I became interested in this phenomenon of constraints inspiring creative outbursts.
And if you look at the last century there were three really profound examples of that.
I would say the earliest that I found incredibly interesting was the limit of the speed of
light leading Einstein to the theory of relativity.
Where a lot of other scientists wanted to remove the limit, they wanted to say there
is no limit to the speed of light.
That doesn't make any sense.
That's impossible.
Einstein actually, despite the word relativity, adhered to a very strict absolute.
And that absolute was the speed of light.
He took that to be his guiding constraint.
And by sticking to it rigidly he said I'll give up anything else but the speed of light,
the constancy of the speed of light.
And by doing so he gave up on the absolute nature of space and time.
I mean that's just much harder to let go of intuitively and a much greater violation of
our common sense, but it was right.
And so this was an example where this tight constraint led to a creative outburst.
From this one constraint you could trace the line, not only to the relativity of space
and time but the expansion of the universe; the existence of black holes; the ideal that
the entire space has a shape, all of these things burgeoned from this really tight constraint.
Another great example is the Heisenberg uncertainty principle.
So Heisenberg begins to believe that we can't precisely know the location of a particle
and its motion and its momentum.
And this seems to violate what we believe that things objectively exist, that there
should be no such limit, but he takes it very seriously.
He doesn't just say oh it's often cast in this way; oh disturb a particle when we observe
it therefore we can't also know it's momentum once we've located it because in the process
of measuring it we've somehow disturbed it.
That's not really true.
That's much deeper than that.
Heisenberg took very seriously that this was profound that in some sense of the particle
doesn't have a location or a momentum, that in some sense the particle doesn't really
exist in the old-fashioned way we used to think it existed like a marble exists.
So by taking it that much more seriously it leads to the discovery of the deeper phenomenon
of quantum mechanics and that incredibly strange world that even though we don't actually understand
it, even today, we verify experimentally over and over again it's the most well tested paradigm
in all of physics, and yet it's the one we understand it the least.
My third example would be Gödel's limit theorem.
So the crate mashed notation Hilbert sent out a call to all mathematicians just to confirm
that all mathematical facts could indeed be proven within the context of mathematics.
It wasn't the case that he wanted every infinite proof, that's obviously impossible, he just
wanted to prove that the proofs existed.
It seems like a sort of meta level question.
It is, it's a meta level question, can we prove that all facts are knowable, is a simpler
way of saying it?
And Gödel comes along in the 1930s and proves that even in the context of something as basic
as arithmetic that there are facts among the members that can never be proven to be true
or false.
There are literally facts we can never know in the context of mathematics.
And that was a real blow to this idea of a mathematical theory of everything.
We've recovered from that blow and it turned out to have profound consequences and the
profound consequence was the invention of the computer and AI.
So you can trace Turing's creation of the idea of a machine that can think directly
to his work on the limit theorems and the fact that there are certain things we could
never know.
And that limit is severe.
And from that thinking about that limit he was able to imagine how to mechanize thought
and begin to think about making machines that thing and to begin to think that we're just
machines that thing and therefore there could be an artificial intelligence just like there's
a biological intelligence.