jgill

My first few years as an asst prof I taught college algebra out of a textbook by Vance, I think. It incorporated the "New Math", an idea that had most...

For which you should be profoundly thankful. :roll:

The various branches of physics seek answers to "how" rather than "why". You philosophers are charged with answering the latter. Good luck.

That's good. I'm not convinced, but I'm sure others here are. My experience with mathematical dynamical systems that progress forward or backward in t...

@TonesInDeepFreeze or @fishfry might be able to help. I was a math prof years ago but can't assist you here. You might send them a message and see if ...

That's beyond simplistic. Time and length dilation under high velocities should have no effect on applications of logic in respective settings. But I ...

I like a truly simplistic explanation: When embedded in spacetime logical necessity becomes physical causation. :nerd:

It's in Cyrillic. Nevertheless math symbols are the same, but to no avail for me - gobblygook. Feynman's path integral is not the functional integral ...

It's hard to discern on TPF if a poster really knows what they are talking about, especially topics in physics. I think Haglund does have a graduate d...

It does look that way, doesn't it? Confusion arises when 4D spacetime is introduced with a different metric, and said to curve, etc. But space itself ...

The distance between objects changes in some sense.

Kinetic energy minus potential energy? Or that functional used in path integrals? The term comes up over and over it seems.

The arithmetic of infinities is a subject of axiomatic set theory. IMHO little to do with the real physical world. Others would disagree. As for the "...

:chin:

Well, there are different metrics involved, but I can see your point. My first grad course in math in 1962 was differential geometry, and it was a puz...

Just examples of little interest apart from the imagery.

The world is in too much chaos right now to get anything of substance done about climate change. Best to start adapting. For example, the Colorado riv...

Theorema egregium. (Wiki)

Coupled Differential Equations There is a tremendous amount of complex variable theory that is not covered in a typical course (which I taught a numbe...

In fact, as fundamental tools it has everything to do with mathematics. The algebra and trigonometry and perhaps basic calculus you learn is useful th...

G'nite my friend. :yawn:

Not more than a fraction of a second. It awaited a smaller, stronger body.

Moments of clarity like this make a mockery of claims that all that is worthwhile has been mined from philosophy. :chin:

It's refreshing that, having assumed all avenues of original philosophical exploration had been traveled, something novel and appealing bubbles up fro...

Sadly that's the strongest part of my body now. :worry: Hidden within those intricate folds are the secrets of the universe. Well, maybe not. :sad:

I knew Lester Germer slightly, as a famous physicist (wave/particle duality) but more as a fellow rock climber. My impression of him grew considerably...

Yes, the bizarre addition example.

Not so. He was an officer on the front lines, decorated several times. (But I kind of agree regarding his wondrous rule-following paradox.)

Sound like elementary cellular automata, championed by Wolfram some time ago. I've written programs that show a constant sort of development, then a j...

I do also. In this case the talk section makes one's head spin!

If things were not bizarre enough: Rydberg polaritons

You live in Shanghai ? :smile:

More a form of entertainment. :cool: You too. :smile:

The guy who believes rocks have feelings?

I've often wondered how the aether affects ectoplasm.

Wiki: Gotta move up to the 21st century, buddy.

Suppose my random number comes from an observation of unpredictable minute changes in atmospheric pressure?

Lots of notes/articles as a hobby. Here's an example: Woven Contours I've written all my computer programs in BASIC.

You have an algorithm that, once begun, leads to an outcome - thus determined. But halfway through the algorithm is a step requiring the input of a ra...

It's not a fractal, but sometimes one can focus on a spot and enlarge it and find additional intricacies. Iterations are done at pixel levels with lig...

Here is a non-chaotic image arising from an iteration process that involves differing functions rather than a single function. Its' beautiful intricac...

The computer calculations define the dynamical system in C (complex plane). Iteration of a function carries an initial point in C to a new position - ...

Not entirely true. Complex numbers arose in the study of roots of polynomial equations, more pure math than physics.

The word "same" means persistence over a span of time in this case. The instant (t=0) your toe touches the flowing water all is frozen in time. Think ...

Not really: Mathematical physics. A person engaged in this pursuit seeks mathematical ideas and procedures that might illuminate aspects of physics. S...

Sure you can. But not twice. :roll:

A minor point, but when a mathematician explores a possible theorem, searching for a hypothesis that will guarantee a certain outcome, he does so over...

Here's the first article I've seen that discusses the possibility of determining whether alternate universes might exist. It still seems a reach. In m...

I find a certain merit in your arguments. By making philosophy equivalent (?) to science hypotheses you have put the subject on a firm foundation, dis...

How would you categorize the many worlds interpretation of QM? At this stage it is not a scientific hypothesis since testing it is a distant objective...