The language he [Wigner] uses is deeply religious throughout — Moliere

It's funny you say that - his Wikipedia page says he was a convinced atheist — Wayfarer

Interesting observations. My ex-wife's father, a friend of Wigners, was an architect and intellectual in Hungarian society. He had no use for organized religion, but was something of a disciple of Tielhard de Chardin, an intellectual and Catholic priest who advanced the idea of an Omega Point, toward which the world moves and reaches in its final days. A curious blend of science and something like religion.

First off. How did things get this out of hand? — TiredThinker

Bat Masterson and others with their tales of the Wild West. Every generation having veterans of a previous war. ???

Measurement doesn't affect anything in the past. — Andrew M


It does! It collapses wave function in space and time. The past was in superposition untill we measured it. Remember Copenhagen... — Landoma1

Welcome back, quantum mysticism. "Collapse of the wave function!" carries us away from Earthly distractions into the cirque of the gods where ectoplasm interacts with aether causing spacetime curvature. Superposition is annihilated with a bolt from Zeus!

It's a mystery to me. All I know is we mathematicians observe physical phenomena and extract and abstract patterns.

↪jgill

There are many branches of metaphysics not just the one. Perhaps some metaphysics as a philosophy of mathematical fundamentals done by mathematicians might be illustrative. — magritte

Of course there are. I've long considered infinitesimals metaphysical objects within mathematics. Transfinite set theory seems metaphysical to me. Like pornography, I know it when I see it.

Not knowing the existence of unknowns can trip one up.

Also, what fixed point do you have in mind? — TonesInDeepFreeze

This caught my attention although I am not following the discussion, not in my bailiwick. I've worked with these things quite a bit in Banach spaces, etc. but not in this context. What's going on?

I never read posts about wiki — Jackson

I understand. Don't read this one.

You could say that of logic — Jackson

Logic is the study of correct reasoning or good arguments. It is often defined in a more narrow sense as the science of deductively valid inferences or of logical truths. In this sense, it is equivalent to formal logic and constitutes a formal science investigating how conclusions follow from premises in a topic-neutral way or which propositions are true only in virtue of the logical vocabulary they contain

Wiki

It is a branch of philosophy like epistemology or ethics — Jackson

Then it should discipline itself by agreeing upon a definition.

What does the discipline of metphysics have to do with quantum entanglement? — Jackson

Calling metaphysics a "discipline" is quite a stretch. Here, on TPF, several philosophers have tried to interpret QE without a clue about the math that seems to support the phenomenon. That's an example of metaphysics as I see it.

When does metaphysical border on mystical? Eliminating metaphysics (which I consider impossible without severely crippling philosophy) would remove all the entertaining babble about quantum entanglement, for example.

The word metaphysical itself is ill-defined. This is a step further into the void.

Acceleration has never been adequately understood by human beings. — Metaphysician Undercover

From past posts I assume you refer to instantaneous acceleration.

paradoxes; they're an existential threat — Agent Smith

That's a paradox itself. :cool:

I'm curious what you think of Schaums Outline of Logic. I found math outlines that worked well in several courses I taught. Would you recommend this for students such as ToothyMaw? I've never looked at a copy.

Wagner, not wigner

Good question. I was much younger and I think an associate professor at the time, and my interests then might not have been my interests now - hard to recall. But probably I would have discussed the origins of mathematical concepts, those ideas that seem to pop out of nowhere and can become so important. Without such breakthroughs math would stagnate. An example is the notion of metric spaces, an abstraction or generalization of Euclidean distance.

I missed a golden opportunity years ago to exchange letters with Wigner or talk with him. My ex-wife's father, who lived in Montana, was a Hungarian aristocrat who corresponded regularly with Wigner. I could have discussed this very issue, being an academic math person. Sometimes we skirt by greatness without recognizing an opportunity.

From Wigner's paper:

The principal emphasis is on the invention of concepts

, and he goes on to observe that we would run out of interesting theorems were it not for the creation or discovery of new concepts.

The basic observation piece being subject to probability seems crucial. Once the superposition is resolved it would seem that it is like the coin split down the middle to a head half and a tail half. But it's got to be more than that. Wish I had studied QM years ago.

My best friend, a fellow math prof, departed a physics major after he enrolled in QM.

The statement of a theorem is a way of understanding what has been proved. In modern abstract mathematics, however, one would need advanced knowledge to understand even that statement.

It is possible for the researcher to argue step by step, building a logical edifice, without stating the theorem. Then stating the formal structure of the theorem by say, "Thus we find that . . . ". I just did that in a math note, in fact:

"
A Brief Analysis . . ." (page 2)

What if it applied conversely and allowed us to determine that the proof behind a principle or theorem assumed to be true couldn't be observed or determined? — ToothyMaw

If a theorem is "true", then it is so subject to foundational axioms. Changing the axioms could change the designation of "true". "True" means derivable in this way. "True" isn't out there all by itself.

Well, yes. If God spoke to me saying, THIS THEOREM IS TRUE, then that would remove a nagging uncertainty in the proof process. But it might end up making little difference in the future effort. On the other hand, if He said, DON"T WASTE YOUR TIME, I wouldn't. :cool:

Well, I might think, I'll use mathematical induction and see where that goes. And it might work, or not. I can essentially do a simple proof in BASIC and see all the constituent parts, and I might have thought of the various parts before designing my program. But to know for certain the following 10 parts will be used before I begin experimenting with them is a stretch. And a rather foolish and non-productive expenditure of energy.

Virtually any mathematical conjecture would be of this type. When I compose a possible theorem I'm not certain about the argument I will ultimately use, although I am almost sure it is correct - but not absolutely. This is true of most mathematicians. Fermat's Last Theorem was assumed true long before the proof was established. But no one was absolutely certain.

Classical logic works just fine for a vast amount of the logic for the sciences — TonesInDeepFreeze

And "traditional" mathematics. But with over 26,000 topics in math it's getting harder to pigeonhole.

I haven't kept up here, so this may have been discussed upthread. As a child during and after WWII I identified with Cowboys in games of Cowboys and Indians. Imitation six shooters in the form of cap pistols were it seems everywhere. Boys were encouraged to engage in imaginary conflicts, popping away. A few years older and friends and I would have actual bb-gun fights, mimicking what occured in popular war movies. During the Vietnam conflict all kinds of plastic imitation weapons were available for kids - mostly if not all, boys.

Even today all those B&W TV shows of the '50s and '60s, like Gunsmoke, are available and have followers. But I think there's a trend away from games of gun violence, so there is hope a future America will be less inclined to imaginary and actual violence. There's even a chance the 2nd amendment wil be reinterpreted by a future Supreme Court. When little boys have other interests the entire culture might change.

Edit: Whoops, I neglected to include modern computer games that are more violent than the stuff of past generations. Guess we'll see.

A system that includes fossils, renewables, recycling is a possible answer. A bit like where we are now, but looked at as a system, not individual components in isolation. Good thread, Crank.

Look at the period at the end of this sentence. Now keep on staring at it. — Joshs

Look into this box of apples. They are all Delicious apples, a kind of apple. Now look closely at each one after carefully counting them - there are 24. Each apple is unique, being distinguished from the others in small ways. We see this as we contemplate these apples, a particular kind of apple. After a bit each apple seems to turn its best side toward our gaze, and we begin to contemplate what may lie on their opposite sides. In so doing we drift into a meditative state in which apples prevail, even those not Delicious.

Our mathematics begins only after we have concealed what happens within ‘kinds’. — Joshs

:chin:

The Schrödinger equation is linear and so linear combinations of solutions are also solutions. This is the superposition concept in its mathematical garb. The superposition principle leads to quantum entanglement, since a measurement identifies a state and illuminates a solution. Thus entanglement can occur, since otherwise an entangled pair would be nothing more than the common example of a coin split into a head half and a tale half. So the roots of this notion arise in elementary differential equations or linear algebra. Or so it seems to me.

Not that this solves anything.

So put in steps to make mass murder harder, e.g strict gun regulations — Michael

I wish. Apart from the over abundance of guns in the US is the fact that those guns can last for many generations. It's not like your TV set wearing out and being replaced or your car collapsing and being replaced. Each new gun produced does not replace one that is trashed. But a nation that cannot refrain from indulging in war is unlikely to stifle the production of weapons for its citizens.

Better than random. That's all? I would have hoped for better reliability than that. — noAxioms

:up:

Ergodic theory says you get the same distribution of walks — Jarjar

Surprised to see this thread resurrected. Yes, the math and physics definition of ergodic is technical about averages. Lem used this term to imply averaging out of incidents in strong social movements. More or less the opposite of the butterfly effect (SDIC) of chaos theory.

What can take most of the guns out of circulation? — TiredThinker

A miracle.

We are caught in a whirlpool of violence in which gang members are arrested for gun crimes, then processed and released back into the streets. Most gun ownership is not promulgated by a desire to keep the federal government in check, but for feeling a need to protect oneself and one's family from lethal criminal attacks. I know, all those statistics about suicide and accidental shootings. But the cops usually aren't there when the crime occurs, they can only pick up the pieces of carnage and seek the culprit.

Einstein did not like the quantum model. He still understood physics under the old deterministic model. — Jackson

What does that have to do with fishing?

There's something fishy about entanglement. Years ago, as a kid fishing in the gulf of Mexico I would experience it often. Why did Einstein make such a big deal of it? :chin:

Something's Wrong!? :grin: — Agent Smith

Your perspective.

What I see on TPF sometimes is a circular argument beginning with hypotheses and ending with hypotheses.

we're quite alike — Hillary

:cool:

I don't think that as has been said absence of evidence is evidence of absence. — Andrew4Handel

Yes, but as you say it makes the supernatural implausible.

I can't see where this discussion is going.