Computing Limit – Computerphile
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Computing Limit – Computerphile


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 science 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 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 computing 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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