There doesn't seem to be any current interest in this topic, so I'll make a few observations, then let the thread fizzle away.

I have some expertise in two areas: mathematics and a certain outdoor sport. Articles I have read in Wikipedia of advanced topics in math have generally been very good, excellent at times. Usually these are written by experts in the areas, and when they make mistakes other experts chime in. Articles on more elementary topics, however, sometimes demonstrate the limitations of amateurish contributions. And articles on advanced topics of very limited interest may also be less dependable than one would hope.

I have published papers in a number of international refereed math journals, and I have found that peer review has its limitations as well. Topics that are popular in a particular clique, particularly breakthroughs, are usually well-vetted, but those not as popular might receive cursory reviews. Also, if the researcher is respected in a community their paper might not be as rigorously inspected as an unknown, reviewers assuming the known colleague has a history of making few if any mistakes.

Every day between 100 and 135 new math research papers arrive at ArXiv.org . Lots of them have errors. Eventually some will be corrected. Most are destined for publication.

As for the outdoor sport, Wikipedia is much softer and too often relies on books and articles on both the sport and its participants for verification, when these references may have numerous flaws. Rumor may become fact over time.

We're probably long out of time, in terms of the climate disaster that's already happening and will inevitably become worse, if not destroy the human species altogether, but there's little else we can do at this point. — Xtrix

Probably, you are correct. Desalinization itself will require huge amounts of dependable energy. I think the human race will adapt. But it won't be pretty.

The interpretation of infinite I use as a mathematician (complex analysis) coincides with one employed in the physical world: unbounded. Were I to be a set theorist this probably would not be the case.

Even as a mathematician, beyond equivalence relations the word "symmetry" has always left me a bit uneasy, so I have avoided it. And in modern physics I not infrequently look it up.

I suspect Kim's calculations came directly from the subconscious.

Here's an operation of arity n: $\bigcap\limits_{k=1}^{n}{{{A}_{k}}}$

↪jgill
about 15yrs of practice in lucid dreaming I found that their are for lack of a better term levels to existence and very dramatic ones at that — MAYAEL

I'm sure you will agree that the actual experience of these mental states cannot be adequately described to those who haven't enjoyed them. Years ago Steven King in one of his books narrates an instance of one of his characters emerging into an alternate reality in a country meadow so fresh and invigorating that one could smell an onion pulled from the earth a mile away.

However, this thread includes possible physical realities as well. Nevertheless, I encourage Tired Thinker to study the sort of practices you and I have enjoyed. Excursions into the realm of pure will.

The key to your dilemma is practice rather than philosophical babble.

How did you achieve your experiences?

If, then, being different they are still equal, then their equality is based in some standard not the things themselves. — tim wood

Yes. More like the legal standard of equitable. A fair assessment, not necessarily equal, as in a divorce proceeding where assets should be shared in an equitable but not equal manner. A softer and more congenial approach.

Ditto for the explanation.

Conversely, alpine mountaineers often speak of the feeling of intense and total aliveness that comes with the most difficult climbs — Wayfarer

I recommend climbing in this regard.



Read Art of Dreaming for a practical technique.

The only truly clean energy of which I'm aware is the passive solar type that is built into my house. Outside ten degrees, inside seventy. Virtually no pollution involved.

Cold when the sun goes down.

On the other hand, you can't just make up anything and apply it anything equally successfully. It's a very tight fit, especially at the most basic (aka fundamental) level. This is what makes the fit seem to remarkable. — SophistiCat

How true. My dabbling in complex dynamics seems entirely devoid of physical applications, other than amazing imagery. Few of my colleagues spent time thinking beyond the particular game we were playing, like curious cats.

Maybe this thread should die here. — tim wood

It never came alive in the right way. Governmental policies directed toward equality are debatable. Little to do with genetics.

The Art of Dreaming did it for me. The practice takes you into amazing mental worlds, far outshining everyday existence.

The worlds according to Tegmark — Goldyluck

Bless his heart. I pray he comes to his senses. :worry:

I assume those that mathematically try to calculate how many different worlds there are . . . — TiredThinker

Medieval scholasticism rises anew. :roll:

Perhaps it's this sort of thing to which you refer: Proposed Math Curriculum in California

I have mixed feelings about the issue, having dealt with college students who were exposed to calculus in high school, so perhaps alternatives aren't all that bad. On the other hand any effort to eliminate fast tracks for talented students to keep "everybody together" doesn't bode well for a system that is not at the top of international scales to begin with. Just my opinion.

Mathematicians prosper as mathematicians by undermining previous mathematics, by thinking of new things to do — Banno

It's more likely new math extends, generalizes, abstracts what is known, and/or connects what had been thought of as disparate results.

Most math is embedded in academia minds — Goldyluck

That's been my experience. That's where it usually starts. But mathematical physics is academic as well.

But what are the implications of having more universes that 2 or more universes are exactly identical to one another? — TiredThinker

None. Probability is a notion having arisen by observation and ideation in this universe.

Gödel claims that given an axiom set A, there are true propositions (say p) that are true but not provable in A. — Agent Smith

Are you sure about that? :chin:

What philosophical rules or mechanism are in role here? — Kanye18

Are you the Man of the House, or are you a Man or a Mouse? Investigate the subtle linkage.

You're Paul Erdös! — Agent Smith

Wrong. He would not be seen dead in my image. :snicker:

Have fun with The Book. — jgill


:up: So your Erdős number is low. I think someone with a mathematical background can shed light on what I'm trying to say. — Agent Smith

Yes, proud to say it's 0. I'm happy to shed no light on what you are trying to say. :cool:

Years ago, when I was giving a talk about one of my research projects, Erdős sat in the front row and listened intently for a few minutes, then lost interest and began doodling, then took a short nap.

He was a very unusual character, traveling around the world with a grocery bag of belongings, staying with fellow mathematicians. He never married and would live with his ageing mother in her apartment in Budapest when not going from place to place. He once stayed at the home of my advisor.

Have fun with The Book.

"Hard and easy is a matter of perspective" about says it all.

Although Crowley came from wealth and later made a living as the founder of Thelema, one should observe he had a wicked sense of humor and it's quite possible he chuckled at the naivety of his numerous followers while lurking behind the Green Curtain. He was a pioneer British climber and wrote of his adventures on the rock and his feuds with other notable climbers, like Owen Glynn Jones. Here is an anecdote that may give one pause when asking, Was he really serious about "Magick"?

Another very amusing incident occurred at Arolla. A little way above the old hotel is a large boulder, which had never been climbed from the hotel side. I spent some time before I found out how to do it. One had to traverse the face to the right, with a minimum of hand hold and foot hold, until one came to a place where the slope eased off. But this point was defended by a bulge in the rock which threw one out. It was just possible for a very slim man with a prehensile abdomen. But it was a matter of a quarter of an ounce one way or the other whether the friction grips were sufficient or not. It was one of the most difficult pieces of rock climbing I had ever tackled.

I decided to have some fun with it and taught a girl how to do it. I then offered a hundred francs to any guide who could get up. We got together a little party one afternoon and I proceeded to show off. Several other people tried, but without success. I began to mock them and said, 'But this is absurd --- you fellows can't climb at all --- it's quite easy --- why, I'd back a girl to do it --- won't you have a try, Miss So-and-so?' My pupil played up beautifully and pretended to need a lot of persuasion. Ultimately, she offered to try if she were held on a rope from above. I said, 'Nonsense, you can do it perfectly well by yourself!' The company protested that she would kill herself; and she pretended to be put on her mettle, refused all help and swarmed up in great style.

This made everybody very much ashamed. Even the guides were stung into trying it. But nobody else got up. So I started to coach them on the rope. Several succeeded with the moral support and without being hauled. A fair number, however, came off and looked rather ridiculous, dangling. People began the urge the chaplain to try his hand. He didn't like it at all; but he came to me and said he would go if I would be very careful to manage the rope so that he did not look ridiculous, because of the respect due to his cloth. I promised him that I would attend to the matter with the utmost conscientiousness. I admitted that I had purposely made fun of some of the others, but that in his case I would tie the rope properly; not under his arms but just above the hips.

Having thus arranged for the respect due to his cloth, I went to the top of the rock and sat sufficiently far back to be unable to see what was happening on the face. When he came off, as the rope was fastened so low, he turned upside down. I pretended to misunderstand and jerked him up and down for several minutes before finally hauling him up, purple in the face and covered with scratches. I had not failed in the respect due to his cloth. But quite a number of people were sufficiently lacking in taste to laugh at him"

And yet, Cartuna, who is an actual physicist, is banned. :roll:

↪jgill
At the back it has to expand. But how can this be? How can space be distorted near mass? — Cartuna

Can space by itself be distorted? Without its connection to time. :chin:

"Hard vacuum and soft vacuum are terms that are defined with a dividing line defined differently by different sources, such as 1 Torr,[43][44] or 0.1 Torr,[45] the common denominator being that a hard vacuum is a higher vacuum than a soft one." :chin:

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.