0:00

You're listening to the Stephen

0:02

Wolfram podcast, an exploration of

0:04

thoughts and ideas from the

0:07

founder and CEO of Wolfram

0:09

Research, creator of Wolfram Alpha

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and the Wolfram Language. In

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this ongoing Q&A series, Stephen

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answers questions from his live

0:19

stream audience about science and

0:22

technology. This session was originally

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broadcast on January 10th, 2025.

0:27

Let's have a listen. science

0:29

and technology Q&A for

0:32

kids and others. So I

0:34

see a variety of questions

0:36

here. Let me see what I

0:38

can do with them. Well, first

0:41

one, Lana says, in class

0:43

we learned that light behaves

0:45

both as a wave and

0:47

a particle. How is that

0:49

even possible? Okay, so

0:52

there's a long history to

0:54

this. People wondered what

0:56

light is. And starting,

0:59

well, by 300 years

1:01

ago, people were arguing

1:03

a lot. Is light

1:05

a series of little

1:07

packets of light? Or

1:10

is light a wave like

1:12

a wave on the surface

1:14

of water, but a

1:17

wave somehow of

1:19

something electromagnetic? They

1:21

thought in some medium.

1:24

Well, what happened?

1:26

This is a slightly

1:28

complicated

1:30

story. So I guess

1:32

we should think about

1:34

how we observe things

1:37

about light, and

1:39

that's perhaps the

1:41

place to start.

1:43

So when light is, when

1:46

we're detecting light,

1:49

there's the question

1:51

of... Are we detecting something which

1:53

behaves like a particle where it's like,

1:55

boom, we just detected a particle, a

1:57

photo on a light, boom, we detected

1:59

another... and so on, or

2:02

is it instead something

2:04

where we're saying we're

2:06

just finding the intensity

2:08

of some wave that's changing

2:11

continuously with time?

2:14

So what happens is

2:16

that there are certain kinds

2:18

of things where what one

2:21

detects of light is sort

2:23

of the particle-like. character

2:26

and there are other

2:28

places where what one

2:31

detects is a wave-like

2:34

character. How can it

2:36

be both a wave and a

2:38

particle? Well, here's a

2:40

way to start thinking

2:43

about that that isn't

2:45

quite right, but it's

2:47

a beginning at least. And

2:49

it would be to say, well,

2:51

let's, it's the best way

2:54

to do this. Boy, this is

2:56

a, this is surprisingly

2:59

tricky. The, think about

3:01

it this way. Just imagine

3:04

you have lots and

3:06

lots of photons, lots

3:08

and lots of particles

3:11

of light. Well, in, together,

3:14

those can, for example, have,

3:16

be, there can be

3:18

more, there can be

3:20

less and so on.

3:22

So, for example, when

3:25

we have... Yeah, this

3:27

is a little

3:29

tricky. Okay. We

3:31

can explain this

3:34

in kind of the

3:36

way the formalism

3:39

works from

3:42

quantum mechanics,

3:45

but again, that's

3:47

a little tricky.

3:50

Boy, this is... I'm telling

3:52

you... these kinds of Q&As

3:54

is that the questions that

3:56

seem to me the most

3:58

obvious are the ones that

4:00

turn out to be the

4:02

hardest answer. And this one,

4:04

let's first of all, let's

4:06

talk about phenomena where what

4:08

light is like as a

4:10

wave, what light is like

4:12

as a particle, and then

4:14

we'll talk about how those

4:16

two mix together. So as

4:18

a wave, what's happening is

4:20

that light is electric field,

4:22

a magnetic field, both varying

4:24

rapidly. in fact varying about

4:26

a trillion times per second.

4:28

That's what visible light has

4:30

electric fields and magnetic fields

4:32

varying that quickly. And it

4:34

turns out that there's a

4:36

way that you can have

4:38

kind of a freely propagating

4:40

combination of electric and magnetic

4:42

fields that wiggle that quickly

4:44

and they travel in a

4:46

certain direction. So it's... You

4:49

are just having, there's, again,

4:51

one of the things that

4:53

confused people for a long

4:55

time is that other kinds

4:57

of waves are, exist in

4:59

a medium. So for example,

5:01

a water wave, it's the

5:03

water is going up and

5:05

down, but there's water there,

5:07

and it's the thing that's

5:09

going up and down, or

5:11

a sound wave, is regions

5:13

of compression. and rarefaction in

5:15

air. There are air molecules

5:17

squashed together, there are air

5:19

molecules moved further apart, that's

5:21

what sound waves are like.

5:23

People sort of assumed that

5:25

light waves would be the

5:27

same kind of thing, that

5:29

there would be this change

5:31

of electric field, change of

5:33

magnetic field, and that that

5:35

would exist in some medium.

5:37

They called it the ether.

5:39

And up through the end

5:41

of the 19th century, that's...

5:43

pretty much how people assumed

5:45

that light worked, that it

5:47

was kind of like instead

5:49

of being a compression and

5:51

rarefaction of air molecules, of

5:53

a gas, it was kind

5:55

of these distortions of this

5:57

thing that was called the

5:59

ether. Now it turned out

6:01

that in 1900 there was

6:03

this experiment done, the Michelson

6:05

Morley experiment, which kind of

6:07

demonstrated that in the most

6:10

obvious way of there being

6:12

an ether, just some kind

6:14

of material that filled the

6:16

universe and where the Earth,

6:18

for example, was moving relative

6:20

to that medium. that that

6:22

such a thing did not

6:24

exist. And so what had

6:26

to be going on was

6:28

that there was sort of

6:30

disembodied electrical magnetic fields that

6:32

just existed independent of anything,

6:34

just existed and moved through

6:36

even a vacuum. That was

6:38

the picture. It was that

6:40

picture that led, for example,

6:42

its relativity theory, and that

6:44

was kind of trying to

6:46

make consistent the idea of

6:48

there is no ether. It's

6:50

just disembodied electricity and magnetism

6:52

that's leading to light, for

6:54

example, and the characteristics of

6:56

that, making that consistent with

6:58

the laws of mechanics and

7:00

space and time was what

7:02

led to special activity in

7:04

1905. Well, this idea that

7:06

it's sort of a disembodied

7:08

electric and magnetic field abstractly

7:10

defined That has been the

7:12

dominant view of how kind

7:14

of light works. It's a

7:16

little more complicated than that.

7:18

The idea that there isn't

7:20

really a medium in which

7:22

the thing exists isn't really

7:24

the story in modern quantum

7:26

field theory. kind of a

7:28

constant kind of zero point

7:31

fluctuation everywhere in the universe

7:33

there are all kind of

7:35

quantum fluctuations happening and what's

7:37

happening when you have something

7:39

like light is that you

7:41

have extra stuff beyond the

7:43

quantum fluctuations that's made of

7:45

the same stuff that makes

7:47

the quantum fluctuations. In that

7:49

model it's all sort of

7:51

disembodied electromagnetic field that both

7:53

makes the quantum fluctuations and

7:55

makes the actual light that

7:57

we see. Actually in our

7:59

model of physics now in

8:01

the last few years our

8:03

physics project, things become a

8:05

bit more concrete. And we

8:07

actually have this kind of

8:09

model of space, and we

8:11

have models that we don't

8:13

yet know exactly how they

8:15

work, of things like photons

8:17

that sort of do exist

8:19

in the context of something

8:21

that isn't like the ether

8:23

that people imagine in the

8:25

19th century, but it is

8:27

this kind of medium, this

8:29

thing that makes up space

8:31

that is the thing in

8:33

which things like photons like

8:35

photons exist. We're sort of

8:37

back to that same kind

8:39

of idea, and we don't

8:41

have to just say, oh,

8:43

there's the mathematics of the

8:45

electromagnetic field, and that's what

8:47

determines the structure of light.

8:49

It can be described in

8:52

a slightly more kind of

8:54

almost mechanical way. And by

8:56

the way, as I mentioned,

8:58

in modern fancy quantum field

9:00

theory, that's effectively what's happening

9:02

as well. Okay, so the

9:04

the idea that so this

9:06

idea of sort of light.

9:08

as a wave is this

9:10

notion of sort of disembodied

9:12

electrical fields varying? As I

9:14

said, there's the slightly more

9:16

concrete versions of that that

9:18

show up in quantum field

9:20

theory and now even more

9:22

so in our physics project.

9:24

What effect does it have

9:26

when light behaves like a

9:28

wave? Well, one feature of

9:30

waves is they can go

9:32

up and they can go

9:34

down. And if you have

9:36

two trains of waves coming

9:38

along and you end up...

9:40

in a situation where the

9:42

peak of one wave, one

9:44

train of waves is sort

9:46

of coming to the same

9:48

place as the trough of

9:50

the other train of waves,

9:52

those two will cancel each

9:54

other out. There will be

9:56

destructive interference of those waves.

9:58

And that's a phenomenon that

10:00

you see in light. You

10:02

see that there can be

10:04

two sources of light, and

10:06

if they are producing waves

10:08

that are out of phase

10:10

like that, so that the

10:13

peaks of one sort of

10:15

are the same places of

10:17

the troughs of the other.

10:19

then you will get destructive

10:21

interference. An example of something

10:23

related to that is the

10:25

phenomenon of diffraction. So let's

10:27

just talk about what these

10:29

light waves are kind of

10:31

like. If you have a

10:33

source of light, it will

10:35

be producing, well, a source

10:37

of light that is sort

10:39

of a carefully enough organized

10:41

source of light. So a

10:43

laser is an example of

10:45

such a thing that produces

10:47

coherent light. what will happen

10:49

is there'll be a series

10:51

of peaks of this of

10:53

the collection magnetic field for

10:55

the light and there'll be

10:57

kind of at every there'll

10:59

be a peek a trough

11:01

a trillion times a second

11:03

or so and that what

11:05

if if you have that

11:07

source a long way away

11:09

what you'll find what what

11:11

you'll observe is just a

11:13

collection of so-called plane waves

11:15

basically the the front of

11:17

those waves. Well, so if

11:19

you have a point source

11:21

of light, you'll have waves

11:23

that come out in a

11:25

sphere around that point source

11:27

of light. But if you're

11:29

far enough away, then you're

11:31

on this kind of shell

11:34

of the sphere, and at

11:36

a particular place, it'll seem

11:38

like it's just a flat

11:40

part of the sphere, because

11:42

the sphere, you're, you're, the

11:44

place where you're looking is

11:46

small compared to the radius

11:48

of the sphere. And so...

11:50

you'll have this kind of

11:52

series of wave fronts that

11:54

will be kind of a

11:56

plane as a series. of

11:58

sort of flat planes of

12:00

where the electric field is

12:02

largest. Okay, so what you

12:04

might have happened is you've

12:06

got something where you've got

12:08

some light and it's coming

12:10

through, it comes through a

12:12

hole, for example. And you

12:14

might think, okay, there are

12:16

these, these sequence of plane

12:18

waves, they get to this

12:20

hole, it goes through and

12:22

wherever. you can, wherever sort

12:24

of the light wasn't blocked

12:26

by the things that weren't

12:28

the hole, it'll keep going

12:30

and wherever there was, it

12:32

was blocked, it won't go

12:34

through. Well, there's a phenomenon

12:36

of diffraction. Diffraction is that

12:38

light always spreads a bit.

12:40

Once it's gone through that

12:42

hole, the light always spreads

12:44

out to the sides. And

12:46

it does that because when

12:48

you're thinking about this, the

12:50

effectively, it will. Again, this

12:52

is kind of complicated. The

12:55

way to think about how

12:57

light is moving is that

12:59

one way to think about

13:01

it is the light reaches

13:03

some particular place and wherever

13:05

it gets to, that's a

13:07

source of new light. So

13:09

when light is moving through

13:11

a medium like a crystal

13:13

or something, that's literally what

13:15

happens. The light is absorbed

13:17

by one atom. then it's

13:19

reemitted by that atom very

13:21

short time later, then it's

13:23

absorbed by another atom, and

13:25

that's how it moves through

13:27

the crystal or whatever, is

13:29

continuous or through water or

13:31

any material, it's continuously being

13:33

absorbed and reemitted. And so

13:35

when it's reemitted, the reemission

13:37

effectively, it is reemitted equally

13:39

in all directions. And so

13:41

what you get is that

13:43

you're forming kind of, you

13:45

can think of the light.

13:47

as the kind of the

13:49

waves produced by the light

13:51

has been formed by adding

13:53

up lots of little spherical

13:55

waves. And if you have

13:57

lots of little... spherical waves

13:59

on the front of this

14:01

plane wave, they'll make another

14:03

plane wave. But if you're

14:05

at the edge of the

14:07

plane wave, if the plane

14:09

wave has got stopped by

14:11

kind of the edges of

14:13

this hole that it's going

14:16

through, at the edges of

14:18

that region, you'll still have

14:20

little spherical waves, but those

14:22

spherical waves that don't, that just

14:24

start sending light. away from

14:26

the direction that corresponded to

14:28

going straight through the hole.

14:30

In other words, the light

14:32

will be as it will

14:34

kind of spread out around

14:36

the direction it was already

14:38

going in. And that's the

14:40

phenomenon of diffraction. And that's

14:42

a typical phenomenon that comes

14:44

from the kind of wave character

14:47

of light. So that's one kind of

14:49

one phenomenon that goes from

14:51

sort of the wave side of

14:53

thinking about thinking about light.

14:55

that comes from the particle

14:57

side of thinking about light

14:59

is the photoelectric effect,

15:02

that you can have light that when

15:04

you shine light on some metal

15:06

or something, you can end up

15:08

in a situation where a little

15:10

piece of light causes an

15:12

electron to get ejected. And

15:15

it's like the light comes in

15:17

and there's a certain amount of

15:19

light and it just makes

15:21

one electron. get ejected. So

15:23

it's kind of like it's

15:25

not half an electron because

15:27

there's no notion of half

15:29

an electron, it's the electron gets

15:32

ejected. And so there, kind

15:34

of from the particle nature

15:36

of the electron, you're kind

15:38

of working backwards to say,

15:40

well, okay, that might seem

15:42

like it's kind of a

15:44

particle of that electron be

15:46

ejected. And so that's kind of

15:48

the sort of particle character

15:51

of light showing up in that

15:53

case. And a lot of devices that

15:55

we have today, the best way

15:57

to think about them is a

15:59

photon of light is absorbed

16:01

and some electrical effect, some

16:04

electron is ejected or something,

16:06

that's what happens in a

16:08

typical, the sensor of a camera,

16:10

things like this. Again, it's a

16:12

little more complicated than that, and

16:14

it has to do with the

16:17

way that a photon can kind

16:19

of move an electron from one

16:21

energy level to another. It can,

16:24

by absorbing the photon, the electron

16:26

gets the energy that the photon

16:28

had. Okay, so those

16:31

are two cases, diffraction

16:33

and interference in general

16:35

is a wave-like phenomenon,

16:38

and things like kicking

16:40

an electron out as

16:42

a particle-like

16:44

phenomenon. So the

16:46

question is, sort of, how do

16:49

those merge together? And the

16:51

way to think about this,

16:53

I think, is the way it's done

16:55

in quantum mechanics.

16:58

is to say really what we're talking

17:00

about is a kind of probability

17:02

for the, for there to be

17:04

an electromagnetic effect

17:07

right here. It's the, in quantum mechanics,

17:09

it's usually called the

17:12

wave function. And it's the

17:14

thing that gives you the,

17:16

the, sort of, the, it's

17:18

not quite the probability, it's

17:20

the so-called quantum amplitude, which

17:22

is not quite the probability,

17:24

which is not quite the

17:27

probability. It's kind of the,

17:29

it gives you a kind

17:31

of a quantum mechanical

17:34

version of the chance

17:36

that you find a

17:39

piece of electromagnetic wave

17:41

at this particular point.

17:44

And what, what then one

17:46

has to think about

17:48

is how those

17:50

probabilities, those probabilities

17:52

kind of have

17:54

a character that

17:56

is like. a

18:00

wave, so maybe this is a way to

18:02

explain it. The mathematically

18:05

calculating the

18:07

probability gives you something

18:09

that makes the probability

18:11

vary in a wave-like way.

18:13

But that's just the

18:15

probability. What will sort of

18:18

actually happen is that there

18:20

will be a particular photon

18:22

that either is there or not.

18:24

There's a certain probability the

18:26

photon will be there.

18:28

What's actually there is either a

18:31

photon or not a photon. And

18:33

in fact, this is probably the

18:35

best way to explain this whole

18:37

story, is to think about the

18:39

wave as being a sort of a

18:42

wave that describes how the

18:44

probability of there being a

18:46

photon there varies with position

18:48

and time and so on.

18:50

And that's something that can

18:52

be described mathematically

18:55

by something that... is like the

18:57

waves that you see in

18:59

sound waves and things like

19:01

this. It's mathematically described in

19:04

that way, using equations that

19:06

look like the equations that

19:08

are used to describe

19:10

waves. But that's just

19:13

probabilities. In terms of

19:15

what's actually there, one can better

19:17

think about it as particles

19:20

of light. where there's a

19:22

probability of point two or

19:24

something, that means one-fifth of

19:27

the time there'll be a

19:29

particle there, and the rest of

19:31

the time there won't be. So

19:33

that's the first approximation

19:35

at least, is that the kind

19:38

of the wave-like character is

19:40

operating at the level

19:42

of individual particles. Now

19:45

unfortunately it's not as

19:47

simple as that. Unfortunately,

19:49

the... There's, yeah,

19:52

there's sort of,

19:55

there's a, it's really

19:58

partly. a question of

20:00

whether you're just basing what you're

20:03

talking about on the mathematics of

20:05

the theory or whether you're trying

20:08

to kind of have a mechanical

20:10

explanation of what's going on. By

20:12

the time you're trying to have

20:15

a mechanical explanation of what's going

20:17

on, I don't think that's doable

20:19

in anything other than our recent

20:22

physics project. And let me

20:24

see if I can give an indication

20:26

of how that works. Oh gosh, it's complicated.

20:30

I think this is going to be too

20:32

complicated. I think I need to think

20:34

about this offline to come up with

20:36

a good clean way to talk about

20:38

this. Roughly what I will say is that

20:40

in our physics project, the

20:42

thing that happens that is

20:44

sort of characteristic of quantum

20:46

mechanics is this idea that

20:49

there are many possible branches of

20:51

history for the behavior of the

20:53

universe and what you end up seeing

20:55

is the branching and merging of those

20:57

paths and phenomena... like interference,

21:00

are associated with kind

21:02

of things that happen in the

21:05

branch and emerging of those paths

21:07

of history. So one that's a

21:09

little bit confusing is

21:12

destructive interference, when

21:14

the peaks of one sort of

21:16

wave kind of combine with the

21:18

troughs of the other and you

21:20

get nothing there, so to speak.

21:22

And what happens, I think,

21:24

in our physics project is

21:26

something kind of tricky. which is

21:28

that the kind of parts of

21:30

history corresponding to those two

21:33

possibilities of the peaks and

21:35

the troughs, those parts of

21:37

history kind of get so

21:39

separated in this thing we call

21:41

branchial space that observers like us

21:43

never combine them. And so for

21:46

us, it's like, well, both of

21:48

these possibilities just disappeared because we

21:50

can't combine them together to say

21:52

this is the definite thing that

21:55

happened. This is complicated and we

21:57

certainly haven't worked the whole thing

21:59

out. Let me just

22:01

mention in terms of

22:03

waves and particles and so

22:06

on. It's pretty typical

22:08

that what, as you change the

22:10

kind of electromagnetic

22:13

radiation you're talking

22:15

about, that it behaves

22:17

more particle-like or more

22:20

wave-like. For example,

22:22

in a radio wave, there are

22:24

in a sense lots of... very

22:26

low energy photons associated with

22:28

the radio wave, and what's

22:30

most important is the kind

22:33

of collective probabilities of all

22:35

those photons being there or not,

22:37

and that can be thought of like this

22:39

wave, which has, you know, a wavelength that

22:41

might be afoot or more long. So that's

22:43

at the radio end of the

22:45

electromagnetic spectrum. As you go down

22:48

from radio waves, you get to

22:50

infrared, then you get to visible

22:52

light, and then you get to

22:55

ultraviolet. and then you get x-rays and

22:57

then gamma rays. As you go down

22:59

to x-rays and then gamma

23:01

rays, things are behaving much

23:03

more particle-like, because every individual

23:06

photon is packing a whole

23:08

bunch of energy. And so when

23:10

you, when that individual photon interacts

23:12

with your detector or whatever it

23:14

is, it does something very, very

23:16

definite. It's not like a whole

23:18

collection of lots and lots of

23:20

photons that are doing it. It's

23:23

that one photon. You can register

23:25

that one photon because it's packing

23:27

all that energy. In the case

23:29

of radio waves, every individual photon

23:31

has absolutely tiny energy. It's only

23:33

the collection of many of those

23:35

photons that can have an effect

23:37

that you can detect with your radio

23:39

antenna and so on. And in fact,

23:42

one of the features of detecting radio

23:44

waves is that you, all those photons

23:46

behave what's called coherently. That is... All

23:48

those photons are in the radio wave.

23:50

They're all making a little contribution, but

23:52

their contributions are all adding up. And

23:54

really, the only thing you get to

23:56

observe with an antenna or something like

23:59

that is all. those added-up

24:01

contributions. In the case of

24:03

gamma rays, for example, with that

24:05

one gamma ray photon that's packing

24:08

all that energy, its behavior is

24:10

really quite independent of the

24:12

behavior of other gamma ray

24:14

photons. The interaction between those

24:17

things is very small. It's

24:19

not, it's not, it's kind of one

24:21

photon at a time kind of thing,

24:23

whereas in the radio wave, it's the

24:26

whole sort of collective probabilities

24:28

that matter. Well,

24:30

another thing to mention is that

24:32

light particles, photons, are

24:35

not the only kinds of things

24:37

that have this kind of, it's

24:39

a bit like a wave, it's

24:41

a bit like a particle. Every

24:43

kind of particle has that

24:45

characteristic, electrons,

24:47

protons, all these kinds of

24:50

things. But they have a

24:52

certain characteristic wavelength that

24:54

corresponds to kind of

24:56

their... the scale on

24:58

which they're kind of

25:00

wave-like behavior observed, it's

25:02

called the DeBroy wavelength,

25:04

spelt to broadly, wavelength.

25:07

And what happens is that

25:09

that wavelength is, as the

25:11

mass of the particle

25:13

increases, that wavelength goes

25:16

down. And so the higher the

25:18

mass of the particle, the shorter

25:20

the wavelength, over which things

25:23

sort of behave in a

25:25

wave-like way, and show things

25:27

like diffraction. So for example,

25:30

in the case of electrons,

25:33

you can see electron diffraction,

25:35

but it's a small

25:37

effect compared to diffraction

25:40

with photons because of

25:42

the mass of the electron.

25:44

And that so, but

25:46

all particles. all the kinds of

25:49

standard particles what talks about have

25:51

this characteristic that in some sense

25:53

the sort of the probabilities of

25:56

where they are kind of have

25:58

wave-like characteristics whereas The oh you

26:01

can count them as one

26:03

proton, two protons, three protons

26:05

has a particle-like characteristic.

26:08

Sorry, that was a little

26:10

bit more complicated

26:12

than I expected. Let's

26:14

see, we have another question

26:16

here from Yahoo, saying my

26:18

teacher says there's no up or

26:21

down in space. Why is that

26:23

and how do astronauts navigate?

26:25

Well, if you're in orbit near

26:28

the Earth, There is an up and

26:30

down in the sense that there's

26:32

a way that's going towards Earth,

26:34

and there's a way that's

26:36

going away from Earth. But there isn't

26:38

an up and down in the sense

26:41

that it isn't the case that

26:43

one can define down by where things

26:45

fall to if you drop them. I

26:47

mean, on the Earth, if you drop something,

26:49

it will fall down. In orbit

26:52

around the Earth, if you drop something,

26:54

it won't go either up or up

26:56

or down. It will just stay... in

26:58

one place. Now why is that? Actually,

27:00

it's staying in one place

27:02

relative to you. You're moving

27:05

in this orbit. If it's low Earth

27:07

orbit, you're going at about 17,000 miles

27:09

an hour. And in a sense, you

27:11

are sort of falling in the gravity

27:14

of the Earth. And as you fall, you know,

27:16

by the time you've sort of fallen

27:18

to the Earth, you've already gone

27:20

over the side of the Earth.

27:22

And so you're actually just going

27:24

in this orbit around the orbit

27:26

around the Earth. And the whole

27:29

point is that the things

27:31

that are near you are

27:33

also going in that orbit.

27:36

And they are, they're,

27:38

they're, they don't move

27:40

towards the earth any

27:43

more or less than you

27:45

move towards the earth. And

27:47

so if you put that

27:50

eraser right in front of

27:52

your nose and your... on

27:55

the International Space Station or

27:57

something, it will stay right

27:59

there because... It is moving

28:01

relative to you. It's

28:03

not moving relative to

28:05

you. You're moving and it's

28:07

moving. And there's no,

28:09

and gravity is not

28:12

having, the effect of

28:14

gravity is that there's no

28:16

direct effect of gravity

28:18

on that other than that

28:21

it maintains both you and

28:23

it in orbit around the

28:25

Earth. Now in general. gravity

28:27

is produced by objects that have mass

28:29

or in general energy, and the earth

28:31

is a big such thing, the sun

28:33

is another big such thing, the amount

28:35

of gravity produced by something decreases

28:37

like the square of the distance

28:39

you are from the thing. You

28:42

can kind of see why that is.

28:44

It's kind of like imagine, and we

28:46

were just talking about particles and waves

28:48

and so on, there's yet another piece

28:50

to that picture, which is fields. We

28:52

talk about a gravitational field where

28:55

there is an effect. of gravity

28:57

from a massive object, but that

28:59

field is actually implemented in a

29:01

sense by lots of particles streaming

29:03

out, which can themselves be thought

29:05

of as associated with waves and

29:07

the particles that are relevant for

29:09

gravity of gravitons, and although we've

29:11

never observed one directly, we kind

29:14

of can think about gravity as

29:16

being sort of packaged into gravitons,

29:18

just as we can think about

29:20

electromagnetism as being packaged into photons.

29:22

And so in a sense, with

29:25

any massive object, there are all

29:27

these gravitons streaming out in all

29:29

directions. And that's the effect of the

29:31

presence of mass makes these gravitons

29:33

stream out in all directions.

29:36

A little bit confusingly, they're

29:38

not real gravitons, they're so-called

29:40

virtual gravitons, but let's put

29:42

that aside for a second.

29:44

Basically, they're streaming out in

29:46

all directions. So if you have this

29:49

ball of mass here, you've got

29:51

these things streaming out in all

29:53

directions, you can ask how many

29:55

of them if you are sort

29:57

of a, if you're at a

29:59

particular place. away from this ball of

30:01

mass, how many of these gravitons will

30:03

be, will hit you if you're

30:05

just in this little region far

30:07

away from this object? Well, if

30:09

you think about it, they're all

30:12

streaming outwards. And so the further

30:14

you are away from the object,

30:16

the less dense those gravitons will

30:18

be. Close to the object, they'll

30:20

all be that they'll be right

30:22

there, but they're just keeping streaming

30:24

out in straight lines. It's kind

30:27

of like some kind of... some

30:29

bursts coming out from the

30:31

massive object. And so if

30:33

you try to work out, well,

30:35

how many gravitons will hit you

30:37

if you have a fixed size

30:40

and you're close to the object,

30:42

some number, if you move further

30:44

away, how many will hit you?

30:47

Well, the way to think about it

30:49

is in terms of the surface

30:51

area of a sphere. So... The

30:53

volume of a sphere is four-thirds

30:55

pie R cubed, the surface area

30:58

is four pie R squared, and

31:00

that means that the R squared

31:02

is telling you that that's the,

31:04

that as a function of the

31:06

radius, that surface area is proportional

31:08

to R squared. And so

31:11

if you're looking at a single

31:13

part of that area, if you're

31:15

looking at a fixed size region

31:17

in that area, as the, as

31:19

the, as that sphere gets larger,

31:21

that fixed size area is a

31:24

smaller fraction of the whole sphere.

31:26

If the area of the whole

31:28

sphere is 4.5r squared, and you

31:30

have, let's say, a size 1

31:32

region on that sphere, the fraction

31:35

of the whole sphere will be

31:37

1 over 4.5r squared. And so

31:39

that's why the force of

31:41

gravity decreases like the square

31:44

of the distance, because it's

31:46

kind of all these gravitons

31:49

streaming out. And you... are sampling

31:51

one particular area, but as

31:53

they stream out, they're occupying

31:55

the whole area, but the area

31:57

that your sampling decreases the

32:00

fraction decreases like 1 over R

32:02

squared. And so that's what happens

32:04

is that the sort of force

32:06

of gravity goes down like 1

32:08

over R squared. The picture I

32:10

just told you, it's not quite

32:12

as simple as that in reality,

32:14

but that's a rough kind of

32:16

mechanical picture of what's going on.

32:18

Well that means if you're far away

32:21

from all objects that are

32:23

producing gravitons, producing gravity,

32:25

then there just won't be any

32:28

pull of gravity on you. And so

32:30

that's, and for example, if

32:32

you are somewhere in

32:35

space between galaxies, for

32:37

example, you're far away

32:39

from all the galaxies,

32:41

then there really won't

32:43

be much of a

32:45

pull of gravity on

32:47

you associated with any

32:49

of those galaxies, because

32:51

it's just too far away.

32:53

And so that's a, and

32:56

even in, so that... That's another

32:58

situation in which you just don't have

33:00

any gravity sort of the pulling on

33:02

you. Now, there's a little bit of trickiness

33:04

there because there's always a little

33:06

bit of force on things associated with

33:09

the expansion of the universe. In a

33:11

slightly complicated way, everything is being

33:13

sort of pulled outwards by the

33:15

expansion of the universe. That's sort

33:18

of a force a bit like

33:20

gravity, but you can think of

33:22

it as being... a force of

33:24

gravity because it's related to the

33:27

curvature of space-time, but it's a

33:29

sort of an additional force that's

33:31

independent of there being a galaxy

33:34

right there that's pulling on

33:36

you. Okay, so now a question will

33:38

be, well, how do you navigate

33:40

when, how do you know which way to

33:42

go if you're in space? And,

33:44

well, that's quite tricky, because

33:47

on the Earth, for example,

33:49

right now, Well, how do

33:51

you know where to go on

33:53

the earth? You could look

33:55

at the stars and

33:58

you could use a... You could

34:00

use something where you know where the

34:02

positions of the stars are and so

34:04

on. You know what time it is

34:06

that tells you where you are on

34:08

the Earth. In modern times, you'd use

34:10

GPS. GPS is a

34:12

collection of satellites orbiting

34:15

the Earth, where one knows where

34:17

the satellites are, and one can work

34:19

out any GPS receiver, works by

34:21

working out how far it is

34:23

away from each satellite. So if you

34:25

just have three satellites, you can triangulate,

34:27

you can say, oh, I know I'm

34:29

this distance away, you know, I'm 200

34:31

miles away from that satellite, I'm 500

34:33

miles away from that satellite, I'm 400

34:36

miles away from that satellite, I'm 400

34:38

miles away from that satellite, and you

34:40

can just sort of draw the lines

34:42

and figure out, well, I must be

34:44

exactly here. Well, for GPS to

34:47

work, one has to know where

34:49

the satellites are going to be,

34:51

and one has to be able

34:53

to measure that distance. The distance

34:55

is measured because the satellites produce

34:57

a radio signal where the radio

34:59

signal is constantly changing

35:01

and the receiver knows that

35:03

at this particular moment of time,

35:05

the signal as sent will have

35:07

been this. But because the receiver

35:10

receives it later, then it was

35:12

sent because it takes time for

35:14

the signal to travel from the

35:16

satellite to the receiver, the

35:18

receiver can just work out, oh, I'm off

35:20

my... I know, either receiver, know that

35:23

the time is exactly noon, let's

35:25

say, but the signal that

35:27

I'm receiving is the signal

35:29

that was sent at 1159 and,

35:31

you know, some amounts of

35:33

seconds or whatever, and therefore

35:36

I can work out, I

35:38

must be this distance away

35:40

from that satellite because that

35:42

signal is delayed by this

35:44

amount. So I can work out

35:46

where I am based on those satellites.

35:48

Okay. The GPS satellites are in

35:50

orbit, fairly low orbit around

35:53

the Earth. If you are far

35:55

away from the Earth, if you're

35:57

tooling off to Jupiter or something...

35:59

you don't get to use the GPS

36:01

satellites to find out where you are. Even

36:04

if you could detect the signals from

36:06

the GPS satellites, it's not really going

36:08

to be good enough because all those

36:10

GPS satellites are really close to the

36:12

Earth. They don't give you a good

36:14

way to sort of triangulate to know

36:16

where you are if you're near Jupiter.

36:18

So a typical thing that's been

36:20

done in deep spacecraft, but navigating is

36:23

to use stars. And to use the

36:25

fact that you know in which

36:27

direction you lock on to particular

36:29

bright stars, for some reason Canopus,

36:31

was one that was used at

36:33

least in the early Deep spacecraft.

36:35

And as one of the, you

36:37

lock onto those stars, you know

36:39

those stars are in exactly these

36:41

directions, and then you can again

36:43

use this kind of triangulation idea

36:45

to work out, well, if those

36:47

stars are in exactly those directions,

36:49

then either spacecraft must be right

36:51

here. There are slightly fancier techniques that

36:54

people have talked about. One of

36:56

them is to use pulsars, rapidly

36:58

rotating neutron stars that produce radio

37:01

signals, and the radio signals are

37:03

a bit like the GPS radio

37:06

signals in the sense that they

37:08

are continually, that they have sort

37:10

of a continual sequence of pulses.

37:13

They're not as nicely distinguished as

37:15

the pulses in GPS satellites, which

37:17

are specially built so that... essentially

37:19

at every moment you're seeing a

37:21

slightly different form of radio signal

37:23

so you can tell where in

37:26

the time series you are. But

37:28

the idea is to use the

37:30

kind of a rival time of

37:32

these different pulses from pulsars as

37:34

another kind of form of navigation.

37:36

But it's not such an easy

37:39

thing to find out where you

37:41

are in deep space. And as I say,

37:43

the main way you do it is by

37:45

just looking at the directions of these

37:47

different stars. Let's see. Okay,

37:50

well Craig asks, is

37:52

the universe as small

37:54

as it is big? That's

37:57

sort of an

37:59

interesting... question, where

38:01

are we in the scale of

38:03

the universe? So we are

38:05

a meter and a bit tall,

38:08

roughly. The universe is 10

38:10

to the 26 meters across.

38:13

So that's a one

38:15

with 26 zeros meters, or

38:17

if I can count it

38:19

down correctly, it would be

38:22

a billion, billion. Can

38:24

I do my arithmetic?

38:26

Yeah, it's about a

38:28

billion, billion. meters across.

38:30

And so that's how big it

38:33

is. Now the question is, as you

38:35

go down to greater levels of

38:37

smallness, how far do you have

38:39

to go down? Well, so for example,

38:41

an atom is about 10

38:44

to minus 10 meters across.

38:46

So that's a one 10

38:48

billionth of a meter across.

38:50

So if the universe is

38:52

a billion billion billion billion

38:54

meters across, an atom is

38:56

a 10 billionth of a meter across.

38:59

An atom is in a sense,

39:01

the universe is big compared

39:03

to the amount that an atom

39:06

is small, so to speak. If

39:08

you ask about a nucleus,

39:10

nucleus about 10 to the

39:13

minus 15 meters across, so

39:15

that's roughly a million billionth

39:18

of a meter across. So

39:20

that's, so we're kind of getting

39:22

down to, you know, we

39:24

got a million billion versus

39:26

a billion billion billion. So

39:28

we're getting down to a

39:31

slightly smaller level of smallness

39:33

there. But so that's the

39:35

size of a nucleus. Proton's

39:37

about the same size as a

39:39

nucleus. Big nuclei, a bit bigger protons,

39:41

depends on how you sort of

39:43

count the size of the proton,

39:45

because it's kind of a bit

39:47

of a fuzzy thing. But then you

39:50

might ask, well, what's even smaller

39:52

than a proton? What do we

39:54

even know about what happens on

39:56

sizes smaller than a proton? Well

40:00

we can use particle accelerators

40:02

to kind of probe the kind

40:04

of like giant microscopes that can

40:06

be used to kind of probe

40:08

what happens at shorter distances. So

40:10

I actually happen to mention

40:12

the phenomenon of diffraction, the

40:14

phenomenon that when you sort of think

40:17

light is going in a particular direction,

40:19

it will always spread out a bit

40:21

as a result of its wave nature.

40:24

And diffraction actually limits

40:26

the resolution of things

40:28

like microscopes. So, when if you

40:30

can't get to see with

40:32

the microscope something that's

40:34

smaller than the wavelength of

40:36

the light or whatever you're

40:39

using to make that observation,

40:41

it's sort of obvious that

40:43

that would be the case, because

40:46

in a sense, if what you're

40:48

detecting is the peaks and troughs

40:50

of that wave and you have

40:53

a thing... that's smaller than the

40:55

distance between those peaks and troughs.

40:57

It's like, it's not going to

41:00

have any effect on the

41:02

peaks and troughs. And so you

41:04

don't get to notice it. So

41:06

that's, if you're using visible

41:09

light, for example, which

41:11

has a wavelength 500

41:13

nanometers, that's about, that's,

41:16

well, it's large compared to the

41:18

size of an atom, which is

41:20

like a tenth of a nanometer.

41:22

And so visible light, you

41:24

can't make a visible

41:26

light microscope that will

41:29

see individual atoms, that

41:31

they're too small relative to

41:33

this big sort of fat-fingered

41:36

kind of light that is

41:38

trying to probe them. If you

41:40

want to see atoms, you have

41:42

to have something where the wavelength

41:44

of the thing you're using to

41:47

see them is smaller than the

41:49

size of atoms. And there are...

41:51

For example, in x-ray

41:53

crystallography, you can effectively

41:55

see positions of atoms by

41:58

using x-rays which have shorter...

42:00

wavelength, and the way that

42:02

x-rays are reflected from crystals

42:04

depends on the way that

42:06

the atoms are lined up

42:08

in the crystals, but it

42:10

needs a wavelength that is

42:12

comparable to the distance between

42:14

the atoms. So in any

42:17

case, generally you need kind

42:19

of higher energy particles. higher,

42:21

shorter wavelength particles to be

42:24

able to kind of probe

42:26

shorter distances and particle accelerators

42:28

are sort of an extreme

42:31

version of that producing particles

42:33

of very high energy and

42:35

therefore very small wavelength.

42:37

And so, but the smallest

42:40

distances that have been

42:42

probed with particle accelerators

42:44

directly are around 10 to

42:46

the minus 20 meters. So that's a,

42:48

whatever it is, roughly. a

42:50

hundredth of a billionth, billionth

42:52

of a meter. So again, the big side

42:55

is billion, billion, even that

42:57

small side is about billion,

42:59

billion. So we're off by

43:01

a factor of a billion there

43:03

on the small side. So what

43:05

happens even below the scale that

43:07

particle accelerators can see? Well, you know,

43:10

one question that comes up

43:12

is, what about electrons? How big

43:14

is an electron? Well, in

43:16

usual theories that have

43:18

existed... an electron is

43:21

infinitely small. Now there are

43:23

features of electrons where there are

43:25

kind of a, is a whole

43:27

cloud of photons around and so

43:30

on, and that big fluffy thing

43:32

is bigger than that. But

43:34

the core electron is

43:36

effectively of zero size in

43:38

the traditional theories of,

43:41

of, of, so that's, that's

43:43

kind of that, so far

43:45

as people have known electrons

43:47

of, Now as you go down to

43:50

sort of smaller and smaller distances,

43:52

things start to happen. For example,

43:54

the effects of quantum

43:57

mechanics start to be important

43:59

and if... of quantum mechanics even

44:01

start to be important on

44:03

the structure of space, and

44:06

there's a distance, the plank length,

44:08

about 10 to the minus 34

44:10

meters, which has, at which the

44:12

kind of, the quantum effects

44:14

on the structure of space

44:16

necessarily become important. We

44:18

usually think of space

44:20

as nice and uniform and,

44:23

and, and consistent, but... when

44:25

we're dealing with sort of

44:27

quantum mechanical space, it necessarily

44:29

becomes a very kind of

44:31

a place where lots of

44:33

variation is happening all the time.

44:36

So that's the plank length, 10

44:38

to 934 meters, is sort of more

44:40

on the small side than the 10 to

44:42

the 26 meters is on the big side

44:45

when you look at the whole universe.

44:47

In our models of physics, there

44:49

is structure... in space, distance is

44:52

quite small compared to the plank

44:54

length, perhaps the smallest 10 to

44:56

minus 100 meters. And in our

44:59

models, space is actually made of

45:01

this kind of network of discrete

45:03

elements. We can think of them

45:05

as atoms of space. There really

45:08

isn't, there's nothing in between, it's

45:10

just space is this network of

45:12

atoms of space. And the... effective

45:14

distance between those atoms of space,

45:17

even though there's no ambient space

45:19

in which we can talk about

45:21

distance, but what, when we line

45:23

up enough atoms of space and

45:26

their connections, we could sort of

45:28

deduce that the effective distance between

45:30

atoms of space maybe is around

45:32

10 to the minus 100 meters. So

45:35

in that picture, going down to the

45:37

smallest, one would be going down a

45:39

lot further than one has to get to

45:41

the whole size of the universe. from

45:43

us, from our one meter scale

45:45

size, up to the whole size

45:47

of the universe, is less than

45:50

going down to the elementary

45:52

length. So it's an interesting

45:54

question whether what structure might

45:57

exist in the universe

45:59

on very... small scales. We know

46:01

on very large scales we have galaxies,

46:03

we have clusters of galaxies, all

46:05

those kinds of things. On the

46:07

small scale we know we have

46:09

particles like protons and so on,

46:11

we have electrons, we don't know

46:13

how big those are in our

46:15

models of physics, they have to

46:17

have a definite size. In fact

46:19

my guess is that they are as

46:21

big as 10 to the 30th elementary

46:24

lengths. But 10th of the

46:26

30th elementary length is 10

46:28

to the minus 70 meters.

46:30

So absolutely tiny compared to,

46:33

for example, the size of

46:35

a proton. But that's some

46:37

kind of sense. But what

46:39

happens at these very, very,

46:41

very small scales and how

46:43

much structure there is there, we

46:46

just don't really know. And that

46:48

would be, yeah, so it

46:50

is interesting that we exist.

46:52

at this size that is

46:54

sort of intermediate between the

46:56

size of the universe and

46:58

the size of the smallest

47:01

things in the universe and

47:03

probably our experience of the

47:05

universe critically depends on that

47:07

sort of scale size of us

47:09

relative to biggest and smallest

47:11

so to speak but

47:13

interesting question. Okay let's

47:15

see. Okay so obvious is asking

47:18

when will we reach the

47:20

physical computer chip? size limit.

47:22

They say I heard in two or three

47:24

years. Okay, so what is a

47:26

computer chip made over? Computer

47:28

chip starts with a

47:30

very pure silicon crystal.

47:33

So it's basically, you know,

47:35

silicon is the one of

47:37

the main ingredients of rock,

47:40

silicon and aluminum of the sort

47:42

of main typical ingredients

47:44

of rock. Actually, silicon

47:46

is the number one ingredient.

47:49

And with great effort. Silicon

47:52

is purified and turned

47:54

into perfect crystals. Perfect

47:56

enough that there are very few

47:58

atoms out of... in a big

48:01

wafer of silicon. And you get

48:03

this, the atoms are all lined

48:05

up in this very particular array

48:07

that silicon crystals put

48:09

atoms into. And then what

48:11

happens when you make

48:14

a microprocessor, for example,

48:16

is that you are etching out

48:18

little channels that sort of serve

48:20

as wires out of that silicon,

48:22

and you're doping them with

48:24

atoms of other materials.

48:26

that have different numbers

48:29

of electrons associated

48:31

with them and so on. And

48:33

so the big issue in getting a

48:35

big sort of figure of merit

48:37

in making microprocessors is the

48:40

feature size, essentially how big

48:42

those wires can be. And

48:44

so sort of three nanometer

48:46

wire sizes is kind of

48:48

a sort of the high

48:50

end of what's achieved today.

48:52

And that means, so the actual

48:54

silicon atoms might be a

48:56

tenth of a nanometer across,

48:58

so that means we're talking

49:00

about 30 atoms across the

49:03

width of a wire. And the question

49:05

is, how do you etch something

49:07

at that size? Well, the wavelength

49:09

of light might be 500 nanometers.

49:11

It's way too big to be

49:13

able to etch something of that

49:15

size. And so you can't use

49:17

visible light. In the early

49:19

days when microprocessors were made,

49:22

Well, what was typically used

49:24

was ultraviolet light, which has

49:26

slightly shorter wavelength. But the

49:28

thing that's been done in more recent

49:31

times is to use x-rays and

49:33

electron beams and other things that

49:35

have shorter and shorter wavelength so

49:37

that they can successfully etch out

49:39

those very, very tiny wires. And

49:41

there's not really a limit to how

49:43

far you can go with that. You just

49:46

have to have higher energy particles.

49:48

Of course, you're going to reach

49:50

the point where the wires... are

49:52

comparable in width of the distance

49:54

between silicon atoms and then you're

49:57

really stuck. You can't go beyond

49:59

that. But then... Why does it matter how

50:01

wide the wires are? So one reason it

50:03

matters is because you want to

50:05

pack more and more components. So

50:08

roughly a transistor, which is sort

50:10

of the key ingredient of circuits, it

50:12

acts as a switch. A transistor

50:14

is roughly made by crossing two

50:17

wires. It's not quite that, but

50:19

roughly what happens is there's

50:21

usually in a so-called field

50:24

effect transistor, there's usually sort

50:26

of current flowing... from the

50:28

source side to the drain side, that's

50:30

sort of one wire, and then there's

50:32

a wire that goes across, that's the

50:34

so-called gate wire, and when you

50:36

put a voltage on that gate wire,

50:38

you prevent, you can prevent current from

50:40

flowing the other way. And so that

50:43

provides a switch, and by making just

50:45

a very small change of that voltage,

50:47

you can have a big effect

50:49

on the current, and so that

50:51

can be used to amplify things,

50:53

but... when you're making a modern

50:55

microprocessor, you might have a billion

50:57

of those little wire crossings that

50:59

make these components. And you want

51:01

those wire crossings to be, you

51:03

want to pack as many of

51:06

them as possible into a small region

51:08

for many reasons. Probably the

51:10

most important ultimate

51:12

reason is capacitance, basically

51:15

how much, how many electrons you

51:17

really have to slip around to

51:19

make. to send a signal, to

51:21

change the signal you're sending through

51:23

the wires. If there's a really

51:25

big sort of clump of electrons

51:28

there, then it's just more effort

51:30

and it takes longer and the

51:32

speed of the microprocessor will be

51:34

slower. But so that, and there

51:36

also effects, like if you make

51:39

two wires, be too close to

51:41

each other, you'll have sort of

51:43

the electrons going through one wire,

51:45

will affect the electrons going through

51:47

the other wire and so on. But you...

51:49

In general, you just want to

51:51

pack in more wires, more transistors, and

51:53

so on. And that's also important that

51:56

the capacitance effect is also important in

51:58

terms of the heat dissipation. that you

52:00

get and so on. You know,

52:03

you can't run your microprocessor so

52:05

hot that it melts the silicon,

52:07

for example, or even so hot

52:10

that the electrons and the dopant

52:12

atoms in the silicon kind of

52:14

start moving around. Then your microprocessor

52:17

will no longer work. But this

52:19

question about how do you pack

52:21

in more components? Well, one of

52:24

the things that tends to happen

52:26

right now is that a microprocessors

52:28

are made in many layers. I

52:31

don't know how many layers it

52:33

is these days. I'm going to

52:35

make a wild guess of 20,

52:38

but I'm not sure that's right.

52:40

But you're making these layers, but

52:42

fundamentally things are in two dimensions.

52:45

The things are wires are mostly

52:47

going, just in a plane, maybe

52:49

there'll be one that goes up

52:52

a bit. and so on. But

52:54

people have talked for 40 years

52:57

at least about making truly three-dimensional

52:59

microprocessors where there really are wires

53:01

going sort of equally well in

53:04

the up down direction as in

53:06

the sort of flat direction. That

53:08

hasn't happened yet and I think

53:11

there's just a lot of technical

53:13

difficulties in making that work. Now,

53:15

you know, in terms of... how

53:18

do you deal with sort of

53:20

getting very small wires, very small

53:22

numbers of electrons, there will be

53:25

limitations. For example, right now, a

53:27

single bit in a typical memory

53:29

chip, for example, or microprocessor, is

53:32

I think around 100,000 electrons. And

53:34

that's fine because with 100,000 electrons

53:36

you can be pretty certain about,

53:39

yup, we moved this 100,000 electrons

53:41

here and we moved them away

53:43

from there and so on. If

53:46

you got down to five electrons,

53:48

that would much less obvious. It'd

53:50

be much more like, well, did

53:53

they really all move there? Yeah,

53:55

a few of them kind of

53:58

were stragglers and they got left

54:00

behind, but maybe actually that bit

54:02

was a zero, not a one

54:05

type thing. And as soon as

54:07

you're going down to the level

54:09

of... of very small numbers of

54:12

electrons, you have to start doing

54:14

things like error correction, where you

54:16

have many, that's already done in

54:19

microprocessor chips, but that, in, sorry,

54:21

it's already done in memory chips.

54:23

It's not done in microprocessors. Nobody

54:26

knows really how to do error

54:28

correction for operations. They only know

54:30

how to do error correction for

54:33

something you're just statically storing in

54:35

memory. Well, the. In any case,

54:37

as you get down to two

54:40

smaller number of electrons, then yes,

54:42

you'll have trouble just by being

54:44

sure about what happened. And that's

54:47

sort of one of the directions.

54:49

But I think, you know, one

54:51

of the disappointments, I suppose, with

54:54

microprocessors, there's just amazing amounts of

54:56

engineering work. amazingly sophisticated engineering and

54:58

physics that's gone into kind of

55:01

gradually increasing the density of transistors

55:03

on microprocessors and improving all sorts

55:06

of different characteristics. But in the

55:08

end, the clock speed, the rate

55:10

at which you're kind of pulsing

55:13

electrons through the circuit, hasn't really

55:15

increased that much in quite a

55:17

few years. It's in the a

55:20

few billion, a few gigahertz, a

55:22

few billion pulses per second, so

55:24

to speak. And... the whole so-called

55:27

Moore's Law of things double every

55:29

18 months hasn't really been true

55:31

for quite a while. And it's

55:34

sort of this idea of how

55:36

much faster will computers get. A

55:38

lot of the, oh my computer

55:41

is getting faster, comes not from

55:43

the individual pieces of circuitry getting

55:45

faster, but the fact that you

55:48

can have more pieces of circuitry

55:50

running in parallel, for example, in

55:52

GPUs, so that in effect, if

55:55

you're processing can be broken up.

55:57

into many things being done in

55:59

parallel, like you're dealing with an

56:02

image, and you can deal with

56:04

one part of the image in

56:06

a separate, separately from another part

56:09

of the image, then you can

56:11

effectively get a speed up. even

56:14

though the individual processing of individual

56:16

pieces didn't get any faster. And

56:18

there's, I think, the kind of

56:21

the notion that you can kind

56:23

of, by improving the algorithms, by

56:25

improving how parallel things can be,

56:28

you can get lots of speed-ups.

56:30

That's been the story of the

56:32

last quite a few years. So,

56:35

let me see. The organ is

56:37

asking, do you expect the propagation

56:39

of light in your physics project?

56:42

How do you expect it to

56:44

work out? Will you get frequency-dependent

56:46

propagation or not? Okay, so this

56:49

is where things get a bit

56:51

tricky. So light, as I mentioned,

56:53

in a vacuum, the kind of

56:56

simplest model for things is this

56:58

very mathematically oriented, disenbodied. kind of

57:00

electric and magnetic fields kind of

57:03

idea. When light goes through a

57:05

material, then what's happening is that

57:07

it keeps on getting stopped by

57:10

atoms, and then when it's stopped

57:12

by an atom it has to

57:15

be reemitted again to keep going.

57:17

The photon is stopped, the photon

57:19

is absorbed, the photon is reemitted.

57:22

Now the issue is that that

57:24

absorption and reemitted. takes a certain

57:26

time. There's a certain, as the

57:29

atom goes from one state to

57:31

another after it's absorbing the photon,

57:33

and it goes back down to

57:36

the previous state again, that all

57:38

takes a certain amount of time.

57:40

And that means that light traveling

57:43

in a material goes slower than

57:45

light traveling through a vacuum. It's

57:47

sort of tricky because in our

57:50

models, this idea of, There is

57:52

sort of a carrier. There is

57:54

a thing in which the light

57:57

is traveling, which in the kind

57:59

of usual theory of so-called Maxwell's

58:01

equations. It's just disembodied mathematics. But

58:04

in a material, it's not disembodied

58:06

mathematics. In a material, its atoms

58:08

are absorbing photons and reemitting them.

58:11

And the question is, what's the

58:13

delay? And some materials, that delay

58:15

is longer than others. And the

58:17

effect of that delay is to make

58:20

light effectively going slower in the material

58:22

than it does in free space.

58:24

So for example, in water, light

58:26

goes one point three times slower

58:28

than it does in... in a

58:30

vacuum and it's pretty much goes

58:33

at the same speed in a

58:35

vacuum as an air because in

58:37

air it's just not hitting atoms

58:39

very often so it's not getting

58:41

absorbed and reemitted

58:44

very often. But so in

58:46

water the the delay I should

58:48

know the actual delay in in

58:50

femto seconds or something I

58:52

don't I could work it

58:54

out but the you're there's a

58:57

certain delay every time a photon

58:59

is absorbed and reemitted by

59:01

an atom. In something like

59:03

diamond, there's a longer delay.

59:06

Diamond slows light down by a factor

59:08

of 2.7. And that quantity

59:10

is the so-called refractive index

59:13

of the material. But what happens

59:15

is that depending on

59:17

the frequency of the photon,

59:19

the time it takes those

59:22

atoms to reemit the photons

59:24

again, and in fact, the

59:26

mostly the reemission varies. with

59:28

the energy of the photon.

59:30

So there are cases

59:33

where there is some, well,

59:35

so-called resonance

59:37

absorption, where, yeah,

59:39

I mean, there's really,

59:42

one question is,

59:44

does it remit the atom,

59:46

the photon again at all,

59:48

or does it just say,

59:50

great, I got a photon,

59:52

now I'm a slightly higher

59:54

energy atom. but I'm not

59:57

going to spontaneously make a

59:59

photon again. And so that can

1:00:01

happen that the material effectively

1:00:03

absorbs the photon and doesn't

1:00:05

remitted at all. When a

1:00:07

material is not transparent to visible

1:00:10

light, that's what's happening. The

1:00:12

photons are being absorbed but

1:00:15

not reemitted. When a

1:00:17

material is transparent, what's happening

1:00:19

is the photons are being absorbed

1:00:22

and reemitted again. And the,

1:00:24

the, depending on the time delay, that

1:00:26

will affect the refractive index. And

1:00:29

in general, that time delay

1:00:31

varies with the energy of

1:00:33

the photon, and so that

1:00:35

means the refractive index varies

1:00:37

with, for example, the color

1:00:39

of light. So, for example, that's how

1:00:41

a prism works. A prism,

1:00:43

you have, for example, white light

1:00:46

comes in, which is a mixture

1:00:48

of all different frequencies of photons,

1:00:50

ones that are lower energy like

1:00:53

redder, and ones that are higher

1:00:55

energy like bluer, and... What

1:00:57

the prism is doing is

1:00:59

in glass the refractive

1:01:02

index varies with

1:01:04

frequency and so

1:01:06

which way which gets

1:01:08

bent more I think

1:01:11

red light gets bent

1:01:13

more so the I think that's

1:01:16

right in glass that the

1:01:18

that there's some a

1:01:20

that a photon that is

1:01:22

has lower energy I think

1:01:25

is it's made to go

1:01:27

proportionately slower in glass than

1:01:29

a blue photon. And so

1:01:31

that means when you have a

1:01:34

prism which, you know, has that

1:01:36

nice sort of prism shape, if

1:01:38

you work out where the, if

1:01:41

you work things out, you'll find

1:01:43

that that causes the ref- okay,

1:01:45

as light enters a material

1:01:48

that has a different

1:01:50

refractive index, the- direction in

1:01:52

which the light travels changes. You can

1:01:54

work that out pretty easily by looking

1:01:57

at the wave fronts and the light

1:01:59

and as the as the speed of

1:02:01

the light changes, the distance

1:02:03

between wavefronts changes, because

1:02:05

the light has a

1:02:08

fixed frequency. You're saying

1:02:10

every, I don't know what

1:02:12

it is, nanosecond, let's

1:02:14

say, for light, every

1:02:17

femto-second, there's another sort

1:02:19

of peak in the

1:02:21

electromagnetic wave. That's the frequency

1:02:24

of the light. The wavelength is

1:02:26

the distance between those peaks.

1:02:28

And that distance is related

1:02:31

to the frequency by the

1:02:33

speed at which the wave is

1:02:35

going. So if the speed the wave

1:02:37

is going is the speed of

1:02:39

light, you just have that the

1:02:42

frequency is equal to the speed

1:02:44

of light divided by the wavelength.

1:02:46

But if the speed at which

1:02:48

the thing goes changes, then that

1:02:51

means the wavelength will

1:02:53

get correspondingly longer and shorter

1:02:56

with a fixed frequency. And when

1:02:58

you work out the geometry, it

1:03:00

means that when a sequence of

1:03:02

wave fronts hit a thing with

1:03:04

a higher refractive index, what

1:03:07

happens is if the, if the, if

1:03:09

those waves are coming at a, at

1:03:11

an angle that's far away

1:03:13

from the kind of the

1:03:15

normal direction, the direction sticking

1:03:17

straight out of the material,

1:03:19

let's say you have a

1:03:21

surface. of water or glass

1:03:23

or something, and it's horizontal,

1:03:25

and the normal direction sticks

1:03:27

straight out of that. It's

1:03:29

kind of the thing that's

1:03:31

at right angles to the

1:03:33

plane of the interface. Then

1:03:35

if you have that pile of

1:03:38

waves coming in an angle,

1:03:40

then what will happen is,

1:03:42

if the refractive index is

1:03:44

larger, those waves will be

1:03:47

turned to go more vertically.

1:03:49

So... It's as you get

1:03:51

into that slower material the

1:03:54

waves go more vertically.

1:03:56

So let's see that was

1:03:58

explaining. So that's

1:04:00

so that's why in a prism

1:04:02

you split red light and blue

1:04:04

light because they because they

1:04:07

have different refractive index

1:04:09

they go at different speeds

1:04:11

therefore they're bent less or

1:04:13

more by refraction and

1:04:15

that means because of the shape

1:04:18

of the prism that that means

1:04:20

that those those beams of light

1:04:22

will be split into the different

1:04:25

colors. So in general this phenomenon

1:04:27

this phenomenon of when

1:04:30

you're splitting light, it's called

1:04:32

chromatic aberration. And

1:04:34

most lenses made of

1:04:36

glass, for example, have a

1:04:39

certain amount of chromatic aberration.

1:04:41

So when you look at things,

1:04:43

you see, actually it's for some

1:04:46

reason it's become more... pronounced in

1:04:48

recent years when you're looking at,

1:04:50

you know, car headlights coming at

1:04:52

you and this also happens as

1:04:54

eyes get older, but I don't

1:04:56

think it's the result of my

1:04:58

eyes getting older that the effect

1:05:00

is larger. I think it's because

1:05:02

of halogen and LED lights. But

1:05:04

in any case, you'll see these

1:05:06

kind of rings of different colors,

1:05:08

for example. And by the way,

1:05:11

that same effect is what leads

1:05:13

to rainbows. It's in the water

1:05:15

drops that sunlight is being... is

1:05:18

being refracted and reflected through the

1:05:20

angle depends on the frequency of

1:05:22

the light and so the red

1:05:25

light and blue light have different

1:05:27

frequencies and so they will be

1:05:29

they have they come out at

1:05:32

different angles. Okay so there

1:05:34

are materials that are so-called

1:05:36

dispersive they have refractive index

1:05:38

that changes the frequency and

1:05:40

that are the do not.

1:05:43

As far as we know

1:05:45

the vacuum has A is not a

1:05:47

dispersive medium. As far as we

1:05:49

know, the speed of light is

1:05:51

the speed of light for all

1:05:53

frequencies of light going through a

1:05:56

vacuum. So the question is, in

1:05:58

our physics project... Is

1:06:00

that true for all frequencies

1:06:02

or not? And my guess would be

1:06:05

when the frequencies are

1:06:07

outrageously high, comparable

1:06:09

to the, so that the wavelength

1:06:11

would be comparable to

1:06:14

the elementary length, the effective

1:06:16

distance between the atoms

1:06:19

of space, then all bets are

1:06:21

off. then the speed of that propagation,

1:06:23

the speed of which those waves

1:06:25

will go through the medium, so

1:06:28

to speak, will be dramatically different.

1:06:30

Away from that I would not

1:06:32

expect much difference. The one thing

1:06:34

that is different in our models

1:06:36

is that space is not

1:06:38

necessarily precisely three-dimensional. There

1:06:40

are dimension fluctuations, places

1:06:42

where space might be

1:06:44

3.01 dimensional or 2.99

1:06:47

dimensional, and that has

1:06:49

presumably a dramatic effect.

1:06:51

on the propagation of light through

1:06:53

those regions. You might remember I

1:06:55

was talking about the inverse square

1:06:57

law as this thing that determines

1:07:00

kind of how much of well

1:07:02

gravity or actually also a little

1:07:04

minute waves that start from a

1:07:06

point you'll get at a certain

1:07:08

distance. How much you'll get depends on

1:07:10

the dimension of the space. So if

1:07:13

you go in in 3.01 dimensional space,

1:07:15

then your it will the amount of that

1:07:17

you get on a radius R will go

1:07:19

like 1 over R to the 2.01, not

1:07:22

1 over R to the 2, i.e. 1

1:07:24

over R squared. So my guess is that

1:07:26

there are some probably some very interesting

1:07:28

effects from dimension fluctuations. We

1:07:30

don't know how many dimension

1:07:33

fluctuations might have been left

1:07:35

over from the early universe,

1:07:37

and I have to say

1:07:39

I am... I am sort of frustrated

1:07:41

that I still don't know

1:07:44

exactly what happens to an

1:07:46

electromagnetic wave propagating through a

1:07:48

dimension fluctuation. I've been kind

1:07:51

of hoping that somebody

1:07:53

else will figure that out. And

1:07:55

I'm kind of, I have to, I

1:07:57

haven't, I haven't worked out something in

1:08:00

class. classical dynamics like that for

1:08:02

many decades, but I think that

1:08:04

might not be true. I think

1:08:07

I might have figured things out.

1:08:09

Yeah, I think I have actually.

1:08:11

But that particular thing, I feel

1:08:14

like I have to sort of,

1:08:16

it's a, I have to kind

1:08:19

of retool a bunch of things

1:08:21

from classical electromagnetism to try and

1:08:23

deal with fractional dimensional space, which

1:08:26

they've never been set up to

1:08:28

deal with. So, so there will

1:08:30

be effects like that. For gravitational.

1:08:33

One of the things that seems

1:08:35

to be true is that gravitational

1:08:38

waves that come from the defamation

1:08:40

of masses, just like electromagnetic waves

1:08:42

come from moving around electric charges,

1:08:45

gravitational waves come from moving around

1:08:47

masses, gravitational waves are really hard

1:08:50

to detect, and mostly we only

1:08:52

get to see them from incredibly

1:08:54

violent events, like we've gotten to

1:08:57

see, or probably once a week

1:08:59

now, the mergers of black holes,

1:09:01

somewhere in the universe. they produce

1:09:04

huge amounts of gravitational radiation. They'll

1:09:06

take in one second, they'll convert

1:09:09

the mass of the sun, the

1:09:11

equivalent to the mass of the

1:09:13

sun, into pure gravitational radiation. And

1:09:16

if that happens anywhere in the

1:09:18

universe, gravitational wave detectors can now

1:09:21

detect that, more or less. And

1:09:23

the question is, those gravitational waves

1:09:25

that were produced in that one

1:09:28

second of the merger of black

1:09:30

holes. Do those gravitational waves, how

1:09:32

fast does gravitational waves go? And

1:09:35

the answer is, they seem to

1:09:37

go at the speed of light.

1:09:40

But in our models, my guess

1:09:42

is that there will be deviations

1:09:44

from that. And I just don't

1:09:47

know what, I mean, it's a

1:09:49

complicated piece of physics to work

1:09:52

out, even given our models, what

1:09:54

the effect on a large gravitational

1:09:56

wave would be, because our models

1:09:59

are dealing with what happens at

1:10:01

the scale of the scale of...

1:10:03

sort of very elementary pieces of

1:10:06

space, yet a gravitational wave involves,

1:10:08

you know, 10 to the 100

1:10:11

different atoms of space, and you

1:10:13

have to kind of see what

1:10:15

the collective effect of that. is

1:10:18

on the gravitational wave. So, let's

1:10:20

see, there's one question here from

1:10:23

Greg. If light has no mass,

1:10:25

how can gravity, like, from a

1:10:27

black hole, pull it in? Okay,

1:10:30

the reason that happens is that

1:10:32

the, how best to say this?

1:10:34

The way that one thinks about

1:10:37

gravity in, well, ever since General

1:10:39

relativity was invented in 1915, is

1:10:42

that gravity has to do with

1:10:44

the curvature of space. So what

1:10:46

does that mean? Well, normally, let's

1:10:49

say that things, whether they're photons,

1:10:51

that doesn't have forces acting on

1:10:54

it will just go in a

1:10:56

straight line. Well, what is a

1:10:58

straight line? Actually, we don't say

1:11:01

it really goes in a straight

1:11:03

line. We say it goes on

1:11:06

the path that takes it in

1:11:08

which it has to go the

1:11:10

minimum distance to get from one

1:11:13

point to another. It doesn't just

1:11:15

sort of wander around. It always

1:11:17

just goes the minimum distance to

1:11:20

get from one point to another.

1:11:22

So in ordinary flat space, the

1:11:25

minimum distance between two points is

1:11:27

a straight line. That's not true

1:11:29

if the space is curved. If

1:11:32

you're on the surface of a

1:11:34

sphere, like on the Earth, for

1:11:37

example, the minimum distance between two

1:11:39

points is a great circle path

1:11:41

on the surface of the sphere.

1:11:44

And the idea is that in

1:11:46

the structure of space time, that

1:11:48

one can think of space as

1:11:51

being curved, and sort of the

1:11:53

big idea of general relativity is

1:11:56

that the presence of mass produces

1:11:58

curvature in space. And so these

1:12:00

particles, they still think that they're

1:12:03

going the shortest distance. They're going

1:12:05

on the shortest paths, so-called geodesic

1:12:08

paths. But those shortest paths, when

1:12:10

space is deformed, those shortest paths

1:12:12

are no longer straight. And in

1:12:15

particular, the shortest paths are exactly

1:12:17

the paths that you follow if

1:12:19

you were to say, well, it's

1:12:22

being deflected by gravity. We don't

1:12:24

really have to talk about gravity,

1:12:27

we can just talk about the

1:12:29

fact that things follow their shortest

1:12:31

paths, but the shortest path is

1:12:34

deformed by the presence of mass

1:12:36

making space be curved. So that's

1:12:39

what's happening to photons, for example,

1:12:41

a light is bent when it

1:12:43

goes around the sun. In fact,

1:12:46

that's even true without general relativity,

1:12:48

but you get double the bending

1:12:50

with general relativity when light goes

1:12:53

around the sun. That was something

1:12:55

that was well supposedly detected in

1:12:58

19, although that experiment may have

1:13:00

been a bit of a fudge,

1:13:02

but it's certainly well known by

1:13:05

now that this deflection, you can

1:13:07

think about it's the result of

1:13:10

it still going in the shortest

1:13:12

path, but and it's going in

1:13:14

the shortest path, but consistent with...

1:13:17

with the defamation of space. I mean,

1:13:20

the thing that happens is when something

1:13:22

is going fast enough, it will be

1:13:24

able to escape the gravity of a

1:13:27

thing. So for example, for the Earth,

1:13:29

if you shoot something up in the

1:13:31

air, faster than 25,000 miles an hour,

1:13:34

it will have enough momentum that it

1:13:36

will escape. the gravity of the earth.

1:13:38

It will not be, the amount that

1:13:41

the gravity of the earth is pulling

1:13:43

it back and slowing it down will

1:13:45

not be sufficient to overcome the inertia

1:13:48

it already has, and it will escape

1:13:50

from the gravity of the earth. For

1:13:52

the sun, the number is 100,000 miles

1:13:55

an hour. For the galaxy, it's a

1:13:57

million miles an hour. But in any

1:13:59

case, there's this question of how. how

1:14:02

fast you have to be going to

1:14:04

escape the gravity of the thing, and

1:14:06

the question is, well, is there something

1:14:09

where it has so much gravity that

1:14:11

even if you're going at the speed

1:14:13

of light, you can't escape the gravity

1:14:15

of the thing, and that's what black

1:14:18

holes are, there are things where the

1:14:20

escape velocity, how fast you have to

1:14:22

be going to escape the gravity of

1:14:25

the thing, is the speed of light.

1:14:27

And what forms the... Yeah,

1:14:30

that's that's that's basically what's

1:14:32

happening. And I mean in

1:14:34

the most extreme case, photons

1:14:36

can actually orbit black holes.

1:14:38

So just as, now normally

1:14:40

with the earth, a photon

1:14:42

absolutely wouldn't orbit the earth

1:14:44

because the speed of light

1:14:46

is 186,000 miles per second

1:14:48

and the escape velocity of

1:14:50

the earth is 25,000 miles

1:14:52

per hour. So light. is

1:14:54

way faster than the escape

1:14:56

velocity of the Earth. So

1:14:58

it just zips right past

1:15:00

Earth without getting sort of

1:15:02

captured by the Earth, without

1:15:04

getting, preventing it from escaping.

1:15:06

But around a black hole,

1:15:08

light can get sort of

1:15:10

pulled into the black hole.

1:15:12

But if you arrange the

1:15:15

light, just like if you

1:15:17

just dropped something from high

1:15:19

above the Earth, it would

1:15:21

just fall to the Earth.

1:15:23

But if it is traveling

1:15:25

at a certain speed relative

1:15:27

to the Earth, it can

1:15:29

be in orbit around the

1:15:31

Earth. when a spacecraft is

1:15:33

sent up it goes up

1:15:35

for a while and then

1:15:37

it's kicked sideways to insert

1:15:39

it into an orbit around

1:15:41

the earth. And the, well

1:15:43

it's complicated because the earth

1:15:45

is spinning and things like

1:15:47

this, but in any case

1:15:49

the thing that that can

1:15:51

happen with a black hole

1:15:53

is normally that photon that's

1:15:55

just coming towards the black

1:15:57

hole will be just pulled

1:15:59

into the black hole. But

1:16:02

if the photon is going

1:16:04

just the right angle, the

1:16:06

photon can end up being

1:16:08

in orbit around... black hole.

1:16:10

And that's what there's maybe

1:16:12

actually has been observed kind

1:16:14

of photons in orbit around

1:16:16

black holes around the central

1:16:18

black hole about galaxy. And

1:16:20

that's that's kind of an

1:16:22

effect that comes about where

1:16:24

you can have where you

1:16:26

can have that phenomenon of

1:16:28

the the photon gets trapped

1:16:30

in the orbit, but it's

1:16:32

still sort of going. It's

1:16:34

not falling all the way

1:16:36

into the black hole. It

1:16:38

gets trickier when there are

1:16:40

black holes that behave as

1:16:42

if they're spinning and all

1:16:44

sorts of fun things happen

1:16:46

there. But it looks like

1:16:48

I have to go back

1:16:51

to my day job here.

1:16:53

So I think we should

1:16:55

wrap up for today. I

1:16:57

see all sorts of other

1:16:59

questions here, which I will

1:17:01

be happy to try to

1:17:03

address. I will say that

1:17:05

I've been trying to think

1:17:07

about sort of what how

1:17:09

I should be organizing these

1:17:11

these live streams. I currently

1:17:13

have four series of live

1:17:15

streams this science and technology

1:17:17

Q&A for kids and others.

1:17:19

I have a Q&A about

1:17:21

history of science and technology,

1:17:23

Q&A about future of science

1:17:25

and technology, and Q&A about

1:17:27

business innovation and managing and

1:17:29

that particular set for must

1:17:31

be a couple of years

1:17:33

now. And I think they

1:17:35

work pretty well. Some things

1:17:38

that I've not been doing

1:17:40

are things where I'm actually

1:17:42

showing kind of live computational

1:17:44

things and actually seeing results

1:17:46

come up live. I've done

1:17:48

that a few times. I

1:17:50

did a kind of math

1:17:52

storytelling day fairly recently along

1:17:54

those lines. but I've been

1:17:56

wondering whether I should mix

1:17:58

in some of those. things

1:18:00

that we can sort of

1:18:02

actually see things happening on

1:18:04

the screen with these more

1:18:06

sort of audio first kinds

1:18:08

of kinds of things. I'm

1:18:10

also wondering if I should

1:18:12

do some slightly more technical

1:18:14

discussions. I mean I make

1:18:16

every effort here to be

1:18:18

able to explain whatever I

1:18:20

need to explain at a

1:18:22

level that people I hope

1:18:25

will understand, but for example...

1:18:27

that if I was explaining

1:18:29

that question about wave particle

1:18:31

duality, if I were allowing

1:18:33

myself to use a little

1:18:35

bit more mathematics and so

1:18:37

on and talk about differential

1:18:39

equations and all kinds of

1:18:41

things like this, I will

1:18:43

have a different kind of

1:18:45

explanation that I can give.

1:18:47

So I'm sort of, I

1:18:49

am interested in people's input

1:18:51

on what they would like

1:18:53

to see. Oh yes, I

1:18:55

see people commenting that it's

1:18:57

fun to see me in

1:18:59

my natural computational habitat. Yeah,

1:19:01

okay, okay, all right, we

1:19:03

have some, some comments, some

1:19:05

encouraging actual, do it with

1:19:07

live computation. I have to

1:19:09

say, I feel like it

1:19:12

is more intense for me

1:19:14

to do that. because I

1:19:16

don't want to be too

1:19:18

boring and end up with,

1:19:20

oh, this code just doesn't

1:19:22

work, there's a bug, I'm

1:19:24

trying to find this bug,

1:19:26

and it's 10 minutes of

1:19:28

messing around and looking at

1:19:30

things and trying things, and

1:19:32

oh my gosh, that's still

1:19:34

not working, etc., etc., etc.

1:19:36

But I think technological help

1:19:38

is on its way. And

1:19:40

in fact, some things that

1:19:42

we've been working on very

1:19:44

recently, which hopefully will be

1:19:46

announced fairly soon. may make

1:19:48

it a great deal easier

1:19:50

to do that kind of

1:19:52

interactive debugging and to get

1:19:54

started on things and not

1:19:56

have to say, oh, I

1:19:59

need to go and... read

1:20:01

the documentation on that and

1:20:03

so on. So okay, well

1:20:05

I'm, I'm, okay, okay, but I'm

1:20:07

seeing a lot of positive feedback

1:20:09

for this idea. All right, I

1:20:11

will, then, then I will, I

1:20:14

will try to do that. All

1:20:16

right, well I should run off

1:20:18

now, but thanks so much

1:20:20

for joining me and look

1:20:22

forward to talking to you

1:20:25

another time. Bye for now.