really what we’re talking about is the
relationship between information and energy and in fact we’ll talk 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’s not going to happen so we’re going to focus on this one one idea which has really fascinated
physicists for, well let’s see, since ’round 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 stored 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 all stored formation processes that were 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 gotta stress as well that there has
been a couple of videos and it’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 of very different concept because what Michael
Vsauce did was it was basically think about electrons electrons the massive
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 what’s 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
its back in the eighteen sixties and he’s talking about something which is
known as the Maxwell’s demon is our demon will get back to our attention on– let’s lift her veil. “If we can conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be will be able to do what is at present impossible to us.” And I’m gonna explain what exactly what that means original
version of Maxwell’s demon we 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 a demon is going to follow the trajectories of the
molecules and what she’s going to do is if she has a fast-growing molecule which
is moving in this direction she’s going to open the thing open that
the partition opened the gate and let it through only the fast ones what we’re
doing here is we’re dividing up the Fast and Slow molecules let’s say this one
for example is zipping around so it’s coming towards that the get she sees
this one zipping man and it’s going very fast much faster than the average
selected throw 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 one’s true so this is quite slow approaching here
this one goes for was the first one she keeps on 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 a throw on this side you end up with a
slow cultures and what’s wrong with that there’s an awful lot wrong with that
because what we’ve done is we’ve generated our temperature difference
without putting any working because what when this we assume and maxwell made the
assumption that when you lift this partition this is frictionless you can
just lift this without doing any work so it’s all entirely smooth and this can
come up without doing any 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 sorted the molecules into well… we sorted the molecules in both partitions
in terms of their speeds. Second law of thermodynamics tells us that really what
that’s what wants to happen is you randomize. The even simpler version of this which
is a another type of demon you don’t even think about the speeds what you going to do is approaching this
way you let it through you let it through you let it through you let it
through let it through and what you end up with is a pressure difference and
major pressure difference and now here’s another problem because now we have a
pressure difference in principle of 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 couple to one big temperature bath
outside we’ve designed a gradient we’ve managed
to put a gradient in the system without effectively doing any work and now we
can get workout we’re getting a free deal will get no you know we’re getting
a free lunch and that is a major problem in this Court’s so many headaches and
still in some regards causes headaches that’s a very very good– Ah, no, that’s a very good
point, but the history of physics and the history philosophy is riddled with
Gedanken experiments. You think about quantum mechanics you think about
relativity. Those Gedanken and those thought experiments are very very
important you can just dismiss this until this is never going to happen in
fact you can never have a purely you know frictionless any type of frictional
system or there are many issues here in terms of setting this up experimental
although it has been setup experimental version of it has recently been setup
experimentally but those Gedanken experiment are really important because
they drive your thinking and one particular when the thing is you gotta
stand back from this angle there’s a problem here so where where is
the problem and ultimately took a long time and a lot of beds 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 of this as we saw in terms of the
molecules which means the direct link link 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 costs and I’m afraid really it’s not just the energy costs it’s actually
we’ve got to think about entropy and so that’s ever really we’ve tried answering
number times we find sixty symbols let’s have a really simple explanation
of entropy here’s a low entropy state all the
molecules and outside 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
about a droplet of cream or whatever or milk on the top of your coffee it spreads out it diffuses this is a low
entropy state that’s not a natural state of affairs particularly when you 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 the molecules on there and we put a
partition in bingo were very very happy because those molecules can knock this
partition that and we can see we can extract work if however we’ve got a high
entropy state and we work our petition in the middle or valve this is just
going to go by and 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 a guy called saleyard 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 took he
went down the spherical Cairo route Thank let’s simplify this what’s the
simplest possible thing we can have one molecule that’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 that’s chances to a piston right so now what we have is
a piston and we’ve got this molecule in the Box here’s is the key thing if we
don’t know the position of the molecule in the box what’s bouncing around what
it’ll do is it’ll keep jumping off that something of that moving that 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 one is going to move that way
if and this is this is sea Lords key inside if however we bring our demon
back in who’s now a slightly stupid or demon in fact she doesn’t really have to
do anything other than see what’s at work out which
side of the box the particles on the molecules on doesn’t have to worry about
the velocity of the molecule and indeed there was one of them so i think even i
could probably handle one molecule let’s say they the molecules here at one
instance of time now if the demon knows that what you can do and she can insert
this piston on either side of the box that’s important you can insert the
piston either side of the box just to make the station if the markets 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 molecule starts bouncing
back and start pushing it back you’re extracting work for you know again you
get a free lunch but it all relies on the information here and all realize 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 constructed just on Tuesday see campbell
but the problem is that we don’t know what sights on it is likely to go that
way as it is to go that with so and that’s in terms of different direct know
but the important thing is very good . pretty but the important thing is to the
balls here the molecules here if we now start pushing this piston forward it we’ve got an issue because the the
molecule is is acting against the piston as well so we’re not getting this free
lunch anymore so it’s important the key aspect of this is known which side of
the container the molecule is actually on and of course is sixty symbols I’m simplified before the comments
section starts filling up I’m simplifying this a great deal yeah let me go to the chest there’s this
clear link between entropy and information and knowledge of the system
in fact many now we’ll catch any of you explain entropy in terms of missing
information and it’s a whole area of entropy which is different from going to
stress that but related to thermodynamics and thermal processes in
communication and computers and information technology and everything
around us is something called Shannon entropy as well again these incredibly
close links with with information i did say that cut the cheese so how does that connect with thoughts
very clever guy who called landowner who back in the sixties 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 a bit of information is it on the left or isn’t the right that’s that’s
our one bit of information and from the thermodynamics of this modern you can
connect that bit of information to the to the the energy and so if we worked
out going to me right one equation in the largest one let’s put it energy and
we’ll say it one bit this is something called Boltzmann’s constant right
Boltzmann’s constant is a pretty small number all you need to worry about is
boltzmann’s constant is the conversion factor is like it’s like having two
different currencies and you’re converting between this is the
conversion rate 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 is going 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 worked out at in terms of what we have at room
temperature say turns out that that is something like 3 x 10 to the minus 21
jewels that’s the energy associated with one
bit of information about mars bar for lunch if we look in the back here to my
eyesight’s get anybody mind of the whole time 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 magnitude it’s 960 killer Jews
that’s 960 x 10 to the 3 this is we’re going to do the equal sign is three x 10
to the minus 21 jewels the amount of energy you get from this E(mars bar) is
about one megajoule which is 1 by 10 to the 6 Jules you can see that there were
an awful lot of those in one of those huge huge amount in one of those so then we come to the really tricky
question which are physicists is really not equipped to address which is what is
a thought so for me, as a physicist thoughts just information let’s say we’re going to assume i don’t
know maybe you thinking pictures like I do so let’s say this picture that you’re
currently looking at that’s 1920 x 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 out what we get is that for that would look the energy just saw if i
can get the board to move number of bits of information is about i’ll do a abide
sign 50 by turned to the 650 million now we know from there that the energy for
one bit is three x 10 to the minus 21 so what we’re going to do the energy of our
thought is going to be 3 by 10 to the minus 21 x 50 x 10 to the 6 workout
throw that’s 450 x 10 to the minus 15 which is equal to 1.5 x 10 to the minus
13 and I hope you’re screaming at me what are the units units or 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 read up here is about a
megajoule so let’s put Energy(mars bar) is about one megajoule. this is its
chemical this is the energy you get from it if you eated 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 Dead the energy you get from eating it is associated with a thought
it turns out well as you can see it’s going to be a really really small number
if we put the energy of our thought over the energy of our mars bar that’s this
incredibly small number / this rather large number just ended the sixth which is about 1.5
x 10 to the minus 19 so this is just a ratio so it means that the energy
associated with your thought is about 10 million million million times smaller
than the energy you get from eating your Mars bar. If you were to eat this it
will be roughly– very, very roughly about an attaogram. You’re not going to be
able to see that that’s an invisible quantity of of mars bar how much I’m gonna try to get this
domain that’s I don’t know maybe that’s that’s a few thousand thoughts just for you, Brady