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

Principles are much lighter than facts. I can walk around with a world of principles in my head, but I can only carry around a small set of facts.

Facts can be used to establish principles. Once established, I only need to retain the most important facts.

Fluxions, Daniel! How about his ridiculous fluxions!

Philosophy requires no infrastructure, no training, and no certification. It just requires curiosity and time.

Philosophy requires no infrastructure, no training, and no certification. It just requires curiosity and time.

If you have not experienced a theoretically good idea failing in practice, then you don't understand why actually-good theories are precious and rare.

There's a difference between "theoretically good" theoretical ideas, and "actually good" theoretical ideas.

The marker of an actually-good theory is that it works in practice. The marker of a bad theoretical idea is that it doesn't work in practice.

I do not believe it is possible to sincerely pursue the truth for a long period of time and end up with a worldview that looks remotely "respectable" according to contemporary opinion.

Delusions of grandeur are insidious, but so are delusions of delusions of grandeur.

Magnus Carlson is grand, and it is good that he knows it.

Mere conceptual incoherence is not a strong enough reason for a modern intellectual to abandon his ideas.

The congregation of the Cathedral could be called The Keepers of Officialdom.

The group is composed of individuals, but most individuals are composed by the group. There is two-way composition.

Most people's self-identity is shaped by their membership in a group. Their values, goals, preferences, and ideas are not their own.

Lockdowns are sufficient justification for secession.

"Atheism or Treason may be the Names given in Britain, to what would be Reason and Truth if asserted of China."

-Burke

Seek truth and live in accordance with it.

Geocentricism worked just fine for a long time. But eventually, it needed to give way to superior theories.

Discrete space will be the same. Already useful in physics, and it will become more important as micro-microtech improves.

Right - Euclidean geometry is arguably the most practical mathematical theory of all time.

But like the Ptolemaic model of the solar system, "practicality" often does not translate into "truth," and I'm interested in truth.

Set /trolltoll @14519 $5

Yes it is, if you think about it thoroughly enough.

As I keep saying, you are trying to map Euclidean objects onto discrete space. That's a mistake. If space is discrete, lines are composed of points.

In this example, the "lines" are somehow magically between the points in continuous space.

Self-evident doesn't always mean "immediately obvious." It means "simply by examining the concepts, you can know it."

Multiple professors have told me that logical contradictions exist. They are self-evidently wrong but haven't thought enough about it yet

Second, the Pythagorean theorem gives you a number that's relevant in Euclidean space. In discrete space, it doesn't work. There isn't enough information (i.e. there are changes in two dimensions that cannot be capture by a single number)

It is harder to learn in victory than in defeat.

One more time, just to rephrase it:

"The diagonal of a square whose side has a length of 1" is a Euclidean object.

There are no Euclidean objects in non-Euclidean space.

All actually-existing space is non-Euclidean.

Therefore, there is no such diagonal

It seems backwards to me to be wary of tying math and computation together. We should be wary of untying them.

Thinking that math floats disconnected from computation is a modern aberration. The "bit" has nothing to do with it.

In discrete space (in the real world), units of length refer to spatially-extended points. When we say "That square has a side whose length is 9", that means "there are 9 units which compose its side."

So, you can't have a composite object made of 1 unit.

I know. I'm saying you are working within Euclidean geometry when you ask about the diagonal of a square with a side the length of 1.

I'm saying that no spatially-extended square has a side the length of 1, since actual squares are composite objects.

You're working within Euclidean geometry. Space is discrete, not continuous, so there are no "squares" that have a distance of 1 unit.

Create a square on your computer screen. You'll see it's composed of a countable number of units (pixels).

If you understand the meaning of the words, you can understand it's universally true and literally cannot be false - i.e. to deny it would yield a logical contradiction.