And about everybody who wasn't late probably ended up in here.

The results look reasonable except in one place we have to look at that.

Okay?

So...

I've...

We've been talking about the language of mathematics.

I don't know

I would like to kind of drill in on this because that's actually one of the things that is

apparently most difficult to many of you.

So...

Maybe here? How about that? Yes.

So...

The language we're using in math

this funny mixture of English

some weird new words and a lot of expressions and formulae is called mathematical vernacular.

Vernacular really comes from the fact that the Catholic Church had all masses in Latin and all the monks could talk Latin to each other.

And everything that wasn't Latin, right?

The language, the normal people were talking what's called vernacular.

So this is kind of what normal mathematicians talk.

And right

it's a technical language

but it's also a natural language which means it's not designed by a committee

it's actually evolved by use.

And the things that work have been adopted and the things that don't work fall by the wayside.

Okay?

It's a smaller community than the community that kind of decides to speak Chinese and evolves the language, but still it's a community effort.

And we basically have three levels of things when we talk about mathematics.

One is the mathematical objects

something like the number three

or the concept of a constraint satisfaction problem in symbolic AI.

Those kind of things, big objects, small objects.

But also the next level up is when we say the object has some kind of a property or two objects are related to each other

that we call statements.

Statements are statements about mathematical objects in our purview here.

Or CS objects

you know that we're using math to express knowledge about CS.

And the third level is the level of essentially truth.

Statements can be true or false.

Objects cannot be true or false.

They can be plurisoparamonic or sparse of all kinds

but they are not per se true or false.

Mathematical statements are true or false.

And then there's the layer that basically says

oh

and this is why we're sure they're actually not false.

They're true. They're a theorem.

The layer of justifying knowledge.

OK, so the first level is just we talk about objects.

And I did show you this Egyptian stuff with hieroglyphics and so on.

And the only reason I showed you this is to show you how inefficient the whole thing is.