From Wikipedia:

Outer space, commonly shortened to space, is the expanse that exists beyond Earth and its atmosphere and between celestial bodies. Outer space is not completely empty—it is a hard vacuum containing a low density of particles, predominantly a plasma of hydrogen and helium, as well as electromagnetic radiation, magnetic fields, neutrinos, dust, and cosmic rays

In mathematical research it is not uncommon for ideas to be discovered and rediscovered during the passage of time. An idea may "belong to" its original conciever I suppose. My advisor years ago stated he didn't think there were any truly original mathematical ideas anymore. I disagreed.

Sometimes this process leads to embarrassing revelations like having a paper rejected because Newton had your idea first!

Can space be compressed? Or merely substances in space? There is a theory of FTL travel which involves compressing spacetime before the moving vehicle.

Excellent post!

As long as the Military-Industrial Complex controls education we are not going to get there. — Athena

Might as well include the NFL, NBA, and MLB regarding athletics at schools.

Perhaps the answer to the issue at hand lies in the fact that it involves "more or less traditional Americans", within which population there appear certain psychic idiocyncracies conducive to conflict and irresponsibility — Michael Zwingli

A bit heavy-handed, but not without merit. :cool:

The second assigns an objective existence to a mathematical entity (the wavefunction), which is absurd. — Cartuna

:up:

How can a mixture of Germans, Frenchmen, Italians and Romansch be considered homogeneous? — Michael Zwingli

More or less traditional Europeans. Middle Eastern and African refugees bring in different cultures, religions, etc. I could easily be wrong. I haven't traveled in Europe in the last fifteen years.

I haven't kept up, so I'm not sure how actualism and determinism relate to climate change.

I read that parts of Europe have an energy problem now, and that all those windmills - predicted to have no more than seven days a year of less than 10% output - have gone 65 days so far.

Where is geothermal? Where is tidal energy? When the sun don't shine and the wind don't blow there's trouble a'brewin.

Why can we not be more sensible in this country, more like....well, more like the Swiss, who know well enough to avoid conflict and to focus on their own prosperity? — Michael Zwingli

Well said, Michael. But my impression has been that the Swiss have or had a very homogeneous population. Perhaps that has changed. And homogeneity may be simplistic.

This is all part of the bigger picture of mob rioting, looting, and smash and grab incidents and the failure of law enforcement to control. Should a responsible citizen simply stand by and observe their car being torched or their store being decimated? Is there any justification of vigilantism? Is there justification of smash and grab? Should one stand by and applaud? Or hide in the basement until all is done?

There are no easy answers.

Central Planning - to what extent? It worked well for Mussolini and Fascism for a short time after WWI.

I believe what you are talking about are limits like in calculus? Or are you talking about the limits of precision? For example, .1 becomes .11, becomes .111, etc? — Philosophim

Here's a mathematical analogue of a causation chain involving an esoteric kind of dynamical system that most math people would disown (but I have enjoyed them): Assume that each causality step is described as a function of the previous step, starting with a first cause $\alpha =f(\delta )$ taking a state point $\delta$ to a state point $\alpha$.

We go back n-time steps into the past and begin the chain there, ${{z}_{1,n}}={{f}_{n}}(\alpha )$

Assume the observed present result is $\beta$. For each value n there arises an observed present value that differs from $\beta$, but the discrepancies grow less and less the further back we start the causal chain.


${{z}_{1,n}}={{f}_{n}}(\alpha )$

${{z}_{2,n}}={{f}_{n-1}}({{f}_{n}}(\alpha ))={{f}_{n-1}}\circ {{f}_{n}}(\alpha )={{f}_{n-1}}({{z}_{1,n}})$

${{z}_{3,n}}={{f}_{n-2}}\circ {{f}_{n-1}}\circ {{f}_{n}}(\alpha )={{f}_{n-2}}({{z}_{2,n}})$

${{z}_{n,n}}={{f}_{1}}\circ {{f}_{2}}\circ \cdots \circ {{f}_{n}}(\alpha )={{f}_{1}}({{z}_{n-1,n}})$


So that $\underset{n\to \infty }{\mathop{\lim }}\,{{z}_{n,n}}=\beta$. We have a first cause but no first time.

This example has lots of holes.

Big Deal! :cool:

From a mathematical POV there are unusual dynamical systems that describe a sequence of forward causal steps extending back in time that account for an incident, F, that has occurred at a specific moment in time in the near past, and for which there is a first cause; but the accuracy of that process in producing F improves as that first cause is initiated earlier and earlier in an unbounded trip into the past.

So, there is a “first cause” (not necessarily unique) for an F, but that first cause has no set position in an infinite span of past time and is only completely reliable in a limiting sense. (this has nothing to do with a “point in time at negative infinity” that set theorists might consider)

If anyone is interested, I will briefly sketch out this scenario. Otherwise, ignore and continue with philosophical conversations.

Just removed instructions for recording episodes of Yellowjackets on Showtime. Ghastly.

Lots of WFH people will be returning to the workplace society simply to be around their fellows. I am a retired prof and a colleague of mine who has been teaching online from our university is relieved, even delighted to return to the classroom. He was on the verge of retiring.

↪Enrique
I've labored within the social service industry and have observed various kinds of problems. What I have not seen first hand is anything like the kind of behavior you ascribe to doctors — Bitter Crank

I've been a US citizen for 84 years and have never seen the sort of narrative you describe, Enrique. But I'm not saying it doesn't exist. Are you a US citizen? What I have seen are the horrors of guardianship laws that allow companies to take over an individual's assets while supplying minimal support. This varies with states.

but what if these citizens are actually being effectively abducted into group home or low income neighborhood situations while commonly drugged by a predatory medical establishment and forced to assert that they have an incurable ailment, in essence ostracized to various degrees by their communities? — Enrique

This seems like a pretty big assumption. Maybe you could flesh it out a bit by citing a country, then giving some examples. Otherwise, your comments are speculative.

A point in 7-D: (x,y,z,u,v,w,t)

I doubt matter underlying the wave function ever fully collapses, as if an absolute demarcation between coherence and decoherence exists, but rather morphs into different shapes and formations depending . . . — Enrique

Are you speaking of a matter wave or a probability wave in QM? Kenosha Kid is probably out making millions with his guitar rather than really important work like clarifying physics on this forum. :sad:

Will one of you logicians write out in English the defining expressions for abstract objects at the beginning of this article from Stanford? This seems to form the basis of Stanford's Metaphysical Laboratory.

Theory of Abstract Objects

Edit: OK, it looks like there is an explanation of sorts in the article. If you don't feel it's worth the effort I might agree.

Lots of extra dimensions in math - one just defines them. So Tegmark's Mathematical Universe Hypothesis implies all sorts of things.

A touch of humor from Quora Digest a few days ago, apparently a joke that's been around for awhile in academia: The dean, when asked for funding for the physics department which requested a new particle accelerator and other expensive equipment said, "Why don't you guys do like the math department and ask for a pen, sheets of blank paper, and a wastebasket? Or. better yet, like the philosophy department that asked only for a few sheets of blank paper and a wastebasket?" :cool:

I got my union card in math in 1971 and was fortunate to get hired in a developing department in a state college that was beginning to grow to becoming a branch of the state university. The job suited me, not requiring research but rewarding it when it was done. Full professor in less than a decade, and a short stint as department chair.

I cannot imagine such opportunities exist today. My timing was very fortunate. I am saddened to know that young academics have so few paths available.

Thanks. A couple of quotes from the article:

"Physically, we don’t have a 4D spatial system, but we can access 4D quantum Hall physics using this lower-dimensional system because the higher-dimensional system is coded in the complexity of the structure.”

“Right now, those experiments are still far from any useful application,” he said. Yet, physics in the 4th dimension could be influencing our 3D world. As for applications Rechtsman said, “Maybe we can come up with new physics in the higher dimension and then design devices that take advantage the higher-dimensional physics in lower dimensions.”

The second paragraph is intriguing. A couple of weeks ago Gravitty - before he was banned - made another thought-provoking comment when he said that light does not travel in time.

I think physicists have shown with experimentation strong evidence that a 4th spacial dimension may exist — TiredThinker

No kidding? — jgill

A link would suffice.

I think physicists have shown with experimentation strong evidence that a 4th spacial dimension may exist — TiredThinker

No kidding?

Academia tries to firm up the ectoplasm called metaphysics:

Metaphysical Resarch Lab

Theory of Abstract Objects

Metaphysics of Science

From my perspective (as one of Leibniz's many, many professional descendants), I think of infinitesimals when thinking of Leibniz. He made many contributions to math, but an infinitesimal lies within the definition of metaphysics for me.

Sorry to interrupt a lively discussion.

:up:

Marco confided he has a masters in physics. With all the pseudo-scientific babble here about collapsing the wave function, superposition, entanglement, etc. I thought it worthwhile to have a genuine physicist on board. Kenosha Kid was excellent, but he hasn't been around for a couple of months. Lookin' for that Pot 'O Gold with his guitar probably.

Do you see the connection? — apokrisis

You must not be talking to me.

Do you mean in the models of dynamical systems? Which models exactly? — apokrisis

Simplest example in the complex plane. $f(z)={{z}^{2}}\Rightarrow {{f}^{-1}}(z)=\sqrt{z}$ Single-valued to multi-valued. One could toss in a t for time.

Thanks for your reply.

Depends on your definition of "eventually". It's not required that monkeys on typewriters eventually compose Shakespeare.

But the point is that it you can construct a machinery of asymptotic approach to a fixed point, then the inverse of that mathematical operation has to be able to pop back out of that point to — apokrisis

Just a minor point, but in dynamical systems this is not necessarily so.

It's too bad Graveltty has been banned. He has a grad degree in physics and some interesting ideas. Do you, by chance, have such a degree? You seem very knowledgeable.

I'm 75; I don't have a lot of water and climate worries, provided I don't live too much longer. I wonder what plans informed adolescents and young adults are making in light of the ongoing crises which they will have to live with. — Bitter Crank

I'm ten years older, so much of what happens will be beyond my awareness. Here in Colorado there is a looming water issue that extends to the Pacific. Over sixty million people rely on the Colorado River.

Shankar Vedantam, the host of the public radio program, Hidden Brain, put it this way: We face an existential threat from survive climate change. Compared to WWII, are we at D Day, or are we at Dunkirk? — Bitter Crank

I heard part of that. An excellent discussion. I was a meteorologist long ago and my opinion is that it's far more important now to prepare for the inevitable. Sure, we can push intelligently toward green energy, but Miami could take a clue from the Maldives where efforts focus on building up the ground levels on the islands. As Shanker stated, we have lost the battle with climate change and must adapt. Little Greta notwithstanding.

You responded to baker’s traditionalism-rich musing about prancing about and showing off as humorous. — kudos

Indeed it is. Somewhere on the downhill spectrum between love of wisdom and love of money. I fear I just enjoyed math and the lifestyle provided by academia. :cool:

Photons have the strange quality not to move in time — GraveItty

It's space that prevents everything from happening at once, and time from everything being everywhere at once — GraveItty

Very nicely put, and thought-provoking.

↪jgill
It is more interesting about how this discussion inevitable turns into a conflict for power between one who sees this long standing institution of the university from a higher moral ground and another with an equally extreme materialist mindset. — kudos

Is that what's happened here? Am I arguing from a "higher moral ground"? Thanks for telling me.

I only taught math (and was a college administrator for a short time). Here in the USA, not the USSR.

What are your thoughts on what this game reveals? — Benj96

With me, it would reveal the difficulty pulling words from my memory at my age. :worry:

Personally, I don't normally take such anomalies too seriously, since I'm not a professional mathematician — Gnomon

Most of us don't either.