Tim Poston - Keynote: Data Comes in Shapes

I feel very honored to be invited here.

Thank you very much.

I like to, I think I've seen one

maybe two other people with gray hair here

[audience laughter]

The last talk I gave a few weeks ago

was to a meeting of ophthalmologists

and that was a bunch of

much older people, okay, and

a homage here to the Fifth Elephant

This is the novel, the cover of the novel

from which it was taken and, well actually

I'm using this as a connection for a

little bit of boasting because

Terry Pratchett wrote the book

I am a co-author of a co-author of
Terry Pratchett

and I actually signed a publisher contract

on my 70th birthday

a few weeks ago to publish a

science-fiction novel with Ian Stewart

and I mention that not just
as boasting but,

ok, this is a Data Geeks meeting rather

than the Graphics Geeks meeting, but if

anybody has graphics enthusiasm, there is

all kinds of stuff that would be fun

to build for the website we are putting

together for that novel. strange things

happening on that planet, so do make

contact if you're interested in drawing

strange and beautiful things because

I have some strange and beautiful things

to draw and some to interact with.

What I don't have is a budget

you have to just like it

ok, that is pure digression

I was originally a mathematician and

that was my PhD back before almost anybody

here was born, and I've kinda wandered

around the world and the sciences and

I've turned into some sort of an engineer

But what I'm going to talk about here is

the power of particular mathematical

point of view, which is that numbers are

not just numbers

They belong together in shapes, so

What are data?

Mostly, they're numbers

I know there are fields and things

We've been hearing about that, but

then you keep counting

Lots and lots of it is numbers

But are numbers only numbers?

Well, no they gather together in things

They come in patterns

and really big data is all about

the arrangements those things make

just knowing the numbers, you don't
know anything

You got to know how they fit together

Patterns are shapes

So, studying shapes, data shapes,
any kind of shapes

Space-time shapes. That's Geometry

But not the kind that I was doing when I
was 13 or 14 years old

Mind you, I had some taste for it and it
was quite fun

but it was all flat in the sand,
just like that

and here is Euclid

Stuff we would write in little triangles

and fun things

This I remember as a remarkable theorem,

but I have never ever, ever, ever
seen a use for

[audience laughs]

It's weird, it's very much something

about the plane, it's strange

and I have never encountered it or

referred to it in anything useful since I
left school

It's a bizarre theorem,
which is occasionally useful

Everything is so much in the plane

Data shapes don't live mostly in the plane

Geometry doesn't mean that you replace

now this, by the way, is highly superior
pointer technology

Much better than those twinkling little

red things that you lose track of
where it's pointing to

and 10% of your audience can't see red

Now, here is something serious

Children think in 3D

They think brilliantly in 3D

They naturally work in 3D

They are connecting how their vision

is working with their hands

they can reach out and grab your nose

If you watch a small child, it's doing
a lot of practice at building

a 3D model of the world, and then,

and these days that continues into
primary school

a hundred years ago, ugh..

but now primary school's good

but their secondary schools suck rocks

It's still, if you get any geometry

it's flat, flat stuff.

It can get more and more complicated

yeah.. but,

I just grabbed that off the web

as one particular complicated 2D diagram

but fix your mind in 2D, you
get to the point where you can't think

Are the x- and y- axes this way
or this way?

I found my UCLA students

if I switched drawing on the blackboard

from this way to that way

because something could be seen better
that way

they couldn't turn it in their heads.

Well data doesn't live in the plane.

It's not flat.

If we have three variables, we have
three dimensions.

That might be how far this way,

how far this way, and how far up.

And if you're doing graphics, it's three
very directly spatial dimensions.

But if it's, if you've just got numbers
about people

I look at everybody here, I know their

height, well I don't know their height but

you guys do because you're big data guys.

Know the height, know the weight, know
the age.

Three numbers, that's a three
dimensional set.

And the pattern that you make, that's

three dimensional geometry.

But of course, you typically have

a lot more. So you've got 'n'
dimensions

and 'n' can be quite big.

So you need to think about 'n' dimensions.

And there's two ways to do it.

One is to turn it all into algebra, which

is what people spend a lot of their time
doing.

And in this talk I'm only going to talk
linear algebra

which doesn't mean it's the only kind
there is,

but I've only got a few minutes.

Or you can practice thinking in 3D and

build up insights that help you very

seriously in 'n'-dimensional thinking.

I took up carving things when I was a grad

student because I realized that my mind

had been flattened by my high school

and my undergraduate. I needed to loosen
up

my mind and think in 3D, so I started

using my hands. You got, this is the

visual part of the brain, this is the

motor part of the brain, and the motor
cortex

just has to be 3D because you've got to

pick things up, you got to twist them,

connect it all up. So seriously, for 3D

thinking, take up sculpture.

So practice thinking in 3D, and the more

3D you can think, the readier you are to

think in other dimensions, general
dimensions.

But 2D? Nah, it's not enough.

So, question for you guys.

Most people here have done things - are

doing things with matrices sometimes,
right?

What does a matrix even mean?

Whats it represent?

Blah, you have told me the data structure.

It's, yeyah, it's an array.

This is the data structure.

It's an array this way, and this way.

But, at the level of algebra, and geometry.

It's something a bit more.

It's something that operates on vectors.

Transforms vectors, and in particular

there was a rule that they taught me

yea back at first or second year of graduate

of which way you multiply the
matrix and the vector.

And, I swear to you it took
me a year to remember

When I'm multiplying 2 matrices
do I go along this way

or along that way. Because it
was a damn silly rule.

That came from the Algebra book.

But, trying to avoid spending
too much time on this.

You do know the rule most of you.
So, if you have this 3x3 matrix.

And, apply it to this vector.
[column of '1,0,0']

You get this. Which is this column.
[points to 'a,c,f' columns]

And, if you apply to this vector.
[column of '0,1,0']

You get this column.
[column of 'b,d,g']

And, if you apply to this vector.
[ column of '0,0,1']

You get the last column.

Now, '1,0,0' means lets suppose
this is the x direction.

X this way. It says anything
that is purely in the

X direction goes to 'a,c,f'.

Wherever that is.
Which is a 3 dimensional vector sum.

Anything that is in the Y direction.
Like, '0,1,0' goes to something else.

Specifically, it goes to 'b,d,g'.

And, anything that starts vertical
goes to 'c,e,h'.

So the matrix is actually a list of vectors.

It's saying, where does the first one go

where does the second one go,
and where does the third one go.

And, believe me if you're doing 3d
computer graphics;

understanding that point
will make it much easier

than anything I've ever seen
in an OpenGL manual

of what you ought to be do.

They don't explain matrices very well.

It's just a list of where
these 3 things go.