Steve Patterson Name and picture from twetch — not on-chain. The signature is; the profile is not.

If your geometric investigations have only been within Euclidean geometry, or only working within continuous space, then discrete space can be unintuitive or shocking.

But alas, all space that we encounter, mental and physical, is actually discrete.

If we're talking about actually-existing geometric objects - not Euclidean nothings - then sure. A "square" is a composite object, made up of a finite number of points. The "diagonal" is another composite object whose units can be counted.

There are definitely self-evident truths.

"Every thing is exactly the way that it is, and it isn't however it isn't."

Self-evidently true.

Few mathematicians would have ever thought that until the 20th century. "Axioms" used to mean a self-evident or easily demonstrate truth. Now, because of the blunders modern math, "axioms" mean "any set of assumptions we take as a given and cannot prove."

A theory that doesn't talk about real things, or makes no attempt at connecting fictions to the world, is a bad theory.

Math can talk about real things, and it can say important things about the world.

"Quantity" is a real feature of the universe.

Gödel's theorems presuppose the meaningfulness of infinitary processes. Zeilberger and I touch briefly on it in this interview: https://www.youtube.com/watch?v=uNYRUUkuhuo

That's the nice way of putting it. I think most pure mathematicians are closer to being mentally handicapped than being intelligent.

Sentences can be associated with quantities, sure. Words are just symbols with a different form.

"If you take three apples and add them to three apples, you'll have a total of six apples." That concept can be expressed, "3a + 3a = 6a".

Mathematical language just uses a different set of symbols. Like sentences, some constructions are valid and some are invalid.

I can write down the symbols "15/0" and say the words "fifteen divided by zero." Doesn't mean that refers to any real quantity.

Actually draw a diagonal on a square, and you will see that, in fact, the diagonal is composed of a finite, countable number of points.

Euclidean geometry mistakenly assumes that space is continuous. With discrete space, there is no incommensurability.

There is no reason to posit "getting closer to a quantity."

Imagine we're talking about English sentences. I can give you a formula to construct a sentence. After each iteration, it contains more words. That doesn't imply it's "approaching" anything.

Perspective A: "The sqrt(2) is a quantity whose value we don't know, can never know, and can only approximate"

Perspective B: "The sqrt(2) is a formula that generates outputs of increasing decimal length, starting with 1.41 and never repeating"

"The square root of two" is a way to describe a formula. The formula is a construction that generates outputs. The outputs differ depending on how many iterations you run.

There is no "converging" on a quantity. The outputs just gain decimals.

Depends on what "it" is. The formula doesn't change, but the output of the formula does, depending on how many times you iterate.

1.41 is different than 1.414 is different than 1.4142, etc.

The formula stays the same. The output changes.

Why "definitely"? Mathematics is a language, and just like any language, the symbols don't necessarily correspond to some independently existing part of the universe.

What explanatory benefit do you gain from saying the sqrt(2) is a fixed quantity?

So, there's no fixed quantity that equals "the square root of two."

Instead, there's a symbol that represents a formula for the generation of numbers.

The generated numbers begin with 1.41 and get more decimals added with more cycles.

I can't speak for him, but I'd say they are formulas for the construction of numbers, not numbers themselves.

As you run more iterations of the formula, the number that's generated slightly changes / gets additional decimals added to it.

You might enjoy this @24

Excellent video by Dr. Wildberger explaining why concept of "real numbers" is rotten.

I second his call to research the sociology and history of these ideas, so we can put mathematics on sounder foundations.

https://www.youtube.com/watch?v=H84VyZCOCew

Masks are a peculiar mixture of tinfoil hats and armband identifiers.

https://news.yahoo.com/amid-coronavirus-surge-california-expands-182259828.html

"The experts"

"Scientific socialism" is excellence in marketing. Might as well call it the "smart love" philosophy.

Power that can only be maintained by lies is weakness.

Friendly reminder than the father of game theory, John von Neumann, advised sitting US Presidents to preemptively drop nuclear bombs on the Soviets because his mathematical models told him that nuclear war was inevitable.

IQ does not equal intelligence.

/trolltoll @5937 $5

"The news" attempts to change reality rather than describe it.

Confusion is the source of political power.

Most people do not think. They believe that they think because they've only be exposed to a tiny amount of ideas.

The've been told the official smart-person ideas and believe that if they can repeat those, that's the same thing as thinking.