0:00

You're listening to the Stephen Wolfram

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podcast, an exploration of thoughts and

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ideas from the founder and CEO

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of Wolfram Research, creator of Wolfram

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Alpha and the Wolfram Language. In

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this ongoing Q&A series, Stephen answers

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questions from his live stream audience

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about science and technology. This session

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was originally broadcast on March 7th,

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2025. Let's have a listen. Hello

0:25

everyone, welcome to another

0:27

episode of science and

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technology Q&A for kids

0:31

and others. So I see a whole

0:34

bunch of questions saved up here. Hmm,

0:36

this is one that's, well, okay,

0:38

one from Atari. Can you talk

0:41

about Lambda calculus? I'll try.

0:43

This would be easier if I

0:45

was allowing myself to show you

0:47

things on the computer and so

0:49

on, but let me try and

0:52

give some. some background and try

0:54

and explain this. So,

0:56

uh, Lambda calculus is an

0:58

idea from 1935, actually, that

1:01

was one of the different

1:03

possible models for

1:05

what computation might consist of.

1:08

So, these days, you

1:10

know, we use computers

1:12

all the time, we have some

1:14

idea of what it means to

1:17

do a computation. One can think

1:19

of a computation as being something

1:21

where you define certain rules and then

1:23

those rules get automatically applied many

1:25

times. That's what the computation

1:28

is. Back in the early part of the 20th

1:30

century, there was an attempt to

1:32

particularly take all the things that sort of

1:35

happen in mathematics and say what's

1:37

in common between all these different

1:39

things one does in mathematics, whether

1:42

one's doing geometry or whether one's

1:44

doing algebra or whether one's doing

1:46

arithmetic arithmetic arithmetic. What is the

1:48

kind of common infrastructure, the common

1:51

raw material from which one can

1:53

build up all those different areas

1:55

of mathematics? And people had

1:57

a bunch of different schemes for...

2:00

what that might consist of.

2:02

The fundamental thing people

2:04

imagine doing is just write down

2:06

sort of a symbolic expression, make

2:08

something that has, you know, things

2:11

like an F of X or

2:13

F of G of X or

2:15

whatever. These are things where we're

2:18

not necessarily saying what F and

2:20

GDR, they're just kind of a

2:22

structure. Now, for example, when we

2:25

have an algebraic expression, like

2:27

something like 2x plus

2:29

y squared. We can think

2:32

of that, and this is what

2:34

we do with morphmal language, as

2:36

a times of 2 and x.

2:39

There's a plus outside the whole

2:41

thing, and then there's a power

2:43

of y and 2, whatever I

2:45

said. And we can think of

2:47

it as a symbolic expression

2:50

plus of times of x of

2:52

2, of 2, of power. of Y and

2:54

2 or whatever. Well, the idea, the big

2:56

idea, was that sort of all these

2:59

different things that come

3:01

up in math, whether

3:03

you're representing arithmetic, algebra,

3:05

geometry, group theory, other kinds

3:07

of things, could all be

3:09

represented in this kind of

3:12

symbolic expression way. It was kind

3:14

of an idea that sort of came

3:16

into existence, I would say, in the

3:18

late 1800s, 1880s, 1890s, and so on,

3:21

and then people as a chap. David

3:23

Hilbert who pushed this idea, Whitehead and

3:25

Russell kind of pushed this idea, they

3:27

kind of wanted to, they thought of

3:30

it as being, sort of derived everything

3:32

from logic, not that they, although implicitly

3:34

they were also using the symbolic

3:37

expression idea. Now I have to

3:39

say that, that I kind of

3:41

coddened onto the symbolic expression idea

3:43

in the end of the 1970s when

3:45

I was designing the sort of forerunner

3:47

of what's now often language. and it's

3:49

all based on everything that I've

3:52

done in sort of our computational

3:54

language and so on is all

3:56

based on the symbolic expression idea

3:58

which really dates originally from the

4:00

early part of the 20th century, and

4:02

it had some uses in the intervening

4:04

years, but what we've been able to

4:06

build the kind of tower of capability

4:09

that we've been able to build in

4:11

the Wolfman language is certainly something I

4:13

hadn't imagined one could build such a

4:15

tall tower, but it's all based on

4:18

this idea of symbolic expressions. Okay, how

4:20

does this relate to Lamba calculus?

4:22

Well, you have these symbolic expressions.

4:25

and they might represent some

4:27

algebraic formula, they might

4:29

represent some piece of geometry,

4:31

whatever else. What are you going

4:34

to do with them? You have to have

4:36

some kind of way in which they

4:38

kind of do operations. So for

4:40

example, if you had a piece

4:43

of that symbolic expression that represented

4:46

two plus two. You want it to

4:48

be the case that that

4:50

gets evaluated to four. You

4:52

have to have something which

4:54

is kind of animating this

4:56

symbolic expression, making it do things.

4:58

And that's, so you have these

5:01

rules that define what to do.

5:03

If you see a piece of

5:05

symbolic expression that looks like this,

5:07

what are you going to do with it?

5:09

The first, well, there were, you could

5:11

think of logic as being a little

5:14

bit like that. If you say P

5:16

and P. you can transform that, you

5:18

can transform that to just

5:20

P. Just like if you say,

5:22

you know, you said P plus P,

5:24

where plus is an arithmetic addition,

5:26

then that's equal to two times

5:28

P and so on. Well, kind

5:31

of the question was, what's the

5:33

sort of general way to

5:35

represent those transformations? There

5:37

were several different ideas.

5:39

First one, a studio trap

5:41

called Moses-Schhenfinkle in 1920.

5:44

was the idea of

5:46

combinators. They're very, very abstract.

5:48

They're very hard to understand. I

5:50

wrote a book about them a

5:52

few years ago. They are, even

5:54

100 years later, they're very

5:56

hard to understand. And people

5:58

didn't understand. them then

6:00

and it sort of didn't really

6:02

engage in and get a lot

6:04

of people to pay attention. There

6:07

was a chap called Emmel Post

6:09

who started talking about essentially

6:11

string rewriting systems where it's

6:13

kind of a bit like

6:15

a text editor where you

6:17

say if you have a

6:19

string that goes, you know,

6:21

A-A-A-B-B-B-B-B-B, you should replace that

6:23

with B-A or something. That

6:25

was another idea that was

6:28

from 2021. Well, there was

6:30

another idea from 1931,

6:32

which was called general

6:34

cursive functions, which were

6:36

Kurt Gertel used that

6:38

idea in proving Gertel's

6:41

theorem. And then in 1935,

6:43

Alonzo Church, mathematician

6:45

of Princeton, had the idea

6:47

of what he called Lander

6:50

calculus. And how to

6:52

explain Lander calculus? Lander

6:54

calculus is a way

6:57

of... describing kind of

6:59

transformations for symbolic

7:01

expressions. And the idea is

7:04

more or less this. So let's say

7:06

you say I have a function F,

7:08

and you're going to say F of

7:10

X is X squared. What does

7:12

that really mean? In Wolfram

7:14

language, the way that that would

7:16

be specified is F of X

7:19

blank, where blank is an underscore

7:21

character, colon equals X

7:24

squared. What does that mean? It

7:26

means there is a pattern of the

7:28

form F of any expression, that's the

7:31

blank. We're going to name it X. F

7:33

of any expression should be transformed

7:35

to that expression squared. So

7:38

that's kind of a way of thinking

7:40

about what a function is. It's

7:42

a thing where you have the

7:44

symbolic expression of the form F

7:46

of any expression, and that is

7:48

then transformed in the way

7:50

that I just specified. Okay, so that's

7:52

one view of sort of what

7:54

functions are. is there are things

7:56

that transform symbolic expressions to other

7:59

symbolic expressions. Okay, so the

8:01

lambda calculus idea is if

8:03

you've got something like F of

8:06

X is X squared, how do

8:08

you make a kind of pure anonymous

8:11

function that is what F

8:13

itself is in a sense? You've

8:15

said what F of X is

8:17

that it's X squared, but can

8:20

you just say what is F

8:22

itself without talking about the

8:24

X? And the idea is that

8:26

F itself is Landa of...

8:28

Let's call it Z. Z squared.

8:30

What does that mean? When we're

8:33

saying lambda of Z, one says,

8:35

we're going to expect something that's

8:37

going to be fed into that

8:39

Z slot, and we're going to

8:42

take that thing and square it.

8:44

And so the idea of a

8:46

lander expression, a pure function,

8:48

sometimes called an anonymous function,

8:51

because it doesn't have a

8:53

name, as it's not F.

8:55

It's what F. is what you can

8:57

think of as being the pure

8:59

F function. It's this thing that

9:02

says Landry of Z, which means

9:04

basically I'm expecting something,

9:07

I'm expecting something that's

9:09

going to be fed in Landry

9:12

of Z Z squared. So that

9:14

means I'm going to eat any

9:16

expression and I'm going to take

9:18

that expression and square

9:21

it. So that's a lambda function.

9:23

And the idea is that you

9:25

can write. sort of something you

9:27

can that that lambda function is

9:30

then reduced so if you say

9:32

land of z z squared and

9:34

then you say apply that to x

9:36

plus one let's say the it'll

9:38

bind the x plus one to

9:41

the z sort of eat the

9:43

x plus one and turn the

9:45

result to x plus one squared

9:47

so this sort of a reduction

9:49

rule that's some it's usually

9:52

called beta reduction that

9:54

essentially takes the pure lambda

9:56

expression and you're feeding it things,

9:58

you're applying it. that lander expression

10:01

as a pure function, two

10:03

things, and then it is being reduced

10:05

to the result of feeding that thing

10:07

into its bound variable and then

10:09

turning it into the body of

10:12

lander expression. This is hard to

10:14

explain. I probably shouldn't have attempted

10:16

this without actually typing things on

10:18

a computer. But to give you

10:21

sort of the flavor of it,

10:23

a lander expression is a pure

10:25

function, a disembodied function, a

10:27

disembodied function that has no

10:29

name. It is just a thing that says

10:31

I am expecting to eat an expression

10:33

and this is what I will do

10:36

with that expression if I am fed it.

10:38

And the point is that you

10:40

can write programs and things as

10:42

big collections of lander functions. And

10:44

then the running of the program

10:46

is just the lander function doing

10:49

the transformations that lander functions

10:51

do. And you can, it gets

10:53

very kind of funky because you

10:55

can have sort of very pure

10:58

lander expressions. that aren't really applied

11:00

to anything, they're just doing reductions

11:02

like beta reduction by being applied

11:04

to other lander expressions. And actually

11:07

I was just studying this recently,

11:09

the kind of ruelliology of lander

11:11

expressions, and trying to understand if

11:13

you have just pure lander expressions,

11:16

you can have a situation where you basically

11:18

can the lander expression will sort

11:20

of eat another lander expression and

11:23

produce another lander expression, it will

11:25

keep going. It'll never stop. It'll

11:27

never stop. It's a, or even

11:29

it will even grow and

11:31

it will produce more, it's

11:33

eating lander expressions, it's producing

11:35

lander expressions, it's just producing

11:37

this bigger and bigger structure.

11:40

So those are, those are sort

11:42

of obscure pure computation ideas, but

11:44

the main idea is it's this

11:46

way of sort of abstracting the

11:48

function out of the sort of

11:50

the pure function. If F of

11:52

X is X squared, what is

11:54

F itself itself itself itself? You

11:56

can think of it as a pure function.

12:00

Things like that are very useful.

12:02

I mean in Wolfram language,

12:04

we call it the function function.

12:06

It is a function whose name is function.

12:09

It gets written with an ampersand and

12:11

things. It has a nice short

12:13

form, but it is the function function.

12:15

And you might say, well, why do I

12:17

want a function function? Well, then

12:20

it turns out to be very, very

12:22

useful. I would say that in people

12:24

learning Wolfram language and

12:26

so on, one... At first, people will say,

12:28

I don't need anything that abstract. I

12:30

don't need that pure function thing. It's

12:33

way too abstract. And they don't

12:35

use it at first. And then at some

12:37

point when they've sort of by hand

12:39

done the things for which pure

12:41

functions are really useful, eventually you can

12:43

show them a pure function and it'll

12:46

be like, aha, okay, now I get

12:48

it, now I can automate, simplify a

12:50

lot of things I've done in the past.

12:52

A typical example is you want to

12:54

apply some operation. to lots of the

12:56

same operation, to lots of different things.

12:59

So let's say you have a bunch of

13:01

images and you're going to invert the colors,

13:03

find the edges, etc., etc., etc. What you

13:05

want to do is you might say, well,

13:08

I'll write a function that does all those

13:10

things and then you'd map that function over

13:12

all those images. But you might say, I

13:14

don't want to bother to write out that

13:16

function and write F of X, blank, colon

13:19

equals, and then that definition of edge

13:21

detection of edge detection, whatever. I

13:23

just want to put something to

13:25

put something in. that stands for

13:27

that function. And that's what

13:29

you can do. You can just

13:31

say something like, you know, edge

13:34

detective, hash sign, and then ampersand,

13:36

that thing is a pure function

13:38

which can now be served the

13:41

role of a function that can

13:43

be applied to all those images.

13:45

So that's kind of the idea,

13:47

and that's how it ends up

13:49

being useful. Very different

13:52

question here. asks any

13:54

thoughts on numerology? Actually, let

13:56

me just see if there

13:58

are more comments on them. Okay,

14:00

well, what is numerology?

14:03

Numerology tends

14:05

to be, oh, I noticed

14:07

that this thing in the

14:10

world, like the mass of

14:12

the muon divided by

14:14

the mass of the

14:16

electron, which is roughly

14:19

206, that really that

14:21

that ratio is actually

14:24

very close to the

14:26

square root of pie

14:28

divided by seven to

14:30

the power of three, who knows

14:32

what, something that's just pure

14:35

numbers. So numerology is the

14:37

real, is the, is sort

14:39

of the, the correspondence between

14:41

things that are purely made

14:44

of numbers and things that

14:46

you see kind of in the

14:48

real world. That's the most common

14:50

use of that term.

14:52

Occasionally there's kind of

14:55

within mathematics numerology. People

14:57

notice that's that. there is

14:59

some kind of coincidence that,

15:01

oh, this series of numbers

15:03

that appear in this mathematical

15:05

problem are the same series

15:08

of numbers that appear in

15:10

that mathematical problem. There have

15:12

been a number of cases,

15:14

most notably in studying large

15:16

finite groups and things, where

15:18

that kind of numerology has

15:20

paid off, where noticing in

15:22

mathematics that this sequence is

15:25

the same as that other

15:27

one, that then a connection

15:29

was found between the source of

15:31

those sequences. Numerology has

15:33

a much less good history

15:35

in natural science and even

15:38

worse history probably in

15:40

kind of more human

15:42

oriented areas. It's kind of,

15:44

you know, there are many examples

15:47

of people trying this. It's

15:49

really basically, as I'm thinking

15:51

about it's ever worked. One

15:54

thing that's often the target of

15:56

this is the thing of the

15:58

fine structure constant, which is a... characterization

16:00

of the strength of

16:02

electromagnetic forces, it happens

16:05

to be dimensionless. It's just a

16:07

number. It's roughly one over 137.

16:09

And people say, well we should

16:11

be able to just derive this

16:13

from something lower level if we

16:15

have a fundamental theory of physics,

16:17

for example, we should just be

16:19

able to derive the fine structure

16:21

constant. And one day I would hope that

16:23

our theories of theory of physics will be

16:26

able to do that. It's worth realizing,

16:28

just sort of a footnote to

16:30

that story, is that the fine

16:33

structure constant as a

16:35

strength of electromagnetic forces

16:37

really depends on the observer

16:40

observing those forces. The value

16:42

of one over 137 is only

16:44

really correct for an observer that's

16:46

operating in a sense at very

16:48

low energy. An observer who in

16:50

the uncertainty principle kind of relates

16:53

to length scales. an observer who

16:55

is kind of measuring electromagnetic forces

16:57

on a very large length scale,

16:59

as you probe them on shorter

17:01

length scales, the effective value of

17:03

the of the fine structure constant

17:05

changes. So it's a little bit

17:07

tricky to just sort of say,

17:10

oh, well, we should have the

17:12

fine structure constant and just fall

17:14

out of the theory. It's the thing

17:16

that falls out of the theory has to

17:18

be something whose value depends on the observer

17:20

who's observing the thing. But in any

17:22

case, there's sort of a an effort. to,

17:25

it's not been a good story of

17:27

people trying to find, you know, oh,

17:29

it's really square to pie, terms this,

17:31

and the other. Now, you know, it's

17:34

worth trying to understand

17:36

the sort of theory of numerology.

17:38

I will tell you something

17:40

that if you type into

17:43

Wolfmalfa, some just random number,

17:45

1.284643, whatever, it will have a

17:47

pod that comes out that lists

17:50

possible closed forms. It will tell

17:52

you... what ratios of pies and

17:54

things like this are close to

17:56

the number you typed in. Now it has

17:58

a bit of a tradeoff. because you

18:00

could get something that's exactly the

18:03

number you've typed in, but it's

18:05

a sum of eight powers of

18:07

pie divided by lots of powers

18:10

of e and so on. It

18:12

could be a really

18:14

complicated formula. It's sort

18:16

of completely unsurprising that

18:18

there is a really

18:20

complicated formula that represents, you

18:23

know, the six digits you

18:25

typed in of that number,

18:27

plus seven over a hundred.

18:29

and that's a nice in terms

18:32

of whole numbers formula. It's

18:34

just not telling one very

18:36

much because that really is just

18:38

the number you put in. Now, if

18:40

the number that I put in was

18:42

3.1.4.159, then it might be telling me

18:45

something to say that's just pie.

18:47

I could say that number is 3 plus

18:49

1 over 10 plus 4 over 100

18:51

plus whatever, but that's a kind

18:54

of a long description of the

18:56

number. The thing that's interesting is

18:58

if there's a short description

19:00

of the number in terms

19:02

of things like pie or whatever

19:04

else. And in a sense, the

19:06

mission of numerology, I suppose, is to

19:09

say, is there a small formula for

19:11

all the digits that you know of

19:13

that number? It's kind of a thing

19:15

where it's like asking, you know, you

19:17

can think of that powers of pie

19:20

or whatever else, as like a program

19:22

for making the number. And so essentially

19:24

numerology is this question of is there

19:26

a short program that makes my number?

19:28

I can clearly have a program that's

19:31

about the same length as the number

19:33

itself that just writes down the number,

19:35

but is there a short program that

19:37

makes the number? Now, even that's a

19:39

tricky thing to say, because the question

19:42

of what kinds of operations can be

19:44

in that program. For example, I talked

19:46

about pie and so on. People have

19:48

heard of pie, but how about if I talk about,

19:50

I don't know the... Well, next level

19:52

of obscurity would be the

19:55

Euler-Masharoni constant, where another level

19:57

would be, you know, the Madelang sum

19:59

of some... These are all kinds of

20:01

things that can be thought

20:03

of as mathematical constants, but

20:05

they have an increasing level

20:08

of obscurity to them. And so then

20:10

you have the tradeoff of, well,

20:12

you know, how many pies is

20:14

one Madeline constant equivalent to? Because

20:17

if I introduce obscure enough constants,

20:19

then again, I'm kind of,

20:21

you know, for example, I

20:23

could just invent a constant

20:25

that is... the my personal constant that is

20:27

the number I just typed in and

20:29

then I've got a very short description

20:32

but you still you don't know what

20:34

my personal constant is that you have

20:36

to have a whole sort of chain

20:38

of knowledge of that so in a sense

20:40

sort of the question is if you have

20:43

a certain language for describing your

20:45

number that might include pies square roots

20:47

things like that how small can

20:49

the description of your number be

20:51

and that's a reasonable question

20:53

There are clearly, if you

20:55

think about all possible numbers,

20:58

most of them can't have

21:00

short descriptions because those short

21:02

descriptions are much fewer in

21:04

number than all the possible

21:06

numbers with all their digits. But

21:08

this question of sort of how

21:10

much is a pie versus, you

21:12

know, what's the effective sort of

21:14

description length of saying I've got

21:17

a pie? as opposed to I've got

21:19

a Madelan constant. Interesting question, not

21:21

obvious what the answer should be,

21:23

like 15 years ago when we

21:26

were building that capability

21:28

in Wolfram Alpha, what we did

21:30

was this. We looked at basically

21:32

all kind of easily available

21:34

math papers, academic papers. And

21:36

we simply say, how often

21:38

do these constants appear? Pie

21:41

appears all over the place.

21:43

The Euler-Mascheroni constant, much less

21:45

frequently. The Madelone constant, even

21:47

much less frequently. And then what

21:50

we said was, let's say that

21:52

the sort of effective information content

21:54

of saying it's pie is much smaller

21:56

in proportion to how much more

21:59

frequently. it appears in mathematical

22:01

literature. Like if I say

22:03

it's pie, I probably not

22:05

have to tell you anymore. If

22:07

I say it's the Smith constant,

22:09

I'm going to have to define

22:12

what I mean by the Smith

22:14

constant. And so that was sort

22:16

of a way of getting a

22:18

proxy for sort of what the

22:20

effective amount of information associated with

22:22

saying it's constant such and

22:25

such. having thought about that,

22:27

you know, you're kind of in this

22:29

position of saying, well, if I've got

22:31

some number that I just measured in

22:34

the world, you know, how small a program

22:36

can I make for that number? And

22:38

is that significant and

22:40

so on? And if I have that

22:42

small program for the number, can

22:44

I imagine a mechanism by

22:46

which that number would be the value

22:48

that it is? Let me give you

22:51

an example within mathematics.

22:53

If you look at pair of

22:55

numbers, let's say 12 and 4,

22:57

okay, 12 and 8, okay, 12 and

22:59

8 are not relatively prime,

23:01

what does that mean?

23:04

It means there is a divisor of

23:06

8, 8 is 2 times 4, 12

23:08

is 4 times 3, okay, the 4

23:10

is uncommon between those. So

23:13

those numbers have a divisor

23:15

in common, they are not

23:18

relatively prime. If we were

23:20

to talk about... Let's say, oh

23:22

gosh, let me not fail my

23:24

arithmetic here. Let's talk about

23:26

10 and what's a good example.

23:29

10 and 21, okay? 10

23:31

is 2 times 5, 21 is 7

23:33

times 3. I'm so proud of myself

23:35

I'm now beginning to know

23:38

my multiplication tables. I didn't

23:40

know that when I was

23:42

a kid, I've gradually learned

23:45

them over the course of

23:47

my life. But in any case,

23:49

10. and 21 are relatively prime

23:51

because they have no factors in common.

23:53

Okay, so I can ask the question. Let's

23:55

say I try a whole bunch of

23:57

different numbers and I ask what's the...

24:00

chance that two numbers are

24:02

relatively prime. And the answer,

24:04

I'll get some number, I

24:06

forget what the exact number

24:08

is, but I go in

24:10

to get more and more

24:12

and more digits. And then

24:14

maybe I type it into

24:16

Wolfram Alpha and I say,

24:18

what is this number? It's

24:20

gonna say it's six over

24:22

pie squared. Well, that turns

24:24

out to be a piece

24:26

of numerology that works, because

24:28

it really is six over

24:30

pie squared, and there is

24:32

a mathematical argument. for why

24:34

it has to be six

24:36

of a pie squared. And

24:38

so that's a case where

24:40

sort of the numerology works

24:42

out. And as I say,

24:44

sometimes it does in math.

24:46

I'll mention this question of

24:48

kind of numbers and kind

24:50

of how produceable is that

24:52

number. So let's say that

24:54

I've got a number and

24:56

it is it is produceable

24:58

as six over pie squared,

25:00

for example. I can imagine

25:02

that if I'm just looking

25:04

at all possible numbers, I

25:06

might type in six over

25:09

five square and that might

25:11

be the number I generate.

25:13

But let's say that you've

25:15

just got the number one

25:17

point seven, three, four, two,

25:19

six, five, four, three, seven,

25:21

four, three, seven, nine, one,

25:23

whatever. I don't think I'm

25:25

very good at generating random

25:27

digits, but it's just some

25:29

sort of randomly generated sequence

25:31

of digits. and it's really

25:33

a number that I'm very

25:35

unlikely to find. Is it

25:37

a number which whose chance

25:39

of occurring is about proportional

25:41

to 10 to the minus

25:43

the number of digits that

25:45

I've specified? So you might

25:47

say why would anybody care

25:49

about knowing whether a number

25:51

is produceable in that sense?

25:53

I'll give you an example.

25:55

Back in the early 1990s

25:57

there was a big disaster,

25:59

Intel, semiconductor company, had made

26:01

a the pantium chip with

26:03

the 856 microprocessor. Lots of

26:05

fanfare, exciting, fast, better, the

26:07

new technology microprocessor. Somebody noticed

26:09

that a particular set of

26:11

numbers, if you divided one

26:13

number by the other, you

26:15

got the wrong answer. The

26:18

Pentium chip just gave the

26:20

wrong answer for a particular

26:22

division of two particular numbers.

26:24

So then the question was,

26:26

how much does that matter?

26:28

If you were just picking

26:30

numbers at random based on

26:32

their digits, the chance of

26:34

hitting the number that was

26:36

one of these bug numbers

26:38

was incredibly low. I mean

26:40

ridiculously low to the point

26:42

where certainly wouldn't have happened

26:44

in human history with people

26:46

running Pentium chips all the

26:48

time. But if that number

26:50

was a produceable number that

26:52

turned out to be really

26:54

it's six over pie square

26:56

or something to enough digits,

26:58

then much bigger deal because

27:00

one could really imagine that

27:02

that number would actually show

27:04

up in practice. Turns out

27:06

so far as I could

27:08

ever tell the numbers that

27:10

led to the bug were

27:12

not produceable numbers. By the

27:14

way this term produceable number

27:16

I just invented that three

27:18

minutes ago or something it's

27:20

not a standard term in

27:22

the literature of mathematics and

27:24

so on. But I think

27:26

it's a good term for

27:29

this particular idea. That's sort

27:31

of an application of this,

27:33

that's sort of an inverse

27:35

numerology kind of question of,

27:37

oh, there is no simple

27:39

version of this number, so

27:41

we don't have to worry

27:43

as much about the fact

27:45

that there is a bug

27:47

in that case because the

27:49

chance that that number occurs

27:51

is really, really small. Well,

27:53

so that's a few comments

27:55

on numerality. I mentioned one

27:57

more thing. So think of

27:59

Benford's law. And it's one

28:01

of these things where it's

28:03

like, well, this is a

28:05

weird numerical numerical feature. So

28:07

if you can. kinds of

28:09

numbers that occur in practice,

28:11

like I don't know, the

28:13

market caps of public companies.

28:15

or the kinds of numbers

28:17

that you'd see on a

28:19

bank statement. And you ask

28:21

the following question. You say,

28:23

what's the first digit of

28:25

that number? Is it $131?

28:27

Is it $372? Just take

28:29

the one or the three

28:31

or whatever. Question is, do

28:33

all leading digits of numbers

28:35

occur with equal frequency? Well,

28:38

the answer is that in

28:40

most sort of practical numbers

28:42

that show up... in accounting

28:44

statements or whatever else, they

28:46

don't occur with equal frequency.

28:48

One is much more probable

28:50

than two and so on

28:52

going down to nine. It

28:54

turns out, so why is

28:56

that? Well, the reason is

28:58

that when you do mathematical

29:00

operations, the, in a sense,

29:02

the, the, what matters, what,

29:04

yeah, the, the, what matters,

29:06

is the logarithms of these

29:08

numbers are equally distributed, but

29:10

the numbers themselves are not.

29:12

And what happens, let's see

29:14

how to explain this. Well,

29:16

roughly, the point is that

29:18

if you're picking a number,

29:20

independent of its size, the

29:22

point is that numbers that

29:24

are... as you

29:26

reduce it to be a number that

29:29

you write out in terms of digits,

29:31

when you pick the number, sort of

29:33

independent of size, you're more likely to

29:35

land in that part of the digit

29:38

representation of the number that begins with

29:40

a one, and that begins with a

29:42

nine, and so on. It's kind of

29:44

a standard trick for trying to detect

29:47

fraud and accounting, for example. Just look

29:49

at all the numbers, and you just

29:51

say, well, if there are really a

29:53

lot of numbers that begin with a

29:56

nine, that are, you know, the amounts

29:58

of payables and things like this. that's

30:00

kind of fishy. And it's sort of

30:02

a common heuristic for that. It works,

30:04

Benford's law works for many kinds of

30:07

things. It works, I think, for the

30:09

powers of two. It doesn't happen

30:11

to work. That's in a pure

30:13

mathematics setting, not in a sort

30:15

of human world setting. I don't

30:17

think it works for primes, and I

30:20

don't think it works for some other

30:22

kinds of numbers. And it's an interesting

30:24

question, which there isn't really a great

30:26

answer to, of why it works. Anyway,

30:29

a few thoughts about

30:31

numerology. Oh boy, there's some

30:34

following questions here. Okay,

30:36

so Technic says that their

30:39

current favorite approximation

30:42

to a constant, in this case,

30:44

E, is some combination

30:46

of digits here. Wow, that's

30:49

interesting. That's

30:51

accurate. They claim to

30:53

18 septilian digits. That

30:55

seems very. Hard to believe

30:58

to me, but that's an

31:00

interesting claim. I mean, this whole question

31:02

about the coincidences of numbers that

31:05

are sort of approximately this or

31:07

that, a famous one is e

31:09

to the power pie times square

31:12

root of 163, I think. That

31:14

number is really close to being

31:16

an integer. It doesn't have to

31:18

be. Could be any number, but

31:20

it's very close. It's, you know,

31:22

something. 99, 99, 99, 99. Many

31:24

times. Is that significant?

31:26

It turns out this mathematician named

31:29

Ramanujan, who was working in the

31:31

early part of the 20th century,

31:33

kind of noticed this and realized

31:36

that it was significant and in

31:38

fact built the whole theory based

31:40

on it, which among other things

31:42

is one of the main ways

31:44

that people compute the digits of

31:46

pie is using Ramanujan's theory that

31:48

came from kind of noticing this

31:50

kind of numerical coincidence. that E

31:52

to the pie square of 163,

31:55

I think that's the right one,

31:57

is close to an integer. You

31:59

know, I will... say that this thing about

32:01

you generate numbers and then you

32:03

say what are these numbers where do

32:06

they come from that's something

32:08

that as a you know when I do research

32:10

on things which I do all

32:12

the time but you know I'll

32:14

generate sequences of numbers and there's

32:16

a function and more from

32:19

language fine sequence function

32:21

which attempts to find

32:23

what function describes that sequence

32:25

of numbers and quite often it's useful.

32:27

I kind of say, yeah, I should

32:30

have been able to figure out why

32:32

these numbers are, you know, powers of

32:34

three minus powers of two or something.

32:37

But it notices, and I didn't, so

32:39

to speak. There's an online

32:41

system, OEIS, the online

32:43

encyclopedia of integer sequences,

32:45

built by a chap called Neil

32:47

Sloan, he started in the 1960s,

32:50

on index cards, and then a

32:52

book, and so on, collecting integer

32:54

sequences. And it's like, what is

32:56

the sequence? Oh, it's the number

32:58

of ways that you can assemble

33:00

sort of squares together and get

33:03

patterns that are distinct when you

33:05

rotate them around, or it's the

33:07

number ways that you can assemble

33:09

a tree with up to some

33:11

number of nodes and so on.

33:13

But it's quite often the case

33:16

that sort of you get, you generate

33:18

this from some completely

33:20

different method, then you might. you

33:23

just find sequence function, you might look it

33:25

up in OAIS, and it'll tell you, oh,

33:27

by the way, that's the number of trees,

33:29

you know, as a function of

33:31

that, the number of nodes or

33:33

something. And that's a useful thing.

33:35

That sort of mathematical coincidence is

33:38

useful. I would say that it's much

33:40

more, that has been much more successful

33:42

than the case of applying this to

33:44

the natural world. There is sort of

33:46

another case of this, which is

33:48

sort of an archaeology. and so

33:50

on, where people say, oh, the

33:52

height of the great pyramid divided

33:54

by the size of the nose of the

33:56

sphinx is, you know, very close

33:59

to pie square. something. That must

34:01

have been significant. Usually, the truth

34:03

is, those things were not significant

34:05

and nobody knew that that was

34:07

what was going on at the

34:10

time when the thing was being

34:12

built. But it is the case

34:14

that there was quite a tradition

34:16

of sort of hidden information, I

34:18

would say, particularly in the, well,

34:20

early printing, you know, 1500, 1600s,

34:23

and so on, of kind of

34:25

like hiding. kind of messages in

34:27

the weird numbers that would show

34:29

up in places. There's a whole

34:31

kind of tradition of that in

34:33

the the Kabala sort of Jewish

34:36

tradition is a lot about sort

34:38

of noticing weird numerical coincidences from

34:40

the from the Old Testament and

34:42

such like. And you know, did

34:44

the people who were writing this

34:46

were they sort of hiding a

34:49

secret message in the number of

34:51

Hebrew characters between here and there?

34:53

or is that just a coincidence?

34:55

That's the question. That's always a,

34:57

it's always a difficult question. Once

34:59

you have a thing to know

35:02

was that thing made for a

35:04

purpose or not is a very

35:06

difficult problem. I mean, it's, you

35:08

know, famously things like, well, famous

35:10

statement from the philosopher Emmanuel Kant,

35:12

if you see a hexagon drawn

35:15

in the sand, you can reasonably

35:17

assume that it was made for

35:19

a purpose by an intelligence of

35:21

some kind. That goes a certain

35:23

distance until you discover that there

35:26

are wind-produced kind of patterns in

35:28

the sand which can be hexagons,

35:30

but it's just the wind. And

35:32

unless you think of the wind

35:34

as an intelligence, which perhaps you

35:36

should, it's certainly not an intelligence

35:39

of the humankind. And even more

35:41

dramatically, if you look at the

35:43

North Pole of the planet Saturn,

35:45

it has a giant storm that

35:47

is a pretty good approximation to

35:49

a hexagon. So it's like on

35:52

the North Pole of Saturn, there's

35:54

a hexagon right there. And so

35:56

in Emmanuel Kant's heuristic, for... was

35:58

it made for a purpose? Was

36:00

it made by an intelligence? Saturn

36:02

was made by an intelligence, which

36:05

is sort of an interesting conclusion,

36:07

but it kind of, it talks

36:09

about the difficulty of recognizing what's

36:11

intelligent and what's merely the natural

36:13

world doing its thing. I mean,

36:15

another famous example from the beginning

36:18

of the 20th century was both

36:20

Marconi and, well, Tesla. had noticed

36:22

that if you just put a

36:24

radio mask up, there wasn't a

36:26

lot of radio transmission going on

36:28

in the world at that time,

36:31

and just put a radio mask

36:33

up, like in the middle of

36:35

the Atlantic, if you were on

36:37

a yacht going across the Atlantic

36:39

or something, you would hear all

36:41

kinds of radio emissions. What were

36:44

they? Tesla said there must be

36:46

the Martian signal link. Marconi didn't

36:48

know what they were. But what

36:50

they actually are, are particular... magnetohedodynamic

36:52

effects in the Earth's ionosphere and

36:54

they are essentially a pure piece

36:57

of nature but yet they make

36:59

these sounds that you might think

37:01

were of kind of intelligent origin.

37:03

Now to confuse things even further,

37:05

days later, whale songs were discovered

37:08

and whale songs sounded awful a

37:10

lot like these kind of emissions

37:12

from the ionosphere. and the emissions

37:14

honestly radio, but if you play

37:16

them as sound, they sound a

37:18

lot like the sounds from whales

37:21

and so on. So it's very

37:23

confusing. You know, the whales are

37:25

sort of intelligence like us. We

37:27

think the honest for us is

37:29

not an intelligence like us, but

37:31

can we tell what was for

37:34

a purpose and what wasn't? And

37:36

it's the same kind of thing

37:38

when we're looking at a hinge

37:40

or something and we're saying, you

37:42

know, was it set up in

37:44

this way? were the equinox or

37:47

was it set up this way

37:49

just because you know druid I

37:51

don't know what druid names would

37:53

have been druid Zestericks or something

37:55

was, I have no idea if

37:57

that's a valid druid name, but

38:00

I'm sort of remembering the the

38:02

asterisk series of comic books that

38:04

I think had had some druids

38:06

in it, so guessing it might

38:08

be something like that, although who

38:10

knows, but any case, we did

38:13

this druid or whatever, who decided

38:15

what Stonehenge should look like, were

38:17

they thinking about astronomy and the

38:19

equinox and so on, or were

38:21

they just like, oh, put it

38:23

this way, and it's hard to

38:26

know. And sometimes, you know, in

38:28

some of these cases, when it

38:30

says, yes, it's very accurately aligned,

38:32

so that it, you know, so

38:34

the light falls on exactly this

38:37

stone at the time of the

38:39

equinox or whatever, and then it's

38:41

like, well, how accurately is it

38:43

aligned that way? And, you know,

38:45

maybe they meant it to be

38:47

for the equinox, but they didn't

38:50

know their astronomy well enough, and

38:52

so it isn't quite aligned. So

38:54

it's always very difficult to tell.

38:58

Rebot comments, atmospheric noise is about

39:00

as random as we can get,

39:03

I think. Well, actually, the thing

39:05

I was just telling about the

39:07

atmosphere is a little bit of

39:10

a, giving a bit of a

39:12

twist to that. I think, you

39:15

know, the wind and kind of

39:17

turbulence in the atmosphere is pretty

39:19

random in some sense, but there's

39:22

definite regularity to it. For example,

39:24

the very fact that wind has

39:26

gusts is a piece of regularity

39:29

that, I mean, why does wind

39:31

have gusts? It's because, well, in

39:34

the end, motion of fluids is

39:36

sometimes motion of fluids is very

39:38

smooth. That's so-called laminar flow when

39:41

the fluid just sort of slides

39:43

past an obstacle. But when the

39:45

fluid is going faster, it's going

39:48

faster, it's going faster. produces turbulence

39:50

and turbulence. You can think of

39:53

it as it's making all these

39:55

little eddies of air or water

39:57

if it's if it's water that

40:00

one's dealing with and there's a

40:02

sort of a general cascade that

40:04

happens when you start with a

40:07

big eddy it gets ground down

40:09

to small and small and small

40:12

eddies and eventually the eddies kind

40:14

of dissipate away but that cascade

40:16

of eddies is from the big

40:19

to the small as kind of

40:21

a somewhat accurate universal law that

40:23

the the energy of the of

40:26

a certain eddy as a e

40:28

to the minus 5 thirds law,

40:31

or k to the minus 5

40:33

thirds actually, no, that's in that,

40:35

sorry, that's the wave number, the

40:38

size of the eddies varies like

40:40

the minus 5 thirds power of

40:43

their size. And that sort of,

40:45

the reason for the gusting has

40:47

to do with that kind of

40:50

cascade of eddies sizes and so

40:52

on. It's one of these things

40:54

where when you look at it

40:57

on a small enough scale, if

40:59

you look at the individual molecules,

41:02

you'll be like, yeah, they're pretty

41:04

random. Now, of course, if you

41:06

roll the clock back and you

41:09

say, well, how did the molecules

41:11

start off? In principle, you can

41:13

do the computation to work out

41:16

where the molecules will be. It's

41:18

sort of a big story that

41:21

I've tried to clarify, actually, in

41:23

recent years that this phenomenon of

41:25

computational irreducibility tells one, well, well,

41:28

But in practice, it will take

41:30

you a computation far beyond any

41:32

computation you can do to figure

41:35

that out. So for practical purposes,

41:37

you can't know whether the molecules

41:40

are going to be, and you

41:42

just have to say, well, they

41:44

seem random, because there's nothing we

41:47

can say that can predict where

41:49

they'll be. All right, let me

41:51

see. Other kinds of questions. Here's

41:55

a question that might be

41:57

reasonably simple from ego. The

42:00

question is, how does

42:02

IBM Watson AI stand

42:05

against modern LLLMs? Well,

42:07

so for those who remember

42:09

it, IBM Watson was

42:12

a system that was put

42:14

up in 2009 or 2010,

42:16

and it was kind of

42:19

a publicity stunt. So

42:21

IBM had for many, many

42:23

years worked on text

42:26

retrieval, which is the problem

42:28

of you've got a big

42:30

piece of text online, you want to

42:33

find these words from that piece

42:35

of text that would be just

42:37

searching for the keywords, you want

42:39

to kind of say, well, where is

42:41

there something in my text that's

42:44

similar to this sentence that I'm

42:46

typing in? And the fact that

42:48

you have a lot of sentences which

42:50

have the in them. just like the

42:53

sentence you typed in has a V

42:55

in it, that's not terribly significant. So

42:57

there are a bunch of different ways

42:59

to find out, well, what is the,

43:01

what is a relevant match? What is

43:03

a significant match? What's not a

43:05

significant match? There's a technique, actually

43:08

not a mentored IBM, but it

43:10

was sort of used there, a

43:12

thing called TFIDF, term frequency, inverse

43:14

document frequency, which essentially is the

43:17

thing that says, if there's a

43:19

really obscure word, you know, you

43:21

know, a a rhombic hexacontahedron, to

43:23

pick an obscure word. That happens

43:25

to be the name of the

43:27

three-dimensional solid that is our company

43:30

logo and so on. But it's

43:32

an obscure word, a rhombic hexacontahedron.

43:34

If your document somewhere in it

43:37

has the world hexacontahedron and

43:39

your search query has

43:41

hexacontahedron, the place where

43:43

you find hexacontahedron in

43:45

the document is probably

43:47

really significant. you what

43:49

you found in your query and what

43:52

you found the document is the word I

43:54

don't know significant let's say

43:56

that's less significant it's

43:58

the word the is

44:00

completely insignificant. So there are

44:02

these methods for figuring out what's

44:04

the relevant thing to pick out

44:07

of a document. So IBM had

44:09

worked on a bunch of these

44:11

techniques and then they kind of

44:13

wanted to have an IBM as

44:16

a company with a long history

44:18

of doing this to have sort

44:20

of a publicity stunt of You

44:22

know, can we show off all

44:25

this technology? I have to say,

44:27

I know quite a few of

44:29

the people who are involved in

44:31

this whole story. So I'll give

44:34

you just the external version of

44:36

this. The thing that, so somebody

44:38

figured out, well, what's, you know,

44:40

the Japanese game? Again, I don't

44:43

watch television, so I've not really

44:45

seen this, but I, it's kind

44:47

of like you have a bunch

44:49

of clues. and then you're kind

44:52

of asked, you know, given these

44:54

clues, you know, who does this

44:56

correspond to, you know, who's a,

44:58

who's a person, what's a, what's

45:01

a kind of animal that has

45:03

some pointing ears and a bushy

45:05

tail and climbs trees and this

45:07

and that and the other, and

45:10

it's sort of, is it a,

45:12

I don't know what does that,

45:14

but that kind of thing. So.

45:16

The sort of publicity stunt was

45:19

to try to use text retrieval

45:21

methods to sort of beat the

45:23

game of Jeopardy and which is

45:26

a television TV game show. And

45:28

the idea was to use web

45:30

content and things like this and

45:32

essentially to do text retrieval searching

45:35

based on the clues that were

45:37

given in the Jeopardy game and

45:39

then surface the answers. So this

45:41

was done in a kind of

45:44

televised thing the one time I

45:46

watched Japanese on television. What was

45:48

quite interesting to see was that

45:50

at the bottom of the screen

45:53

they showed the runner-up kind of

45:55

possible answers. And that was very

45:57

revealing because it was revealing that

45:59

this... was the textatory or play

46:02

because some of those answers had

46:04

incorrect capitalization and things like this.

46:06

They were really coming from the

46:08

source document. It's like here's the

46:11

sentence that comes from the source

46:13

document that seems to be a

46:15

match. So anyway, they did that

46:17

the the the big thing was

46:20

that the the IBM machine that

46:22

was very dramatically presented as this

46:24

big physical machine, won against the

46:26

then reigning jeopardy champion. I think

46:29

in reality, part of the way

46:31

that that game works is do

46:33

you lock in a win or

46:35

do you try for the next

46:38

clue? And that's kind of a

46:40

probability estimates question. And humans are

46:42

really not very good at that.

46:44

Humans are always too hopeful. or

46:47

two pessimistic. And humans don't just

46:49

kind of coolly weigh the odds

46:51

and make their choices based on

46:53

those. Machines are much better at

46:56

that. And I think that's in

46:58

the end why the machine won.

47:00

It was more or less you

47:02

know the clues it was doing

47:05

sort of similarly, but it could

47:07

win on doing the probability estimates

47:09

correctly. So that was the story

47:11

of Watson came out soon after

47:14

the Wolfram Alpha. Well, if my

47:16

offer came out and it was,

47:18

it never really went too far.

47:20

It was, I think as a,

47:23

you know, as a piece of

47:25

corporate commentary, it's, it was sort

47:27

of a publicity stunt that got

47:29

people to pay attention to IBM.

47:32

I mean, they spent billions of

47:34

dollars advertising Watson as a way

47:36

to do for your corporate data,

47:38

what it had done for Japanese.

47:41

And to kind of find a

47:43

needle in a haystack. in sort

47:45

of corporate data or medical data

47:47

or something like this. you know,

47:50

find the needle in the haystack

47:52

and win big. The truth is,

47:54

in many ways, and this is

47:56

maybe more of a business statement,

47:59

it was sort of solving the

48:01

wrong problem because most companies have

48:03

their data in a pretty organized

48:05

form and databases and things like

48:08

that. It's all just rows of

48:10

numbers and so on. And the

48:12

problem ends up being, can you

48:14

answer a question that is maybe

48:17

stated just in plain English? answer

48:19

a question relative to all that

48:21

structured data. And actually that's the

48:23

technology we built in Wolfmalfa was

48:26

very suitable for that. It's been

48:28

used many many times for that.

48:30

And it's something for which this

48:32

text retrieval approach of Watson really

48:35

wasn't a good idea. There are

48:37

more there's more to this story

48:39

of our interactions with IBM and

48:41

Watson, but I don't think I

48:44

should at least not yet tell

48:46

that on a live stream. I

48:48

have to think about that. Maybe

48:50

in a few years from now,

48:53

maybe it's an interesting story, it's

48:55

an interesting story and maybe it

48:57

can be told. But in a

48:59

case, how does that relate to

49:02

a modern LLM? Well, the methodology

49:04

was different. As I said, it

49:06

was really about text retrieval, much

49:08

more like a search engine. In

49:11

fact, right after the Japanese win,

49:13

I tried, how well could you

49:15

do just with a search engine?

49:17

And the answer was pretty well.

49:20

The main issue with the search

49:22

engine was... that yes, you could

49:24

get the right answer on the

49:26

first search engine result page, but

49:29

knowing which of those answers from

49:31

the search engine result page was

49:33

the absolute winner, that was more

49:35

difficult. That final ranking was a

49:38

bit more difficult. But, okay, so

49:40

for an LMLM, LEM's work in

49:42

a rather different way. They are

49:44

taking the input text, might be

49:47

a huge amount, trillion tokens, whatever

49:49

it is, and they're really grinding

49:51

it up. They're getting trained to

49:53

replicate that text. That's their training

49:56

task. But the way that they

49:58

represent that text is really ground

50:00

down to all these numbers inside

50:02

the neural nets and so on.

50:05

There's no lump of text there

50:07

that says, you know, John Smith

50:09

or something as a potential answer.

50:11

It's the John Smith is encoded

50:14

in this way that nobody really

50:16

understands very well as all these

50:18

little detailed numbers that are part

50:21

of the neural net weights that

50:23

are part of the 100 billion

50:25

neural net weights, let's say. When it

50:27

will be interesting actually, and I

50:29

see an easy experiment, I'm sure

50:32

somebody's tried it, I don't know

50:34

the answer, of how well does

50:36

the modern LLLM do on the

50:38

original televised jeopardy competition

50:40

that Watson did? My guess is

50:42

that a modern LLLM will do very well

50:45

at that. My guess is that we'll pretty

50:47

much nail it. And almost effortlessly so.

50:49

I might be wrong, be a good

50:51

experiment to try, but that would be

50:53

my guess. But the way it's doing

50:55

it's doing it. is very different.

50:58

And even though the effect might

51:00

be, well, somewhat, somewhat the same.

51:02

But that's a thought on that. I

51:04

mean, it's a very different term.

51:06

These approaches are all very

51:08

different from what we're doing with

51:11

Wolfram Alpha or Wolfram language,

51:13

where we're actually computing answers.

51:16

In the text retrieval case,

51:18

you're literally pulling out that

51:20

piece of text. In the LLM case,

51:22

you're pulling out that sort

51:25

of statistical pattern. that you

51:27

learn from the pattern of a piece of

51:29

text. It's not, you are using essentially

51:32

an algorithm to compute the

51:34

answer, or you're using sort

51:36

of the structured, curated data

51:38

to be able to figure

51:40

out the answer. That's what

51:42

we're doing in Wolfram Language.

51:44

It's something where Wolfram Language

51:47

is a useful tool for humans.

51:49

It's also become a useful tool for AIs.

51:51

More and more of our customers now are

51:53

AIs. Presumably there's a human at the end

51:56

of the chain who's asking the AI to

51:58

do something and then the AI is

52:00

asking our technology to do something,

52:02

one assumes, maybe one day it'll

52:04

be AIs for themselves, so to

52:06

speak. But the dynamic is that

52:09

the the LLM is providing this

52:11

kind of linguistic interface to ultimately

52:13

this computation. So it's sort of

52:15

a hierarchy of things, from the

52:17

pure text retrieval to the kind

52:19

of statistical ground up thing to

52:21

the actual computation side of things.

52:24

Let's see. Okay, Opie comments, would

52:26

the LLLM have the same reaction

52:28

time to compete and press the

52:30

buzzer? That's an interesting question. That's

52:32

a good sort of, you know,

52:34

assessment of LLLM's because the fact

52:37

is that LLLM's, well, an LLLM,

52:39

the way it works, like chat

52:41

GPT, I think, had about 400

52:43

layers in the neural mat. And,

52:45

you know, you're kind of, you're,

52:47

you're sending that. data through those

52:49

layers and that takes a certain

52:52

amount of time and it has

52:54

to go through all those layers

52:56

for every token it produces every

52:58

piece of a word every word

53:00

every character whatever that it produces

53:02

now you know can one distill

53:05

the neural net so that it

53:07

has fewer layers can one have

53:09

faster hardware to run it on

53:11

those are all things one expects

53:13

to be possible and so they'll

53:15

speed up but it's a good

53:17

question at what point you reach

53:20

the jeopardy point so to given

53:22

the timing information. Oh, there's a

53:24

question here from Reebok. Is it

53:26

possible that one day will predict

53:28

the weather years in advance? I

53:30

think the answer is no. Plain

53:32

and simple. I think that there

53:35

are two different things. One is

53:37

the sort of computational irreducibility of

53:39

all that turbulence and all those

53:41

kinds of things. The other thing

53:43

is that in the end... you

53:45

need to know precisely the way

53:48

the world is set up and

53:50

precisely you know what tree is

53:52

growing on what hill and what,

53:54

you know, how much plankton is

53:56

there in this piece of the

53:58

ocean that causes this or that

54:00

thing. So to know, and even

54:03

in the case of predicting the

54:05

weather far in advance, you know,

54:07

how much traffic is they going

54:09

to be on this road that's

54:11

going to stir up the air

54:13

in this or that way? So

54:16

I think the sort of lack

54:18

of knowledge of the future of

54:20

the world kind of precludes that.

54:22

Now what level... of general prediction

54:24

can you make? This is kind

54:26

of one of the challenges of

54:28

climate work is, okay, the weather

54:31

is one thing. That is the

54:33

details of, you know, what will

54:35

the temperature be? Will it be

54:37

raining in this place or that?

54:39

Really hard to predict things about

54:41

clouds and when clouds form and

54:44

etc., etc., etc. Now if you

54:46

say, well, can I say something

54:48

about the weather a year from

54:50

now, it's very challenging. Because, you're

54:52

sort of, are there things that

54:54

you can say in generality and

54:56

approximately, versus things that you can

54:59

say as a matter of something

55:01

like weather prediction? The transition between

55:03

those things is really tricky, because

55:05

when you're predicting something, you know,

55:07

far in advance, you can't simulate

55:09

every single blade of grass for

55:11

sure not, but even, you know,

55:14

the size of the region on

55:16

the earth that you're simulating, I

55:18

don't know how big it is

55:20

these these days. I think it's

55:22

like 10 kilometers on a side,

55:24

something like that, is the grid

55:27

of kind of what you can

55:29

do very long term sort of

55:31

climate prediction from. It's a very,

55:33

a very coarse grid. So anything

55:35

that's happening that matters about, you

55:37

know, this particular cliff that has

55:39

this particular airflow and so on,

55:42

it's like you're out of luck.

55:44

It's just a 10 kilometer square

55:46

grid, grid section. And it's, it's

55:48

super hard to know what will

55:50

happen and you know there's one

55:52

thing is to do a computer

55:55

simulation the other thing to do

55:57

is to say, given this effect,

55:59

like increasing carbon dioxide levels, increasing

56:01

retention of water vapor in the

56:03

atmosphere, all these kinds of things.

56:05

Given these effects, can we make

56:07

a kind of physics understandable, human

56:10

understandable argument for why this or

56:12

that thing should happen? Sort of

56:14

two competing methodologies. One is the

56:16

kind of reason it through kind

56:18

of almost natural philosophy style, but

56:20

whether you and the other is

56:22

run the computer simulation, and hope

56:25

you've got all the parameters right

56:27

and just trust the answer. They're

56:29

both fraught with difficulty and you

56:31

know if you can if you

56:33

can kind of make them agree

56:35

and not cheat in doing that

56:38

then you have something going for

56:40

you but it's really hard and

56:42

I think the I mean my

56:44

observation has been that the closer

56:46

you get to people who actually

56:48

do climate modeling really on the

56:50

ground with computer systems, the more

56:53

they say, hey, we want to

56:55

just make these physics arguments, and

56:57

vice versa, so to speak. It's

56:59

a pretty difficult area to know,

57:01

sort of to be able to

57:03

say what's going to happen. But

57:06

that's kind of the story of,

57:08

and to know, you know, will

57:10

this happen three years from now,

57:12

there are some large scale atmospheric

57:14

effects like El Nino's and so

57:16

on, which have effects on timescales

57:18

of order a few years of

57:21

order a few years. Similarly, things

57:23

changing in ocean currents and so

57:25

on. And there there's some predictability

57:27

on multi-year timescales, usually with the

57:29

kind of physics argument type methodology,

57:31

not the detailed closer to weather

57:33

forecasting type argument. Reebelke is asking,

57:36

then it is whether a good

57:38

random sequence. Well, up to a

57:40

point, but you know, there is

57:42

some predictability. I mean, like if

57:44

you say the temperature... here is

57:46

random. Well, it's not really. In

57:49

the course of the year, you

57:51

know, in places inland, for example,

57:53

you have this essentially sinusoidal temperature

57:55

is a function of time through

57:57

the year. That's the overall temperature

57:59

profile. Now in detail day to

58:01

day there may be all kinds

58:04

of seemingly random fluctuations, but there's

58:06

still an overarching pattern to the

58:08

whole thing. Let's see, there's a

58:10

question here from Brianna, how do

58:12

you calculate wind speed if wind

58:14

is a pressure difference? So I

58:17

mean the easy way to generate

58:19

wind speed is to the an

58:21

animometer where you know it's been

58:23

the same forever and ever. It's

58:25

just this little thing you see

58:27

that's twirling around and has little

58:29

cups that catch the wind and

58:32

it gets twirled around at a

58:34

different speed depending on on how

58:36

fast the wind is going. That

58:38

works okay if you're dealing with

58:40

like you just stick it on

58:42

a pole and you're measuring it

58:45

at the surface. It's a bit

58:47

trickier to measure the wind speed

58:49

when you're you know, in the

58:51

air, because among other things, it's

58:53

like you don't have, you don't

58:55

have the pole that you're attaching

58:57

things to, to measure winds aloft

59:00

is a trickier thing. These days,

59:02

I guess, you know, it's some,

59:04

let's see how, I mean, clearly

59:06

you can have a balloon, if

59:08

you have a balloon and you

59:10

send the balloon up, the balloon

59:12

is going to get blown by

59:15

the wind, and you can just

59:17

watch the balloon and see how

59:19

fast it goes, and with modern

59:21

GPS, that's not difficult. I'm trying

59:23

to remember how this, I mean,

59:25

planes can, I'm trying to think,

59:28

it's sort of an application of

59:30

vectors, so to speak. The plane

59:32

thinks it's going in this direction,

59:34

but and it has a certain

59:36

thrust that it's pushing with, but

59:38

the wind is blowing it in

59:40

that direction, and it's sort of

59:43

the vector sum that determines what

59:45

the actual direction is. And I

59:47

think you can deduce... In fact,

59:49

yeah, I know you can deduce

59:51

something about the winds at different

59:53

altitudes by looking at what's happening

59:56

to planes. But the whole question

59:58

about is the wind, for example,

1:00:00

constant as you go up, no it

1:00:02

isn't at all. The wind is

1:00:04

going in very different directions as

1:00:07

you go as sort of as

1:00:09

you go up and winds at

1:00:12

high altitudes are routinely very fast.

1:00:14

I mean, there would be, you

1:00:16

know, if you're if you're

1:00:18

in a plane flying at,

1:00:20

you know, 36,000 feet, 40,000

1:00:22

feet or something, the winds

1:00:25

can routinely be 200 miles

1:00:27

an hour. And which at the

1:00:29

surface just doesn't happen that way.

1:00:31

I mean in general what's happening

1:00:33

is there's friction between the air

1:00:36

and the surface of the earth

1:00:38

and that that causes the the

1:00:40

air that's close to the surface

1:00:42

to be moving well in the

1:00:44

end it's moving very slowly at

1:00:47

the you know right down you

1:00:49

know an inch from the ground

1:00:51

or something and as you go

1:00:53

further up there's kind of that

1:00:55

sort of that effect becomes less

1:00:57

important than that it's just how

1:01:00

much is the air getting blown

1:01:02

around, so to speak. Let's

1:01:04

see. If the Earth started rotating

1:01:07

in reverse, ask Kuki, would

1:01:09

that have an effect on

1:01:11

the weather? Absolutely. I mean,

1:01:14

at the moment when

1:01:16

it started turning backwards,

1:01:18

you know, all hell will break

1:01:20

loose, but let's assume that

1:01:22

we just picked an Earth.

1:01:24

that was otherwise the same but

1:01:27

was rotating the other way around. The

1:01:29

point is that, let's see if I

1:01:31

remember which way around this goes.

1:01:33

Cyclones are in the northern

1:01:36

hemisphere, rotate in one direction

1:01:38

in the southern hemisphere, and

1:01:40

not remember, I think cyclones

1:01:42

go clockwise in the northern

1:01:44

hemisphere. So that's regions of

1:01:46

low pressure that have essentially

1:01:49

wind circulating around them.

1:01:51

They, because of the rotation of

1:01:53

the earth... those have the rotation of the

1:01:55

earth leads to this sort of asymmetry

1:01:57

between what happens in the southern hammers.

1:01:59

in the northern hemisphere, at

1:02:02

least in the direction

1:02:04

of rotation of these

1:02:06

things. That's a result

1:02:08

of this thing called

1:02:10

the Coriolus force, which

1:02:12

is a force that, let's

1:02:14

see, it's a force that you

1:02:17

get on a rotating object.

1:02:19

It's roughly that if you,

1:02:21

well, yeah, let's let's give

1:02:24

an example, a practical

1:02:26

example. If people

1:02:28

are shooting. guns, artillery, and

1:02:31

they have a shell and they shoot it

1:02:33

20 miles. It goes up in

1:02:35

this parabolic trajectory more or

1:02:37

less than it comes down again.

1:02:39

And the question is, as that

1:02:41

happens, as the thing is going

1:02:43

through the air, so to speak,

1:02:45

the earth is turning underneath it.

1:02:47

And that effectively, as you work

1:02:50

out all the math and so

1:02:52

on, that ends up having an

1:02:54

effect on then where relative to

1:02:56

where the earth is. If you're

1:02:58

fixed, if you're in knowing if

1:03:01

what matters is where the shell

1:03:03

is going to fall, is it

1:03:05

going to fall, you know, on

1:03:07

that, you know, battalion

1:03:09

or that other one or something,

1:03:11

or on that, you know, where

1:03:14

is it going to fall, that's

1:03:16

that question of where

1:03:19

those troops are is fixed on the

1:03:21

surface of the earth. But where the

1:03:23

shell goes is... during the time the

1:03:26

shell is in the northern hemisphere and

1:03:28

the southern hemisphere. And so that you

1:03:30

can think of that as being like

1:03:32

a force if you if you fix

1:03:35

yourself to the coordinate system of

1:03:37

the folks on the ground, it's as

1:03:39

if there's a force that's pushing the

1:03:41

shell on a certain direction. And

1:03:43

that force, as you think about sort of

1:03:46

the coordinates of how you how

1:03:48

you define things, is in an opposite

1:03:50

direction in the northern hemisphere in

1:03:52

the southern hemisphere and the southern hemisphere.

1:03:55

And so, for example, when when people

1:03:57

have artillery tables back in the day

1:03:59

with and they were still kind

1:04:01

of, you know, to set a

1:04:04

gun or something, you had to

1:04:06

actually look up this table of

1:04:09

numbers. They had to have different

1:04:11

ones for the Northern Hemisphere and

1:04:13

the Southern Hemisphere. That effect

1:04:16

in a less troublesome

1:04:18

setting, perhaps, is what

1:04:20

leads to the different circulation

1:04:22

in the Northern Hemisphere and

1:04:25

the Southern Hemisphere of these

1:04:27

high pressure. cyclones and

1:04:30

so on. By the way, there's

1:04:32

a fun story of a long

1:04:34

time ago. There was a, perhaps

1:04:36

not so directly relevant,

1:04:39

but it's an interesting

1:04:41

story anyway. There was

1:04:43

a plane that a fighter plane,

1:04:46

I think, that was sort

1:04:48

of electronically controlled fighter

1:04:50

plane. This was

1:04:52

in the 80s, I guess. And

1:04:54

one feature that it had was,

1:04:57

it had had was, verified

1:04:59

the code for this plane and it's

1:05:01

correct. Of course, what does it

1:05:03

mean for the code for a fighter

1:05:05

plane to be correct? Because it

1:05:07

depends what you want the fighter

1:05:09

plane to do. And the thing that happened

1:05:12

was the fighter plane was being

1:05:14

tested and it flew over the

1:05:16

equator to the southern hemisphere and

1:05:19

it turned upside down. And that,

1:05:21

and now, is that correct? Is

1:05:23

that not correct? You probably don't

1:05:25

want the plane to fly upside

1:05:27

down. But... That was a thing

1:05:29

I think it had to do

1:05:31

with correcting for the Coriolus force,

1:05:33

I'm not sure, but that was

1:05:35

a sort of an interesting case

1:05:37

of you think you've defined what

1:05:39

it means to be correct, but unless

1:05:42

you've thought of all the things

1:05:44

that could happen, it's very hard

1:05:46

to imagine what it means to

1:05:48

be correct, so to speak. And

1:05:50

that was a case where rather

1:05:52

dramatically it was not what you

1:05:54

would have hoped it would do, so to

1:05:56

speak. Let's see. Um,

1:05:59

oh. So I see there was

1:06:01

a question here, let's see, just as

1:06:03

asking, what would it take to

1:06:05

stabilize the weather, like using

1:06:08

wind farms in reverse or

1:06:10

controlling ground albedo so that

1:06:12

we know it exactly? That's

1:06:14

a good question. I mean, this is

1:06:17

the whole area of geoengineering,

1:06:19

which is, you know, if we don't like

1:06:21

the way the climate is going,

1:06:23

how about we engineer it to

1:06:26

be something different? And we might

1:06:28

not like it because we feel bad

1:06:30

about the fact that we humans are

1:06:32

having an effect on it. We might

1:06:34

not like it because it's causing some

1:06:36

part of the earth to turn into a

1:06:38

desert. You know, we might not like

1:06:40

it for all kinds of reasons. But

1:06:42

let's just say we could turn the thermostat

1:06:44

of the earth and say this is what

1:06:47

the weather is going to be like.

1:06:49

It's of course a very complicated

1:06:51

question if one had that capability

1:06:53

and it was global. Where should

1:06:55

we set the temperature to be? Do we

1:06:58

want it to be the case that, you

1:07:00

know, Northern Canada is a great place for

1:07:02

growing bananas or something? Perhaps not. Perhaps

1:07:04

we say that's too far off. Do we

1:07:06

want it to be the case that doesn't

1:07:08

get quite as cold in the winter on

1:07:10

the east coast of the US or something?

1:07:13

Or do we want it to be the

1:07:15

case? You know, there are lots of different

1:07:17

things. It's very hard to decide what you

1:07:19

would want to do if you could just

1:07:21

control the thermostomat of the earth. It would

1:07:23

be much easier if you could

1:07:25

say, for, you know, this county

1:07:28

wants to pick this or that

1:07:30

thing to happen, that I think

1:07:32

is a more plausible, very difficult

1:07:34

to achieve, but a more sort

1:07:36

of socio- politically achievable kind of

1:07:38

objective. But in any case, this

1:07:40

question of can we in fact make

1:07:42

control these things, the answer is

1:07:44

almost certainly yes. There are all

1:07:47

kinds of different approaches, a,

1:07:49

well, I mean, to list a few of few

1:07:51

of them. And sometimes you hear about

1:07:53

these approaches and then I'll hear about them

1:07:55

from people and then a few years we'll

1:07:57

pass and I'll say well what what happened?

1:07:59

to that approach. And I say, well, it

1:08:02

doesn't work because of this and that

1:08:04

and the other thing. But a few

1:08:06

approaches are you put aerosols, little

1:08:08

particles in the upper atmosphere

1:08:10

of the Earth, it changes the albedo,

1:08:13

the amounts of sunlight that the Earth

1:08:15

reflects, as opposed to getting absorbed on

1:08:17

the surface. That means that the sky

1:08:20

will be a little bit dimmer, but it

1:08:22

means that less sunlight will reach the

1:08:24

Earth, and so you'll cool the

1:08:26

Earth. That's an example of an

1:08:28

approach. Another approach is... to seed the

1:08:30

oceans with iron so that you grow

1:08:33

more algae and those algae will will

1:08:35

ingest carbon dioxide. It's very

1:08:37

much like what plants do

1:08:39

in the, you know, plants. If

1:08:42

you plant more trees, you know,

1:08:44

there are a couple of trillion

1:08:46

trees on the earth right now.

1:08:48

If you planted another trillion trees,

1:08:50

you would have some effect as

1:08:53

well. It might be easier to

1:08:55

seed the oceans, kind of fertilize

1:08:57

the oceans and get the algae

1:08:59

in the oceans to do this.

1:09:01

That changes carbon dioxide levels. It's

1:09:03

not clear that the albedo change

1:09:06

is mostly to do with retention

1:09:08

of water vapor. So it's a

1:09:10

slightly less direct thing, but

1:09:12

it's presumably related.

1:09:14

Then there approaches, let's

1:09:16

see, there are all kinds of

1:09:18

approaches. What are some other ones?

1:09:21

There are the artificial

1:09:23

trees. That's another approach.

1:09:25

You know, controlling the wind.

1:09:27

You know, the fact that wind

1:09:30

farms work insofar as they

1:09:32

do is and they're tricky

1:09:34

business because wind farms

1:09:36

are very expensive, very

1:09:38

hard to maintain giant

1:09:40

pieces of equipment that, you

1:09:43

know, it's not clear that

1:09:45

the economics are complicated. But

1:09:48

insofar as it's not people

1:09:50

don't usually say, oh, there's

1:09:52

a wind farm there, so it took all

1:09:54

my wind, so to so to speak. There

1:09:57

is some of that, but that's a very

1:09:59

small effect. the amount that's removed

1:10:01

from the circulation of

1:10:03

the atmosphere is absolutely

1:10:05

tiny. I mean, it's the same thing as

1:10:08

you could say if we're using hydroelectric

1:10:10

power and we're doing things like,

1:10:12

you know, for example, we're storing

1:10:14

energy by pumping water up to

1:10:17

a higher level and then letting

1:10:19

it cascade down to a lower

1:10:21

level, in a sense that pumping act

1:10:24

is is doing something that that

1:10:26

is, well, let's see is that. Well, no,

1:10:28

if you're harvesting energy from the

1:10:30

tides, for example, I think that

1:10:32

pumping thing does it as well,

1:10:34

but to a smaller extent, if

1:10:36

you're taking energy from the tides,

1:10:39

you are effectively reducing the tides

1:10:41

of the earth, and ultimately you

1:10:43

will affect the rotation rate of the

1:10:45

earth. But that effect is so

1:10:47

absolutely infinitesimal that all the power

1:10:49

us humans could ever want would

1:10:51

not have a big effect on the rotation

1:10:54

of the earth. I think the question of,

1:10:56

you know, could you do something that

1:10:58

has a climate effect by using,

1:11:00

and so on, is because, but

1:11:02

that's mostly due to things like

1:11:04

earthquakes and so on. It's things

1:11:07

beyond what us humans, you know,

1:11:09

the levels of energy that us

1:11:11

humans can make use of. But I

1:11:13

think in the question of, you know,

1:11:15

could you do something that has a

1:11:17

climate effect by using sort of

1:11:20

wind farm level technology? I kind

1:11:22

of suspect the answer is no.

1:11:24

I kind of suspect that it's

1:11:26

just way too weak to have any

1:11:29

effect there. I think that a

1:11:31

sort of intermediate case is cloud

1:11:33

seeding. This question of whether

1:11:36

you can make clouds form,

1:11:38

make clouds rain, that's been

1:11:40

a thing that people have tried

1:11:42

for a hundred years. It's typical,

1:11:45

it's the one of the

1:11:47

things that is generally believed

1:11:49

to be true, is that sort

1:11:51

of every raindrop. was nucleated by

1:11:53

something like a piece of dust

1:11:55

or something, that when you have

1:11:58

water vapor in a cloud... It's

1:12:00

just going to stay as water vapor

1:12:02

unless something kind of reminds it that

1:12:04

it could all be clumping together.

1:12:06

And then at the right humidity level

1:12:09

and so on, right temperature level, it

1:12:11

will start to clump typically around that

1:12:13

nucleation site, which might be a

1:12:15

piece of dust might even perhaps

1:12:17

be to do with cosmic rays

1:12:19

and ionization in the atmosphere, things

1:12:22

like this. It's not clear whether

1:12:24

that's important. It's not clear whether

1:12:26

it may be the path of

1:12:28

lightning is determined by that as

1:12:30

well. the idea is, so the

1:12:32

idea is, let's put sort of

1:12:34

artificial nucleation sites into a cloud

1:12:36

and make it nucleate more

1:12:38

quickly and then rain. And Silver

1:12:41

Ride, I guess, is one of

1:12:43

the common substances used, I think.

1:12:45

But the basic point is, you're

1:12:47

sort of trailing behind a

1:12:49

plane, you've got a plane

1:12:51

flying around, and it's splirting

1:12:53

out stuff into a cloud,

1:12:55

and then the idea is...

1:12:57

for that to form the

1:12:59

nucleation sites that cause the

1:13:02

water vapor to form into

1:13:04

droplets and then drop as rain.

1:13:06

And people have been trying

1:13:08

to do this for 100 years. And

1:13:10

there have been some claimed, there

1:13:13

have been a bunch of claimed

1:13:15

successes, a bunch of, I guess, the, I

1:13:17

think an Olympics in Beijing a

1:13:19

few years ago, there was a

1:13:22

claim that cloud seeding had

1:13:24

been successful there are, there's

1:13:26

a company I know that's, well one of

1:13:28

the challenges of cloud seeding is were

1:13:30

you actually successful or was it going

1:13:32

to rain anyway? It's kind of like

1:13:34

one of these medical tests type things,

1:13:37

you know, if you didn't take the

1:13:39

drug would you have gotten better anyway?

1:13:41

And so it's sort of a challenge

1:13:43

to be able to figure out, you

1:13:45

know, what would have happened anyway, so

1:13:47

to speak? And one's getting better at

1:13:49

that because weather radar and once

1:13:51

able to sort of more accurately say

1:13:53

these were the droplets and this cloud

1:13:56

And another thing you can do is

1:13:58

just have your plane flying. a pattern

1:14:00

and if it rains in a pattern

1:14:02

that spells out a word, which I

1:14:05

don't think anybody has quite achieved yet,

1:14:07

but if it did that, if the

1:14:09

pattern of the rain as seen by

1:14:12

a plane or a satellite or something

1:14:14

was spelling out the word hello or

1:14:16

something, you would be, that would be

1:14:19

a pretty convincing argument that It was

1:14:21

really, you know, the clouds are not

1:14:23

kind of spontaneously rain in the pattern

1:14:26

of the word hello. So you probably

1:14:28

really did succeed in doing cloud

1:14:30

seeding. But that's sort of

1:14:32

an intermediate case of local,

1:14:34

in a sense, local climate.

1:14:36

It's still been very challenging

1:14:39

to make that work. Let's see. Well,

1:14:41

Jogan is commenting, oh gosh,

1:14:43

got a couple of comments in

1:14:45

that should go up on my way

1:14:48

here, but Jillian is is asking

1:14:50

can the Earth's tilt

1:14:52

ever be affected?

1:14:54

What changes would

1:14:56

this cause? So the

1:14:58

Earth is tilted at

1:15:01

23 degrees relative

1:15:03

to the plane in which

1:15:05

it orbits the sun.

1:15:08

That's the... Oh my gosh.

1:15:10

That tilt is... What is

1:15:12

that? The obliquity,

1:15:14

I think of the Earth. I

1:15:17

think that's right. I

1:15:19

mean, most of the planets rotate

1:15:21

around in more or less the

1:15:23

same plane as they orbit the

1:15:26

sun. Famously, Uranus is tipped the

1:15:28

other way and rotates backwards, but

1:15:30

mostly it's close. The Earth is

1:15:33

23 degrees away. That's what leads

1:15:35

to the seasons is the fact

1:15:38

that that the Earth is not

1:15:40

rotating one with the amount of

1:15:42

sunlight you get depends

1:15:44

on a different times of

1:15:47

the year depends on. on

1:15:49

where you, depends on, on,

1:15:52

it varies because of

1:15:54

that tilt. There is a,

1:15:56

there is a, the, the,

1:15:59

the earth. It's its axis

1:16:01

processes around every 23,000 years,

1:16:03

I think. And so the

1:16:05

this this question of kind

1:16:07

of so so it's tilt is it's

1:16:09

like a top that's if you if

1:16:12

you watch a top before it

1:16:14

topples over, you'll see it

1:16:16

process the axis of rotation

1:16:18

will make this little circle.

1:16:20

The the axis of the earth

1:16:23

is doing the same thing every

1:16:25

23,000 years or so. But in

1:16:27

terms of. of things that affect the

1:16:29

tilt of the earth, I'm not

1:16:31

sure that much does. I mean,

1:16:33

and ultimately, you know, the moon

1:16:35

is very tied into what's happening

1:16:37

with the earth, and I don't know,

1:16:40

the moon is gradually receding from

1:16:42

the earth, and I don't know

1:16:44

whether when the moon has receded

1:16:46

far from the earth, or in

1:16:48

earlier times when the moon was

1:16:50

closer to the earth, I don't know

1:16:52

what that will have done to the, to

1:16:54

the tilt of the earth. Joggen comments,

1:16:57

there's a large difference between what

1:16:59

an ideal climate would be and what

1:17:01

changes would mean trouble for us

1:17:03

given our current infrastructure. Yes, absolutely.

1:17:05

I have no idea what an ideal

1:17:07

climate would be. I think it will

1:17:09

be dependent. The 8 billion people on

1:17:11

the earth would probably all have different

1:17:13

opinions about that. You know, the thing that

1:17:15

is probably the most difficult aspect

1:17:18

of climate change is that, you know,

1:17:20

we have an infrastructure that in...

1:17:22

recent years has been built up to

1:17:24

a high degree of precision, so to

1:17:26

speak. I mean, you know, a thousand years

1:17:28

ago, the climate changed the bunch

1:17:30

of times. You know, in the

1:17:32

1600s, it was much colder in

1:17:34

the middle of the 1600s, still

1:17:36

not clear quite why, the so-called

1:17:38

mourned minimum, that might have had

1:17:40

something to do with the output

1:17:42

from the sun. It's not really

1:17:44

clear, but it was much colder

1:17:46

then. and you know and there were

1:17:49

times when you know different parts of

1:17:51

the earth were very fertile versus not

1:17:53

and so on and you know in

1:17:55

past times over the course of a

1:17:57

hundred years people would just move their

1:17:59

sheep from one place to another, and

1:18:01

it wasn't sort of a big deal.

1:18:03

But in modern times, you know, we've

1:18:05

built up a lot of, you know,

1:18:08

we've built our condos on the beach

1:18:10

type thing, and we've built up a

1:18:12

lot of detailed things that depend

1:18:14

on the climate, the sea level,

1:18:16

and so on being the way that

1:18:18

they are right now. And, you know, that's,

1:18:20

I think, one of the challenges, which

1:18:23

at some level, as an economic challenge,

1:18:25

at some level, you know, people... people

1:18:27

have built up things the way they

1:18:29

want them to be and don't want

1:18:32

them to change type thing. But I

1:18:34

think that's, it's absolutely true that

1:18:36

the, you know, the number one issue

1:18:38

is the effect on modern infrastructure. And

1:18:41

even things like, you know, questions of,

1:18:43

you know, how much is that piece

1:18:45

of land worth? If you can grow

1:18:48

crops on it, it's worth more than

1:18:50

if it's just random, you know, tundra

1:18:52

that you don't seem to be able

1:18:55

to do much with. But I think,

1:18:57

so yes, that's, that's, and that's, you

1:18:59

know, that's the challenge is to

1:19:02

unravel kind of, sort of,

1:19:04

I don't know, economic

1:19:06

effects from kind of

1:19:09

the actual sort of

1:19:11

physics of climate. And

1:19:13

then, you know, I think

1:19:15

there's a certain kind of

1:19:18

ethical view that, you know,

1:19:20

the earth has been going along

1:19:22

just fine. and we shouldn't, you

1:19:25

know, we shouldn't affect it. That's more

1:19:27

of, I think, an ethical kind of

1:19:29

statement that it's unclear what that, you

1:19:31

know, from an ethics point of view,

1:19:34

that's a complicated story, because it's like,

1:19:36

you know, we got 8 billion people

1:19:38

and, you know, we think ethics is

1:19:40

really a pretty human thing, and it's

1:19:42

sort of more important in a sense,

1:19:44

in ethics as we do it, normally

1:19:46

as humans, because humans is really only

1:19:49

defined relative to humans, the ethics of

1:19:51

a very hard to very hard to

1:19:53

define. what we mean by you know

1:19:55

what should we what should we do

1:19:57

relative to the rock what should the

1:19:59

rock be doing, so to speak, that's

1:20:01

not really a, you know, ethics as

1:20:04

a human story. And so when

1:20:06

it's a question of sort of

1:20:08

ethics of the ethics of the

1:20:11

inanimate earth, that's a complicated story.

1:20:13

And that maybe is a is

1:20:15

a good thing to leave for

1:20:17

another time. Not that I know

1:20:20

how to unravel that question, but

1:20:22

that's, you know, that's a different

1:20:24

kind of overlay is some, the, is

1:20:27

what of what's going on and

1:20:29

sort of how to think about,

1:20:31

you know, the sort of the

1:20:33

theory of whether we should or

1:20:35

shouldn't be doing things to the

1:20:37

earth. And, you know, if we were

1:20:40

in a position to do, let's say,

1:20:42

we realize that it was going

1:20:44

to be a big win to

1:20:46

change the seasons. We, you know,

1:20:49

let's imagine in, you know, in

1:20:51

science fiction stories that, you know,

1:20:53

put engines, rocket engines on the

1:20:56

earth. And, you know, let's say we could

1:20:58

do that, which we cannot. It's far

1:21:00

far away from being possible. But let's

1:21:02

say we could, and we could change

1:21:04

the tilt of the earth and make

1:21:06

it be the case that we no

1:21:08

longer had seasons. You know, there's a

1:21:10

whole complicated question of what that would

1:21:12

mean and whether how we should think

1:21:14

about that ethically and otherwise. And spare

1:21:16

parts comments, even the weather can't agree

1:21:19

on what the weather should be. Yes,

1:21:21

and maybe that's a good place to end

1:21:23

for today. But thank you for asking

1:21:25

a lot of interesting questions. Get

1:21:27

me to think about a lot of

1:21:30

different things and well, thanks for asking

1:21:32

these questions and for joining me

1:21:34

and see you another time. Bye

1:21:37

for now. You've been listening to

1:21:39

the Stephen Wolfram podcast. You can

1:21:41

view the full Q&A series on

1:21:44

the Wolfram Research YouTube channel. For

1:21:46

more information on Stephen's publications, live

1:21:49

coding streams and this podcast, visit

1:21:51

Stephen Wolfram.com.