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August9,1985

Contents

2495

1. Parallel Computers
2. Reducing the Energy Loss

Questions and Answers

ー︑3. Reducing the Size

1

The Computing Machines in the Future
Nishina Memorial Lecture
given at Gakushuin, Tokyo, August 9, 1985
Richard P. Feynman
California Institute of Technology, Pasadena, California, U.S.A.

・

It s a great pleasur
e and an honor to be here as a speaker inmemorial for a scientist that I have respected and admired as much as
Prof. Nishina.

To come to Japan and talk about computers is likegiving a sermon to Buddha. But I have been thinking about computers
and this is the only subject I could think of when invited to talk.
The first thing I would 1ike to say is what I am not going totalk about.

I want to talk about the future computing machines.

But

the most important possible developments in the future, are things
that I will not speak about. For example, there is a great deal ofwork to try to develop smarter machines, machines which have a better
relationship with the humans so that input and output can be made withless effort than the complex programing that s necessary today.

Thisgoes under the name often of artificial intelligence, but I don't likethat name. Perhaps the unintelligent machines can do even better than
the intelligent ones.

Another problem is the standardization ofprograming languages.

There are too many languages today, and it

would be a good idea to choose just one.

(I hesitate to mention thatin Japan, for what will happen will be that there will simply be more
standard languages; you already have four ways of writing now andattempts to standardize anything here result apparently in more
standards and not fewer.) Another interesting future problem that is
worth working on but I will not talk about, is automatic debugging
programs; debugging means to fix errors in a program or in a machine.
It is surprisingly difficult to debug programs as they get more

2complicated.
machines

Another direction of improvement is to make physicalthree dimensional instead of all on a surface of a chip.

That can be done in stages instead of all at once; you can haveseveral layers and then many more layers as the time goes on. Anotherimportant device would be a way of detecting automatically defective
elements on a chip, then this chip itself automatically rewiring
itself so as to avoid the defective elements.

At the present time

when we try to make big chips there are flaws, bad spots in the chips,
and we throw the whole chip away. But of course if we could make itso that we could use the part of the chip that was effective, it would
be much more efficient.

I mention these things to try to tell youthat I am aware of what the real problems are for future machines.
But what I want to talk about is simple, just some small technical,
physically good things that can be done in principle according to thephysical laws; I would like in other words to discuss the machineryand not the way we use the machines.
I will talk about some technical possibilities for making
machines. There will be three topics really.
One is parallel
processing machines which is something of the very near future, almost
present, that is being developed now.

Further in the future arequestions of the energy consumption of machines which seems at the
moment to be a 1imitation, but really isn t.

Finally I will talkabout the size; it is always better to make the machines smaller, andthe question is how much smaller is it still possible to make machinesaccording to the laws of Nature, in principle. 工 will not discuss
which and what of these things will actually appear in the future.
That depends on economic problems and social problems and I am notgoing to try to guess at those.

1. Parallel ComputersFirst about parallel programing, parallel computers, rather.
Almost a11 the present computers, conventional computers, work on alayout or an architecture invented by von Neumann, in which there is a3very large memory that stores al1 the information, and one central
location that does simple calculations.

We take a number from thisplace in the memory and a number from that place in the memory, send
the two to the central arithmetical unit to add them and then send theanswer to some other place in the memory.

There is, therefore,

effectively one central processor which is working very very fast andvery hard while the whole memory sits out there like a vast filingcabinet of cards which are very rarely used． 工 t is obvious that if
there were more processors working at the same time we ought to beable to do calculations faster. But the problem is that some one who
might be using one processor may be using some information from thememory that another one needs, and it gets very confusing. And so it
has been said that it is very difficult to work many processors inparallel. Some steps in that direction have been taken in the largerc<;>nventiona1 machines, what they ca11

vector processors .

Whensometimes you want to do exactly the same step on many different items
you can do that perhaps at the same time. The ordinary hope is thatthe regular program can be written, and then an interpreter will
discover automatically when it is useful

to

use

this

vectorpossibility. That idea is used in the Cray and in the super‑computers
in Japan.

Another plan is to take what is effectively a large numberof relatively simple (but not very simple) computers, and connect them
all together in some pattern. Then they can all work on a part of the
problem. Each one is really an independent computer, and they willtransfer information to each other as one or another needs it. Thiskind of a scheme is in a machine for example called Cosmic Cube, andis one of the possibilities; many people are making such machines.
Another plan is to distribute very large numbers of very simple
central processors all over the memory.

Each one deals with just asmall part of the memory and there is an elaborate system ofinterconnections between them.

An example of such a machine is theConnection Machine made at M.I.T.

It has 64,000 processors and asystem of routing in which every 16 can talk to any other 16 and thus
4000

routing

connection

possibilities.

It would appear thatscientific questions like the propagation of waves in some material

4might be very easily handled by parallel processing,

because what

happens in this part of space at a moment can be worked out locallyand only the pressures and the stresses from the neighbor needs to be
known for each section can be worked out at the same time, andcommunicate boundary conditions across.• That s why this type of designis bui1t for such a thing.

But it has turned out thaヒ very large

number of problems of all kinds can be dealt with in parallel.

Aslong as the problem is big enough so that a lot of calculating has tobe done, it turns out that a parallel computation can speed this up
enormously, not just scientific problems.
And what happened tρthe prejudice οf 2 years ago, which was thatthe parallel programing is difficult?

It turns out that what wasdifficult, and almost impossible, is to take an ordinary program andautomaticallyfigureout

how

to use the parallel computation

effectively on that program. Instead, one must start all over again
with the problem, appreciating that we have parallel possibility ofcalculation, and rewrite the program completely with a new attitude towhat is inside the machine. It is not possible to effectively use theold programs. They must be rewritten. That is a great disadvantage
to

most

industrial applications and has met with considerable

resistance. But, the big programs belong usually to scientists orothers, unofficial intelligent programmers who love computer scienceand are willing to start all over again and rewrite the program if・they can make it more efficient. So what s going to happen is that thehard programs, vast big ones, will first be programed by experts inthe new way, and then gradually everybody will have to come around,and more and more programs will be programed that way, and programmers
will just have to learn how to do it.

2. Reducing the Enerqy Loss
The second topic I want to talk about is energy loss incomputers.

The fact that they must be cooled is the limitation

apparently to the largest computers; a good deal of the effort is

5

N。、
、−

spent .
in cooling the machine.

Fig. lI would like to explain that this issimply a result of very poor engineering and is nothing fundamental at
all.

Inside the computer a bit of information is controlled by a wire

which either has a voltage of one value or another value.
calledone bit，

工t is

and we have to change the voltage of the wire fromone value to the other and have to put charge on or take charge off.
I make an analogy with water: We have to fill a vessel with water andget one level or to empty it to get to the other level. It's just an
analogy. If you like electricity better you can think more accurately
electrically. What we do now is analogous, in the water case, tofilling the vessel by pouring water in from a top level (Fig.1), andlowering the level by opening the valve at the bottom and letting it
all run out. In both cases there is a loss of energy because of thedrop of the water, suddenly, through a height say from top level where
it comes in to the low bottom level when you start pouring it in tofill it up again. In the cases of voltage and charge, there occurs thesame thing.
It s like, as Mr. Bennett has explained, operating an automobile
which has to start and stop by turning on the engine and putting on
the brakes, turning on the engine and putting on the brakes; each time
you lose power. Another way with a car would be to connect the wheels

6

Fig. 2

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Stop the car and speed up the flywheel saving the

Fig. 3energy, which can then be reconnected to start the car again. The
analogy electrically or in the water would be to have a u‑shaped tube
with a valve at the bottom in the center connecting the two arms of
the U (Fig.2). When it is full here on the right but empty on theleft with the valve closed, if we open that valve the water will slipout to the other side, and we close it just in time to catch it. Then
when we want to go the other way we open the valve again and it slips

・to the other side and we catch it. There is some loss and it doesn t
climb as high as it did before, but al1 we have to do is to put alittle water in to correct the little loss, a much smaller energy loss
than the direct fill method. But such a thing uses the inertia of thewater and the analogue 1.
n the electricity, is inductance. However it
is very difficult with the silicon transistors that we use today tomake up inductance on the chips.

So this is not particularly

practical with the present technology.
Another way would be to fill the tank by a supply which stays
only a little bit above the level lifting the water supply in time as
we fill it up (Fig.3), because then the dropping of t
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In the same way, we could use an

7

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so that the heat loss would not appear at the position of thetransistor, or would be small; it will depend on how high the distanceis between the supply and the surface as we fill it up. This method
corresponds to changing the voltage supply with time (Fig.4). So if
we would use a time varying voltage supply, we could use this method.
Of course, there is energy loss in the voltage supply, but thatis all located in one place, that is simple, and there we can makeone big inductance. This scheme is called ・hot clocking ，because thevoltage supply operates also as the clock which times everything.

And

we don't need an extra clock signa1 to time the circuits as we do inconventional designs.
Both of these last two devices use less energy if they go slower.
If I try to move the water supply level too fast, the water in the・tube doesn t keep up with it and I have a big drop. So to work I mustgo slowly. Again, the U‑tube scheme will not work unless that central
valve can open and close faster than the time it takes for the waterin the U‑tube to s1ip back and forth. So my devices are slower. I ve
saved an energy loss but I ve made the devices slower.

The energy

loss multiplied by the time it takes for the circuit to operate is8constant.
But nevertheless, this turns out to be very practicalbecause the clock time is usually much larger than the circuit time
for the transistors, and we can use that to decrease the energy. Also
if we went, let us say, three times slower with our calculations, we
could use one third the energy over three times the time, which isnine times less power that has to be dissipated. Maybe it is worthit.

Maybe by redesigning using parallel computations or otherdevices, we can spend a little longer than we could do at maximum
circuit speed, in order to make a larger machine that is practical andfrom which we could still get the energy out.
For a transistor, the energy loss multiplied by the time it takes
to operate is a product of severa1 factors (Fig.5): (1) the therma1energy propotiona1 to temperature, kT; (2) the length of thetransistor between source and drain, divided by the velocity of theFelectrons inside (the thermal velocity 百五） ;(3) the length of thetransistor in units of the mean free path for collisions of electrons
in the transistor; and finally (4) the total number of the electrons
that are inside the transistor when it operates. All of these numbers
come out to tell us that the energy used in the transistor today issomewhere around a bi11ion or ten bi11ions or more times the therma1energy kT. When it switches we use that much energy.
It is verylarge amount of energy.

工t is obviously a good idea to decrease thesize of the transistor. We decrease the length between source anddra,in, and we can decrease the number of the electrons, and use much

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It also turns out that a smaller transistor is much

faster, because the electrons can cross it and make their decisions toswitch faster. For every reason, it is a good idea to make thetransistor smaller, and everybody is always trying to do that.
But suppose we come to a circumstance in which the mean free path
is longer than the size of the transistor, then we discゐver that the・transistor doesn t work right any more. 工t does not behave the way we
expected. This reminds me, years ago there was something called thesound barrier・ Airplanes cannot go faster than the speed of soundbecause, if you design them normally and try to put them in thatspeed, the propeller wouldn t work and the wings don't lift andnothing works correctly.

Nevertheless, airplanes can go faster than

the speed of sound. You just have to know what the right laws areunder the right circumstances, and design the device with the correctlaws. You cannot expect old designs to work in new circumstances.
B u t ~ designs can work in a
主主 circumstances, and 工 assert that it isperfectly possible to make transistor systems, that is to say morecorrectly, switchingsystems,computingdevices

in

which

the

dimensions are smaller than the mean free path. I speak of course in
principle and I am not speaking about actual manufacture.

Therefore,

let us discuss what happens if we try to make the devices as sma11 as
possible.

3. Reducing the Size
So, my third topic is the size of computing elements and now I
speak entirely theoretically.

The first thing that you would worry

about when things get very sma11, is Brownian motion; everything isshaking and nothing stays in place, and how can you control thecircuits then?

And if the circuits did work, it has a chance ofaccidentally jumping back. But, if we use two volts for the energy ofthis electric system which is what we ordinarily use, that is eighty
times the thermal energy (kT=l/40 volt) and the chance that something
jumps backward against 80 times thermal energy ise, the base of the10

natural logarithm, to minus eighty power, or 10‑43•

What does thatmean? If we had a billion transistors in a computer (which we don • t・have, we don t have that many at all), working all of them 1010 times
a second, that i̲s, tenth of a nanosecond switching perpetually,
operating for 10

seconds, which is 30 years, the total number of28
switching operations in that machine is 10 and the chance of one of〆‑43them going backward is only 10; there will be no error produced by・

thermal oscillations whatsoever in 30 years. 工f you don t like that,use 2.5 volts and then it gets smaller. Long before that, the real
failure will come when a cosmic ray accidentally goes through thetransistor, and we don't have to be more perfect than that.
However, much more is in fact possible and I would 1ike to refer
you to an article in a most recent Scientific American by Bennett andLandauer.

工t is possible to make a computer in which each element,each transistor, can go forward and accidentally reverse and still thecomputer will operate.

All the operation in succession in thecomputer go forw
ard or backward. The computation proceeds for a while
this way and then it undoes itself, uncalculates, and then goesforward again and so on. If we just pull it along a little, we canmake it go through and finish the calculation by making it just alittle bit more likely that it goes forward than backward.
It is known that all the computations can be made by putting
together some simple elements like transistors; or, if we be morelogically abstract, a thing for instance called NANO gate (NANO means
NOT‑AND).

It has two wires in and one out (Fig.6). Forget the NOT

first. What is ANO? ANO is: The output is 1 only if both input wires
are 1, otherwise the output is 0
. NOT‑ANO means the opposite. The
output wire reads 1 (i.e. has the voltage level corresponding to 1)
unless both input wires read l, if both input wires read 1 then the
output wire reads O (i.e. has the voltage level corresponding to 0).
Here is a litモle table of inputs and outputs. A and Bare inputs and
C is the output. Unless A and Bare both 1, the output is 1 otherwise0. But such a device is irreversible．

工nformation is lost.

If I

・

only know the output, I cannot recover the input. The device can t
be expected to flip forward

and thencome back and compute

1
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correctly anymore. Because if we know for instance that the output is・

now 1, we don t know whether it came from A=O, B=l or A=l, B=O or A=O,
B=O and it cannot go back. Such a device is an irreversible gate.
The great discovery of Bennett and, independently, of Fredkin is that
it is possible to do computation with a diffferent kind of fundamental
gate unit, a reversible gate unit. I have illustrated their ideawith this unit which I could call a reversible NAND or whatever． 工tha!
:: three inputs and three outputs (Fig.7l. Of the outputs, two, A'
and B', are the same as two of the inputs, A and B, but the third
input works this way: C ls the same as C unless A and B are both 1.
Then it changes whatever C is.

For instance, if C is

1

it is

changed to O, if C is O it is changed to l only if both A and Bare1.

If you put two in succession, you see

through, and if

C

A

and

B

will gois not changed in both it stays the same or if C

is changed twice it stays the same.
No information has been lost.

So this gate reverses itself.

It is possible to discover what

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went in if you know what went out.
A device made entirely with such gates will make calculations if
everything moves forward, but if things go back and forth for a while
and then eventually go forward enough it still operates correctly. If
th色 thingミ flip back and then go forward later it is still all right.
It's very much the same as a particle in a gas which is bombarded by
the atoms around it, usually goes nowhere, but with just a little
pull, a little prejudice that makes a chance to move one way a little
higher than the other way, the thing will slowly drift forward andreach from one end to the other, in spite of the Brownian motion thatis made. So our computer will compute provided we apply a force ofdrift to pull the thing more likely across the calculation. Although
it is not doing the calculation in a smooth way, but calculating likethis,forward and backward, it eventually finishes the job. As withthe particle in the gas, if we pull it very slightly, we lose very

13

little energy, but it takes a long time +‑.
o get to one side from theother． 工 f we are in a hurry, and we pull hard, then we loose a lot ofenergy.

And the same with this computer. If we are patient and go

slowly, we can make the computer operate with practically no energy,
even less thankT per step, any amount as small as you like if you

have enough time.

But if you are in a hurry, you must dissipate

energy, and again it s true that the energy lost to pull the
calculation forward to complete it multiplied by the time you areallowed to make the calculation is a constant.
With these possibilities how small can we make a computer?
big must a number be?

How

We al1 know we can write numbers in base 2

as strings of "bits each a one or a zero. But how small can I write?
Surely only one atom is needed to be in one state or another todetermine if it represents a one or a zero. And the next atom could
be a one or a zero, so a little string of atoms are enough to hold anumber, one atom for each bit. (Actually since an atom can be in morestates than just two we could use even fewer atoms, but enough islittle enough!)
So now for intellectual entertainment we consider whether we
could make a computer in which the bits writing is of atomic size, inwhich a bit is for example whether the spin in the atom is up for 1 or
down for O. And then our transistor changing the bits in different
places would correspond to some interaction between some atoms, whichwil.
l change their states.

The simplest would be a kind of 3‑atominteraction to be the fundamental element or gate in such a device.
But again, it won t work right if we design it with the laws
appropriate for large objects. We must use the new laws of physics,
quantum mechanical laws, the laws that they are appropriate to atomic
motion.

And so we have to ask whether the principles of quantum

mechanics permit an arrangements of atoms so small in number as a few
times the number of gates in a computer that could still be put
together and operate as a computer.

This has been studied inprinciple, and such an arrangement has been found. The laws of quantum
mechanics are reversible and therefore we must use the invention ofreversible gates, that principle, that idea of Bennett and Fredkin,

14

but we know that's alright now. When the quantum mechanical situationis studied it is found that quantum mechanics adds no further
1imitations to anything that Mr. Bennet has said from thermodynamic
considerations.

Of course there is a limitation, the practicallimitation anyway, that the bits must be of the size of an atom and atransistor 3 or 4 atoms; the quantum mechanical gate I used has 3・atoms. （工 would not try to write my bits on to nuclei, I 11 wait till
the technological development reaches the atoms before I need to go
any further!)That leads us just with (a) the limitations in size tothe size of atoms, (b) the energy requirements depending on the time
as worked out by Bennett, (c) and the feature that I did not mention

・

concerning the speed of 1ight; we can t send the signals any fasterthan the speed of light. Those are the only physical limitations that
I know on computers.
If we make an atomic size computer, somehow, it would mean thatthe dimension, the 1inear dimension is a thousand to ten thousands
times smaller than those very tiny chips that we have now. It means‑11
that the volume of the computer is 100 billionth, 10of the present‑11
volume, because the transistor is that much smaller 10, than thetransistors that we make today. The energy requirement for a single
switch is also about eleven orders of magnitude smaller than theenergy required to switch the transistor today, and the time to makethe transisions will be at least ten thousands times faster per stepof calculation.
So there is plenty of room for improvement in thecomputer and 工 leave you, practical p告 ople who work on computers, thisas an aim to get to. I underestimated how long it would take for Mr.
Ezawa to translate what I said, and 工 have no more to say that I have
prepared for today. Thank you!

・

I will answer questions if you d like.

1
5

Questions and Answers

Q: You mentioned that one bit of information can be stored in one
ato
m, and I wonder if you can store the same amount of information in
one quark.
A: Yes. But we don t have control of the quarks and that becomes areally impractical way to deal with things. You might think that what

・

I am talking about is impractical, but I don t believe so. When I am
talking about atoms, I believe that someday we will be able to handle
and control them individually. There would be so much energy involvedin the quark interactions it would be very dangerous to handle becauseof the radioactivity and so on.

But the atomic energies that I am

talking about are very familiar to us in chemical energies, electricalenergies, and those, that I am speaking of, are numbers that arewithin the realm of reality, I believe, however absurd it may seem at
the moment.
Q: You said that the smaller the computing element is the better.
But，工 think equipments have to be larger, because•.
A:
You mean that your finger is too big to push the buttons? Is
that what you mean?
Q: Yes, it is.
A: Of course, you are right. I am talking about internal computers
perhaps for robots or other devices.

The input and output issomething that I didn t discuss, whether the input comes from looking
at pictures, hearing voices, or buttons being pushed. I am discussing
how the computation is done in principle, and not what form the output
should take.

It is certainly true that the input and the output

cannot be reduced in most cases effectively beyond human dimension.
It is already too difficult to push the buttons on some of thecomputers with our big fingers. But with elaborate computing problems
that take hours and hours, they could be done very rapidly on the verysmall machines with low energy consumption. That s the kind of

1
6

machine I was thinking of.
Not the simple applications of adding two
numbers but the elaborate calculations.
Q:

I would like to know your method to transform the informationfrom one atomic scale element to another atomic scale element. 工f you
will use a quantum mechanical or natural interaction between the twoelements then such a device wil1 become very close to Nature itself.
For example, if we make a computer simulation, a Monte Carlosimulation of a magnet to study critical phenomena, then your atomic
scale computer will be very close to the magnet itself. What are yourthoughts about that?
A: Yes. All things that we make are Nature. We arrange it in a way
to suit our purpose, to make a calculation for a purpose.

In a magnet

there is some kind of relation, if you wish, there are some kind ofcomputations going on just like there is in the solar system in a wayof thinking・But, that might not be the calculation we want to makeat the moment. What we need to make is a device for which we canchange the programs and let it compute the problem that we want tosolve, not just its own magnet problem that it likes to solve foritself.

I can t use the solar system for a computer unless it justhappens that the problem that someone gave me was to find the motionof the planets, in which case all I have to do is to watch.
There was an amusing article as a joke. Far in the future thearticle appears discussing a new method of making aerodynamical
calculations: In只 terid of using the elaborate computers of the day, theauthor invents a simple device to blow air past the wing. (Hereinvents the wind tunnel.)
Q: I have recently read in an newspaper article that operations of

the nerve system in a brain are much slo
wer than present day computers
and the unit in the nerve system is much smaller.

Do you think thatthe computers you have talked about today have something in common
with the nerve system in the brain?
A:

There is an analogy between the brain and the computer in that

there are apparently elements that can switch under the control of

17

others. Nerve impulses controling or exciting other nerves, in a waythat often depends upon whether more than one impulse comes in;something like an AND or its generalization.

The amount of energy

used in the brain eel1 for one of these transitions? I don t know thenumber. The time it takes to make a switching in the brain is verymuch longer than it is in our computers even today, never mind the
fancy business of some atomic computer. But, interconnection system
is much more elaborate.

Each nerve is connected to thousand othernerves, whereas we connect transistors to two or three others.
Some people look at the activity of the brain in action and seethat in many respects it surpasses the computer of today, and in manyother respects the computer surpasses ourselves. This inspires people
to design machines that can do more. What often happens is that anengineer makes up how the brain works in his opinion, and then designs
a machine that behaves that way. This new machine may in fact work
very well.

But, I must warn you that that does not tell us anything

about how the brain actually works, nor is it necessary to ever reallyknow that in order to make a computer very capable.

It is notnecessary to understand the way birds flap their wings and how thefeathers are designed in order to make a flying machine．

工t is notnecessary to understand the lever system in the legs of a cheetah,that is an animal that runs fast, in order to make an automobile withwheels that goes very fast. It is therefore not necessary to imitate
the behavior of Nature in detail in order to engineer a device which
can in many respects surpass Nature s abilities.
It is an interesting subject and I like to talk about it. Your
brain is very weak compared to a computer. I wil1 give you a seriesof numbers, one, three, seven, oh yes, ichi, san, shichi, san, ni, go,
ni, go, ichi, hachi, ichi, ni, ku, san, go. I want you to repeat themback.

But, a computer can taketen thousands numbers

and giveme them back in reverse every other one, or sum them or lots of things
that we cannot do.

On the other hand, if I look at a face, in a・

glance I can tell you who it is if I know that person, or that I don t
know that person.

But, we do not know how to make a computer system

so that if we give it a pattern of a face it can tell us who he is,18even if it has seen many faces and you try to teach it. We do not know
how to make computers do that, ヱ主主−Another interesting example is chess playing machines.

It isquite a surprise that we can make machines that play chess better thanalmost everybody in the room.
possibilities.

But, they do it by trying many many

If he moves here, then I could move here and he canmove there and so forth. They look at each alternative and choose thebest. Now, millions of alternatives are looked at.
chess player, a human, does it differently.

But, a masterHe recognizes patterns.

He looks at only thirty or forty positions before deciding what move
to make.

Therefore, although the rules are simpler in Go, machinesthat play Go are not very good, because in each position there are too
many possibi1ities to move and there are too many things to check andthe machines cannot look deeply. Therefore the problem of recognizing
patterns and what to do under the circumstances is the thing that thecomputer engineers (they like to call themselves computer scientists)
still find very difficult, and it is certainly one of the important
things for future computers, perhaps more important than the things I
spoke about. Make a machine to play Go effectively.
Q:

I think that any method of computation would not be fruitfulunless it would give a kind of provision on how to compose suchdevices or programs.
I thought the Fredkin paper on conservative
logic was very intriguing, but once 工 came to think of making a simple
program using such devices 工 came to a halt because thinking out sucha program is far more complex than the program itself.

I think we

could easily get into a kind of infinite regression because theprocess of making out a certain program would be much more complex
than the program itself and in trying to automate the process theautomating program would be more complex and so on.

Especially inthis case where the program is hard wired rather than being separated
as a software, I think it is fundamental to think of the ways ofcomposition.
A:

We have some different experiences.

There is no infinite

1
9regression; it stops at a certain level of complexity.

The machinethat Fredkin ultimately is talking about and the one that I was
talking about in the quantum mechanical case are both universal

.
￡
￡
l
E
1
2
.
込主主玉三 in the sense that they can be programed to do various jobs;
this is not a hard‑wired program; they are no more hard‑wired than an
ordinary computer that you can put information in, that the program isa part of the input, and the machine does the problem that it isassigned to do. It is hard‑wired but it is unive工sal like an ordinary
computer. These things are very uncertain but I found a minimum.

If

you have a program written for an irreversible machine, the ordinary
program, then I can convert it to a reversible machine program by adirect translation scheme, which is very inefficient and uses many
more steps. Then in real situations, the number of steps can be muchless.

But at least I know that I can take a program with a 2n stepsnwhere it is irreversible, convert it to 3 steps of a reversible
machine. That is many more steps.

I did it very inefficiently; I did・

not try to find the minimum. Just a way. I don t really think that
we 11 find this regression that you speak of, but you might be right.
I am uncertain.
Q: Won t we be sacrificing many of the merits we were expecting ofsuch devices, because those reversible machines run so slow? I am very
pessimistic about this point.
A:

They run slower, but they are very much smaller. I don t make itreversible unless I need to. There is no point in making the machine
reversible unless you are trying very hard to decrease the energy
enormously, rather ridiculously, because with only 80 times kT theirreversible machine functions perfectly. That 80 is much less than
910
the present day 10 or 10 , so I have at least 10 improvement inenergy to make, and can sti1
1 do it with irreversible machines!

・

That s true.

That s the right way to go, for the present.

I

entertain myself intellectually for fun, to ask how far could we go主主principle, not in practice, and then I discover that I can go to a
fraction of a kT of energy and make the machines microscopic,
atomically microscopic.

But to do so, I must use the reversible

20physical laws.

Irreversibility comes because the heat is spread overa large number of atoms and can't be gathered back again. When I makethe machine very small, unless I allow a cooling element which is lotsof atoms, I have to work reversibly. In practice there probably wil1
never come a time when we will be unwilling to tie a little computer10
to a big piece of lead which contains 10 atoms (which is still verysmall indeed), making it effectively irreversible. Therefore I agreewith you that in practice, for a very long time and perhaps forever,
we will use irreversible gates. On the other hand it is a part of theadventure of science to try to find a limitations in al1 directions
and to stretch a human imagination as far as possible everywhere.
Although at every stage it has looked as if such an activity wasabsurd and useless, it often turns out at least not to be useless.
Q: Are there any limitations

from the uncertainty principle?

Are

there any fundamental limitations on the energy and the clock time inyour reversible machine scheme?
A: That was my exact point. There is no further limitation due toquantum mechanics.

One must distinguish carefully between the energy

lost or consumed irreversibly, the heat generated in the operation of
the machine, and the energy content of the moving parts which might be
extracted again.

There is a relationship between the time and theenergy which might be extracted again. But that energy which can beextracted again is not of any importance or concern. It would be like2

asking whether we should add the mc , rest energy, of all the atoms
which are in the device. I only speak of' the energy lost times thetime, and then there is no limitation. However it is true that if you
want to make a calculation at a certain extremely high speed, you haveto supply to the machine parts which move fast and have energy butthat energy is not necessarily lost at each step of the calculation;
it coasts through by inertia.
A (to no Q): Could I just say with regard to the question of uselessideas? I d like to add one more. I waited, if you would ask me, but
you didn t.

So I answer it anyway. How would we make a machine of21such small dimension where we have to put the atoms in special places?
To
day we have no machinery with moving parts whose dimension isextremely small or atomic or hundreds of atoms even, but there is no
physica1 1imitation in that direction either. And there is no reason
why, when we lay down the si1icon even today, the pieces cannot bemade into little islands so that they are movable.

And we could

arrange smal1 jets so we could squirt the different chemicals on
certain locations. We can make machinery which is extremely small.
Such machinery will be easy to control by the same kind of computercircuits that we make.

Ultimately, for fun again and intellectualpleasure, we could imagine machines tiny like few microns across 凶 lth
wheels and cables all interconnected by wires, silicon connections, sothat the thing as a whole, a very large device, moves not like the
awkward motion of our present stiff machines but in a smooth way of
the neck of a swan,which after al1 is a lot of 1ittle machines, thecells a11 interconnected and al1 controlled in a smooth way.
can t we do that ourselves?

Why