What I am arguing is that mathematicians ought not accept such theorems, I am not trying to say that they don't accept them. So, you providing me evidence that they do accept them, just provides me with inspiration to produce a stronger argument that they ought not do what they do. — Metaphysician Undercover

I just took a moment doing what I do to read this post, and now I feel so guilty. :cry:

You have no mercy, MU.

What you'd prefer is to say that they do not have any apples . . . calling 0 a quantity is an abuse of the idea of quantity — Srap Tasmaner

$0=\{\text{ }\}$ ? :roll:

No good. 0+ and 0− are used in limit notation to indicate one-sided limits but have nothing to do with opposites. — Real Gone Cat

Picky picky. Of course they don't. But in the spirit of this discussion they could. There are enough ambiguities in math to satisfy MU. Take $f$ for example. What does it mean? A function? A constant force? Depends on the context. $f=f\left( x+1 \right)$ ? How about 4x/5y-1 ? If these guys want to play around with nonsense don't poop in their sandbox. :cool:

A curious statement. All the years I've practiced math I can't recall using "opposite" in this way. But I suppose some do. — jgill

↪jgill

Major Edit : "Opposite" is perfectly fine when discussing positives and negatives — Real Gone Cat

This discussion revolves around the use of the word "opposite" in math. Apart from integers - the focus here - it arises in discussions of geometry, like a side opposite the hypotenuse, or in a complex vector field with an indifferent fixed point - on one side an attractor and on the other or opposite side a repellor. And so on.

Why not use a pair of these? $0+\text{ }0-\text{ }{{0}^{+}}\text{ }{{0}^{-}}$. They are commonly used in math. You could come up with the first being infinitesimals just to the right of zero, etc.
There are your "opposites" of zero.

Does quantum physics say anything about this?

This user has been deleted and all their posts removed. — Deleted User


That's an excellent username. And what better way to admit that you were wrong, then to delete all your posts. — Metaphysician Undercover

A sort of "Cancel Culture" of TPF.

In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number) — Additive inverse - Wikipedia

A curious statement. All the years I've practiced math I can't recall using "opposite" in this way. But I suppose some do.

I dunno, I don't really feel that way. I find pre-theoretical intuitions interesting and important. No math without 'em. — Srap Tasmaner

Indeed. Centuries ago.

Proof of something like time travel would be more appealing.

Word games full of sound and fury . . . :roll:

Recently I have taken an interest in testing remote viewing. — TiredThinker

Any luck there?

Abstract, "pure mathematics" shows that we dream up universal principles (axioms) first, from the imagination, or they come to us intuitively, then we try to force the particulars of specific circumstances to be consistent with the universals. — Metaphysician Undercover

That's at least in the neighborhood of Sellars's argument and the impasse I expected to reach, that empiricism from a blank slate can't actually get started. — Srap Tasmaner

MU makes a good point regarding some highly abstract mathematics. I'll tell the story again of a PhD student writing a fine looking thesis about a certain class of functions, but when asked to illustrate the class by a specific example discovered the class was the empty set.

Thanks for adding to my vocabulary. I had to look up "eschaton" to see what in the world you are talking about. Now I'm glad I had no knowledge of this word, nor its depressing meaning.

Psychologically, how can we confront this terminal historical moment we have all been thrust into? — hypericin

Don't Google "eschaton". :roll:

Usually the concept of work relates to a change of energy, kinetic or potential. When an object follows a path through a force field, if that field is conservative, the path the object takes from point A to point B is immaterial regarding work; all such paths produce the same work. This idea aligns with Cauchy's Theorem in complex analysis.

The analogy I recall is two people about the same weight standing before a mountain. One takes off directly to the summit over a series of cliffs, and the other follows a trail that winds round and round the mountain, finally reaching the top. Both have done the same work.

A sequence of smooth contours in the complex plane I devised that start at zero and end at one grow longer and longer without bound while converging uniformly to the straight line path along the x-axis from zero to one. Set in the backdrop of a conservative force field an object moving from zero to one along the x-axis does the same work as on a contour that could be unraveled and stretched from Earth to Alpha Centauri and beyond.

:up:

Richard Muller, physics professor emeritus at UC Berkeley, states that energy is the most difficult concept to understand in the basic physics curriculum. It will be interesting to see what people say.

In what sense inaccessible? Do you mean that generalisation actually ends up cutting its connection to the particular? That shouldn’t happen if it is being done right — apokrisis

Mathematical Schemes is an example of current levels of abstraction. If I were an algebraist or topologist I would probably see the values therein. This entity aided in solving Fermat's Last Theorem. But its value in real or complex analysis is debatable. Here's an example that, for me, is vague - which you value. For others that vagueness is merely the ectoplasm of math.

You speak often of systems theory, and in math that begins with dz/dt=f(z,t) in the complex plane. Here the levels of vagueness are low, and chaos may grow out of these scenarios. What scheme theory has to say about this is a question for experts in these areas. But it appears schema theory means something else in biology.

Schema Theory and the Dynamical Systems Theory are the predominant behavior theories that address how the nervous system produces a movement.

The Generalized Motor Program Theory (GMP) or Schema Theory and the Dynamical Systems Theory are the predominant behavior theories that address how the nervous system produces a movement. The debate of movement scientist and the contrasts of these theories centers on whether movement is created through hierarchical control in the nervous system (i.e., cortical control) or if movement control is distributed throughout cortical, subcortical, spinal, and even musculoskeletal levels of the nervous system. While compromise between these two theories may be possible, each theory has its respective adamant supporters who will argue for the support of one over the other. In this assignment, you will evaluate these theories to determine which theory you believe is the more plausible explanation.

At the lower level of technicians perhaps, but I doubt it since thinking involves both hemispheres. Advances in science require imagination, which certainly does.

So that for me is the meaning of metaphysics. The move from the particular to the universal. From the concrete to the abstract. From that which is true of some things to that which is true of all things. — apokrisis

Well, this has happened in mathematics as specifics have given way to greater and greater generalities, an approach that has brought together various ideas under broad umbrellas, and is certainly a popular trend (with virtually every grad student knowledgeable of category theory), but it leaves lower level intricacies inaccessible - particularly in real and complex analysis, the latter being very important in QT.

I wish I knew more about QT so I could assess how beneficial this has become (beyond Hilbert spaces, etc.) :chin:

Einstein had taught himself differential and integral calculus by age 15, and had a teaching diploma in math and physics before the patent office job. His PhD may have been awarded while he still held that job (1905).

Ramanujan had studied mathematics for some time, both on his own reading and in school, before he interested Hardy in his original results.

In both cases these geniuses had backgrounds in mathematical thought before they became celebrated.

In the movie, however, the janitor had no previous math experiences - except a reference to being self-taught - and simply picked up an advanced topic (requiring a background) by simply looking at notes left on a blackboard. One of my relatives asked me my opinion about this, and I told him "possible but unlikely".

That shows in your support of Tonioni for example — apokrisis

Probably you mean Giulio Tononi. His Phi function is untenable.

It could be that a non-specialist somehow cracks the problem — Manuel

Reminds me of the movie Good Will Hunting in which a janitor solves a ridiculously difficult mathematics problem while erasing a blackboard each day. Possible, I suppose, but extremely unlikely since prodigies are so rare. A pretty good film nevertheless. :smile:

A non-differentiable manifold. Live with it. :brow:

Spoken like a mathematician but not a physicist or metaphysician? — apokrisis

True enough. I don't have a Professional Degree in metaphysics. But I respect those who do. :cool:

If mathematicians need sets, for example, even if we're not happy about it, we'll deal with the philosophers who say they can't have them. — Srap Tasmaner

Bless you, young man! :fear:

Plenty of philosophers ignore aesthetics, for instance, or ethics, but I always thought Quine didn't so much ignore them as exclude them. Do you read him differently? — Srap Tasmaner

I only meant I could not find where he might have said this. Nit picking. :wink:

But they smell blood in the water, and won't go away — Gnomon

They still search for fire they can breathe.

We simply never were interested in what might “breath fire” into our equations? I really was wasting my time? :up: — apokrisis

Breathing fire is vastly overrated. Exploring the math can do that job. No need for unicorns.

Quine had this idea that philosophy is the handmaid of science, — Srap Tasmaner

Really? I can't seem to find a reference. Do you have one handy?

On the other hand, among those physicists who are aquatinted with philosophical accounts of realism and anti-realism, most consider themselves philosophical realists. — Joshs

That would be my guess. Were I a physicist I would be in that camp. Actually, I probably wouldn't care one way or the other.

Was it Halmos who said our mathematics is not ready for the Collatz conjecture? — Srap Tasmaner

Paul Erdős

Did you have this sort of thing? $\sum\limits_{{}}^{{}}{\prod{{}}}$ (I use that all the time)

Have fun. It looks dreadfully unappealing.

But the general answer I get from those who know this stuff is NO. It doesn't say anything like that. When I get into the philosophy about it I get stuff like "well that depends what you mean by reality", after that I pretty much tune it out. — Darkneos

If you search for "real" in your Schaum's Outline of Quantum Mechanics you will find nothing, save mentions of the real number system. "reality" is in the domain of speculation by both experts and quantum mysticists.

It looks like progressives vs regressives. I guess I don't see the purpose of it.

Well yes. It’s the difference between tossing a classical coin to discover if it lands head or tails, and knowing that if you toss one of a pair of quantum entangled coins — apokrisis

I was thinking only of a more mundane application of S's equation, with wave packets and probabilities of a particle being at a particular place at a particular time. But I have zero knowledge of the experimental mechanisms involved. So I should avoid talking about things I do not understand. :confused:

Breathe fire :cool:

How do you mean? The act of measurement that picks out a solution is the tricky issue. — apokrisis

From a purely mathematical perspective, when one solves a kind of partial DE there may be many linear combinations of solutions. Question: which one applies to a particular experiment? Answer: the one correlating with an observed measurement. It seems that these are just possible solutions to the problem being investigated, not "possible worlds" or "superpositions" in quasi-mystical senses.

Like a simple problem in d=rt, where one gets two possible solutions, one negative, one positive, and the physical situation determines the positive solution is appropriate. There are not two possible worlds, just two possible answers, one of which correlates with observations. I suspect you are saying this kind of distinction is much trickier in QM?

Thanks for taking the time to answer these questions.

Who wrote the "laws" limiting how far amateur philosophers can speculate, beyond the "revealed Word" of physical Science? — Gnomon

There are few restrictions here. But when views are presented others are free to poke at them.

You keep looking for the "stuff" that breathes fire into the equations.

But I'm not. I'm saying its a mistake to presume it. — noAxioms

Yes, I agree. The mistake is to assume the universe was created to raise human emotions.

What would you say about the idea that there is happening no collapse at all.But we just think that we "spot"one ,cause we are condemned from our own consciousness to see it like that? — dimosthenis9

Good point. , to what extent is the "collapse" simply the experiment being resolved by identifying one of the many solutions of the Schrödinger equation, all of which "exist" together?

Here is a graph summarizing the results of a survey of physicist's opinions of the correct interpretation of quantum mechanics: — T Clark

It's interesting that the survey showed zero percent in favor of a transactional approach. I seem to recall that one of the few actual physicists on TPF, Kenosha Kid, argued for that.

Compossibility

Euler diagrams

If you have a program on your computer you need to pay and be a subscriber to upload an image to a post.

to make someone understand what you yourself don't understand? — Agent Smith

I see this attempted on TPF when someone starts talking about quantum theory or relativity. Now, there are a few individuals on the site who know what they claim to know, but others shovel out the terminologies and key words from stockpiles only a few centimeters thick, thinking they do understand while not knowing the extent of their misconceptions. To some extent this is due to books and articles attempting to convey information to the masses in ways palatable to those masses.

Sean Carroll is now attempting to remedy this unfortunate practice by going deeper into the mathematical basis of ideas in physics and cosmology in a book describing popular science notions.

One deplorable example I see over and over here is "curvature of space", exemplified by the ubiquitous image of the Earth sinking into a basketball net of gravity.

which is that the behavior of a small percentage of the world population is responsible for most problems. — Xtrix

Spare me clichés — Xtrix

OK