Really what we're talking about is the
relationship between information and
energy. And in fact, we're talking about
the relationship between information and
entropy. So just let me stress if you're
thinking of getting all of
thermodynamics in the next five minutes,
it it's not going to happen. So we're
going to focus on this one one idea
which has really fascinated physicists
for oh oh let's see since around about
1860 and it comes up time and time and
time again which is the relationship
between heat and energy entropy and in
particular
information. We're going to think of it
in terms of bits of information because
you could have a very complex thought.
You could have a very as you say
fleeting thought you could have a
snapshot. I don't know, you could see an
image appear in front of you and it's
gone the next minute. And we could think
about that image in terms of the number
of bits of information. Now, I'd love to
be able to say that our knowledge of the
brain is such that we can understand
those thought formation processes as
we're nowhere near understanding just
how that happens. But we can think about
it in terms of bits of information. And
that's that's really where I'm going
with this. I've got to stress as well
that there has been a couple of videos
and there's quite a lot of discussion
online which is actually one of the
reasons we're doing this video about you
know for example how much does the
internet weigh and that was a video that
oh I believe Vsauce did number of years
ago this is a different concept a very
different concept because what Michael
what Vsauce did was was basically think
about electron electrons the mass of
electrons charge and how much charge
electronic charge you need to store bits
of information what we're going to talk
about is much more fundamental much more
subtle much more conceptually
challenging and therefore I would argue
much more
fun. I'm going to start with as it says
here one of the most heavily quoted
passages in physics and this is from
Maxwell and it's back in the 1860s and
he's talking about something which is uh
known as the Maxwell's demon. Here's our
demon. We'll get back to our demon.
Let's lift our veil. If we conceive a
being whose faculties are so sharpened
that he can follow every molecule in its
course, such a being whose attributes
are still as essentially finite as our
own will be able to do what is at
present impossible to us. And I'm going
to explain what exactly what that means.
The original version of the Maxwell's
demon, we've got molecules moving around
in a box. So they've got some energy and
that energy is coming from the just the
heat energy from the environment. We
have a partition in the box. And so what
we're going to do
now is the demon, and here's our demon,
is going to follow the trajectories of
the molecules. And what she's going to
do is if she has a fastgoing molecule
which is moving in this direction, she's
going to open the thing, open the the
partition, open the the gate and let it
through. Only the fast ones. What we're
doing here is we're dividing up the fast
and the slow molecules. Let's say this
one, for example, is zipping around. So,
it's coming towards the the the gate.
She sees that this one's zipping around
and it's going very fast, much faster
than the average. So, she lets it
through. This one's moving more slowly.
So, this one doesn't get through. And on
this side, okay, it's the opposite way
around. So, what's happening is that
she's going to let the slow moving ones
through. So, if this is quite slow
approaching here, this one goes through.
Whereas the fast one she keeps in this
side. So over time what happens of
course is that we end up with all the
molecules over here. These are all the
speed demons that have made it through
and on this side you end up with a slow
coaches. Now what's wrong with that?
There's an awful lot wrong with that
because what we've done is we've
generated a temperature difference
without putting any work in because what
when this um we assume and Maxwell made
the assumption that when you lift this
partition this is frictionless and you
can just lift this without doing any
work. So it's all entirely smooth and
this can come up without doing any work
and the demon wasn't doing any work.
What we've done is we've broken the
second law of thermodynamics because
over here we've we've sorted the
molecules in ter well we've sorted the
molecules in both partitions in terms of
their speeds. Second law of
thermodynamics tells us that really what
what this what wants to happen is you
randomize the even simpler version of
this which is another type of demon. You
don't even think about the speeds. What
you're going to do is if it's
approaching this way, um, you let it
through, you let it through, you let it
through, and what you end up with is a
pressure difference, a major pressure
difference. And now here's another
problem. Because now we have a pressure
difference. In principle, that pressure
difference can do work. And yet, the way
an engine works is we have a temperature
gradient. Here we have no temperature
gradient. Remember, this is just coupled
to one big temperature bath outside.
we've designed a gradient or we've
managed to put a gradient in the system
without effectively doing any work and
now we can get work out. We're getting a
free deal. We're getting a you know
we're getting a free lunch and that is a
major problem and this caused so many um
headaches and still in some regards
causes headaches. Phil, why does it
cause headaches when it's a thought
experiment with a demon that doesn't
exist and is not possible? That's a very
very saying if a unicorn walked in that
would be confusing but a unicorn can't
walk. Uh no that's a very good point but
the the history of physics and the
history of philosophy is riddled with
gdankan experiments. You think about
quantum mechanics you think about
relativity those gdank and those thought
experiments are very very important and
you can just dismiss this and say this
is never going to happen. In fact you
can never have a purely um you know
frictionless any type of frictionless
system. There are many issues here in
terms of setting this up experimentally.
Although it has been set up
experimentally or a version of it has
recently been set up experimentally. But
those Gdankan experiments are really
important because they drive your
thinking in one particular way. And the
thing is you got to stand back from this
and go there's a problem here. So where
where is the problem? And ultimately and
it took a long time and a lot of debates
and a lot of controversy. It's the
information that's stored by the demon.
That's that's that's the key thing.
That means that there's a direct link
between information and as we can see
we've set up a pressure difference here
or we can set up a temperature gradient
as we saw in terms of the molecules
which means there's a direct link um
link between what this demon knows and
what's going on physically and we've got
to think about what the energy cost of
the information of what this demon
knows. That's the key thing is what's
the energy cost and I'm afraid Brad it's
not just the energy cost it's actually
we've got to think about entropy and so
let's have a really we've tried entropy
a number of times before in 60 symbols
let's have a really simple explanation
of
entropy here's a low entropy state all
the molecules in that side of the box
that's a very low entropy state that's
not you know what's going to happen is
if you've got some milk on the top of
your coffee, you put a droplet of cream
or whatever or milk on the top of your
coffee, it spreads out. It diffuses.
This is a a low entropy state. That's
not a natural state of affairs,
particularly when you've got thermal
energy pouring in. What's going to
happen is that they're going to
randomize. That's a high entropy state.
Now, here's a very interesting aspect of
this. If we've got all our molecules on
there and we put a partition in, bingo,
we're very, very happy because those
molecules can knock this partition and
we can we can extract work. If however,
we've got a high entropy state and we
whack our partition in the middle or or
valve, this is just going to go bounce
back and forth and it's not going to go
anywhere. That's a key difference
between a high and a low entropy state
in terms of the amount of work we can
generate. There's um a guy called
Sillyard who is really famous because he
came up with nuclear chain reactions. He
was fascinated by Maxwell's demon and
like a very good physicist like all good
physicists do he thought he went down
the spherical cow route. Think right
let's simplify this. What's the simplest
possible thing we can have? One
molecule. Let's make it even simpler.
Let's not let it move in three
dimensions or two dimensions. Let's just
make it move in one dimension. And
what's very interesting now is that you
can imagine having a piston. Let's
change this to a piston now. Right? So
now what we have is a piston and we've
got this molecule in the box. Here's
here's the key thing. If we don't know
the position of the molecule in the box,
so it's bouncing around. What it'll do
is it'll keep thumping off that thumping
off that moving the the piston forward
as long as the piston doesn't fall over.
Or it could be in this side of the box
and it'll drive it back. But if we have
no idea where the position of the ball
is on on average, it's going to move
that way and it's going to move that
way. If and this is this is Celod's key
insight. If however we bring our demon
back in who's now a slightly stupider
demon. In fact, she doesn't really have
to do anything um other than say what's
work out which side of the box the
particles on, the molecule is on.
Doesn't have to worry about the velocity
of the molecule. And indeed there's one
of them. So I think even I could
probably handle one molecule. Let's say
the the molecule's here at one instance
of time. Now if the demon knows that
what she can do and she can insert this
piston on either side of the box. That's
important. She can insert the piston on
either side of the box. She has to make
a decision. If the molecules over here
and she knows she can insert the piston
here. And here's the key thing. Remember
this is frictionless. There's no
molecules here. There's only one
molecule. No work. No work. No work. No
work. No work. comes up here, a molecule
starts bouncing back and starts pushing
it back. You're extracting work for, you
know, again, you're getting a free
lunch. But it all relies on the
information here. It all relies if we
don't know which side of the box the
molecule is on. We're not going to be
able to extract this work reliably,
reliably. We can extract it. Just on
Tuesdays we can, but on Thursdays we
won't. But the problem is if we don't
know which side it's on, it's as likely
to go that way as it is to go that way.
So, and that's in terms of still
extracting work just in a different
direction. No, but the important thing
is very good point Brady, but the
important thing is let's say the ball's
here, the molecules here. If we now
start pushing this piston forward, it
we've got an issue because the um the
molecule is is acting against the piston
as well. So, we're not getting this free
lunch anymore. So, it's the important
the key aspect of this is knowing which
side of the container the molecule is
actually on. And of course it's 60
symbols. I'm simplify before the comment
section starts filling up. I'm
simplifying this a great
deal. Yeah. Let me cut to the chase.
There's this clear link between entropy
and information and knowledge of the
system. In fact, many now will uh couch
entropy or explain entropy in terms of
missing information. And indeed there's
a whole area of entropy which is
different from got to stress that but
related to thermodynamics and thermal
processes in communication and computers
and information technology and
everything around us. There's something
called Shannon entropy as well. Again
these incredibly close links with with
information. I did say I'd cut to the
chase. So how does that connect with
thoughts? very clever guy who called
Landau who back in the 60s was again
thinking of this problem and he worked
out precisely the energy associated with
one bit of information from this model
from this type of model because here
we've got one bit of
information which is which side of the
box is the particle on. That's our bit
of information. Is it on the left or is
it on the right? That's that's our one
bit of information. And from the
thermodynamics of this model, you can
connect that bit of information to the
uh to the the energy. And so if we work
that out, go on, let me write one
equation on the just one. There we go.
And let's put it energy and we'll say
one bit. This is something called
Boltzman's constant, right? Boltzman's
constant is a pretty small number. All
you need to worry about is Boltzman's
constant is the conversion factor is
like it's like having two different
currencies and you're converting between
them. This is the the um conversion
rate. Um and what it does is it converts
from temperature to energy. Units are
really really important for physicists.
This doesn't have units. So this has got
to have units energy. K translates
temperature to energy. That's that's the
formula and it's really straightforward
for one bit of information. Now if we
work that
out at in terms of what we have at room
temperature say turns out that that is
something like 3x 10 the
minus21 jewels that's the energy
associated with one bit of information
got me Mars bar for lunch if we look in
the back here though my eyesight's
getting really bad might have to help
out. So if we work in proper units like
physicists do which are jewels not this
calorie nonsense we find that it's
actually nearly a megajoule it's 960 kJ
so it's
960 by 10 to the 3 this is we're going
to do the equal sign is 3x 10us 21
jewels the amount of energy you get from
this e marbar is about 1 megle which is
1x 10 to the 6 jewels. You can see that
there are an awful lot of those in one
of those a huge huge amount in one of
those. So then we come to the really
tricky question which a physicist is
really not equipped to address which is
what is a thought? Um so for me for as a
physicist thoughts just information.
Let's say we're going to assume I don't
know maybe you think in pictures like I
do. So, let's say this picture that
you're currently looking at, that's
1920x 1080 pixels. And we're going to
assume that each pixel is 24 bits of
information. Put those numbers together,
multiply them up, and we find that what
we get is that that's for that lovely
image you just
saw. If I can get the board to move
number of bits of information is about
I'll do a about sign 50 by 10 the 6 50
million. Now we know from there that the
energy for one bit is 3 by
10us21. So what we're going to do the
energy of our thought is going to be 3
by 10us
21 multiplied by
50 by 10 the
6. Work that through. That's 150 by 10
-15 which is equal to 1.5 by 10us3. And
I hope you're screaming at me. What are
the units? The units are jewels.
So how much of a Mars bar is that amount
of energy? So we've already told you
that the energy of a Mars bar in terms
of the nutritional energy that we've
read up here is about a megajoule. So
let's put energy Mars
bar is about one megajoule. So this is
its chemical. This is the energy you get
from it if you you eat it. So let's
let's look at what that that's gonna we
can work out what fraction of the Mars
bar in terms of the the the energy you
get from eating it um is associated with
our thought. And it turns out well as
you can see it's going to be a really
really small number. Or if we put the
energy of our thought over the energy of
our Mars bar, that's this incredibly
small
number divided by this rather large
number which is 10 6 which is about 1.5
by 10 the minus19. So this is just a
ratio. So it means that the energy
associated with your thought is about uh
10 million million million times smaller
than the energy you get from eating your
Mars bar. If you were to eat this, it
would be roughly very very roughly about
an atgram. You're not going to be able
to see that. Um, that's an invisible
quantity of of of Mars bar.
How much? How much? I'm going to try and
get that that's I don't know. Maybe
that's that's a few thousand thoughts
just for you really.