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Cell["The Future of Computation", "Title"],
Cell["Stephen Wolfram", "Author"],
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"It is a pleasure to be with you all today. My main excuse for not being \
there in person is that we really have to finish the next version of ",
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". I think it is probably fair to say that almost nobody thinks I should be \
doing anything other than working very hard on the upcoming version of ",
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", which I can assure you is going to be something extremely exciting, that \
we have been working on for a great many years. "
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"But I thought today that I would not talk mainly about near-term ",
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" technology. The original title for this talk was ",
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" and the Future of Computation, but then I saw it had been changed to just \
The Future of Computation. The modification to the title got me thinking \
about what I really should be talking about. So I am going to talk about the \
modified title. I decided that would give me more license to talk about a \
broader range of things, and I thought that we might have some fun with that. "
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"What will be the future of computation? To really home in on that question \
some of what we have to think about is what computation is, what computation \
has been, what kinds of things could computation be in the future, what kinds \
of things can we perhaps uniquely learn from our experience with ",
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" about the nature of computation and about its future directions. "
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"But I guess it was during the 1800s the idea of purely abstract kinds of \
mathematical constructs and operators really took root. There were things \
like the work of Galois on groups and the development of Boolean algebra and \
abstract logic by Boole. Then came the development of abstract algebra in the \
late 1800s and so on. Then there was the notion of people like Peano trying \
to formalize, trying to make a human-like language that could be used to find \
a uniform formalization of mathematics. And that, in the 1910s, led to things \
like the Whitehead and Russell venture of ",
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", one of the uses of the \[OpenCurlyDoubleQuote]mathematica\
\[CloseCurlyDoubleQuote] word in the past, where the notion was could one \
take all of the ideas of mathematics and formalize them in a way that was \
somehow based on logic? As you may know, Whitehead and Russell produced this \
giant three-volume work that purported to describe how mathematics worked. \
Unfortunately, it went in rather small steps and it was rather hard to \
understand. It determined that 2 + 2 was equal to 4 somewhere about \
two-thirds of the way through the first book. It was an early attempt to \
formalize a process, in this case a process of mathematical proof and \
presentation."
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"When you look at the pages of ",
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" they almost seem like a uniquely bad notation for actually presenting the \
ideas of mathematics. Nevertheless, as a proof of principle it was something \
very important to take this large volume of potential mathematical knowledge \
and try and formalize it in a uniform way. "
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"Then there were other kinds of ideas that came up in the 1920s about the \
formalization of things. For example, the idea of recursive functions came \
up. In fact the very idea of functions had been a fairly recent construct, \
something that had really cropped up in the 1880s or so. The idea of just \
some abstract thing, ",
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That idea of abstracting a notion of a function was a comparatively late one \
in the history of mathematics.
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"As time went forward, there were a few other strands, a few other kinds of \
primitive operations that were considered for computation. Another one that \
came very early in the history, although was ignored until many years later, \
was an idea called combinators, which are the ultimate functional programming \
construct, in a sense. These typically are set up as two combinators, ",
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" combinators. That was actually an idea that came up in 1921. Although it \
was not really recognized until probably the 1940s or later, that this was a \
significant and worthwhile thing, which has perhaps not even been recognized \
until today. "
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"When I got serious about building what is now ",
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" one of the things that I was interested in was to see how general could we \
make this notion of computation. How could we take the idea of what \
computation could be, the representation of arbitrary processes and arbitrary \
kinds of constructs and to what extent could we build the system that could \
really make use of this potential generality that the idea of computation has?"
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"So this line of thinking is part of what got me started, what fueled some \
of my scientific efforts. For my own personal purposes, the idea that when \
one builds a computer language like ",
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", in a sense what one is trying to do is take all these abstract processes \
that people want to do and find what the primitives are out of which those \
operations can be formed. And then we give those primitives names like ",
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" or whatever else. Those are the primitives from which we build up the \
things that people want to do\[LongDash]the processes that people want to \
carry out. "
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"Before Newton, it was not clear how one should represent processes in \
nature. There were a lot of different sometimes quite wacky ideas about that, \
the great advance of 1687 and Newton\[CloseCurlyQuote]s Principia \
Mathematica, the title of his book was ",
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". His notion was can we take natural philosophy, this systematic study of \
nature, and can we put mathematical principles onto that. That was a great \
idea and a great advance. It fueled the development of the physical and other \
exact sciences for 300 years, this notion that one can take mathematical \
equations, ideas from mathematics, ideas about calculus, and so on and one \
can use them to explain and represent processes in nature. "
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"So in a sense, as I was saying at the beginning, at least my view of what \
computation is in essence, is that it is a way of finding an abstract \
representation of processes. So among other things these ideas of computation \
should be able to find good abstract representations of the processes that go \
on in nature too. What one realizes as one looks at the underlying constructs \
of whether it is Turing machines, whether it is ",
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", the underlying as it is turned out quite uniform constructs that support \
universal computation that allow one to make programs and so on, all those \
constructs are considerably broader than traditional ones that exist in \
mathematics and arithmetic and calculus and so on. "
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"And in fact, the ",
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" function in ",
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", has used this method for generating randomness ever since ",
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" Version 1 was released. And it has been a really good method of generating \
randomness. In fact it has been an embarrassment to us that for some real \
number random generation methods we used, against my better judgment I was \
convinced that we should use more traditional random generators, which were \
slightly faster at the time when these things were first implemented but \
which have turned out to have all kinds of horrible bugs. So, this particular \
way of generating randomness, this little rule 30 thing, which is by far the \
simplest in terms of its rule, has withstood all of these attacks. So this is \
a remarkable thing. It is not one\[CloseCurlyQuote]s common intuition. "
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"One of the things one might start to think about is: What does it mean to \
have a system that does a computation? Usually when we think of computation \
we think of setting a system up to specifically achieve some particular task \
that we have set for it. So for example, Figure 5 is a system, it happens to \
be a cellular automaton, that is set up specifically to achieve the task of \
squaring its input. So you put in ",
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"Well, I think that the answer is really definitely yes, it absolutely \
counts as a computation. It is not a computation where we necessarily know \
the point of it beforehand, but it is a computation that just happens. It is \
a computation that perhaps may be happening in nature quite a bit. And it is \
a computation that sometimes we may find out is actually quite useful. Like \
in the case of this rule 30 system, it has been very useful as a random \
generator in ",
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"For many years I studied what is out there in the computational universe. I \
was using ",
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" as a telescope to look and try to do the natural history of all these \
strange creatures that exist in the computational universe. And having done \
the natural history, try to classify them and then try to find general \
principles about what happens out in the computational universe. "
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"Figure 8 is a particular case where we now know that this is possible. This \
is the rule 110 cellular automaton. It is the ",
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automata. "
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"The big thing that one realizes from this principle of computational \
equivalence and this whole ",
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actually a fairly special case. That out there in the space of possible \
abstract systems, out there in the computational universe, a very large \
fraction of systems are actually doing much more complicated things that are \
in a sense computationally powerful and are in a sense computationally \
irreducible. There is really no way to work out what this system, for \
example, will do by any procedure that is much more efficient I think than \
just running the system and seeing what happens\[LongDash]that is the idea of \
computational irreducibility. That makes this system seem complex to us."
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"And that puts more pressure on us to find the right primitives representing \
natural systems in a way that fits in well with the kinds of computers that \
we actually use. Because we know we are going to have to do a lot of \
computational operations to find out what the natural system does. So those \
operations should be as simple as possible so that we get to do as many of \
them as efficiently as possible. In a sense, that forces us to think about \
the kinds of primitives that should exist, let us say in ",
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well-matched with the kinds of things that actually go on in the natural \
world or not? And I would say that what I have seen from studying NKS and so \
on is that I am very pleased with the extent to which the kind of symbolic \
programming primitives that we have in ",
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models that seem to be relevant in studying the natural world."
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"It could certainly be the case that our universe would be rule number 17, \
or our universe could be rule number ",
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"And the question is: How simple will the rules be? I do not have any \
particular criterion to decide that, although it is a very fundamental fact \
about nature that the rules for nature are not as complicated as they might \
be. For example, the universe has perhaps a little less than ",
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those particles might choose to do a different thing. Yet what we know is \
that there is considerable order in the universe, that the rules are not that \
complicated. Most of the particles choose to follow the same kind of rules \
all the time. And so the rules are simple compared to, in a sense, the size \
of the universe. How simple they are we do not know. We do not have a \
criterion. There is not yet a criterion by which we might guess how simple \
the rules might be. "
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"It is a wonderful application of ",
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" actually. It is a fairly sophisticated, fairly high-tech thing that \
involves feeding in a possible rule for the universe to see what it does. \
Many rules for the universe are completely stupid. One can say immediately, \
this is not our universe. No notion of time, space, expands exponentially in \
a trivial way forever, etc. What you really want to know, for example, is \
given some potential universe, what are the laws that operate in this \
universe and are they the same laws that we know, whether it is the standard \
model gauge invariance or general relativity, or whatever else. Are they the \
same laws that we know from existing physics? "
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"That has turned into this big enterprise of essentially doing automated \
theorem proving and things like that and doing a whole bunch of graph theory \
and combinatorics. It is a wonderful ",
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what we can prove for candidate universes. It is kind of automating the \
process of being a natural scientist or a theoretical natural scientist. \
Given this set of rules, what can we determine from that about laws of this \
universe? "
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"It has been going rather well and there are some nice technology spin-offs, \
which will show up in ",
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". One of the consequences of finding out that our universe is one of these \
universes out there in the computational universe is that it really grounds \
the notion of computation. If our universe is one of these things out in the \
computational universe, we know that is all that is there. We cannot start \
arguing, oh well, computation as we know it right now is not really \
everything that is relevant in the universe, there might be some special \
rule-number thing, there might be some hyper-computation thing, there might \
be some other weird thing going on. We will be able to say, no that \
absolutely is not the case, everything that happens is just determined by \
this particular computational model."
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