jgill

To illustrate non-linear time, this graph shows the correspondence between ground observer time (horizontal axis) and proper time (vertical axis) for ...

I think this is the best contribution to this thread. Thank you, gmba. Kind of like herd immunity in reverse.

You funny. :cool:

I used to teach point-set topology. A delightful topic. I try be brief :smile:

I be brief. Usually by playing with existing mathematics. At first a conjecture, then comes a proof.

Pondering

Eternal, perhaps?

Well, here's a difference between a PhD math thesis and a publishable math paper: In the thesis the grad student is encouraged to spell most arguments...

Can't believe this thread is still going on. :roll:

From my perspective (an old mathematician) philosophy people looove to talk and write, sometimes going on for paragraph after paragraph elaborating up...

Whatever mankind does to itself will ultimately be dwarfed by what nature does. Beyond looming climate change, which might be benign by comparison, th...

(Wiki)

Not sure there is any such thing. As we watch a spaceship fly by at half the speed of light times the linear 0< t<1, both the spaceship crew and you a...

Time dilation during the early stages of the Big Bang makes the notion of an infinite past debatable. It would seem that an "infinite past" would be b...

On the concept of the number of many worlds in quantum theory, David Wallace (2011) has this to say: Not an argument, just an observation somehow rela...

You are assuming another possible universe is simply an extension of the one we are in, adding features here and there. How could you possibly know wh...

OK. At the present time we have a result of causation from an event having taken place 1/2 a year ago. At that time a previous event caused that resul...

Suppose the infinite regress is a causation sequence that, going back toward an origin, is of the form 1/2^n. You never reach the origin, but the chai...

Fortunately, it's the exploratory effort that gives them meaning. Publication and citing gives them reward.

This type of comment comes up every so often. Alexandre used it some time back. Exactly how do you do this encoding? Is it arbitrary? Hence, you asser...

All of us who use Wikipedia should contribute some $ now and then. It will continue to exist but may have to start accepting ads.

Yep. I like the "little pepper-corn" analogy. I've mentioned before that the number of new research papers in math alone arriving at Cornell's ArXiv.o...

Right. Otherwise it could not exist now.

Some time back the president of the American Mathematical Society could do this juggling trick. What is it about these big-shot intellects that they a...

It would make more sense if you questioned whether the number of objects in the universe was finite or infinite, then countable or uncountable. What d...

It's intriguing to think these things "exist", an effort to comprehend the physical universe - or simply a devise to create working models.

nullum sensum facit

Implied by You are completely right. It is wrong to think that ‘geometrization’ is something essential. It is only a kind of crutch (Eselsbrücke) for ...

Once one moves into 4-D, the "curvature" of space becomes an algebraic concept, not a geometric concept. And implications back to 3-D probably remain ...

In four dimensions, yes.

:cool: :up:

That's unreal!!! :gasp:

Thanks. It's nit-picking, but space itself has no substance and does not "stretch" as the balloon analogy suggests. The metric changes and objects not...

Curvature occurs in spacetime, rather than in 3-D space is my (pathetic) understanding. Is it space itself that expands, or matter within space? (A ye...

Mathematicians can play with time, real or unreal: Playing with Complex and Distorted Time If there was any physical substance to time it would be a t...

As the saying goes, just Shut up and calculate. Do what you can with what you have.

https://i.guim.co.uk/img/media/c41374f2d1313cd564257607c476061771a8f8ed/606_420_4626_2776/master/4626.jpg?width=1300&quality=85&auto=format&fit=max&s=...

Do you live there? You must to have witnessed this horror. :scream:

Infinite Compositions of Analytic Functions If F is a functional operating on a function f, then F(f) makes sense, but F(F(f)) does not. Functionals m...

Why? Is time is unreal a mathematical theorem? Since we experience the passage of time it seems quite real. But not physically so like a doughnut.

I like the idea of driving an electric car. As a high school student in the early 1950s I would take the electric buses in Atlanta downtown frequently...

From the Aaronson blog: I'm with him up to an isomorphism. Beyond that is the absurd IMHO.

Whatever. As I mentioned in another thread, a simple isomorphism between physical reality and mathematical structures provides a way of saying they ar...

Try the Taxi Cab metric. Please die, thread. Poor thing, I should never have started you. This is wandering in the direction of threads having hundred...

Whatever this means, the paradox is not that big a deal. Aristotle may have been aware of the fact that arc length is not preserved in this kind of pr...

As a retired mathematician I read the OP and thought, This is utter rubbish. I have worked with infinite compositions of functions for years. But some...

Imagine if all those vehicles stranded on I95 for 24 hours in snow and ice had been electric.

Only if it pleases you to do so.

This is a mathematical can of worms, with definitions and counter-definitions. In the physical world certain phenomena may exhibit what we normally th...

A Short Note: Extending the Diagonal Paradox :sad: The path is continuous. Sounds like you just float up. :gasp: