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