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U1L2d.txt
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#
# File: content-mit-8370x-subtitles/U1L2d.txt
#
# Captions for course module
#
# This file has 127 caption lines.
#
# Do not add or delete any lines. If there is text missing at the end, please add it to the last line.
#
#----------------------------------------
What's the physical cost of realizing such computations?
I just now mentioned energy.
And so it is very interesting to consider the fundamental limits
upon computation imposed by the laws of physics.
And I want to spend a few minutes on that
by talking about this second topic, thermodynamics
and computation.
It's really remarkable, in many ways,
how I've been able to tell you a great deal about computation
so far ignoring the laws of physics.
And really, the physics department
doesn't like this, in many ways, just from a standpoint
of fundamental principles.
Shouldn't everything be governed by the laws of physics?
How come I was able to give you that strong Church-Turing
thesis, which I erased over here,
and it said absolutely nothing about Newton's laws
or about Maxwell's equations?
Why?
It seemed like it was a construct of pure math,
really maybe pure audacity, to be able to ignore
the laws of physics.
And there was a whole group of researchers, scientists
around the world who thought deeply
about that in the early 1990s and the late 1800s.
And they came up with this realization
about thermodynamics and computation.
And this was, in my own journey in science,
one of the starting points about how I got interested
in quantum computation.
And that's one of the reasons I want
to share this little piece of a story with you today.
And the idea starts in 1867 with a construct, which
I think many of you already know about,
known as Maxwell's Daemon.
These were the good days when you did science
by writing letters to each other, researchers,
and postcards.
I don't know how many of you have seen the Stern and Gerlock
results that were sent to Professor in Americas
or in Canada.
Otto Stern took a snapshot and printed it
on the back of a postcard and mailed it.
I don't think I could do that today.
Maxwell's Daemon likewise showed up first,
as far as I know, in correspondence
between James Clark Maxwell and another fellow scientist.
How many of you know Maxwell's Daemon?
OK.
About half.
So let me actually describe this.
And those of you who know it, feel free to ask me questions,
get me to add and fill in some more of the detail.
So here's the scenario.
We have a cylinder with gas molecules in it.
And these gas molecules are careening around
at different velocities.
And some of them are going to be hot, and some of them
are going to be cold.
So if I were drawing this carefully,
I would draw the links of these arrows representing,
in some way, their velocity.
OK?
So longer arrows faster, shorter arrows slower.
Now, this box let's say has a partition in it with a hole.
And this partition has a sliding door.
And this sliding door can be actuated
by this clever little person sitting inside this cylinder,
a very, very small cylinder.
I mean, small person or a very large cylinder, let's say.
A very daemonic person who has his or her hand on this door.
And this daemonic individual, Maxwell's Daemon,
looks at each one of these molecules,
and, say, sees this molecule going about to hit this door.
And what Maxwell's Daemon does is
try to achieve this configuration where
he or she puts all the cold molecules
on the left and the hot molecules
on the right-hand side by virtue of looking at them
and selecting them one at a time as they
can go through the door.
So by doing this, Maxwell's Daemon
should be able to take, like, all the gas
molecules in this room and put the hot ones on one
side and the cold ones on the other side,
and then create an imbalance of temperature,
by virtue of which now Maxwell's Daemon hasn't done
any work, apparently, because all the daemon had to do
was open and close the door.
So it seems like this daemon is able to accomplish something
very useful, create a configuration of gas which
could then be used to extract energy and accomplish work
and so forth, and yet expend exceedingly little energy
in comparison with what the daemon could harvest
from the gas molecules in a room,
because any random distribution of molecules in a room,
like in this room, have a wide [? distribution, ?]
some which are cold, some which are hot.
So why shouldn't the daemon be able to separate them just
like this?
This is a real question.
And it's connected to computation in a way
that I hope you'll see in a moment.
Now, this actually is impossible.
And although I put exclamation points here,
really there should be a question mark,
because at first it wasn't understood why it's impossible.
Is it because of the energy required to move the wall?
Is it because of the measurement?
Maybe it's too hard to measure single molecules.
Maybe by measuring them sufficiently well,
the Maxwell's Daemon would end up
kicking the molecules in the wrong place.
Or is it hard because there's a need for intelligence,
in some way?
Like, maybe no automaton could accomplish this,
but a graduate student could.
So these were really the type of topics