B1 Intermediate 8 Folder Collection
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It's what I want to do is focus on the real fundamental
physical limits of course getting down to the the miniaturization
And the smallest possible structures is an important aspect
But there's also a speed aspect if you even get down to that you get your density up. How fast can you process?
The reason I'm quite keen to come back to computerphile is I spent the first two years of my physics degree going shuddered on computer
and because I'm really quite a per mathematician to put it mildly, but I'm
As a cold or at least back in the dim distant days of the past I used to be okay
I started with the zx81 got into assembly language coding did a lot of from
Zx80 ones that expect from BBC micro all that type of stuff used to love coding my mantra throughout my undergraduate degree
And I was not a great student was if I can't code this. I don't understand it
So there's a piece of physics particularly piece of mathematical physics
I'd always think about how do I call this Fourier transforms convolution correlation?
Can I reduce this to a piece of discrete mathematics and therefore can I actually code it so I've always loved exploring those links between
Programming coding computers information and physics before we start thinking about limits
We've got to start thinking about well
physically what the computers do what do they actually do they they take information in and
They do some computation and they give information out is that a fair enough description Sean sounds good
yeah, so the interesting thing is just how you define information and
There's a guy called wheeler who was the PhD supervisor of
Feynman what wheel also had this very famous phrase which was it from bit
So the idea that the fundamental quantity in the universe is not energy. It's not matter its information and
What does he mean by that well it's it's it's intriguing. Let's play around with these. Let's say. We've got a system
which is
Entirely what we'd call reversible right? What does that mean it means that if I drop that ball?
Let's say you're as you can see I'm slowing it down
But let's imagine that I was actually just dropping it out of my hand and it was coming right back up to the same height
All right
That would be what's called an elastic system
There's no energy being removed
This ball is coming right back up to its same height its end position is exactly the same as its starting position. It's entirely reversible
There is a link to computing a promise so
What happens if we if we add some if we take some energy out of this system and there's this what we call?
dissipation this friction
Does the ball is squishy so when it hits the floor? It's not a perfectly elastic band
It just doesn't bounce as if it's a rigid object. You know what's gonna happen. It's fairly boring
Now we've got a problem because that's our final state. That's a right pot
That's a right part of the system. Do we have any information at all about the input?
From that no not exactly
It's just there you drop it from this height you drop it from that height you drop it from that height
You've lost all information about the initial state
However if it's if there's no energy leaking out of the system, then you drop it from this height
If it was a perfectly elastic system. Let's do it like that just to pretend then it comes back up to the same height
This is already telling us that there are interesting links between information and energy
Now if we look at a standard to get back into computer files territory. There's a direct relationship between the
reversibility of the system
And the information content of the output so in the second case when the balls like that
Energy's leaked out the system isn't reversible and
We've we have no idea what the input was so we've lost
Information in that sense has leaked out into the environment the fascinating aspect of this is if you take a NAND gate
So what we have now is a is a logical connection
Connection and boolean logic to this physical problem because let's set this up as a truth table
Let's put that as output which is not how computer scientist might do it
But I'm a physicist
So I'll do it this way so if we go zero zero you all know how a NAND gate works zero one zero zero
one zero one
one one
Now we've got a problem
Because for three of these outputs. We've got exactly the same. We've got zero
We've got no connection between this iPod
We've lost information because we don't know what our inputs were we have a lack of reversibility and that lack of reversibility is
absolutely key in terms of the connections between the physical world and the
Information world the computing world and therefore because we've got a connection from reversibility and energy
Therefore we've got a connection with the physical world in terms of how we do computation
There are multiple ways of getting to zero is basically what we've got precisely so if we've got this we can traverse the system
To know to work out what exactly are our inputs where there's only
Okay, forgive me for saying this, but is that not just because we've got two inputs that only one output through sir
Thank you for that exceptionally perceptive question John so what was and what was that's exactly the issue
So there's a whole host of gears called fredkin gates. Which are developed which have three inputs and three outputs now
We'll go into them. You don't have to forget setup like this you can have something which is called a reversible gate and
In principle if you've got that reversible gate input in place though actually
There's a difference between the physics and the engineering
engineering one of those gates and actually changing or a computer
Architecture to move towards all type of fredkin gates is going to take an awful lot of effort
and an awful lot of cost but in principle if we could do that and if we had a
Perfect perfect Fred can get then there would be no energy cost to computing
No energy no. No energy cost because here's the fascinating thing. What costs the energy is not the
Computation itself it's a raising information that and gate there
It's the logic of the of the data
but it doesn't show all the physical connections does it usually these gates have multiple things like Earth's and
Of course is that right and in fact exactly they have written in fact
How you clear these in many cases is you ground so if you've got a 1, which is what is a 1 well?
It's a voltage how do you set that to 0 you actually ground it? So that's that's a leaker in that sense?
you're leaking out to the environment, and that's what it's a
Really good way of thinking because that's exactly what's happening here. This is not. This is unravel
because the the information is
Leaking out to the environment effectively or in this case the energy is leaking out to the environment
So you must observe it to see what happens generally?
okay, so with it with the
sort of threat of going down the route of an electric engineering file
How does this relate to somebody who's practicing a modern-day computer?
They saw the key thing here is because it costs a certain amount of energy to erase data and for any
Computation in the way, we've set up or to lose data particularly with these there's an energy cost to doing this because it's irreversible
that means that that is setting a fundamental limit in terms of the the
Amount of energy that it needs to power a computer and in turn you know from both
environmental and also fundamental physics reasons
You know we really need to think carefully about how we actually beat that limit if we could beat that limit
Let's say we do call the DS fredkin gets
What where we really come up hard against another limit is?
something called the Heisenberg uncertainty principle quantum physics
So don't worry
I'm not going to go into a great deal of detail about the uncertainty principle
Apart from to say this is that too often the uncertainty principle is seen as you have a system you make a measurement
your influence on the system is
Affecting the measurement, and there is affecting the system and therefore that gives rise to an uncertainty that's not it at all
It's it's much more fundamental than that there is in quantum mechanics the observation effect of the observer effect
That's a whole we could do 15 hours on that and though indeed there are whole masters courses on that on that
But in terms of the uncertainty principle actually
Every time you play a guitar if you do play a guitar the uncertainty principle comes it comes about in a nutshell
The uncertainty principle is is all about
How waves behave and once you down at the quantum level? You've got to think about
Particles not just as being particles as little billiard balls
They've got a way of like characteristic does that mean they change into waves no that would be far too straightforward
But it means they've got a way of like characteristic and therefore the physics of waves
Translates all the way there it must do because we're in viewing matter with these wave-like
characteristics at the quantum level
So therefore the physics of waves in the world around us and the mathematical framework of waves in the world around us has to
Move down to that level this uncertainty principle is just this if I let that no ring out for a long long time
Or indeed if I just whistle maybe a whistles in pair on
For a long time
And I ask you to tell me what the frequency that whistle is or we look on a signal analyzer
And we look at the spectrum we'd be able to say as particularly if I whistle for a very long time
That's at 400 Hertz or whatever and some of you perhaps if you could spectrum analyzer don't even go back and tell me what?
Frequency that was that the difficulty is this what if I do this?
Or what if I do this?
How do I describe that what frequency is a god and the thing is this wide and time
narrow and frequency
Narrow in time and in fact if you were to look at this on a spectrum analyzer what you'd see is you need a much
Wider frequency spectrum to represent that chunk
So when you hear that happening and lots of metal bands do this
What that is is the uncertainty principle in action, but that's the key thing
wide in time
Narrow in frequency narrow in time wide in frequency. Just get that again
I wish I'd got that idea in my head as an undergraduate about three years before I did get it in my head and
Then quantum physics would have been a hell of a lot easier
How does that relate to this well we coming towards something to do with processing speed?
We are indeed that's exactly what I'm going with this so the question is to ask yourself
Let's say with the ideal technology we had you know everything we could manufacture down to incredibly tight limits
We could get down to the single atom limit principle. We may even get below the single-item limit start controlling nuclei. What is the fundamental?
Physical principle that really limits us
Right down at the lowest possible level we could go to and what it is is it's the uncertainty principle now often
It's that the uncertainty principle is couched in terms of momentum and position
for the physicists among you there's also a
counterpart which is energy and time
At this point what I'd really like to do is put in a little aside to all the physicists out there
So if you've got something which is wide and time it's an hour on frequency similarly if we try to constrain it in time
The problem is that we get a much larger range of energy
so if you want to do a
Operation you've got to think about well the number of operations
you can get by per second that means if you've got a number of operations per second that means you've got a
Frequency of those operations also means you've got a time between those now the uncertainty principle
tells us that we've got a
Fundamental limit on how narrow we can make that time because by narrowing down that time we broaden out the energy
associated with the atom with the operation which sets a
Fundamental limit because the narrow narrow narrow narrow we get that the broad on broader and broader the energy becomes
So that's it's a very fundamental limit when you work it through and there's this grid paper
Ultimate physical limits to computation which was set alight MIT back in 2000. This is a freely available online
Physics is physics, but this papers 2000 and things have moved on quite a bit interview 2
But the point he's making here in fact is he talked about having the ultimate laptop and in fact when he means the ultimate
Laptop. He's not talking about the limit. This is the important thing
That's the engineering limits, and then there's the pure physical limits his ultimate laptop is a plasma at
just a
stupidly high temperature
And that's what his ultimate laptop comes down to and even he talks about let's reach in terms of the density of information
What happens if we get to a density of?
Information which is comparable to the type of effects we have to consider when we're thinking about black holes
We are not talking about where the current semiconductor
Wherever it seemed gonna be in 20 or 30 years were thinking about where our hard limits where for an incredibly advanced civilization
Where are they gonna stop and?
It turns out that if you think about the uncertainty principle
Which sets this this fundamental limit in terms of the time scale, but 10 to the 50 per second, right?
So this is operations. It's not so much clock speed so it's more prison to flops
What's this day of the are the moment for flops
Thank you for asking me that question cuz I look that up because being a lowly physicist. I wasn't entirely certain so the cray are
Reasonably confident that by 2020 we'll be at the point where we have exa flops
I believe let me just check that yeah one extra
Flop by 2020 so exaflop so EXA is 10 to the 18 so 10 to the 18
floating point logic operations per second
There are some suggestions by 2030 will have zetas flops so 10 to the 21
operations per second
Whereas our ultimate physical limit in terms of what Lloyd has suggested 10 to the 50?
right so
that's so 50 compared to 21 doesn't seem like a big number 10 to the 50 compared to 10 to the 21 is a
Huge huge number in fact if you work it through
so we're about I don't know let's say we're off order and meat are shown in terms of height if you compare us to the
diameter of the observable universe
It's 26 orders of magnitude so 10 to 26 is compared to ten to the twenty-nine
So what were we are closer to the size of the observable universe the 92 billion light-years?
Then-current computing technology is from the limit. Yeah from the limit, so we've got a long long way to go
My little question is why have you got some pink D poppers on the corner?
So if you if you start this off and it but you'd see it disappears energy
And it comes to arrest and what's happening there was that Energy's leaking out into the environment
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Computing Limit - Computerphile

8 Folder Collection
林宜悉 published on March 28, 2020
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