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 say 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 that 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 the
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 daemon we'll
get back to our demon sonoma 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 daemon 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 fast going molecule
which is moving in this direction
she's going to
open the thing
open 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
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 this
is quite slow approaching here this one
goes through whereas the fast 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 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 when this
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 into
well we've sorted the molecules in both
partitions in terms of their speeds
second law of thermodynamics tells us
that really what this what wants to
happen is you randomize
the even simpler version of this
which is another type of daemon you
don't even think about the speeds what
you're going to do is if it's
approaching this way
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 our
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 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 but 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 good if a unicorn walked in
that would be confusing but a unicorn
can't wait uh no that's a very good
point but the the history of physics and
the history philosophy is riddled with
gedanken 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 guidance 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
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 really 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 160
symbols well 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 good 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 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 our 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 and 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 th he went down the
spherical cow root think well 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
win it's going to move that way if and
this is this is celiad's key inside 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 uh
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 molecules 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 so you
can insert the piston on either side of
the box she has to make a decision if
the molecule is over here then 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 reliable we can extract it
just on tuesday so we can but on
thursdays but the problem is if we don't
know what 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
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 the 60 symbols
i'm simplified 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
gotta 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
information i did say i'd cut to the
chairs so how does that connect with
thoughts very clever guy who called
landauer 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
board just one there we go and let's put
it energy and we'll say 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 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 3
by 10 to the minus 21 joules 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 really 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 960khz
so that's 960 by 10 to the 3. this is
we're going to do the equal sign is 3 by
10 to the minus 21 joules
the amount of energy you get from this
e marshmallow is about one megajoule
which is one by ten to the six
joules
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
that's 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 1920 by 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 to the six
50 million now we know from there
that the energy for one bit
is three by ten to the minus twenty one
so what we're going to do the energy of
our thought is going to be three by ten
to the minus twenty one
multiplied by fifty
by 10 to the six
work that through that's 150
by 10 to the minus 15 which is equal to
1.5 by 10 to the minus 13 and i hope
you're screaming at me what are the
units the units are joules
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 energy you get from
eating it um is associated with a
thought and 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
divided by this rather large number
which is 10 to the sixth
which is about
1.5 by 10 to the minus 19. 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 atogram you're not
going to be able to see that
that's an invisible quantity of mars bar
how much how much i'm going to try and
get there
that's i don't know maybe
that's a few thousand thoughts just for
you