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00:00Roger Penrose
00:29is the Rouse-Ball Professor of Mathematics
00:31at Oxford University.
00:34He's also a distinguished physicist
00:35who collaborated with Stephen Hawking
00:37on the work which transformed our understanding
00:40of the origins of the universe.
00:42His recent work on computers, minds and the laws of physics
00:46has explored questions of profound philosophical importance.
00:59I believe that some of the most challenging questions
01:04facing scientists in the coming century
01:06will arise out of the nature of the human mind.
01:10I've become preoccupied with a growing belief
01:12that human intelligence can be replicated artificially
01:15in a computer.
01:18It is a fascinating and compelling idea
01:21which, if true, could offer humanity
01:23almost limitless opportunities.
01:25I believe it is an idea
01:29which attracts only to deceive.
01:46Everywhere we go today,
01:48we are surrounded by things
01:49using what's called artificial intelligence.
01:52cameras and video recorders use it
01:54to make decisions for us
01:56how to focus, engage exposure
01:58or record the right program
02:00from the television set.
02:02New generations of sophisticated electronic machines
02:05can diagnose their own problems
02:07and prescribe remedies.
02:08All over the world, scientists are at work
02:17on projects which mimic aspects of human intelligence
02:20giving machines a limited capability
02:21to make their own decisions.
02:26Here scientists are developing a surveillance machine
02:29that reproduces the human ability to track motion.
02:32No one claims that any of this work
02:38will actually replicate human intelligence
02:40in its entirety.
02:41At the moment, everyone agrees
02:43that so-called artificial intelligence
02:45is only partial intelligence.
02:47But some scientists, proponents of what is known
02:55as strong artificial intelligence,
02:57believe this process will, one day,
02:59go much further
03:00and replicate human intelligence fully.
03:03This is a materialist view
03:05where the brain and everything in it,
03:07consciousness, soul and all,
03:09is just physical material.
03:11I think within perhaps 50 years,
03:17machines as intelligent as human beings
03:19but different in many detail will exist.
03:24Sometime after that,
03:25possibly after several generations
03:28of scientists of the robotic variety
03:31work on the problem,
03:33it may become possible
03:34to scan a human brain in sufficient detail
03:39and with sufficient understanding
03:41to replicate its function in other hardware.
03:45So it may be possible essentially
03:46to read out a human personality
03:48and install it
03:49in some kind of future supercomputer.
03:53And then you would, in fact,
03:55have transplanted the soul of a person
03:57into a machine.
04:03What especially excites me
04:04about this line of development
04:06is that it offers a way
04:08to break most of the bounds
04:10built into our bodies
04:12and our biological minds
04:13by transferring our mental skills
04:17into machinery
04:18and re-engineering them
04:20in a way that makes sense.
04:24We can do things like increase memory,
04:28increase computing speed,
04:30increase the skill repertoire.
04:31We can also build bodies
04:33which can live in many places
04:34that biological bodies certainly could not.
04:37and it would allow us to do things,
04:42us in this expanded sense,
04:44that now we can't even imagine.
04:48It's a process of exploration of territory
04:51that's very interesting.
04:55The concept of building robotic progeny
04:59which will exceed us
05:00and essentially take over our functions
05:02and go where we could possibly
05:05not have gone before
05:06is really unprecedented in human history.
05:10There's nothing in our past
05:11that's really quite like it.
05:13So there is really no natural way
05:15to feel about it.
05:17The best we can do
05:18is to map it into things
05:21that are similar to things in our past.
05:23And there are several distinct categories
05:26of things we can map it into
05:27and some of them are bad
05:29and some of them are good.
05:31For instance,
05:32we can imagine
05:33that these artificial mines
05:36are really some kind of foreigner.
05:39They're the people of the next tribe
05:42coming down to take over our territory
05:44and throw us out.
05:46And then we feel very defensive about it
05:48and we would want to stop them at all costs.
05:51On the other hand,
05:53the idea that we're building things
05:56bit by bit
05:57and instilling in them
05:59our values, our skills,
06:01they're gradually becoming more competent,
06:03that's very much like
06:04the way we treat our children.
06:07So thinking of these things as our children
06:09makes them entirely a positive thing.
06:12It's natural that they should
06:13take over from us in the future.
06:15And in fact,
06:16our continued survival is through them.
06:19I'm a scientist
06:20and I too believe in the power
06:22of the human mind to make progress.
06:24But as a scientist,
06:26I also believe in certain inbuilt limitations
06:28on what can be scientifically achieved.
06:31And this is what I shall argue in this program.
06:34The human mind may have invented the computer,
06:37but it has not invented a computer
06:38that can invent a human mind.
06:41Nor will it ever be able to do so.
06:46The prospect of thinking machines
06:55has always fascinated us.
06:57They've long been a staple of popular culture
06:59in films ranging from
07:01Fritz Lang's futurist masterpiece,
07:03Metropolis,
07:04to the androids in modern action movies
07:06like Blade Runner and Terminator.
07:08Here human minds are like human bodies,
07:16just physical artefacts which can be
07:18and are replicated in computers.
07:20But the robot woman is still missing something.
07:31And most people seem to think
07:33this will always be missing.
07:35If you've got the machine programmed by an individual,
07:38the most you can hope to do
07:39is replace some of the emotions of that individual.
07:42But you're never going to have that total individuality,
07:46you know, the emotional side of it.
07:48I mean, it would be impossible, wouldn't it?
07:49Yeah, I think we've got a certain ingredient
07:51you just can't put into a machine, really.
07:54Surely there must be a secret ingredient,
07:56which is soul.
07:57Soul exists, yeah.
07:58And they don't exist in the microchip,
07:59so, yeah, we're pretty definite about that.
08:02It's a function within a human being,
08:06which has been gifted to us, so, yeah.
08:09What's inside, I don't know, human personality,
08:11you can never replicate that in microchips and stuff.
08:14I just don't see it happening.
08:16You couldn't put fuel in anyone.
08:17I don't know how they'd get around that.
08:20I think they'll never, ever be a machine like us,
08:22like humans.
08:23But they, I mean, they're not going to be far away,
08:26but they're just not going to...
08:27Otherwise we can quit now, can't we?
08:28You know?
08:29The distinction many make between physical human bodies,
08:38which they believe could be replicated in androids or whatever,
08:41and our spiritual minds, which they believe can't,
08:45is the philosopher's old dualistic distinction
08:47between mind and body.
08:49And this represents one argument
08:51against strong artificial intelligence.
08:53In order to see the inside of the brain,
09:00what we need to do is actually
09:01to separate the two hemispheres very carefully
09:05and pull them apart from one another,
09:09and that will enable us to have a look
09:10at the brain right from the inside.
09:13So as we begin to open it up,
09:16you can see the medial surfaces...
09:21Most of us find it difficult to reconcile our picture
09:23of the physical matter which makes up the brain
09:25with a vivid consciousness
09:27which appears to result from its action.
09:29...sobes of the brain, occipital, parietal, frontal,
09:33and then deep in the brain...
09:37Surely we feel mind and body
09:39must be totally distinct things.
09:42What link can there be
09:43between that spongy grey matter of cell and tissue
09:45and the glorious, soaring insights
09:48of human consciousness?
10:01Happiness, excitement, sensation.
10:05We might believe that someday
10:06it will be possible to reproduce
10:08the machine that is our body.
10:10But how could we ever hope
10:11to reproduce the mysterious consciousness within it?
10:20Essentially, this is a mystical
10:21and religious view of consciousness,
10:24a profound phenomenon we ordinary humans
10:26would never be able to explain
10:28in physical or scientific terms.
10:31However much progress science makes
10:33in explaining things,
10:34there's always something beyond that explanation.
10:37Where does life come from?
10:38What came before the Big Bang?
10:50In this view,
10:52consciousness can only come from God
10:53and only be understood spiritually,
10:56not scientifically.
10:57And if we can't understand it scientifically,
11:00how can we ever hope to replicate it?
11:02This is a powerful argument.
11:18It is not the reason why I reject the idea
11:20of strong artificial intelligence.
11:22I don't believe there is a straight choice
11:24between such a spiritual viewpoint
11:25and the materialism
11:27of the strong artificial intelligence position.
11:30I believe there's a third option.
11:31It is materialist in the sense
11:33that it argues for a physical
11:35and scientific explanation of consciousness.
11:37But equally,
11:38it is opposed
11:39to strong artificial intelligence
11:41in that it argues
11:43that a materialist view of the mind
11:44does not inevitably mean
11:45that human consciousness
11:47is capable
11:47of being replicated
11:48in a computer.
11:51My option is less obvious
11:52than the other two,
11:54perhaps because it seems
11:55to cut across so much
11:56of late 20th century conditioning.
11:59It depends neither on yearning
12:00for spirituality
12:01or on a sort of mechanistic approach
12:03to learning science
12:04which has become so familiar.
12:06Two and two are four
12:10Four and four are eight
12:14That's all you have
12:17on your business like mine
12:20Three is one.
12:22And the one you would place
12:23above the three
12:25which was the last figure
12:26that you used.
12:27The way we learn mathematics
12:29it is perhaps not surprising
12:31that many have come to believe
12:33that minds and computers
12:34work in the same way.
12:37The apparent link
12:37is a mathematical device
12:39for problem solving
12:40called an algorithm.
12:43You bring down the six.
12:46Much of elementary mathematics
12:47involves the following
12:49of step-by-step mechanical rules
12:51such as in adding
12:52or multiplying numbers together.
12:55These operations
12:56are instances
12:57of what are called algorithms.
12:58I'll leave you with 11.
13:01You then bring down the seven.
13:02725s come to 175.
13:06Examples of these
13:07systematic processes
13:08of calculation
13:08have been known
13:10since the times
13:10of the ancient Greeks.
13:12But it was not
13:13until the 1930s
13:15that the concept
13:16of a general algorithm
13:17was formulated.
13:17The man who formulated it
13:22launched a revolution
13:23that has transformed
13:24our world
13:25and created
13:26the arguments
13:27for strong
13:27artificial intelligence.
13:32Alan Turing
13:33was a mathematician
13:34of genius
13:35who helped break
13:36the Nazis' Enigma code
13:37at Bletchley Park
13:38during the Second World War
13:39and committed suicide
13:41in 1957
13:42after being persecuted
13:43for his homosexuality.
13:45He left behind
13:46a legacy of work
13:47which laid the foundations
13:48of the computer age.
13:59In the 1930s,
14:01Turing had set out
14:02to provide a general definition
14:03of an algorithm.
14:05His approach
14:05was highly imaginative.
14:07He conceived of
14:18an idealized machine
14:19whose mechanical components
14:21operating one after the other
14:22corresponded to the
14:24step-by-step procedures
14:25of an algorithm.
14:29The Turing machine
14:30is essentially
14:31any object
14:32which carries out
14:33any purely
14:34step-by-step
14:35mechanical
14:36calculational procedure
14:37and it is clear
14:38that in formulating
14:39his historic piece
14:40of mathematics,
14:42Turing was inspired
14:43by his vision
14:43of how the human mind
14:45worked.
14:46In his view,
14:47it was a Turing machine
14:49working algorithmically
14:51step-by-step.
14:52In this electronic age,
15:07computers are rapidly
15:08becoming man's best friend.
15:10After the war,
15:11the idealized concept
15:12of the Turing machine
15:13inspired scientists
15:14to make it into
15:15a physical reality
15:16in the form
15:17of computers.
15:20All modern computers
15:25derive from this.
15:26Serial computers,
15:28the kind most of us
15:28come across,
15:29which carry out
15:30computations
15:30one after the other.
15:37Parallel computers,
15:39whose massive power
15:40comes from their ability
15:41to run a multitude
15:42of computations
15:43at the same time.
15:44all work algorithmically.
15:52While most computers
15:53are programmed
15:54so-called top-down,
15:56where their algorithms
15:57are fixed and dedicated
15:58to solving specific
15:59given tasks,
16:01some are programmed
16:02so-called bottom-up.
16:04Here, their algorithms
16:05can modify themselves
16:06in an algorithmic way
16:08so that the computer
16:09can, in a sense,
16:11learn from experience
16:12and can, for example,
16:14recognize the ability
16:14of computers' patterns.
16:16Computers like this
16:17mimic the neural activity
16:19and architecture
16:20of the human brain.
16:22But essentially,
16:23they are still
16:24just acting out algorithms.
16:28The algorithm
16:29is a universal concept
16:31which applies to everything
16:32which works mechanically.
16:34And whatever a Turing machine
16:36is made up of,
16:37silicon chips
16:37or old tin cans,
16:39it will always work
16:40in an algorithmic,
16:41computational way.
16:44Even the spongy grey matter
16:45of the brain
16:46could act as a Turing machine.
16:48And for the proponents
16:49of strong artificial intelligence,
16:51it not only could,
16:53it does.
16:54And that's all it does.
16:56The proponents of strong
17:03artificial intelligence
17:04argue that human intelligence
17:06acts according to
17:07algorithmic processes
17:08just like computers.
17:12When we start out,
17:13they say,
17:14we are like
17:15unprogrammed hardware.
17:16As experiences
17:24crowd in on us,
17:25we learn from them
17:26and process them,
17:28creating new algorithmic rules
17:29and programs
17:30as we go.
17:33According to this argument,
17:34we develop perceptual programs
17:36that allow us to read
17:37the physical world.
17:39We learn, for example,
17:40how to predict
17:41where an object
17:41that has disappeared
17:42will reappear.
17:43We learn to recognize emotions
17:55in others
17:56and in ourselves.
18:01We learn rules
18:03that enable us
18:04to live as social animals,
18:06learn to make sense
18:06of the world.
18:12Of course,
18:13this process
18:13does not mean
18:14we all end up the same,
18:16like a run of
18:16mass-produced computers.
18:19We are individuals,
18:20each with our own personality.
18:23The strong AI position
18:24argues that this arises
18:25because each
18:26and every one of us
18:27is subjected
18:28to so many different
18:29and varied experiences
18:30that the outcome
18:32of the algorithmic process
18:33each brain goes through
18:34is unique.
18:37This algorithmic process
18:38is obviously
18:39highly complex
18:40and sophisticated,
18:41so not even
18:42the most committed proponent
18:43of strong artificial intelligence
18:44believes computers
18:45are yet
18:46anywhere near powerful enough
18:48to replicate
18:49human intelligence.
18:52For them,
18:53we may not be there yet.
18:55It is just
18:55a matter of time,
18:57development
18:58of sufficiently powerful computers
18:59and of the right algorithms
19:01before computers
19:02will be able to replicate
19:03human intelligence
19:04and then race beyond it.
19:05and because in their view,
19:07thinking is computation,
19:09such computers
19:10will be conscious.
19:12I think it's reasonable
19:14to view a nervous system
19:15as an information processing device
19:17built according to its own
19:19peculiar rules
19:20and restrictions.
19:21I see no reason
19:29to believe
19:29that there are any
19:30hidden processes
19:32which cannot be
19:33emulated
19:34in one way or another
19:35in other kinds of hardware.
19:37I don't think
19:38there's any magic
19:39in the nervous system
19:40other than
19:41its very clever organization
19:43and its very large complexity.
19:45On the face of it,
20:07this might seem
20:08a persuasive argument.
20:10We have all experienced
20:11some kind of algorithmic thinking
20:12whenever we do
20:14a long division sum,
20:15or follow the instructions
20:16as to how to use
20:17a calculator to do it,
20:18for example.
20:20Yet,
20:21while there is no doubt
20:21that some aspects
20:22of thinking are algorithmic
20:24and therefore replicable
20:25in computers,
20:27I shall argue
20:28that there are critical aspects
20:30of our consciousness
20:31which do not fit
20:32and cannot ever be fitted
20:34into this computational picture.
20:45I like green
20:59because it makes me feel
21:03like slimer.
21:04I like green
21:08because it makes me feel comfortable.
21:15What is so special
21:17about human intelligence,
21:19consciousness,
21:20that it couldn't be replicated
21:21in a computer?
21:22As human beings,
21:25we experience the physical world
21:26through sensation.
21:27We can feel it.
21:30Take colours.
21:33Green, for example.
21:35We all know
21:36what the experience
21:37of green feels like.
21:38It makes me feel,
21:52erm,
21:53slimy.
21:54It makes you feel slimy?
21:56OK,
21:57what were you going to say,
21:58Jack?
21:58Fresh.
21:59Fresh.
22:00Alfie,
22:00what does it make you feel?
22:01It makes me feel
22:03nice and sleepy.
22:06It makes you feel sleepy.
22:08A computer-controlled robot
22:10could be programmed
22:11to respond to green,
22:12to pick out green materials,
22:14say,
22:14but that would not mean
22:16that the robot
22:16actually experiences green
22:18as the children do.
22:21Instinctively,
22:21we feel a computer
22:22couldn't actually experience
22:24anything at all.
22:27For the proponents
22:28of strong artificial intelligence,
22:30this is an unimpressive argument.
22:32There is no difference,
22:33they say,
22:34between actually experiencing green
22:36and behaving exactly
22:38as though
22:38one is experiencing green.
22:41Well,
22:41that's a philosophical argument
22:42which could go on
22:43until the end of time.
22:45But there are kinds
22:46of human understanding
22:47which I believe
22:48more unarguably
22:49and scientifically
22:50demonstrate
22:51that they cannot
22:52be properly simulated
22:53by any computational
22:55activity whatever.
23:00perhaps the most striking
23:02area of human understanding
23:04which cannot be totally
23:05simulated computationally
23:07is mathematics.
23:09This may seem odd
23:10as mathematics
23:11might be thought
23:12to be a quintessentially
23:13algorithmic science.
23:15In many areas,
23:16like the carrying out
23:17of long division,
23:17it is.
23:18But in others,
23:19it's quite a different story.
23:22Now,
23:22we've been looking
23:23at our times tables
23:24and we have noticed,
23:26or rather you have noticed,
23:27a very interesting pattern.
23:29In a very general
23:30and basic sense,
23:31although computers
23:32can follow rules,
23:34they can never understand
23:35those rules,
23:36which is what we can do.
23:38If we've got
23:39three groups of two,
23:40we can represent that
23:42like this.
23:43where I have now
23:51three groups
23:52of two.
23:53I've put them together
23:54in an order,
23:55but we've got them
23:56there.
23:57One,
23:57two,
23:58three,
23:58each group
23:59with two in.
24:00An example.
24:01How do we know
24:02that A times B
24:04will always equal
24:05B times A,
24:07where A and B
24:07are ordinary numbers?
24:10If we substitute
24:11actual numbers
24:12for A and B
24:12in each case,
24:13we can work it out.
24:15They also give us
24:16the same answer here,
24:18six.
24:19It is also clear
24:20that the computer
24:21can work this out as well.
24:23But how do we know
24:23that this is true
24:24for any A and B
24:25whatsoever?
24:27We don't even have
24:28to know that
24:28three times two is six
24:30to see that
24:31three times two
24:32is the same
24:33as two times three.
24:35We know
24:36that we have
24:37six crosses.
24:39They could have been
24:39sweets,
24:41apples,
24:41whatever
24:42in your problem,
24:43but we have
24:44six of them
24:44in both sets.
24:47Are these two groups
24:49the same?
24:50Are they the same?
24:51Look at them.
24:53Are they the same?
24:55Kia?
24:55Yes.
24:56Yes.
24:57We've got the same
24:59algos inside
25:00but they've been
25:01flipped over.
25:02Rather than flip
25:03this over...
25:04The children can see
25:05that it is
25:05and we can understand
25:07along with them.
25:08To us,
25:08it's obvious.
25:10Casper.
25:10Rotating it.
25:11We've rotated it.
25:13We've turned it
25:14or rotated it
25:15round
25:16to make this shape.
25:17Now imagine
25:29the numbers
25:30are much larger.
25:31We don't have
25:31to count them all.
25:38But if we know
25:39there are A rows
25:40and B columns
25:40then we know
25:42there will be
25:42A times B
25:43and B altogether.
25:49We can turn this
25:50round in our
25:50mind's eye
25:51and see
25:51that this must be
25:52the same
25:53as B rows
25:54and A columns.
26:03No matter
26:04how enormously
26:05big the numbers
26:05A and B
26:06we know
26:06intuitively
26:07that A times B
26:08will always
26:09equal B times A.
26:11But a computer
26:12can only work
26:13it with actual
26:14examples.
26:15And since there
26:16are infinitely
26:16many actual numbers
26:17no computer
26:18no matter
26:19how powerful
26:19would ever
26:21be able
26:21to finish
26:21the computation
26:22which would
26:23enable it
26:23to prove
26:24merely by calculating
26:25that A times B
26:26will always
26:27equal B times A.
26:30Of course
26:31we could
26:31program the
26:32general rule
26:33into the computer
26:33but it would
26:34not know
26:35independently
26:35of our telling
26:36it.
26:37It could not
26:37see as we
26:38can
26:38that the
26:39general rule
26:39must be true.
26:41Indeed
26:42we could
26:42tell it
26:42that sometimes
26:43A times B
26:44is not
26:45equal to B
26:46times A
26:46and the computer
26:47would have no
26:48way of telling
26:49that that was
26:50wrong.
26:52Now let's turn
26:53to something else
26:53in mathematics
26:54which computers
26:55can't cope with.
26:56The general problem
26:57of tiling
26:58the Euclidean plane.
27:01What you may ask
27:02is that?
27:02imagine a plane
27:09stretching away
27:10into infinity.
27:11The task
27:11is to decide
27:12whether it
27:13can be covered
27:13all the way
27:14out to infinity
27:15without gaps
27:16or overlaps
27:17using different
27:18kinds of geometric
27:19shapes
27:19or tiles.
27:20if we have
27:28just one
27:28shape of tile
27:29say this
27:30regular hexagon
27:31the answer
27:32is obviously
27:33yes.
27:33and if the shape
27:48is this
27:48irregular pentagon
27:50the answer
27:51again
27:51turns out
27:52to be yes.
27:52but if the shape
28:05is this
28:05regular pentagon
28:06the answer
28:07now is an
28:08obvious no.
28:14We can also
28:15consider combinations
28:16of tile shapes.
28:18If we allow
28:19the use of this
28:19four-pointed star
28:20as well as
28:21the regular pentagon
28:22then the answer
28:23is now
28:24yes.
28:26Though we do not
28:27ever literally
28:27cover the infinite
28:28plane
28:28when we see
28:29enough of the
28:30pattern
28:30we can become
28:31confident
28:31that it will
28:32cover the plane.
28:34We can see
28:34this.
28:37Could a computer
28:38be programmed
28:39to answer
28:39correctly
28:40yes or no
28:41to the question
28:42of whether
28:43a particular
28:43tile shape
28:44or combination
28:45would cover
28:46the plane?
28:47Being algorithmic
28:48in operation
28:49it would have
28:50to have a
28:50program
28:51rules to follow.
28:52what might
28:53they be?
28:55It's noticeable
28:56with the
28:56example so far
28:57that where the
28:58shapes successfully
29:00tile the plane
29:00in doing so
29:02they created
29:03repeating patterns.
29:10This insight
29:11could be programmed
29:12into the computer.
29:14It would know
29:14to answer yes
29:15if it detected
29:16that the pieces
29:17could be arranged
29:18in a way
29:19that produces
29:19repeating patterns.
29:21But does the
29:22answer yes
29:22occur only
29:23with shapes
29:24that create
29:24patterns that
29:25repeat?
29:27Look at this
29:28pair of shapes.
29:30The answer
29:30is yes.
29:31The shapes
29:32cover the plane
29:33but they do not
29:34create a repeating
29:35pattern.
29:35The computer
29:44would be stumped.
29:48It could use
29:49its brute
29:49computing power
29:50to keep trying
29:51the shapes
29:52to see if they
29:53could fit
29:53and create
29:54a repeating
29:54pattern.
29:56Failing in this
29:56the computer
29:57would wrongly
29:58answer that
29:58the shapes
29:59will not
29:59tile the plane.
30:00we could tell
30:03our computer
30:04that this
30:04particular kind
30:05of non-repeating
30:06arrangement
30:06also gives
30:07the answer
30:07yes.
30:08But that
30:09wouldn't solve
30:10the general
30:10tiling problem.
30:12To do that
30:13we would have
30:13to keep supplying
30:14new insights
30:15like this
30:16forever.
30:18But the
30:18machine's meant
30:19to be computing
30:19this, not relying
30:21on our insights.
30:23No computer,
30:24no matter how
30:25powerful,
30:26could ever be
30:26able to finish
30:27a computation
30:28which would
30:29enable it to
30:29solve the
30:30general tiling
30:30problem
30:31with the
30:31entire
30:32infinite
30:33plane.
30:34The solution
30:35is literally
30:36non-computable.
30:40What might
30:40the strong
30:41artificial
30:41intelligence
30:42people say
30:42to all this?
30:44Well, they
30:44might say,
30:45fine, why
30:46don't we just
30:46build into
30:47the computer
30:47all the rules
30:48that can be
30:49perceived by
30:50human beings?
30:51Then it would
30:52do as well
30:52as we can
30:53and do it
30:53a good deal
30:54faster and
30:54more accurately.
30:56And in any
30:57event, we
30:57humans work
30:58by such a
30:58set of rules.
30:59rules that
31:00we have
31:01built up
31:01not only
31:01by the
31:02process of
31:02logic, but
31:03also through
31:04millennia of
31:04experience and
31:05natural selection.
31:07Well, they
31:08might say
31:08that, but a
31:09remarkable
31:10theorem formulated
31:1160 years ago
31:12by a strange
31:14and brilliant
31:14magician proves
31:16that all the
31:16rules that
31:17can be
31:17perceived by
31:18human beings
31:19cannot be
31:20programmed into
31:21a computer.
31:21better.
31:22The Austrian
31:23mathematician
31:24Kurt Gödel
31:25was a genius,
31:26an eccentric,
31:27lonely man.
31:28He died at
31:28the age of
31:2971 from
31:29malnutrition.
31:31He had
31:31stopped eating
31:31because he
31:32believed his
31:33doctors were
31:33trying to
31:33poison him.
31:37But while
31:38working in
31:38Vienna at
31:39the age of
31:3925 in
31:401931, he
31:42transformed
31:43mathematics and
31:43logic with the
31:44profound and
31:45difficult work which
31:46will forever be
31:47associated with
31:48his name, the
31:49incompleteness
31:50theorem.
31:53Before this,
31:54mathematicians had
31:55been confident
31:55they were working
31:56inside a unified,
31:57complete system and
31:59that any
32:00mathematical truth
32:00within that system
32:01could eventually
32:02be known.
32:05Gödel destroyed
32:06this belief.
32:12Gödel's enigmatic
32:13and challenging
32:14theorem revolutionized
32:15the basis of
32:16mathematics in ways
32:17that are still
32:17being explored.
32:19One thing it
32:20demonstrates is
32:21that whatever set
32:22of mathematical
32:23rules we choose
32:23to define the
32:24action of a
32:24computer, provided
32:26we believe those
32:27rules are right,
32:28then we must also
32:29believe, perceiving
32:30to be actually
32:31true, another rule
32:32that is completely
32:33inaccessible to the
32:34computer.
32:35In other words,
32:37every formal
32:38mathematical system,
32:39every system based
32:40on algorithms, must,
32:42if sound and
32:43perceived to be
32:44sound, be incomplete
32:45and perceived as
32:47incomplete.
32:47there will always be
32:48some propositions
32:49it will be unable
32:50to prove, but which
32:51we can perceive to
32:52be true.
32:54Algorithms are not
32:55the answer to
32:55everything.
32:56They do not
32:57encompass all human
32:58insights.
32:59There are some
33:00areas of mathematics
33:00and hence of human
33:02understanding that are
33:03not susceptible to
33:04algorithms and so
33:05are inherently
33:06non-computable.
33:07people.
33:09But this is not the
33:10full extent of the
33:11importance of
33:11Gödel's theorem for
33:12my own arguments.
33:14Some wonderful
33:14insights that it
33:15contains provide
33:16critical support in
33:17other ways too.
33:23I believe Gödel's
33:24theorem provides
33:25wonderful insights into
33:26the nature of
33:27mathematical truth
33:28itself.
33:30If there's always
33:31another rule beyond
33:32any set of rules we've
33:33thought of at any
33:34given point, then the
33:36view that mathematics
33:37is invented by human
33:38intelligence must be
33:40wrong.
33:42I agree with Gödel
33:43that mathematics is
33:44not invented but
33:45discovered.
33:46It has an existence
33:47independent of human
33:48intelligence.
33:50He tells us the world
33:51of mathematics is out
33:52there anyway,
33:53irrespective of whether
33:55we're here or not.
33:59This follows the ideas
34:01of the ancient Greek
34:02philosopher Plato, who
34:03argued for the
34:04existence of a perfect,
34:06timeless world, an
34:07ideal world.
34:09He believed the
34:10apparently real world
34:11we experience can only
34:13ever be an imperfect
34:14shadow of this
34:15platonic perfection.
34:17We can continually
34:18uncover more of the
34:19truth of this ideal
34:20world through the use
34:22of intellect and
34:23insight, but we will
34:24never reach the end
34:25of the task.
34:27The platonic vision
34:28isn't confined to
34:29mathematics.
34:31A Bach fugue has
34:32much in it of a
34:33deeply personal and
34:34emotional nature, but
34:36it is also continually
34:37striving for perfection,
34:38an ideal platonic form.
34:43Many artists feel in
34:45their greatest works they
34:46are revealing eternal
34:47truths.
34:49Jorge Luis Borges, the
34:50Argentinian writer, said
34:52a famous poet is less of
34:53an inventor than a
34:55discoverer.
34:55But of all the forms of
34:59human intellectual
34:59endeavor, I believe it
35:01is mathematics, with its
35:02high degree of
35:03abstraction and
35:04conceptualization, that
35:06comes closest to
35:07embodying the
35:08platonic ideal.
35:12Plato's ideal world
35:14contains mathematical
35:15truths accessible to us
35:16through our intellect.
35:18The real world consists of
35:20tangible objects
35:21accessible to us in the
35:22ordinary physical way
35:23through our senses.
35:26So the concepts of a
35:28circle, or triangle, say,
35:30belong to the ideal
35:31platonic world, while
35:32their physical
35:33embodiment in
35:34architecture, say, is a
35:35less perfect but real
35:37physical manifestation of
35:39that ideal.
35:46It may seem that there is
35:47little real connection
35:48between these two things,
35:50one abstract, one
35:51physical.
35:52But I believe these two
35:53worlds are inextricably
35:55bound together, and it
35:56is on that relationship
35:57that the next stage of my
35:59argument depends.
36:00I believe there is a
36:22profound harmony between
36:24the physical, actual world
36:25we live in and the
36:26platonic ideal world.
36:28I believe this harmony is
36:30particularly significant
36:31in the case of the
36:32extraordinarily deep and
36:33integrated relationship
36:34that exists between
36:35mathematics, the abstract
36:37science of space, number
36:39and quantity, and
36:40physics, with its
36:41explanations of the
36:42workings of the
36:43physical universe.
36:44Beautiful language
36:46can take any more
36:49Beautiful language
36:52can take any more
36:55I can take any more
36:58I recognize many may feel
37:05this is a somewhat
37:06bizarre proposition
37:07that the extraordinarily
37:08complex workings of the
37:10physical world,
37:11everything from
37:11hurricanes to nuclear
37:12fission to terrifying
37:14fairground rides,
37:16can ultimately only be
37:17understood in terms of
37:18precise but abstract
37:19mathematics.
37:21Yet there is clear
37:21evidence for it.
37:29Perhaps the most striking
37:31demonstration is given by
37:32the most remarkable single
37:34scientific achievement of the
37:36twentieth century.
37:44Einstein's general theory of
37:46relativity formulated in 1915
37:48was a platonic theory,
37:51existing in an ideal world,
37:53beautiful in the
37:54magnificence of its
37:55mathematics, but
37:56unsupported by much in the
37:58way of observations of the
37:59physical world.
38:01Einstein arrived at it
38:02through extraordinary
38:03theoretical intuition and
38:05insight.
38:12It was only afterwards that
38:13observational evidence for the
38:15theory began to accumulate.
38:18During an eclipse in 1919,
38:25light was found to be
38:26displaced in accordance with
38:27the theory.
38:31Most strikingly, in 1964,
38:34astronomers at the Arecibo
38:35Observatory in Puerto Rico
38:36detected a double star
38:38system known as a binary
38:39pulsar, which emitted precise
38:42electromagnetic signals in a
38:44way that is now seen to be
38:45completely consistent with
38:47Einstein's theory.
38:48theory of relativity.
38:51Largely on the basis of these
38:52observations, the general
38:54theory of relativity has now
38:55become the most accurate of
38:57all physical theories,
38:59accurate to 14 significant
39:01figures, one part in a
39:03hundred million million.
39:06What mathematical theory
39:08supposed, physical observation
39:10has proved.
39:11The history of Einstein's general
39:15theory illustrates, I believe,
39:16the profound harmony between
39:19the worlds of mathematics and
39:20physics.
39:21What mathematics conceptualizes,
39:24physics demonstrates.
39:26I would expect to see a
39:27demonstration in the physical
39:28world of non-computability,
39:31which so far has been seen only
39:33in the abstract platonic world
39:35of mathematics.
39:36I would expect to see that
39:39non-computability actually
39:41reflected in physics underlying
39:43the activity of the world we live
39:44in, which includes the behavior of
39:47our brains.
39:48But is it?
39:49Physical theory currently operates
39:58on two levels of explanation.
40:01There is the level of classical
40:02physics, dealing with reasonably
40:04large-scale objects, things that
40:06we can actually perceive, like
40:08these fairground rides which
40:09harness known forces through
40:11familiar mechanics.
40:15Scientists like Newton, Maxwell,
40:17and Einstein have given us remarkably
40:19accurate explanations of how the
40:21physical world we experience
40:22operates.
40:24They reveal the world is built up
40:26of small individual particles
40:28acting on each other through
40:29continuous fields of force
40:31permeating space.
40:37The gravitational force governs
40:39the motions of planets and
40:40physical bodies, while the
40:42electromagnetic force controls the
40:44behavior of charged particles and
40:46explains the nature of light and
40:48radio waves.
40:51There are precise equations which
40:53describe how these fields and
40:54particles change over time, and
40:57these equations can be solved to any
40:59desired degree of precision by
41:01algorithmic computation.
41:03No non-computability here.
41:06So what are the other level of
41:07explanation?
41:12Physicists in the early years of this
41:14century developed the theory of quantum
41:15mechanics to provide an explanation for
41:18the behavior of matter at the
41:19molecular, atomic, and subatomic level,
41:23well below that which we can directly perceive.
41:32It describes nature by what is called the
41:33quantum state, where particles are considered as
41:36spread-out, wave-like structures, inextricably entangled with one another.
41:40It explains a wide range of phenomena from lasers to the
41:44colors and physical nature of substances.
41:48The quantum state evolves according to a very precise equation.
41:52Here, too, the equation can be accurately described by algorithmic methods.
41:56So the quantum level is also computable.
42:02If both the existing levels of physical
42:04explanation of the world are computable,
42:06then it might appear that there must be a serious flaw in the argument.
42:11After all, my claims resting on non-computability in mathematics,
42:15and also on my belief in the profound harmony between mathematics and physics,
42:20suggest that there will be elements of non-computability in the physical
42:24explanation of the world.
42:26And it might appear that this is not the case,
42:30as both the existing levels of physical explanation,
42:33the classical and the quantum,
42:35are completely computable.
42:37But there isn't really a contradiction here.
42:40That's because these two levels of explanation,
42:43good as they are,
42:44do not provide a complete framework
42:46for the explanation of the physical world.
42:48It is in the gap between them
42:51that a new theory of physics is needed,
42:54and where I believe
42:55the non-computability I predict for the physical world
42:58will be found.
43:01The development of quantum theory
43:03at the turn of the century
43:04by scientists like Bohr,
43:06Heisenberg, Schrodinger, and Dirac
43:08was a remarkable scientific achievement.
43:12But it raised as many questions as it answered.
43:14Quantum theory is very difficult to grasp
43:18because it posits a view of physical behavior
43:21which seems to run directly counter to common sense.
43:25At the classical level,
43:27although there is the possibility of many things happening,
43:31only one thing actually happens.
43:34But quantum theory argues
43:35that all the things that might happen
43:37actually happen together,
43:40existing in some strange kind of superposition.
43:43Something common sense
43:45and common experience
43:46tells us is impossible.
43:50One of the originators of quantum theory,
43:52the famous physicist Schrodinger,
43:54was particularly troubled by this discrepancy.
43:57He invented a thought experiment,
43:59much imitated,
44:00to illustrate the profound philosophical problems
44:03that arise as a result.
44:08Imagine my version of it.
44:09A ceramic cat is placed close to a large hammer,
44:13capable of smashing it to pieces.
44:19The hammer is released by a mechanism
44:21triggered by a quantum event,
44:24say the activating of a photoelectric cell
44:27by a photon emitted by some light source.
44:31In between is a half-silvered mirror.
44:33The photon may be reflected off this,
44:36in which case the cat survives.
44:40But the photon has an equal chance
44:42of passing through the mirror,
44:44activating the mechanism,
44:45and smashing the cat.
44:49Quantum theory tells us
44:50the photon is both transmitted through
44:52and reflected off the mirror,
44:55leaving the cat both smashed
44:56and not smashed at the same time.
44:58But this is absurd,
45:02for all our experience
45:04tells us that the cat
45:05must be in one state or the other.
45:10Quantum theory copes with this discrepancy
45:12by asserting that
45:13when a quantum event
45:14is magnified in this way,
45:16so that its effects become large,
45:18like smashing or not smashing a cat,
45:20then something happens
45:21on this journey
45:22from the microscopic to the macroscopic.
45:25That something
45:26is often referred to
45:28as the collapse of the wave function,
45:30when the quantum world
45:31of multiple possibilities
45:32becomes the classical world
45:34of actual outcomes.
45:40Schrodinger invented this thought experiment
45:42to demonstrate a gap
45:43between the explanations
45:45of quantum theory,
45:46operating at atomic
45:48and subatomic levels,
45:49and classical theory,
45:50which explains more massive phenomena.
45:53No one knows exactly
45:54how or why the wave function collapses,
45:57from the quantum world
45:58of multiple possibilities
45:59to the classical world
46:00of actual outcomes.
46:03So it seems to me
46:04that there is clearly a need
46:05for a new physical theory
46:07to bridge the two existing levels
46:09of explanation.
46:10And it is in this bridge
46:12that I believe
46:13we will find the elements
46:14of non-computability
46:15my argument predicts.
46:17We are a long way off
46:20from any formulation
46:21of such a theory.
46:23But there is already evidence
46:24that suggests
46:25that it must operate
46:26in the workings of the brain.
46:30The conventional picture
46:31of brain action
46:32is one of classical level physics,
46:35with the brain cells
46:35known as neurons
46:36carrying and switching
46:38electric signals
46:39through an elaborate network.
46:42This looks very like
46:43the classical model
46:44of a computer,
46:45with the neurons
46:46acting as the computer's
46:47transistors and wires.
46:49But this does not provide
46:51the support it might appear to
46:53for the strong AI position.
46:55For this is not all
46:57there is to the brain.
47:00Deep below the level of neurons
47:01lies a substructure
47:03known as the cytoskeleton,
47:05with filaments
47:05of tube-like fibers
47:07known as microtubules,
47:09acting in complicated ways,
47:11controlling the connections
47:12between one neuron and the next.
47:16The cytoskeleton operates
47:18at a level where
47:18quantum laws apply.
47:20But through the microtubules,
47:22it also influences
47:23the classical level world
47:24of the network of neurons.
47:27And it is at this transition level
47:29between quantum
47:30and classical physics
47:31where a new theory is needed.
47:34Not just for the operation
47:35of the brain,
47:36but for much else as well.
47:39A theory where there will be found
47:40the elements of non-computability,
47:42I predict.
47:44I believe this theory
47:45will surely emerge one day.
47:48In science,
47:50explanation is usually
47:51eventually followed
47:52the perceived need for it.
47:54And when it does,
47:55I believe we shall then have
47:57the physical support
47:58for my mathematical argument
48:00that non-computability
48:02is an inherent feature
48:03of our world
48:04and our consciousness
48:05that perceives it.
48:07and that computers
48:08will thus never
48:10be able to replicate
48:11such human consciousness.
48:14What's one way
48:15of saying this then?
48:18Lawrence.
48:19Two lots of three.
48:33It may be one day
48:34computers will appear
48:35to learn to think
48:36and exhibit intelligent actions,
48:38but they will never
48:39possess consciousness.
48:41Whatever the mind is,
48:43however it gives rise
48:44to human intelligence
48:45and consciousness,
48:46it must be something
48:47that is inextricably
48:48intertwined
48:49with the very laws
48:50that govern the workings
48:52of our actual universe.
48:54And with the deep
48:54and intimate way
48:55these laws relate
48:56to the platonic
48:57mathematical realm.
48:59The place of mind
49:00in the universe
49:01is neither a gift
49:02from God nor a cosmic accident.
49:05It is bound up
49:06with the very foundations
49:07of the mathematical laws
49:09governing physical behavior.
49:13And because some
49:13of the most fundamental
49:14elements of those laws
49:15are non-computable,
49:17computers will never
49:18be able to do more
49:19than simulate
49:20the computable aspects
49:21of human intelligence.
49:23computers are immensely
49:32powerful tools
49:34that will achieve
49:34even greater powers
49:35in the future.
49:37Incredibly powerful
49:38computers, yes.
49:40But as for replicating
49:41human intelligence,
49:43they are the delusion
49:44of the emperor's new mind.
49:46A copy of the transcript
49:59of this programme
50:00is available by sending
50:01a cheque or postal order
50:02for three pounds
50:03payable to Channel 4
50:04to Penrose,
50:06P.O. Box 4000,
50:08London W36XJ.
50:11And if you'd like
50:11to know more about
50:12the Channel 4 Science Club,
50:13please phone 0222 575 444
50:18from Monday to Friday
50:19during office hours.
50:22Next Sunday's Equinox
50:23gets behind the wheel
50:24of the Japanese car industry
50:25to discover just how they do it.
50:28That's next Sunday at 7.
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