesn't
seem to help. So we have to conclude--
do we conclude that this is a bad idea? Well, we don't have to conclude
it's a bad idea yet, because we may just look at
it and ask why five times. And we might ask, well, maybe we
can get a better mechanism in there to translate fitness
into probability of survival. Using this formula is kind of
strange, anyway, because suppose temperature is one of
your fitness characteristics. The hotter, the better. Then the ratio of the
probability that you'll survive versus the person next
to you, that ratio will depend on whether you're measuring the
temperature in Celsius or Fahrenheit, right? Because you've shifted the
origin that shifts the ratio that shifts the probability
of success. So it seems kind of strange to
just take these things right straight into probabilities. So a better idea-- idea number two-- is to say, well, shoot, maybe
we don't care about what the actual fitnesses are. All we really care about is
the rank order of all the candidates. So the candidate with the most
fitness will have the most probability of getting into
the next generation. The candidate with the
second-most fitness will have the second-highest probability,
and so on. But we're not going to use the
actual fitnesses themselves to make the determination. Instead, what we're going
to do with this mechanism number two-- this is the rank
space method-- is this. We're going to say that
the probability of the highest-ranking individual
of getting into the next generation is some constant P
sub c, which, of course, you can select. You have another choice. Then, if that guy doesn't get
selected, the probability of the second-highest-ranking
individual getting in the next generation is going to be the
probability that that guy didn't get in there. That's 1 minus P sub c times the
same probability constant. And so you can see how
this is going. P3 will be equal to 1 minus P
sub c squared terms P sub c. P sub n minus 1 will be equal
to 1 minus that probability constant to the n minus-- n minus 2 times P sub c. And then there's only
one individual left. And then if you got through all
these guys and haven't got anybody selected, then you've
got to select the last guy. And so the probability you're
going to select the last guy is going to be 1 minus P
sub c to the n minus 1. So it's a probability you've
missed all those guys in the first n minus 1 choices. Yeah, it is, honest to God. See, this is the probability
that this last guys is going to get selected. It's not the probability that
it's the last guy getting selected, given that the others
haven't been select. Trust me, it's right. Are you thinking it
ought to be 1? STUDENT: What? PATRICK WINSTON: Were you
thinking it ought to be 1? STUDENT: No, I was thinking that
I was wondering why you were re-rolling the
dice, so to speak. PATRICK WINSTON: You are
re-rolling the dice. You've got a probability each
time, except for the last time, when, of course,
you have to take it. There's nothing left. There's no other choice. STUDENT: I have a question. PATRICK WINSTON: Yeah,
[INAUDIBLE]. STUDENT: So when you jump from
[INAUDIBLE], that makes sense. [INAUDIBLE] you're saying
[INAUDIBLE]. PATRICK WINSTON: It's the
probability [INAUDIBLE] the first two choices. STUDENT: Yeah, but the second
choice had probability one minus P sub c times
P sub c, not-- PATRICK WINSTON: Think
about it this way. It's the probability you didn't
choose the first two. So the probability you didn't
choose the first one is one minus P sub c. The probability you didn't
choose the next one, as well, because you're choosing that
next one with probability P sub c, it's the square of it. So that might work better. Let's give it a shot. Let's go back to our original
space choice, and we set and switch to the rank
fitness method. And we'll run out
100 generations. Whoa! What happened there? That was pretty fast. Maybe I used a big step size. Yeah, that's a little
bit more reasonable. Oops-- what happened? It's really getting stuck
on a local maximum. So evidently, I've choosed a
constant P sub c such that it just drove it right up
the nearest hill. On the other hand, if I change
the step size a little bit, maybe I can get it
to spread out. I sure did. And now that it's managed to
evolve over there to find the maximum value, now I can clamp
down on the step size again. And now it shows no
more diversity. It's just locked on to
that global maximum. So this is not unlike what
evolution sometimes does. Sometimes, species collapse into
a state where they don't change for 500 million or 600
million years, like sharks, for example. Sometimes, they only survive
if they've got a lot of diversity built into their way
of life so that they can adjust to habitat changes. Now, when you increase the
step size, because you're stuck on a local maximum, it's
like heating up a metal. You make everything
kind of vibrate more, make bigger steps. So this kind of process, where
you may start with a big step size and then gradually reduce
the step size, is called simulated annealing, because
it's like letting a metal cool down. So you start off with a big
temperature-- big step size-- that covers the space. And then you slowly reduce the
step size, so you actually crawl up to the local maxima
that are available. So that seemed to work
pretty well. Let's see if we can get it
to work on the harder problem of the moat. So it's not doing very well. Better increase the step size. No, it's still kind of stuck. Even though it's got the
capacity to cross over, it's so stuck on that lower
right-hand corner, it can't get up that vertical branch
to get to a point where a crossover will produce a value
up there in the upper right-hand corner. So we're still not home yet. So what's the trouble? The trouble is that the fitness
mechanism is just driving things up to
the local maximum. It's just terribly
unfortunate. What to do? Well, here's something
you could do. You can say, well, if the
problem is we've lost the diversity in our population,
then we can measure the diversity-- not only the fitness of the
set of individuals we're selecting from, but we can
measure how different they are on the individuals we've already
selected for the next population. In other words, we can get a
diverse population as well as a fit population if, when we
make our selection, we consider not only their fitness
but how different they are from the individuals that
have already been selected. So that's going to be mechanism
number three. So now we have a space,
and we can measure fitness along one axis-- ordinary fitness-- and this is rank space
fitness, so that's going to be P sub c. There will always be
some individual with the highest fitness. And over here-- that might not be P
sub c, actually. But there'll be some individual
with a maximal fitness, and at any given step
in the selection of the next population, there'll be some
individual that's maximally diverse from all of the
individuals that have been selected for the next
generation so far. So what kind of individual would
you like to pick for the next generation? Well, the one with the highest
fitness rank and the one with the highest diversity rank. So what you'd really like is
you'd like to have somebody right there. And if you can't have somebody
right there, if there's nobody right there with a maximum
fitness, a maximum diversity at the same time, then maybe you
can draw in iso-goodness lines, like so, which
are just how far you are from that ideal. So let's summarize. You've got to pick some
individuals for the next population. When we pick the first
individual, all we've got to go on is how fit the individual
is, because there's nobody else in that
next generation. After the first individual is
selected, then we can look at our set of candidates, and we
can say which candidate would be more different from the set
of things we've already selected than all the others. That would get the highest
diversity rank and so on down the candidate list. So let's see how that
might work. So we're going to use a
combination of fitness rank and diversity rank. And we'll just use the
simple one so far. We'll use a small step size,
and we'll let this run 100 generations to see
what happens. Bingo. It crawls right up there,
because it's trying to keep itself spread out. It uses that diversity
measurement to do that. And at the same time, it's
seeking high fitness, so that's why it's crawling up to
the upper right-hand corner. But in the end, that diversity
piece of it is keeping the things spread out. So suppose you're a shark
or something. You don't care about diversity
anymore, And we could just turn that off. Is that thing still running? Go back to fitness rank-- bingo. So there you are-- you're stuck
for 600 million years. So let's see if this will
handle the moat problem. See, our step size
is still small. We'll just let this run. So the diversity of P sub is
keeping it spread out, pretty soon, bingo, it's
right in there. It's across that big moat,
because it's got the crossover mechanism that combines the best
of the x's and the best of the y's. So that seems to work
pretty well. OK, so see, these are some of
the things that you can think about when you're thinking--
oh, and of course, we're a shark, we're going to forget
about diversity. We'll change the selection
method from fitness and diversity rank to
just diversity. It collapses down on to
the highest hill. Yeah, [INAUDIBLE], what? STUDENT: How does step size
translate into mutations? PATRICK WINSTON:
Oh, just the-- question is, how does step size
translate into mutation? Instead of allowing myself to
take steps as big as 1/10, I might allow myself to take
steps as big as 3/10, according to some
distribution. So what to say about all this? It's very seductive, because
it's nature, right? The trouble is, it's
naive nature. And as evolutionary theories
go, this is horrible. This is naive. So we'd like to use real
evolutionary theory, except we don't have real evolutionary
theory. Evolution is still a mystery. Some things are pretty
obvious. You can breed fast
race horses. That works just like so. The trouble is, we don't have
any real good idea about how speciation takes place and how
a lot of evolution works, because all these chromosomes
are connected to their phenotype consequences in very
complicated ways that nobody fully understands. So there's a great deal of
magic in that genotype to phenotype transition
that nobody really understands very well. So when people write these
programs that are in the style of so-called genetic algorithm,
they're taking a photograph of high school
biology, and they're spending a long time building programs
based on that naive idea. But that naive idea has lots
of places for intervention, because look at all the things
you can screw around with in that process of going from one
generation to the next. By the way, what does
mutation do? It's basically hill
climbing, right? It's producing a little spread
out, and you're using the fitness thing to
climb the hill. So you get a lot of choices
about how you handle that. Then you get a lot of
choices about much crossover you're doing. What does crossover do? It kind of combines strong
features of multiple individuals into one
individual, maybe. So you've got all kinds
of choices there. And then your genotype to
phenotype translation-- how do you interpret something
like those zeroes and ones as an if-then rule, for example,
as something that's in the hands of the designer? Then you've got all the rest of
those things, all which are left up to the designer. So in the end, you really
have to ask-- when you see an impressive
demonstration, you have to say, where does the
credit lie? And I mean that pun
intentionally, because usually the people who are claiming
the credit are lying about where it's coming from. But nevertheless, let me give
you a couple of examples of where this has found actual,
bona fide practical application. So when you look for practical
application, you might say, well, in what kind of problem
does a good front piece combine with a good back
piece to produce a good thing overall? And the answer is, when
you're making a plan. So you might have a problem in
planning that requires you to take a series of steps. And you might have two
plans, each of which is a series of steps. And you might combine these to
produce something new that's the front half of one and the
back half of another. So that's practical application
number one. And that requires you to
interpret your chromosome as an indicator of the
steps in the plan. Another example is drawn
from a [? UROP ?] project a student did for
me some years ago. He was a freshman. He came to me and said, I want
to do a [? UROP ?] project. And I said, have you
taken 6.034? And he said no. And I said, go away. And he said, I don't
want to go away. I want to do a [? UROP ?]
project. So I said, have you
read my book? He said no. I said, well, go away, then. And he said, I don't
want to go away. I want to do a UROP project. So I said, I don't have any
[? UROP ?] projects. He said, that's OK. I've got my own. He's a finance-type guy, so he
was interested in whether he could build a rule-based expert
system that could predict the winners
at horse races. So his rule-based expert
system consisted of rules like this. If x and y, then some
conclusion. If l and m, then some
kind of conclusion. And from these, he would
produce rules like if x prime-- that's a slightly
mutated version of the x antecedent-- and m, then some conclusion. So it's mutation
and crossover. And he was able to produce a
system that seemed to work about as well as the
handicappers in the newspaper. So he started losing money
at a less fast rate. He is now doing something in
the stock market, they say. Doesn't talk so much
about it, though. But an interesting
application. He came up with rules like, if
the sum of the jockey's weight on the post position is
low, that's good. Well, that makes sense in the
end, because the jockey's weight is always between 100 and
110 pounds, and the post position is always between 1 and
10 or something, so they were commensurate values. And a low one is
good, in fact. Not bad. But neither of those-- I mean, this is real stuff. My company uses this
sort of stuff to do some planning work. But neither of those is
as impressive as the demonstration I'm about to show
you that involves the evolution of creatures. And these creatures consist of
block-like objects, like so. And they combine like
this, and so on. And so how can you make a
feature like that from a [? 0-1 ?] chromosome? Well, some of the bits in the
chromosome are interpreted as the number of objects. Others are interpreted as the
sizes of the objects. Others are interpreted as the
structure of how the objects are articulated. And still others are interpreted
as fixing the control algorithm by which
the creature operates. So you see how that
roughly goes? Would you like to see a film
of that in action? Yes. OK. [INAUDIBLE] always likes to see the films. STUDENT: How would you measure
diversity in that graph? PATRICK WINSTON: The question
is, how do I measure the diversity of the graph? I did it the same way I
measured the fitness. That is to say, I calculated
the distance-- the actual metric distance-- of all the candidates for the
next generation from all of the candidates that had
already been selected. I summed that up. And from that sum, I could rank
them according to how different they were from the
individuals that were already in the next generation. It's like giving a rank, and
then from the rank, I use that kind of calculation to determine
a fitness, ie, a probability of survival, and
then I just combine the two kinds of probabilities. STUDENT: So you always kept--
every time that you started something, [? you cached ?]
those. And you kept everything that
you've ever [INAUDIBLE]. PATRICK WINSTON: I'm always
using the individuals that have already been selected at
every step, so every step is a little different because it's
working with a new set of individuals that have already
been selected for the next generation. OK? So let's see how this works. So this is showing
the evolution of some swimming creatures. And they're evolved according to
how well they can swim, how fast they can go. Some of them have quite exotic
mechanisms, and some of them quite natural. That looked like a sperm cell
floating away there. Once you have these things
evolving, then of course, you can get groups of them
to evolve together. So you saw already some that
were evolving to swim. These are evolving to move
around on the land. It's interesting-- this was done
by Karl Sims, who at the time was at a then-thriving
company, Thinking Machines, a fresh spinoff from MIT. So he was using a vastly
parallel computer, super powerful for its day,
thousands of processors, to do this. And it was a demonstration
of what you could do with lots of computing. In the early stages of the
experimentation, though, its notion of physics wasn't quite
complete, so some of the creatures evolved to move by
hitting themselves in the chest and not knowing about the
conservation of momentum. I thought that was just great. So here they are, out
doing some further-- So you look at these, and you
say, wow, there must be something to this. This is interesting. These are complicated. I think this is one of the
ones that was trained, initially, to swim and then
to do land locomotion. So eventually, Karl got around
to thinking about how to make these things evolve so that they
would compete for food. That's the fastest, I think,
by the way, of the land locomotors. So that was training them to--
evolving them to jump. This is evolving them to follow
a little red dot. Some of them have stumbled upon
quite exotic methods, as you can see. Seem to be flailing around,
but somehow manage to-- sort of like watching
people take a quiz. Making progress on it. But now we're on to the
food competition. So some of them go for the food,
and some of them go to excluding their opponent from
the food, not actually caring too much about whether
they get it. That's sort of what
children do. There's a kind of
hockey player-- now, here's two hockey
players. Watch this. They're kind of-- one succeeds-- it reminds me a little
bit of hockey, rugby, something like that. Sometimes, they just get kind
of confused, go right after their opponent, forgetting
about the food. Gives up. I think these are the
overall winners in this elimination contest. I can't quite get there. OK, so you look at that, and
you say, wow, that's cool. Genetic algorithms must
be the way to go. I remember the first time
I saw this film. It was over in Kresge. I was walking out of the
auditorium with Toma Poggio And we looked at each other,
and we said the same thing simultaneously. We didn't say that genetic
algorithms were the way to go. What we said was, wow, that
space is rich in solutions. What we were amazed by was not
that simple-minded genetic algorithms produced solutions
but that the space was so rich with solutions that almost any
mechanism that was looking around in that space
would find them. But there's yet another way of
thinking about it, and that is you could say, wow, look at
how smart Karl Sims is, because Karl Sims is the one who
had his hands on all the levers, all those choices. And I kept emphasizing, all
those choices that enabled him to trick this thing, in some
sense, into stumbling across the solutions in a space
that was guaranteed to be rich with solutions. So you have to ask-- so first of all, diversity
is good. We noticed when we put diversity
into the genetic algorithm calculations,
we were much better at finding solutions. But the next gold star idea that
I'd really like to have you go away with is the idea
that you have to ask where the credit lies. Does it lie with the ingenuity
of the programmer or with the value of the algorithm itself? In this case, impressive as it
is, the credit lies in the richness of the space and in
the intelligence of the programmer, not necessarily
in the idea of genetic algorithms.
