Askwith Forum: Stephen Wolfram and Howard Gardner – Best Education in Computational Thinking


(people talking quietly) – We’re gonna set up, so you can chat a bit more if you want. We’ll start in a few minutes. – All right. (people talking quietly) Let’s forget that one. – Okay, sure. Okay, let’s give ’em another
minute and then start. (people talking quietly) Okay. – Okay?
– Yeah, yeah. Good evening everybody. I’m Howard Gardner and welcome to this evening’s Askwith Forum. And I’m sure you all want to
know what the Askwith Forum is, so I’m going to give you the tweet. The Askwith Forum brings
leaders in the field to campus to share knowledge and
engage with our community, the community of the School of Education. These forums help strengthen the intellectual life of the
school through conversation, debate, and the exchange of ideas. They are also a way to open our doors to welcome members of the
greater Harvard community and the general public. And the next Askwith Forum will be held next Tuesday, November
14th, same time, 5:30, same place, and the topic for the forum, which will give you a sense of the breadth of this enterprise is How Mayors are Leading the Way on Child Development and Education. So that’s your primer
on the Askwith Forum. Having fulfilled my official role, it’s my pleasure to
welcome Stephen Wolfram to the Graduate School of Education. Now it’s polite decorum
to introduce speakers, but Stephen presents a
very difficult problem. He’s done so many things and
is doing so many more things, it would take the better
part of the evening to introduce him, and
then we wouldn’t have time to hear from him or to hear from you. So with that as an apology, let me just mention a half
a dozen Stephen Wolframs. Number one, a very young
scholar who was educated in England, UK and the USA, Stephen published his first
scholarly paper at 15, received his PhD in theoretical
physics from Caltech at the age of 20. Number two, he’s a certified genius. At the tender age of 21, Stephen became the youngest recipient of the MacArthur Prize Fellowship, the so-called Genius Award. We’re not sure of anybody
younger ever got it, but I kind of doubt it. Number three, the teacher’s scholar. Stephen has taught in several universities and has written on a wide range of topics, including a very important book called “A New Kind of Science”, a very big book. And more recently, he has
been writing about the history of scientific and mathematical thinking. He’s been doing podcasts. And wrote a very interesting book where he described his own
experiences and interactions either in his own mind
or directly with 11 or so important thinkers historically. And it’s a very, very interesting read. Wolfram, number four, is the
creator of new languages, codes, programs,
knowledge-based languages, that’s his particular focus. Fifth, he’s an entrepreneur. He has started a whole set of enterprises, has a network of people working
with him in many places. And I believe this is all
done under the umbrella of Wolfram Research. – Yep. – Sixth and last and most
relevant this evening, Stephen is an educator, an educator particularly of young people. He has run summer schools, he has supported the National
Museum of Mathematics, and he has a large computational
thinking initiative which I’m sure he will talk
about a lot this evening. So that’s a fair sample of the many hats that Stephen has worn over the years. So we are at an Ed School, and so tonight, I want to focus on educational issues. And many of us, including me, are confused about what
the best education is for young people going forward. We’ve heard many terms, math,
STEM, computing, coding, computational thinking and my motive for asking Stephen to come here and I was very happy that
he accepted was to try to remove some cobwebs from my own mind and perhaps help you think more clearly about these issues. The plan is that we’re gonna
talk here from the podium for 30 or 40 minutes, then open it up to
questions from the audience. We have microphones here and
the usual patterns for people just to go up the mic and
to ask your questions. And I’ll ask you, hold your comments, but whether you’re making
a question or comment, please make it clear and
please make it succinct. So welcome, Stephen. – Thanks.
– Thanks again for accepting our invitation. And when this program was advertised, and I take responsibility for this, I used the word mathematical thinking or mathematical, mathematics, and you said, “Well that’s
not really what I think about “and what I want to talk about.” So as I said to you beforehand, I want to sort of start with
definitions and epistemology so we can have some sense of
what these different terms mean and then move gradually to more specific educational challenges. – So I mean, why change
from mathematical thinking to computational thinking? Computational thinking is a
bigger, more significant thing that is kind of I think
will be kind of remembered as probably the most
important kind of intellectual achievement of the 21st century, it’s kind of the beginning of serious computational thinking. Mathematical thinking is something which kind of was very important
300 years ago in the kind of, the beginning of modern
exact science and so on, and it’s had lots of effects, but computational thinking
is kind of a bigger thing. I view mathematical thinking as sort of a subset of computational thinking. So I mean, if you say what is
computational thinking, right? One definition of it that I might give is it’s the activity for a
human of taking something that they want to know about or that they want to
have happen in the world and formulating it such a way that a sufficiently smart computer
can then know what to do. Now, the sufficiently smart part, that’s what I’ve spent my
life trying to build is the, is to make the computer sufficiently smart that you can go from kind of what you as a human think about doing and have a language in which
to talk to the computer and explain what you want to have done, and then have the computer
as automatically as possible actually go and do it. This is kind of in, when we
talk about mathematical thinking it more tends to be about
the particular methods that have been successful in mathematics, things with equations,
calculus, and so on. These are examples of
kind of formal systems, formal structured systems that
have been quite successful in bringing us a lot of
modern physics and engineering and so on. What I happen to as a
matter of basic science to have spent a certain amount
of time trying to generalize the success of mathematics
to the more general kind of computational world, I
mean so the question is if you’re trying to
make a model of a thing, for example something in nature,
how do you make that model? And the sort of the big
discovery of 300 years ago by people like Newton and so on was you can use math to make models of things like the natural world, and that was a tremendously
successful discovery that’s given us lots of kinds of things. The question is, is that the only way we can make models of the natural world, or is there a sort of more
general category of model that we can use? And in modern times when we understand something about programs
and computers, we realize, well, we’re gonna make
a model of something, we have to have some definite
structured formal rules for how the thing works. But the ones that we
can embody in a program are more general than the ones that we’ve considered in mathematics. And so I got interested
in this question of okay, so can we build kind of a way
of thinking about the world that makes use of programs and computation rather than the specific
constructs of mathematics? And one of the one of the
things that’s happened actually in the last 15 years or so since that big book that you
mentioned of mine came out, I think it’s something to do with the fact that my book came out then, but it might just be a matter of the progress of the world in general. There’s sort of been a transition
for the last 300 years, when you wanted to make
a model of something, the chances are you would use math as the foundation for making that model. You would find an equation for how the thing works, or whatever. Now it is vastly more common to say we’ll make a program
that can define the rules for how the system works, and we’ll then simulate the system or whatever using the program. So in 15 years, after
300 years of dominance of kind of the mathematical approach, we’ve seen this sort of transition to a more computational approach. – So let’s take two figures, let’s take Isaac Newton and
let’s take Charles Babbage. – Yes. – Newton being a great scientist and also inventor of the
calculus, along with Leibniz, and Babbage being the
person who had the idea of a calculating machine,
which was an early computer, what would they be surprised about if they were to come back today, and what would they say, “Well sure”– – You should give more credit
to Ada Lovelace because she’s the one who actually–
– I actually do. – I mean, Charles Babbage
was a good engineer, but Ada actually understood
what the point was. – Happy to do that. – In a way that Babbage did not. He was deep down trying to
calculate mathematical tables, but in any case, in terms of
what’s happened today, I think, let me think, I mean, Newton, Newton was at a time,
lived at a time when people were very surprised that
you could just use math to describe how the world works. And it was like, “But
there’s no mechanism. “What’s the mechanism
by which the earth moves “according to the law
of gravity”, and so on. But in his time, so that
he was fighting the, “No, actually you can just
describe it using math.” Now we’re fighting the opposite battle. It’s people saying, “But we know math is the
way everything works.” Actually, I think this battle has been won in the last few years. I think that the thing
that’s always surprising, for example, in the case of computation, and particularly the idea
of universal computation which was the idea that Ada Lovelace kind of pretty much figured out
from what Babbage was doing, I mean, universal computation
is kind of the idea that if you want to run a
program that does anything that a program can do, you can use the same computer to run all these different kinds of programs. It might have been the case, and people thought that for a while that you want to do addition,
you buy an adding machine, you want to do multiplication, you buy a multiplying
machine, but actually, there’s this idea that you
can have a universal computer that can be programmed to do anything. Now that idea which sort of came between Godel and Turing and so on, that idea really emerged as a real thing, but the understanding of, “Okay, so what can we actually do “with these universal machines?” That has been slow to come,
and we only gradually, in my own efforts to sort of
understand how one can have the broadest abstract
structure for computation. I think I’ve, at the rate
of about once per decade, I understand another major thing that can now be fit into this kind
of paradigm of computation. And I mean, when we saw one of the things that’s sort of strange about, well, the thing I think that
we’re seeing today and that would have surprised, well, I think Newton didn’t know anything about things like computers. That was just, that was out of his world. – Leibniz might have actually known more. – Leibniz would have been,
Leibniz wanted to do, Leibniz was on a path to do
a lot of the kinds of things that I’ve spent my life doing. I mean, Leibniz had the idea, there’s this thing called Wolfram Alpha, which lots of people use and powers Siri and things like that, that’s a computational knowledge engine, and Leibniz had pretty much the idea of building such a thing, but as a cautionary tale to people like me who like to think about
what one should do, he was 300 years too early
and actually formulated it. I mean, he was like, “Let’s build the best calculator we can.” I went to see his calculator, it’s made of brass and has
a bunch of wheels and gears and so on, it took him 30 years to try and get it to be sort of a four
function calculator of its day and then he was like,
“Let’s collect knowledge “that we can feed into these things.” And he went to convince a bunch of Dukes to build libraries and so on. I had it much easier 300 years later. But I think the thing
that is remarkable today is that we see this kind of paradigm of computational thinking about things in computational terms,
and it is becoming, we’re realizing that it
is pretty much applicable to any field that one thinks about. So there’s a, my way of saying this is it’s kind of for any
field X from agriculture to zoology to whatever else, there either is now a computational X, or there soon will be. And that computational X typically defines the future of that field. It is the, it’s the sort of
emerging very broad paradigm that the things that we’re thinking about, it’s a way of structuring
what we’re thinking about, it’s a way of making progress with what we’re thinking about. – Of course, many people, including me, are either afraid or skeptical that computational ways of thinking
will take over every field. – Let’s pick a field, we can talk about– – Well since you said
it, let’s talk about, let’s call it aesthetics, including art history and art appreciation and the making of artwork. Now I think we all agree that you could do lots of computational things. The challenge comes are
you doing the things which are illuminating, or
simply things which you can do? – Yeah, well, that’s always, I mean, that is the story of progress of knowledge is people invent
methodologies and then they, fields end up getting defined
by their methodologies. We happen to have a broad new methodology which allows us to unlock
lots of kinds of things. I don’t know, we can do, let’s actually do something real here, it’s always fun to do an
actual computer experiment. Let me just, let’s see
if can project this. If we can project this then, ah, that won’t work
because it can’t magically, it has to, there we go. Push that in, maybe screw
it in and that would be, I don’t see, did that work? Yes, something came up, okay. Well, let’s just for fun, let us try just, I’m
going to, this is just, I’m just typing into Wolfram language. So let’s say van Gogh,
let’s see if it knows about, let’s see if it knows some, okay, so van Gogh is a person. Can you see this or
should I make it bigger? (crowd laughing)
Bigger. Okay, so there’s van Gogh, it’s a person. And let’s say we say, what are some notable
artworks of van Gogh? So it’ll now have to go
and, so this is just, it’ll go and find, okay, so there’s there’s a
bunch of notable artworks, so let’s take a, now let’s say, let’s take a random sample
of those notable artworks. Let’s take, I don’t know,
10 notable artworks there. Let’s see if we can find, let’s see if we have
images for some of those. Okay, let’s what it does. Okay, so there are some images. And now maybe we can ask ourselves what colors were used in those? So, this is a very, very
science-y thing to ask, but let’s say what colors
were used in those pictures? So we can say, okay, that’s
the distribution in color space of what colors were used, or we can, maybe we could take those
pictures and we could say– – [Howard] That would
be very helpful to me because I’m colorblind so– – Okay, so–
– You sold me on that. – Here’s a good thing to do then. Let’s take these pictures
and let’s see what happens if we take the ones on line five. Let us say, well here, let’s do something very straightforward. Let’s just binarize those pictures. Okay, so that’s the
black and white version of those pictures. Maybe we can actually,
are you a dichromat? – I’m called an anomalous tritanope, but let’s not use me as the subject. (crowd laughing) – But we could start figuring out, given these pictures
we could start saying, “Let’s simulate how you
would perceive these pictures “based on your particular vision system”, and then we could start asking, “Can you distinguish what”, for example, we might take those pictures that are on line five and
let’s say, let’s make, I mean, this is, let’s use some
machine learning method to try and figure out, it wasn’t very exciting in this case, I was going to try and
arrange these pictures in some kind of feature space
where you could perhaps see if you did this and you did
it for all these pictures, you might be able to see some
kind of progression of style. – Yeah let me, this I think is something that you may be able to do. Let’s say could you
rank order the pictures on the range of color
space that they have, how many different colors and so on? – Sure, let’s try that. – What’s of interest to me is that even though I’m colorblind,
Rothko is my favorite, Mark Rothko is my favorite
20th century painter and he’s all color, but obviously, there’s something about that
which transcends the fact that I don’t know what colors they are. – [Stephen] Right, so I mean,
we can, I don’t know what, okay, so we seem to
have some, so let’s say, let’s just take the first
10 of those just for fun, and let’s say, okay, so we don’t have so many images here, but let’s just for fun here, let’s say, let’s just delete the ones
that we’re missing here and let’s say, “What are
the dominant colors?” Okay, so this might be kind
of an interesting thing to do. Let’s take the dominant colors
in there and now let’s say, let’s think how to do this. I can find out what is the nearest, for each of those colors, I can find out the nearest
named color to those colors. Let me think how to do that. – So I can’t see, but are these Rothkos? And what’s on the left
there, is that a van Gogh ? – No, that’s a Rothko, I think. I mean, it says it’s a Rothko. It says it was a thing
called Orbade, Aubade. – [Howard] Oh, okay, yeah. – [Stephen] I mean, we could probably– – [Howard] It’s certainly not a van Gogh. – No.
– I’ll give you that. – Right, it’s some, but so now, we’ve figured out what are
the dominant colors here? We could for example, so for example, here’s an interesting case
of computational thinking that somebody might do. They might say, “How can we
help a person who is colorblind “to appreciate this art?” And what could we do? Well, we might want to
turn this art into words. We might want to say, be able to annotate each piece of art with the names of some colors as a way to give some indication of what’s there. And then we might think,
“How would we do that?” And somebody might say, “Well, what do we mean
by the name of a color?” Because this, that thing
there, we could say, in this case, there are certain, there is a whole range of colors. If we just take that
image there and we say, “What’s a chromaticity
plot of that image?” We’ll find that there’s
a range of colors there. Okay, so in the color triangle, there’s a range of colors. What is the color in that image? Well now we have to get
into sort of this question that might be sort of a
computational thinking question of what do we mean by saying the dominant color in the image? – And even if you didn’t have it, if you formulate it clearly enough, you could create a
measure for chromaticity. – Yes, so for example here, one easy thing we could
do is if you want to know how diverse is the palette of colors, this will be a good indication. So for example, if we
take our pictures here, well, let’s actually take line
five and line 10, line 11. Okay, so let’s say chromaticity plot, chromaticity plot of
the stuff on line five, that was van Gogh. Actually, let’s do this. We’re gonna do that for van Gogh and for those Rothko
pictures there, line 11. And what we’re gonna find I think, let’s take a look, okay. So that’s a comparison of
the sort of color range for van Gogh versus Rothko. Actually, it’s not quite
as broad for van Gogh as I might have expected, but it’s clearly somewhat broader than in the Rothko case,
and we could kind of, we could easily take that and turn it into some quantitative measure of these things. And so–
– What Stephen has done, I hope he’ll accept this characterization, actually is very meaningful for me because I’m a psychologist by training, and when I was 15 or 16, I wasn’t getting my doctorate in physics, my uncle gave me a psychology textbook. He must have had a sense that
I was interested in that, and I became fascinated by
the Ishihara color plates because people who can
see colors, they read 23, to me, it looks like nothing. And one of the powerful
things about Stephen’s work and we’re getting into
education by this example is he doesn’t start with
what the textbooks say kids should be interested in
or what the teachers said, but he starts with what
kids are interested in, the questions they bring up, and then he tries to figure out a way to help them answer the
question and in the process, introducing them to
categories and to analyses, which they may or may not
have thought of on their own. And I listen to a lot of music,
classical music and often, I can’t tell exactly who the composer is but I know approximately when it was done, and I also have pretty strong views about whether it’s any good. And it’d be wonderful to know whether my judgment of quality, I say look, this is clearly a classical piece, I don’t think it’s
Mozart, it might be Haydn, but it’s also not Salieri, you know? And we don’t know that
the computational approach could answer the question but it might be, it might well be able to. – It’s surprising, I
mean, that type of thing of classifying which instrument is playing in a piece of sound, for example. So the modern machine learning, it is remarkably easy to
answer questions like that, to classify things and it’s remarkable, the cues that end up being,
I mean if I just say, we could take, let’s do this, let’s get an image from my computer. There we go, there’s an
image from the computer. We could say image identify that image, and now, this is just a simple case, I know what it’s gonna say here, it may say something
goofy because it’s seeing all kinds of background and so on here, but it might say it’s a
person, it might say it’s a, okay, that’s interesting. (crowd laughing)
Okay, so let’s try, it said it’s a cockpit,
that’s very strange. Let’s ask it just for fun, let’s ask it what were the
probabilities that it assigned? This is the world of machine
learning that, like humans, AIs make mistakes and– – That was so fascinating. Everybody said, “Why did it say that?” – Yeah, so a really
interesting thing to do, let’s try doing this, let’s try feeding it those Rothko pictures as things
to identify what are they and see what it says there. Let’s see, what is it doing here? Wake up computer, there we go. Okay, so it says it’s a cockpit with 27%. It’s a primate with 27%.
(crowd laughing) It’s a hominid, again, a person, okay? So the person has almost made it, the cockpit just beat out the person. It’s an awning deck. And a variety of other things
here, but it’s kind of, as a matter of psychology, actually when we were building
this image identifier, one of the things I like to
do is to feed it abstract art because it’s a way of telling
whether it’s prejudiced. For example, for a
while it was saying that almost any piece of abstract
art was a band-aid– (crowd laughing)
Which is kind of weird and it means something is wrong with the way it’s thinking
about things and so on. – Great. So there’s a question we’d like to ask, and the work that I do, if you were to design a university, we can remain nameless, and you could reconfigure the curriculum, and let’s take Harvard as an example. Harvard has for years been
humanities, social sciences, natural sciences, and within humanities, there’s the arts, English, history, linguistics sometimes, and
within social sciences, from sociology and
anthropology to economics, and then you have natural
and physical sciences, and roughly speaking, that’s
what’s done in certainly, in most liberal arts
schools in this country. Would you keep those categories
or would you shake them up? And if so, how? – It’s a funny thing. How fields are defined is complicated. I mean, so one question is, when you talk about computational thinking and the role of that paradigm, there is, okay, so let’s talk about math and what’s happened with math. So math rather cleverly figured out that there’s this area of pure mathematics that’s this abstract intellectual area that is worth pursuing, okay, let’s go back to the Middle Ages. There were two competing
kind of formal systems; Logic and math. As we notice in sort of the
development of education, math is done today and kids learn math. Logic, not so much,
it’s not really a thing. I think one of the
differences is that math ended up building this
kind of quite substantial kind of independent abstract field that was pure mathematics. Logic didn’t so much build that. It ends up that the
support of pure mathematics as a worthwhile thing to
do is largely a consequence of the fact that there are
applications of mathematics that have flowed out into different areas, but there’s also this
pure abstract thinking kind of activity that is pure mathematics, that is a worthwhile sort of
piece of intellectual heritage that our culture has. I think that we can ask
about computational thinking how should that be, when it comes to math,
there’s this area of pure math that’s really, really good
and clean and intellectual. There’s applied math, which people don’t
completely know what it is. Applied math as a
department at universities has had a troubled history. It was, after the Second World War, it was mostly differential
equations and linear programming. Then it sort of evolved
into different things. It’s been, it’s not
really clear what it means to be applied math. There is this pure area of
intellectual work that is math, and then there are the, well, it gets applied to different things. For computation and computational
thinking, there is also, I think, a sort of basic
science of computation that is actually not so much studied, it’s not quite the same
thing as computer science, and there’s a small piece of
thing that should exist there much like pure mathematics– – And Turing would have
been an example of someone who did that, Alan Turing. – Yes, I mean, I would say he was at the beginning of that, yes, yes, right. These are abstract
ideas about computation. So there’s a pure computational science that deserves to be
its own separate thing, like there’s a department
of pure mathematics, so to speak, and then there
are the applications of that to all different areas, and those things should
be part of those areas. – So in other words, let me just make sure that I’m understanding you, you wouldn’t change the
typography particularly, but you would open it up to computing ways of thinking, and they would go as far as they could go. – But that’s because
a lot of these things, they will be called
computational sociology, computational art history. They’re not going to be called that, and this question of
how we divide knowledge into the things that we choose to teach, that’s an interesting
question in its own right, and I think it’s kind of like the, there are all kinds of things that, how do you estimate how many
departments there might be in a university? It’s like how do you estimate
on the back of an envelope how many countries there
should be in the world? How do you estimate, these are, it’s not easy to know
that there should be, maybe it’s more a matter
of something to do with the way that we humans sort of
choose to organize ourselves that there end up being whatever it is, 50 to 150 or something, I don’t know quite what the number is of sort of different fields that typically get taught at universities. I mean, I think another question is as we look at the progress of technology, what technology tries to do is to automate things getting done, and then
there’s a question of, okay, so what do we teach the humans at a time when there’s this sort of
rising tide of automation? And what do we, and you know, we could still be teaching
flint knapping, but we’re not because the things that, or you know, or a lot of other kinds
of very manual operations that have long ago been sort
of submerged by technology. And I think one of the
things that’s interesting is is there more that needs to
be taught in the world today, or is it that there is a continually a frontier of things that
are worth humans learning, but haven’t yet been automated? And then as we automate more, we can sort of teach
higher-level kinds of things for the humans, so to speak, and leave the lower level things to just get done by machines. And I think that one of the
things that comes up right now is this question of okay,
so what should we teach? Well, we should teach, we’re
getting very powerful tools for achieving lots of kinds
of things in the world, but the one thing we don’t
get to sort of automate is defining still what is it
that we’re trying to achieve? The definition of what our goals are is something that I think
inevitably has to come from us humans. – But no, but it isn’t the fear that much of artificial
intelligence will actually presuppose certain goals whether or not the users of it are aware of it? I mean, let’s just take cars, and what they do when
there’s a potential accident. There has to be something
built into that system which decides do they hit three people or does the driver
sacrificed himself because, so, we could I mean, I would
say and I guess you would say, I’m not sure I want to
leave that to the algorithm, but most people won’t say that, they’ll just do whatever is
built into their car system. – Right, but I mean, and
what all we’re doing here is it’s a question. There’s there’s this very
powerful thing that is computation and computation can do
all kinds of things, but we have to tell it
what we want it to do. You can, one of the things
I particularly like is being able to just sort of go out into the computational
universe of possible programs and just say, “What does
a typical program do?” So I have to, one of my
all-time favorites, this is, it’s a very simple program. There’s kind of the rules for
the program and if we say, “Well what does this
particular program do?” We can just say, “Let’s run this program, “starting off from just one
black dot at the beginning.” Let’s see. Oops. We’re just using using this
program and running it. And that’s what it does. And so this is, even though the rules that we started off from
are these very simple rules, the thing we get is something
that looks complicated and in many ways quite random. – [Howard] This is your
new kind of science. – Yes, this is. This is kind of my analog,
my very junior analog of the kind of being Galileo and seeing the moons of
Jupiter, so to speak, and realizing that there was something that existed in the world
that wasn’t what you expected. And this is the thing for me which is there can be a very
simple rule that produces very complicated behavior, and I think this is a lot about how nature makes the things it makes. But one of the things that, and there’s sort of a
basic science of exploring what’s out there in this
computational universe. – So earlier, we talked a bit
before this public session and you used the word constitution. And of course, I immediately thought about the United States Constitution,
which is pretty important, and then I thought about Antonin Scalia who claimed that he was an originalist, and many of us sort of doubt
that he was an originalist, that he kind of decided
what he wanted to do and then thought, but if
one wanted to think about that question, if you were actually, if Scalia and may he rest in peace, were to come to you and say, “I want to figure out what
the Constitution really meant “about things”, how would
you think about that? – Well, let’s talk about it. I mean, let me just, this
thought about kind of computation and the thing we learn from the science is that there’s a lot of powerful stuff that is easily at hand in
the computational universe. The challenge for us humans is what do we choose to do with it? And as a person whose
spent a lot of my life designing a language for
communicating with machines, the thing that I view
that language is achieving is sort of being a bridge between the way we think about things, and what we can get our computers to do. Now one of the questions
that comes up is okay, if we’re going to build for the future and define sort of how
AIs are going to work and how the trolley problem is
going to be solved by the car and things like this, we
ultimately need to tell the AIs what we want them to do. The AIS are capable of
doing all kinds of stuff, all kinds of things that we
can’t see the point of at all, all kinds of things we could run, computation can do, can generate
all kinds of complex things which they just, they are what they are, we may not care about them and so on. Our challenge is to say,
“What do we actually want “the AIs to do?” And one of the things that
then comes up is okay, so how do you explain some
concept like okay, AIs, be nice to humans. How do you explain that concept? You have to have some way
to go from inside the AI, it’s doing something a bit like this, and I could show you what’s happening inside that image identifier, and it’ll just be a bunch
of bits flapping around. And the question is how does one, how does one then explain a
concept like be nice to humans? And this is a, there’s
a question of sort of the computationalization of
an area of human endeavor. It’s actually one that Leibniz
was very interested in. Leibniz’s original goal, he was originally trained as a lawyer, and his original goal was to sort of turn every legal argument into
something where you could compute who was right and who was wrong. That turned out he was 300
years too early for that. We are just coming to the point where we are starting to be able to do that, and it’s something of great
relevance in the modern world of cryptocurrencies and smart
contracts and things like this to be able to express,
to be able to represent the kinds of things that one
might write in a legal document as something like code that
is in some way executable. So one of the challenges
are talking about the what should we tell the AIs to do? How should we tell them
to sort of globally act? I think what we end up having
to do is write something which is more like a kind of Constitution, than it is like our traditional
notion of a program. And that’s kind of the, one of the challenges is how do we express these things which are
important values to us humans in a way that sort of bridges sort of the abstract computation? – But if I understand you correctly, one could then still ask the same question of this computer-generated
Constitution, namely what does it literally say and as opposed to how expansive it is? – Yeah, right. So I mean one of the issues
is given a set of rules, what consequences can they have? – And how broadly are they applied? – Yeah but also, I mean,
one of the consequences of Godel’s Theorem and
what we now know about universal computation is
in a sense in any system that isn’t trivial, there will always be kind
of unintended consequences. I mean, to put in terms of, in terms of this kind of thing–
– Do you get that, guys? If you didn’t understand Godel’s Theorem– – That’s another version of it which is– – He had a nervous
breakdown, but you get it, you did it very well. – It’s, when you look at a
picture like this and you say, “What’s going to happen? “If I ran this for a million
steps, what would happen?” So one answer, one way to know that is just run it for million
steps and see what happens. There’s a question of can
you figure out an advance? Can we, as sort of smarter humans, figure out what’s going to happen, know whether this will ever
die out or whatever else without having to actually run it? There’s a phenomenon I call
computational irreducibility that implies that in
general, you can’t do that, and it’s closely related to
Godel’s Theorem and so on. And it’s kind of, it’s the same thing, when you set up a set of
constraints that are saying, “Well we want the AIs to be nice to humans “and that means among other
things that this should happen “and this should happen
and this should happen”, it is inevitable that when you set up some set of constraints
that there will always be some unintended consequences. It’s a consequence of
computational irreducibility that that will happen. So one of the interesting
questions for example for just sort of thinking it through for sort of an AI Constitution is okay, if the AI Constitution is in place, and the AIs are acting according to it, then we don’t want the AIs to be able to change
the Constitution do we? Because then we’d kind of end up with, then something that we didn’t
intend to happen would happen. But on the other hand, if we say, “Well let’s set this Constitution now”– – Then they’ll really outthink the ones which we then have to adjust to. Which is what you said.
– Right, right, right. And it’s also, and so it’s
kind of interesting to see when you look at the actual constitutions that exist around the world,
one of the question is how do Constitutions get changed? And it’s like, well there’s this sort of super democracy scheme, there’s
the supreme ruler scheme, and then my favorite which seemed to, from my interpretation was kind of some of the Soviet style ones was it’s almost undecidable what will happen. There is a depth of bureaucracy so great that you can’t figure
out whether it’s possible to ever get to the end of the process. But that’s, Godel thought
he had found a bug actually in the US Constitution. He thought he had found a way in which the US could become
a dictatorship, and that was– – Well, we’re testing that now. (crowd laughing) Anyway, I would love to
continue in this vein, but I would like to move
a bit closer to education for younger people. You have children yourself. – Indeed. – And to what extent were your children, did your children learn different
things from different ways from the way that your generation did? I mean, let’s not talk
about you particularly but– – Oh I think, I have four children so I have four data points. (crowd laughing) And the, I think probably, some of my children inherited from me a certain degree of unteachability. (crowd laughing) Which is, I’m one of these people who I like figuring out stuff for myself. I’m not sure, when I was a kid, one of the things that I
sort of unwittingly did was I wasn’t interested in
doing exercises in textbooks because they’d been done before, but I figured that there were problems that were fairly close to those that were more interesting because nobody had done those before. And I sort of thought, “Okay,
let me try and do these.” – But did you make up these questions or were these questions that,
as far as you could tell, hadn’t been answered? – No, I made them up. I mean that’s, it’s kind of the, and so I think some of my
children might have inherited– – One analogy is if you
were playing an instrument, you could simply play just
the stuff that’s been written or you could begin to you
know improvise, et cetera. – Right. I think I have, of my four
children, one of them is, but they’re all still
sort of being educated, but as I think I’m still being educated, but they’re they’re young enough that they’re officially being educated. – All right, so I’m a parent too, and four kids, four grandkids. Let’s forget about teaching them subjects, but how about teaching them about life like being nice and so on? Do you think about that in
a in a way that’s different than most people do? Do you have a sense of that? – I don’t know. The only thing my kids happen
to have been exposed enough to what I do that they
kind of got the idea that I think one of the things that’s sort of sometimes amusing to them, and it’s like I’ll have some crazy idea. I have ideas, my sort of way of living
is I run a company that I’ve been running for 31 years now and it’s 800 people or something, and I view it as being sort of a machine for turning ideas that I have
into real things in the world. And so every day, I have ideas. And some of those ideas, they start off as kind of some crazy idea, and then they turn into
something real in the world. Now it turns out that computation, and sort of this whole sort
of computational paradigm I found to be an incredibly
efficient vehicle for turning ideas into
real things in the world. It’s something not just for
me, but for everybody else. But I think one of the things that perhaps my kids might have noticed is for them, it’s kind of a natural thing
that one can just have an idea and then it will turn
into a thing in the world where there are websites and everything and people talking about it
and all that kind of thing. So I think that’s a, if anything, that’s a sort of a meta– – Well let me make this
somewhat less intellectual. Let’s say there’s a kid,
could be anybody’s kid, who’s very unhappy because
the other kids are shunning him or her, and the kid cries a lot and you’re actually worried
that the kid may get depressed. How do you think about that as a parent or as an analyst? But it’s a much less happy
story than you should be able to develop ideas
and create programs. – Okay so, fortunately,
my particular kids are rather happy kids, I’m happy to say, so I haven’t had to confront
that particular issue but I think that, so I have been interested
in sort of people and how people sort of evolve in the world and one of those kinds of people who’s kept track of what
happens to everybody they went to kindergarten
with pretty much, because I view that as my
longest baseline kind of data on how people develop. And I’ve also been, as a person who’s been trying to build up a sort
of talented team of people, I’ve been really interested in kind of how do you find
talent in the world, and then how do you match up? And I view one of the things
that I’m often interested in is there’s a set of things that
people are good at doing and there’s a set of things that are to be done in the world today, and it’s kind of this interesting puzzle of how do you fit
together the set of things that people are good at doing with the niches that exist today? I mean, you can be unlucky and you can be a perfect match for being a
traditional pirate or something but you lived at the
wrong time in history. Or you can be a perfect match for building a computational knowledge system and you can live in the time of Leibniz. And so, there’s a certain degree of luck, but there’s also a question of given one’s sort of intrinsic
interests and abilities, there’s kind of how do
you solve that puzzle? I think one of the things
that I see as being, I’m curious about this and I’ve, it’s sort of a hobby of
mine to try and understand how one can help kids in
particular to understand what is the thing that is
the great match for them? – So I’m going to pretend to
be that kid, and you just say, “You know dad, I tried so hard to play “with the kids on the playground, “and Johnny played with me but he’s moved, “and when I try to play with them, “they just don’t want to play with me “and they’re starting to tease
me and I’m really unhappy, “I don’t want to go to school anymore.” How would you think about that? – Well I mean, for me, I would be like, “Well what do you actually want to do? “If you have nothing, if you were, “if you have your free day
when you’re not at school, “what are you gonna do?” So if you give me an answer, I can start the build– – I want to play with
friends, I want to play ball, and they don’t want to play ball with me. – Okay, I’m the wrong
guy to ask this question. (crowd laughing) – He confessed, neither
of us follows sports. – Yeah, right.
– But I think what you’re saying is you’ve got to find what motivates the child that
also he has more control over because we don’t know why the
other kids aren’t playing. – Right, I mean like for
example, in my own life, so I’ve been, I’m not a
professor for example, I’m an entrepreneur. And basically I don’t
think there’s any job, being a CEO is something that
I’ve done for a long time, and I’m probably somewhat competent at it, but I don’t think that in a, will the other kids want to play ball? My strategy is I’m just
gonna build my own thing where I can play whatever ball I want– (crowd laughing) Rather than have to
exist in the environment, so I’m probably the wrong person to ask that particular scenario. – Okay. I do want to ask just a
couple more things about your, about the one of the six
people, the educator, Stephen. You have a summer program? – Yes. – Can you talk a bit about that? – Yeah, actually we have
two main summer programs. One is a summer school for
kind of adults and others, and the other is a summer
camp for high school students. So the summer school has been
running for 15 years now. It’s kind of, we end up getting this very interesting collection of
people from around the world, it’s a three-week thing,
and kind of our goal is to get people to do an interesting project about some topic, and kind of
my role and the whole thing is I’m doing sort of the
extreme professoring thing of going through, we had, I
think, 77 people this this year and it’s like for each
one, okay, what topic, what project should they do? And it’s been very satisfying
over the years because a bunch of the projects
that ended up getting sort of picked out for people
in these summer schools, they’ve done it their whole careers. – Can you give one or two examples? – Yeah I mean, there’s a, even from the very first summer
school we had, there was a, a thing we’re studying, I mean, this is a kind of math-y thing, but we were studying kind of, particular kind of sequences
that are rather unusual and the, a particular person
got really interested by– – By sequences you mean–
– Mathematical sequences. – Like prime numbers,
or something like that? – Yeah, yeah, right. But actually as it happened, this was a sequence that
nobody would have expected to make primes, but it did. And so that ended up being a
whole sort of career thing. – Well actually, what’s the career? So I’m interested, I have to say. – An area of mathematics. Actually, I’ll tell you an example. – Actually one of my, this is
not from our summer school, but in terms of the people’s
niches in the world and so on, one of my, one of the things that’s always interesting about sort of doing new things is that you find that there
are new niches for people you didn’t know exists. So for example, I always like
it when there’s a new job, job category that just
didn’t exist before. So like one that’s common for us now as a linguistic curator. So that’s when we have to figure out for Wolfram Alpha or for Siri and so on, when people say something,
what does that mean? So for example, for all
the companies that exists in the world, what are all the names by which these companies are known? And this is kind of an area
and so we used to have a test, I don’t think we probably use
this anymore but it’s like how many ways are there to give change for 35 cents or something? And there are many, many, many, many different ways to say that. And some people are really good at coming up with all those
different ways to say it. They don’t necessarily
know they have the skill, but it’s sort of an
interesting and fun thing when you realize that
there are these things that some people are really good at, and that people who’ve
had a great time with us being linguistic curators,
they really enjoy it, they didn’t know that that
was a skill that existed. I have to say, my all-time
favorite example of that for many years ago, I was, here, I’ll show you an example. If you have a graph, a network, so let’s say we have a network
and it’s got a bunch of nodes and it’s connected and so on, there’s a question of how do you lay out a network like that? Well we’ve now got machines
to do it fairly well, this particular network is random so it doesn’t look like much,
but back many years ago, for my “New Kind of Science” book, I needed to lay out a bunch of networks, so I wanted to find a person who was good at graph detangling, okay? So we ran this ad and
we were trying to find some student or something
who would be good at graph detangling, and most people were
really pretty bad at it. We just give ’em a test and
they were pretty bad at it. There was this one young woman who turned out to be really good at it, and so she worked for us for a short while doing graph detangling,
so it was like okay, what happened to her? Turns out she does kind of exotic innovative knitting patterns, and has a whole company
in Korea based on– – So she was a knit wit? – Something like that, but a detangler of, but so that’s a particular kind of skill that that this particular
person happened to have that was a, but then anyway,
back to our summer school. I think the thing that is that, maybe I’ll talk about the summer camp which is for high school students. I should say the summer school, we just added a track for educators which has been quite successful, and that’s something that for
people to kind of learn about these kinds of tools and
computational thinking– – So when you say educators, now these are K-12 teachers or– – They’ve been a mixture of K-12. – Okay, and do they come
from certain disciplines or are they across the board? – Across the board.
– That’s good, because– – Kind of random collection, but okay, so the summer camp, which we’ve only been
doing for five years now, that’s kind of an interesting case because it’s a two week summer camp
and most of the kids come in knowing rather little about
computational programming. It is a surprising thing, despite all of this emphasis
on coding education and so on, I mean, I think by the way, coding education is sort of the enemy of computational thinking in the same, in the following sense,
I mean what tends to be, coding education tends to be, “Let’s try and write some
kind of sort of detailed code “in some fairly low-level language “that kind of describes
to a computer in detail “what it should do.” It’s not, “Let’s take sort
of some computational idea “and let’s sort of explore
that computational idea””, it’s, “Let’s do the mechanics
of how the code works.” I mean it’s sort of like, “Let’s understand, we’re
not so much interested “in driving the car, we’re more interested “in going inside the engine
and looking at the details “of how to put together
the pistons and so on.” Now the thing which
has happened in sort of coding education, it’s
gone through multiple waves with multiple different
technologies and so on. The thing that I’m most
concerned about actually is I hope it isn’t too successful because otherwise what it runs
the risk of happening is that kids will conclude, okay,
so when you look at math, one of the really bad
things that kids conclude about their experience of
learning math in school is math is kind of boring
and is not for them. I mean, that’s sort of a meta thing they, some fraction don’t discover that, but some rather large
fraction discover that. And I think with kind of
the sort of low-level coding and so on, it is as mechanical
as a lot of the kind of math that kids find boring. And it sort of runs the risk if you, computational thinking,
this is the kind of thing I’ve been sort of
illustrating here is that it’s a really quite
different kind of thing. If we were to go down to
the sort of lowest levels of what happens inside a
computer and we were to say, “Let’s go figure out what’s going on “with binarizing pictures
and so on”, that’s a whole, that’s a week of writing code
in some low-level language to be able to do that, and
that’s a very different activity than thinking about what does it mean to turn a picture from being colored to black and white, and so on. So I think that, but anyway, what we find, so what we’ve done, I
should have a good example, I wonder where it is of, so anyway, we have these students, I think we had like 45 this
year in our summer camp, and sort of the goal is
to go from zero knowledge of computation and computational thinking to the point where they have
a decent degree of fluency. And what I mean by fluency is given a question that they might ask, like one of the ones we
were just asking here, can they just sit down and be able to answer that question for themselves? Can they get a reasonable
start at being fluent enough with computational
thinking and with the tools to be able to go from
thought that they have to actual execution and implementation? – Let me try to paraphrase
what you’ve done, and then I’d like to open
it up for some questions from the floor, paraphrase
what you’ve just said. I think it’s easier to teach
coding from the point of view of the teacher because there’s
a right and wrong answer. Once you get to computational thinking, it’s a question of what
satisfices for the answer? And that’s more challenging,
and it means you have to have, I mean to use ed jargon, you have to have a more
progressive approach to education rather than the testing,
right and wrong kind of– – I think one of the things
I’ve noticed is that, you see, one of the very nice
things is you could write a computational essay here, we could say there’s a section heading, okay, making pictures black and white. And then we could say, what do we do? We could write some text here. I think this is a very
interesting medium for sort of what kids can
actually do is they are, you might have some prompt that says figure out how a colorblind person might perceive these pictures, then you can go and do
various things, and you write. It’s a mixture of kind of a narrative text together with a lot of kind of, together with expressing your thoughts in a computational language
and then sort of having this sort of power of the
computer kind of filling in the facts, so to speak. Now, a computational essay, how do you grade a computational essay? It’s kind of like the way you
might grade an essay essay. I think it’s something where, and many of the criteria are like is it clear in what it’s saying? It’s actually probably easier to structure a computational essay than to structure, to sort of learn structure
in a computational essay than an ordinary essay, but
yes, I agree with you that the, I mean, you can answer the question. I mean, what’s interesting
about computational thinking is how open-ended it can be. And one of the things
that I find, for example, in our summer camp, summer school, I usually start them off
by doing some kind of live experiment where I will say, “Okay, in the next hour,
we’re gonna discover “something interesting that’s
never been discovered before.” Okay, and so far it’s always
worked, discovered something. And the very fact that that’s possible is really an important– – It’s very exciting.
– Right. – Yeah, and I guess there’s no reason why you couldn’t have a
program which also grades the computational essay. And then the question is how draconian is it? – Right, well for example,
in this I wrote a book about Wolfram language
that has, let’s see, I probably have, we can probably, okay, so the book would have, this is a look at the section
on colors for example. It has exercises, and actually there’s a MOOC
version of this book as well but let’s see how this works. Okay, so let’s see, answer
and check your solution. Okay, so we can type in code
here and we have actually, it’s rather high-tech. We have an auto grading
system that can recognize whether the program is
both doing the right thing and whether the program
is kind of just sort of assuming the answer and so on, and also whether the
program is copy pasted from some place on the web,
we have ways to tell that. And what’s interesting
about the programs is that they are sort of a, unlike math, where the answer might be 17 or something, programs are a more creative kind of thing to produce because in fact, the right answers won’t
always be the same. There are a wide range of
programs which will all be in somewhat different styles, but will all achieve the
objective which was defined. And so I think that
that’s some, and as I say, it happens to be possible
to auto grade programs, it’s somewhat more
difficult than auto grading math where the answer might be, it’s multiple choice where
the answer is 17 or something. But yeah, so I think, but in general, I view
what’s great about sort of writing like Wolfram
language code so to speak, it’s an expressive language like English is an expressive language. And it’s one where for example
kids who get quite fluent, I mean for example for myself,
I’m fluent enough in it, and one of my kids is more
fluent even than I am, which is always interesting, but you can start typing code long before I could tell you what
the code is going to say. Actually the most extreme
thing that I’ve seen in some 11 year olds I guess they were, who’ve been studying Wolfram
language, they were like, I’m like it’s nice to meet them, and they start saying programming– – [Howard] You should tell
them what that sounds like. – [Stephen] I don’t think I can do it. I can’t do it– – [Howard] But you were doing that before. – [Stephen] Right, I mean,
I could take one of these– – [Howard] It’s like Pig Latin but– – I could say something like okay, yeah, I can’t do it. It’s just map dominant
colors over whatever. Actually it’s something
that we’ve realized for some education purposes
that it’s actually important to be able to say code,
because when you tell somebody, “Oh, you didn’t do that quite
right, it should be this”, you have to be able to say it. And what we’re doing
effectively in Wolfram language, the reason that we can make
this language that it’s actually like human languages, it’s
easier to read than to write. And you can take some piece
of code that’s been written and it’s easy, I don’t know,
let’s just do as one example, before we, just to say, okay, let’s get a list
of words in English. Let’s do something like
let’s take the first letter from each of those words, and let’s make a word. So that’s like how many times, and let’s make a word cloud of that. So this is gonna show us
effectively a word cloud of what the most common letters, like if we looked at a dictionary, we’d find the S section of the dictionary was thicker than the K section
or something like that, and that shows us. But if we look at this,
we can sort of understand it’s a word cloud of taking
something from a string and it’s a word list, and
we’re kind of leveraging the fact that there is, that we know English to
be able to understand what’s going on computationally. And this gets more exotic
when you start to have, where you can shorten this
code and have various kinds of other constructs in it
that are a little bit more sophisticated than this, and that’s what these kids
could do that I can’t readily do verbally, so to speak. – Great. So we have about a half an hour. I have a couple final
questions to ask Stephen, but the floor is open. Don’t be shy, and don’t be verbose. (crowd laughing) Okay, we have several people getting up. Why don’t you start and then we’ll go table tennis, yep please. – Hi, my name is Ben Folger,
I’m a Harvard alum and there’s a period in
time where rote thinking was highly valued, the ability
to just memorize things. And now we’ve gone to a
period of where I think a critical analysis is
more valued than education. And I’m just wondering for the future, as we perhaps emphasize more
on computational thinking, what does, if retaining information, memorization is not as valued, and critical analysis itself has evolved into computational thinking, what does it mean to be
intelligent in the new era? – So in terms of the
should you know stuff, yes, it’s really worthwhile to know stuff. I mean I’m lucky enough
that I have a good memory, and so I just know a bunch of
stuff about a bunch of areas and that’s really
useful, and the idea that one should sort of remove
knowing stuff from education I think is crazy. And whether it’s, whether
you have to know stuff by rote memorizing it or whether you have a good enough memory that you just sort of absorb
it, that’s a different issue. In terms of what does it mean to, I don’t know quite what,
how to formulate it. And I think in the question of, sort of there are patterns
of thinking that it’s worth, that there are just things to know about how to think about
different kinds of things, there are patterns of thinking
that it’s worth learning. I’m not sure, I don’t know how to answer, that’s a more global question than I think I may know
how to answer immediately. Do you have any? Can you christen that? – I think that when you talk about it’s good to know a lot of stuff and then you can invoke your memory, our problem in the 21st century is if you don’t have a good memory, you have to know how
quickly how to access it from some kind of a site–
– Right but– – But it’s probably the case that it’s, as I think this gentleman is implying, living by your wits which means
coming up with new questions and figuring out things that
can’t easily be be automated is relatively more important in an age where almost
anything that can be mechanized or simply computed is, how this translates into
what goes on in the classroom from a young age or indeed, what goes on in child-rearing
from a young age, there probably are huge
differences across societies, across demographies, and across
teaching philosophies and… – Look, I have prejudices
because of the way that for example I learned. I learn best by actually
figuring stuff out for myself. Not true of everybody. And so for me, I would sort
of project that onto the world as saying people should just figure out what they want to know
about and then learn about how to do the mechanics
of figuring that out. I doubt that that would work
all people, so I think I’ve, in terms of, I think people
need a certain set of skills. One of those skills is how
to do computational thinking. Computational thinking happens to be a really powerful skill that
those of us who build tools are trying to make that skill ever more, ever more of a powerful skill. You have to have that ability as yourself to sort of formulate to
structure your thinking to the point where you can explain it to a sufficiently smart computer, then it’s kind of our
job to make that computer ever smarter and smarter,
and to leverage that skill, to make that skill more and
more useful in the world. – Thank you, now see, this
is a good computing thinking because the woman saw that
the line was longer here, so she went over there. (crowd laughing) – Hi Stephen, my name’s Noah Heller. I teach math teachers here at the Graduate School of Education. And I should first thank
you, one for being here, also for helping me get
through multivariable calculus however many years ago. The question I have is in math education, a critique, a very real
critique of math education is that we’re teaching students
how to answer questions that they haven’t yet asked. And watching you engineer your language, it was remarkable to see you not just fluently use a language, but also ask meaningful questions. And I wonder if in your
work with students, or in your work developing this language, you’ve thought about how
to promote question asking so that people are simultaneously
learning a language that I’m curious in
terms of technical skill, your critique of the way that
programming is being taught, I wonder if, if that’s avoidable, in the
same way that we teach math in order to ask questions someday. So can you learn, can you learn Wolfram simultaneously with asking meaningful questions? – Right, so I think the first
thing about asking questions is you’ve got to see other people, you’ve got to see it be
something where people are figuring out questions to ask. So my, I don’t really know
because I haven’t spent time in enough classrooms, but my impression is that a lot of classroom teaching ends up being teacher
thinks they know everything, so to speak, and is feeding
that to students, so to speak. In the world of sort of
computational thinking and particularly kind of live
computational exploration, the situation is a bit different because as you start doing
things you are routinely discovering stuff that teacher won’t know, maybe no human knows, it’s
never been seen before. And so even by illustrating
the doing of that for students, I think that’s a very kind of liberating and empowering thing to
see that is that you can just go and you can explore
in different directions. A thing I’ve done, so I’ve
done a bunch of things, I live in Concord, Massachusetts, and I have a little effort, teaching some middle schoolers there because I like to do actual fieldwork on the stuff I’m talking about to, and it’s kind of interesting
because this is kind of child-directed exploration, right? And they’re like, “What
about this, what about that?” And they get the idea very quickly that it’s possible to ask
questions because normally, you ask a question and okay, maybe you just don’t know the answer, nobody knows the answer. Well, there’s nothing very
interesting to explore. But once you see that it’s possible to take the question they ask, do some computational thinking
to formulate it in a way that is feedable to a computer, then they’re kind of empowered to say, “Well now I wonder about this,
now I wonder about that”, and the problem, which I don’t understand in
terms of classroom management is what you end up with very quickly is a stack of 10 questions. And that’s great because
then you’re off and running and questions are being asked. But yeah, I think the first step is just let students see this kind
of open exploration process and it’s for a teacher, so there are many people other than me who can do live programming
with Wolfram language. It’s, for example, one of my
kids is better at it than I am so it’s something I think that the, but I think this process of
let’s just go and explore, and we’ve got this tool, and what’s interesting
about the tool is that you can do enough quickly
enough that people stay interested and that the
questions people ask are like, “Okay, it’s gonna take five or 10 minutes “to answer that question.” It’s not like we have to go
to a library and we have to go sifting through books
or websites or whatever to be able to answer that question. So that’s my, I mean, I think it’s a very, I completely agree with you that the formulating the question thing is a wonderful skill to teach. I mean, when we look
at a lot of fields in, for example, in academia,
there are people who are mechanically very good at doing something, but the people who end up being probably the most successful
academics tend to be the ones who are good at formulating
what should be done, aren’t addressing what question, that’s a great thing to
teach and I think we, we now have a nice
medium for teaching that. – Thanks.
– Thanks, good question, yeah. Please.
– Hi, my name is Kevin Evans. You mentioned several
times the necessity for establishing and stating goals before starting a computational procedure. In education, the goal
that we’re often after is preparing students for
job readiness rather than looking at how jobs actually
fit in society and in life and investigating what
else could fill that need. So I’m curious for you, how
do you go about, for one, structuring, figuring out good goals? And then also how do you
know when you’ve reached deep enough so that you
can begin on the process? – Okay, that’s a, I mean, I think, the trick is to be fluent
enough with the tools that the questions you ask, you’re gonna be able to get
somewhere really quickly. And you may then discover
that the place you thought you were going to go isn’t
the place you should be going because there’s something
else that’s actually a better goal to have. I mean in terms of how do you fit this in to what students can do,
I mean, so for example, in today’s world, one of
the things that I’ve been sort of a personal thing
is get it to the point where random kids in
random places in the world can learn enough about
Wolfram language and so on that they can be productive
employees or whatever else at some young age. And for example, if you take
data science as an area, which is sort of kind of just like, you’ve got data, what does it mean? Pretty much any organization
is in the position where they’ve got data and they want
to know what it means, okay? So it will be the case
that there will be kids who know Wolfram language and so on who can go into any organization and say, “Okay, give me your data, “I’ll tell you something
about what it means.” And that’s an example of, that’s an immediately
employable kind of thing. Now if you ask how does, if you’re saying how do
we map what we’re teaching and to what employers will want, one of my points is this
whole sort of direction, developments of computational X for all X, that’s a critical thing that employers will really care about. I mean it’s not, I find it kind of ironic that there were people for
a long time in my company, we didn’t hire people who had gone through computer science programs, because the computer science
programs were teaching, this is like 25 years ago, they were teaching very theoretical things that were irrelevant to actual, the actual practical
development of software. Then the pendulum really
swung completely the other way and a lot of what’s taught in a lot of kinds of
computer science programs this is extremely practical, how to do agile programming
with Java, or something. And this again is actually
it’s a very short-term thing. It’s not, it’s a trade
basically, it’s not really a, it’s not something, it’s a
trade of this particular moment in history, so to speak. And what’s much more
useful to at least in a, my own little example of as
an employer, so to speak, is people where you can give
them some project, problem, and they can figure
out using, in our case, computational thinking
to how to attack that and how to make progress on it. – Thank you. – Okay. Hi, Stephen, I’m Helen,
I’m a master student here at School of Education. I’m curious among your various
roles as an entrepreneur leading 100 people as an
educator offering camps to both adults and kids
and as a father of four, which role is the most challenging and how computational thinking
help you navigate the role? – Oh, that’s an interesting question. I don’t think any of them have been, I haven’t viewed any of
them as super challenging. I don’t know, you can ask my kids, you could ask my kids what they, I always had the theory
that I’ve been doing management of adults for years, and so kids will be straightforward. Actually, kids turned out to
be a little different but– (crowd laughing) I think that one of the things that I always find interesting is can one live one’s own
paradigm, so to speak. That is, if you invent a paradigm like sort of computational
thinking kinds of things, to what extent do you lead your life with using that paradigm? And so I do find that when it
comes to sort of formulating what should I do and how
should I think about things and how should I set the
company up and so on, I do think about that in terms of if I were designing a
Wolfram language function that did that, how would it work? And that turns out to be
that’s what this department at the company should do. I mean that’s a, it does turn out to be, it’s a way of structuring one’s thinking that I find very useful. Now there are other
things, like for example, I’m a data enthusiast, so I’ve collected, I collect all kinds of data on myself and I’ve been doing that for
30 years, and I somewhat, to my horror discovered a few years ago that I’m the human who’s collected more data about themselves
than anybody else. And that’s kind of another living the paradigm kind of thing. I don’t, I often, I don’t look at this data that much, but occasionally I’ll go and
wonder something about myself and I can just go back and figure out, maybe it’s a simple thing like I’ve just switched
keyboards on my computer. Did I type faster on my old
keyboard or on my new keyboard? I can answer that in five minutes. And that’s because I have all the data, I have every keystroke I’ve typed for the last 20 years or something and it’s actually, so the extent, I mean, I find computational thinking
is a great way to structure thinking about things. And the thing I found in my own efforts, I’ve done a bunch of
big projects in my life and they all seem to
be somewhat different, some were about basic science, some were about technology and so on. I think the thing that I finally
realized is that actually, I only have one skill
and I think people are, the one skill that I’m reasonably good at is taking these big complicated areas, kind of breaking them down
into sort of simple primitives and then kind of doing the engineering to build back up again
to something useful. So it’s kind of the, it’s
sort of what one might think natural science might be about, although it doesn’t to be
that way in most practical, people doing it. It’s like take the world and figure out what are the underlying
components and so on? – But in a sense it’s actually
what scholarship should be. Thank you, we have five more people. Let’s move a bit more briskly. – Yes, hi, thank you. My name is Rosalie Belanger-Rioux. I’m a preceptor in the
mathematics department here, and I’m wondering if you
could address this problem that I see that we have in
mathematics and maybe science and life in general of the genius myth, this idea that you’re born to be a genius, you’re born to be a CEO, you’re born to be good at math. In fact, you were introduced
as a certified genius by Mr. Gardner. And so I’m wondering if
you have any thoughts on how we can break that myth and maybe computational thinking can help? – Yeah, I mean, look, at one point of view as I was mentioning before, I mean, my own perhaps optimistic
view of the human condition, so to speak is that people
have various skills and the, and there are many niches in the world, and the question is is
there a niche into which your skill fits well? And sometimes that’s a challenging process to find that niche. I’m not sure that education
necessarily does a great job of showing people what the
portfolio of possible niches is. I think that it tends to be
quite narrow in the sense that what you teach, it’s like pick even an old-fashioned encyclopedia and say, “What fraction of the encyclopedia “is actually talked about
in standard education?” And even more so, what
you might find on the web, or whatever else. I think that that, so I think
this question of whether, I think that the two, my own view would be that
there are two versions of this genius myth thing. There’s both a version that
says are you born with it? I think there’s a, people are born with all kinds of different skills. Can they figure out how to
take what skills they have and turn them into something that’s going to be successful for them? I think though the other theory is that everybody can do everything,
I don’t think it’s true. I mean, that is, I don’t
think you can take, what I’ve noticed is I’ve
noticed, for example, people learning
computational thinking, okay? Very broad range of people can learn it, but there are people who
really pick it up quickly. And there are people who you might think would pick it up quickly, but they don’t. There are people who might
be very educated in math, but they really, they think
about, oh I don’t know, they’re great at doing math
competitions for example, but when you say let’s study things in a more in a broader way which involves more judgment and so on, they
just, they just don’t get it. So I think it kind of goes
both ways that there’s a, as I see it, it’s a
matching problem of what, can you figure out what
you’re really good at doing, what you really like doing? And can you match that with something that exists as a niche in the world today? And if it doesn’t exist, you
can always try building it. I mean this is my kind of theory of it’s a lot more effort to build a niche than to fit into an
existing niche, but it’s, and it’s always a trade-off
for people when you, if you’re like an academic
or something like that, you can say, “I’ll work
on this super popular area “where there’s tons of
people working on it “and then anything I
do will be immediately, “people will know why it’s important, “but there’ll be a zillion competitors “to everything I’m doing, or I
can pick this total backwater “where nobody’s cared
about it for 50 years”, and then you know you’re the
unique person doing that, but you then have to tell
the world why it’s important. I mean for myself, I’m
much more interested in, I like building what I
call alien artifacts, which means things that you might, things that you might not have thought would exist in the world,
but one can make them exist, so to speak, and which are
typically not things that were kind of in the flow of
what was already happening. – Okay, thanks for the
question, next please. – Hi there, oh, I’m sorry, hi, I’m a master’s
student at the Ed School. Thank you for your thoughts so far. It seems very resource-intensive
educating and for teaching and I’m just wondering
whether you had any thoughts on measures or proposals
that would make sure that it was equitable and that it was accessible for everyone and to ensure that there were equal
opportunities there for engaging this computational
thinking that could potentially lead to sort of considerable discrepancies arising
in terms of inequality? – Yeah, right, I mean,
look, you go to the website, you go into this free thing
that anybody can play with, if they have a smartphone,
they can start playing with it. I’ve actually been really
interested in trying to figure out how do you spread this
as broadly as possible? So for example, our summer camp,
the first few years we got, the kids who came were from
the fanciest schools that, the ones always heard of, and I was sort of kind
of frustrated by that. And so we started off running these ads on the Wolfram Alpha sidebar and we know a decent fraction of high
school kids for example in the US use Wolfram Alpha, so that was a broad range of kids we got. And we were quite
successful in the sense that in more recent years, it’s been a very good
geographic distribution of kids, not just from the the fancy
schools of the big cities. The thing that we haven’t
succeeded at so far is, and I don’t really know why is we were offering scholarships and things, and almost nobody took us
up on those scholarships. So although these kids were
coming from less fancy schools, they were not, they were
socioeconomically still sort of advanced kids, and I think for me, this is a part that I’m very
curious about but I don’t have a good solution for is okay, this is something that’s
going to be important in the best jobs of the 21st century. How do you get some
kid who’s out somewhere away from sort of influences
that say this is important, so to speak, to still kind of have access? I think we’re being quite
successful at having the sort of technological
access be possible. I think the question of how we get the kids to be motivated and to connect, that’s something I don’t, I’d be very interested in solving that I don’t know how to solve. – Well, you have an
audience here, they may– – Yes, right.
– Thank you, yes. Next please. – Hi, my name is Alicia. I’m a sophomore at the college
studying computer science. I’m actually enjoying a
theory of computation class that I’m taking right now. And one of the points of view
that came up in the class was that every natural process, action, even thought could be reduced
to a computable function. And you introduced computational thinking as a way to model the world,
but no model is perfect. And so I was wondering what you, what your thoughts are about what’s lost through computational
thinking or the model? – So I mean, this idea that
the world can be modeled in computational terms, I
suppose I’ve been personally quite involved in people
coming to believe that, so to speak, so I’m sort of
guilty of being an originator of that kind of concept. Now your statement about
models are never perfect, you’re absolutely right. One of the things about models, models are always controversial, in the sense that somebody will say, “This model captures”,
like a classic example I was involved in years ago
was snowflake growth, okay? So I had a model that
explained the basic, elaborate, sort of tree-like structure
of snowflakes, okay? There’s another model that did really well explaining the growth rate
of the arms of a snowflake. And so you might say,
so if you’re interested in the growth rate of
the arms of a snowflake, you pick that second model, because my model didn’t really talk about the growth rate of the arms, but that second model also said that snowflakes should be spherical, which is, it’s fine if you’re interested in the growth rate of the arms, it doesn’t matter that the thing
says it should be spherical but most of the time, modeling is about deciding
what you care about and idealizing everything else away. There is one unique example
where that won’t be the case. If we find a fundamental
theory for physics, there will be a precise
theory that is just this is our universe and
it’s exactly our universe, but that’s the one example
of sort of the perfect model. Now if you ask the question do brains work according to computational, in computational ways, the
answer is I absolutely think so. I think that we are getting to see, in modern neural network stuff, we’re getting to see a
lot of kinds of things which are remarkably
brain-like in their activity. It’s interesting to take
apart a neural net and say what’s happening inside? And to realize how alien that
intelligence is, so to speak. So for example one thing– – Could you explain, neural nets here is not neurons, necessarily, it’s just– – No, no, it’s–
– A program that works a certain way. – Right, neural nets
are a fascinating story in the history of science– – It’s a mathematical–
– Right, it’s a purely, it’s compositions of functions, basically, that happened to get invented in the 1940s as an idealized model for brains. And for many, many years,
they were kind of things that people sort of talked
about but didn’t think were very interesting, and
then suddenly five years ago, because computer power became greater, and also because somebody was lucky to do the right experiment
at the right time, it became possible to see how to take, for example, that image
identifier that I showed you, that was created by training
one of these neural nets on 30 million images. It’s about the same number of
images as a human might see in the first few years of life, and it was trained to
associate those images with about 10,000 words that
describe things in the world. Now what’s interesting, if
you take that thing apart and you say what’s it doing inside? Well inside, it’s making
all kinds of distinctions. It’s deciding, it’s got
to decide is this picture a picture of an elephant or a teacup? And somewhere in the
middle it’s gonna say, well this image, it’s gonna
make a sort of distinction, like a 20 questions type distinction, it’s gonna say, this image
is kind of blobby in this way and this one is not, so that one is gonna go
down the elephant track and that one is gonna go
down the teacup track. What’s interesting about those
distinctions that it’s making is those are distinctions that it’s learnt that we humans don’t
necessarily understand. Society, our culture could have developed in such a way that we would have a word for that distinction,
but we don’t necessarily. Some of those distinctions, we
do happen to have words for, but in a sense what’s
happened is the neural net has learnt its own kind of culture and invented its own
distinctions and its own words. We humans deal with maybe 50,000 words. In what’s emerging in
these kinds of systems, you could readily have hundreds
of thousands of millions of distinctions that are being made, but may turn out to be
very valuable distinctions that we just don’t have them make. Like in the progress of
science, occasionally, people will discover
some way of organizing the way of thinking about the world. It’s kind of a very circular
thing because people realize, like fractals were a good example. Before fractals were talked about, there were images that people
had made that were fractals, but when you read the art history books, the art historians just
ignored those images because they had no way to describe them. So now we know these nested patterns, they’re fractals, we have
a way to talk about them. And so now, but now,
that is really reinforced because we started using them in the world that we build for ourselves, so it’s kind of a very circular thing. And then we have more
words that describe things that are in the world, but
these are things that are, there are things in the world that were just put there by nature, and there are things in the
world that were put there because we understood that
those were interesting things, and so we started building our world to have those things in it. And so it’s an interesting
sort of circular thing that I think also relates
to these questions about what do you end up teaching about, what do you end up caring about? – Thanks for your question. We don’t turn to elephants
or teacups at seven, but I know people have schedules, so why don’t each of you
ask you a question to him, and Stephen will answer them as he wishes? First, young man? – I was curious based on your experience with your summer camp in school, and just your general experiences
with higher education, are there some universally
effective exercises based either in classroom teaching
or just things you can do on your own that develop
computational thinking? – Okay, I can answer
that one because it’s a, you just have to do it. You just have to take
questions you’re interested in and try and make them be computational. I think that’s the, I
don’t know of any kind of exercise you can do that, I think, I think it’s one of these
things you learn it by doing it, so to speak, and the good news is, it’s very easy to start doing it. – Thanks.
– Okay, thank you. – Well, I’m glad that people mentioned about the image
identification that in that, it looks like you’ve done a superb job of doing what used to be called, or still is called fuzzy logic, and giving the probability of whether it’s a canape or a human face. But I wanted to apply that then also to, when you generated sort of that pyramid, that it looked like you had
five black and white boxes which and it looked like that the
computer tried to generate the law which generated
what that sequence was, and it would seem that the
same sort of probabilistic analysis need be done because that series can be generated by even
odd for black white, and can be generated by
any modular arithmetic and base of your number system. So I was wondering why it
had just a unique pyramid with 100% probability that that sequence of black white boxes–
– Yeah, right. So I mean, this is just, it’s just an example of
a really simple program. So here’s another really simple program, I just changed the rules. These are just precise,
deterministic rules. I could run that program, and then I get a different result. Or I could say so each, this number is just a code
that allows us to specify a different program. – [Crowd Member] Right, but
presumably, your, the code, it’s finding code that explains those black and white boxes based on a– – No, no, this is a
very, very simple thing. What’s going on here is
absolutely what you see is what you have, it’s
very, very, very simple. So if I were to just do this, let’s say for 20 steps and
show kind of a mesh there, what would happen is every
place in this picture, like let’s pick that place there, okay, what’s above it is two whites and a black. So we go back in this
rule up here and we say two whites and a black makes a black. So it’s just saying here’s the
rule, this is what it does. So it’s a very minimal example. So in fact, if you were doing
sort of pre-computer science, if you wanted to do this
with with kindergarteners, for example, you can do
pre-computer science. It’s kind of a fun exercise. You can say, “Okay, you’ve just got “a piece of graph paper,
and you’ve got these rules, “start filling in the graph
paper according to these rules.” And what’s kind of neat is they say, “Well I don’t know,
there’s nothing interesting “is gonna happen, it’s
just way too simple rules.” You keep going for a while and suddenly, there’ll be some pattern that emerges. And by the way, that’s a kind of, what you’re seeing there is
a very fundamental feature of kind of the process of computation. It’s an example that
doesn’t involve arithmetic, it doesn’t involve
numbers, you don’t really, this can be done by, well, I’ve seen this in about five year olds, I don’t know what the, and it’s a it’s a great
little example of how, and actually, if you really
want to have fun with this, it turns out, well my favorite
example is mollusk shells turn out to have the patterns
that you make this way, you find mollusks actually
put on their shells. And that’s kind of a
neat thing that you can actually have something where
you can sort of yourself do the computation, so to speak, and then you can realize that gosh, these mollusks do that
same kind of thing too. – Yes–
– I’m gonna thank you for your question ’cause we’re past time. I did want to ask one question of my own curiosity. Clearly, you find your
own mind interesting, and a lot of questions that you raised are ones you’ve raised
yourself, but I’m interested, what do you read, whom do you
talk to, where do you travel? What are the things that you do that you find stimulate your thinking and maybe make you think about things you haven’t thought about before? – Well, I lead a weird life
in a sense because I’m, one, so the main thing I spend
my time doing I suppose is I run a company and what that, and I’m kind of a micromanager
of the kinds of things that we make, and that means
that what I end up doing, strangely, I’m a remote
CEO, so I’m usually, it’s just computer screen and phones, but what I spend my whole
time doing is sort of the thinking and public process of we’re figuring something out, we have an hour to figure this out, this is the problem we’re
trying to figure out, we’re trying to design some
feature of our language, there might be 10 people
involved in this meeting, everybody has some thing
that they’re bringing to it, and I’m just trying to
figure out what will happen. And the most extreme and
outrageous case of that is something where we’ll have something we’re trying to figure
out and somebody will say, “Look I’ve read the literature on this, “people have been trying
to do this for 25 years”, and we’ll say, “Well, we have
an hour and a half here.” (crowd laughing) Well, and the remarkable thing
is that just the very concept that you might be able to do
it is already a very important, gives you a huge step up in number because people often,
and when fields develop and get sort of deeply built out, people forget about the
fact that the foundations may still be, you may still be able to attack
the foundation, so to speak. But anyway, in terms of what, so I suppose the most
stimulating thing for me is that I’ve built up a
group of 800 people or so who I work with a lot
and who are continually, I mean I’m actively
thinking through things all the time every day, and that’s kind of the primary thing. I’m pretty bad at reading, I must admit. I’m a lousy reader of books– – But you’re doing history, and you must be reading it then. – Yes.
– You’re not making it up. – Yes, that’s true. So I find I have sort of a
hobby of studying historical, I mean a typical, I typically write these blog posts and I just wrote one actually about, which I’ve been meaning
to write for years. I usually have to have these excuses. It has to be an anniversary, somebody has to have
died, something like that. This is one about some, a chap, a very interesting kind
of Victorian scientist. Yeah I mean, what happens is, I don’t know how people
did history in the past because for me it’s like, okay, I wanted to find out the
book that this guy’s father had written, okay, I
can immediately find it from the internet archive and I can go and I can make all kinds of connections, and I might be doing, I don’t remember whether
I did, someplace here, yeah, this guy ran a museum
that had, I actually went to, I went eventually to Scotland
to go see that museum. He was, there might be
some computational stuff, let’s see that I have some
computational stuff here. This is mostly just scanned
images of things, but let’s see. Somewhere here, I think I had something, oh yeah, that’s a bit computational. That was a crocodile
skull he collected that we got a 3D scan of, but
someplace here, okay, so that’s an example for
example of the literature, citations to this person’s
work as a function of time over the last 100 years and so on. But in terms of for this, I find these history exercises, what I always find interesting is that for any one of these
ideas that people have, what you know in hindsight is, oh, this person figured out this thing, but it turns out there’s always the story. And I find it really
interesting to try and sort of piece together how did the person actually come up with that idea? And there’s usually a
really long backstory, and it’s often quite a puzzle to see where did they really get these influences that led to that idea? And in the end, there really is a very sort of definite narrative,
and I can see for myself, I’ve gone back and wondered
about that for myself because they’re things where
I figured something out, okay, how did I come to figure that out? So for example, good example
is Wolfram Alpha, actually. How did I come to figure out that it might be possible
to build Wolfram Alpha? So I wondered how did I,
because I just as a matter, and the answer was I’ve been
thinking about kind of AI stuff since I was a kid and I’ve been thinking can we build a general
computational knowledge engine? And my conclusion was no, we’d have to figure out how
to build a brain-like thing to be able to do that. Well then, I did a bunch of basic science and one of the conclusions
of that basic science is there isn’t really
a bright line between brain-like intelligent things
and sort of mere computation. And so that, what was
basically a piece of philosophy ended up being okay, we could actually build something like this. In terms of, I’ve been fortunate in that I know a lot of people in a lot of
different fields who are, kind of have invented lots of
kinds of things and I enjoy chatting with them. I find that in the technological world, it’s interesting because sort
of new companies are coming up new ideas are being created, that kind of provides an environment where you can kind of identify some of the new stuff that’s
happening I also, okay, for many years, I didn’t travel at al, and then one of my kids, my
older daughter actually about, what was it, six years
ago or something now said “You get all these
invitations all over the world “and you turn down 100% of them.” She said, “Let me just look
at these invitations and pick “the ones that we’re gonna go to.” And so–
– Good for you. I think we actually
have to go pretty soon, you and I have another appointment so thank you so much, this
is a memorable evening, and I hope you’ll all join
me in thanking Stephen. (crowd applauding)

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