How to isolate an instant? Take a photo. — jgill

As I've explained above, that is an arbitrarily created "instant". So it provides nothing toward proving that real time consists of a succession of instants — Metaphysician Undercover

I would be surprised if there were a proof to the contrary. Isn't all of non-analytic philosophy speculation?

I don't know if you've had much interaction with the sometime contributor here, Apokrisis, but he has a lot of interesting things to say about biosemiotics, a field I didn't even know existed until he came along. — Wayfarer

I think he has a PhD in biophysics. This thread seems to be in a rut of sorts. He might add something original to the discussion. My own ideas, shallow as they are, is that time certainly exists and is a continuum of instances, like the points on the real line. How to isolate an instant? Take a photo.

Is it intended to be used for research purposes? — javi2541997

It's useful in physics for wave functions that might otherwise be cluttered with sines and cosines. It crops up from time to time in things that interest me. For example, the DE that defines a particular contour

$\frac{dz}{dt}=iz$ , solving for $z(t)$ where $t:0\to 1$

Then
$z(t)={{z}_{0}}{{e}^{it}}$
${{z}_{0}}{{e}^{it}}={{z}_{0}}\left( \cos t+i\sin t \right)=\left( {{x}_{0}}\cos t-{{y}_{0}}\sin t \right)+i\left( {{y}_{0}}\cos t+{{x}_{0}}\sin t \right)$

Euler's Formula: 1740 Considering the complex plane a vector space helps to see the connections.

$e^{i x} = \cos x + i \sin x,$

Neither space nor time come equipped with intrinsic measurements. Relativity sees to that. Without objects in play there is nothing. There is no independent space were it not for at least two objects. Then there is time, but only if those objects move through space. Space and time are the empty stage, coming alive only with actors therein.

But is this really a dream though? It doesn't sound like you were even asleep, if you noticed yourself strolling by a table, and you could even knock on the table to confirm that you were not asleep. — Metaphysician Undercover

Guess where I was walking? In the bedroom towards the closed door - which I walked through, like moving through a panel of smoke. I was fully conscious. (delightful experience, by the way)

But the question is, how can the subconscious so thoroughly deceive the conscious, so that the conscious doesn't even know that it's not awake when the subconscious is producing dreams — Metaphysician Undercover

In the sort of lucid dream I described, one realizes exactly what is happening. I remember testing the state by knocking on a table while strolling by, feeling the fibers of the carpet beneath my feet.

How is this possible, that my mind can allow itself to go into a completely distinct reality (which is not reality, yet I believe it to be reality at the time)? How is it possible, — Metaphysician Undercover

The closer one gets to lucid dreaming the more pronounced this effect. I've commented before on Castaneda's Art of Dreaming, and how the process leads to an awakening into an alternate form of reality, more vivid and compelling than normal, allowing one to become pure will.

The key to accessing this experience is summoning a form of consciousness while in the hypnagogic state. Perhaps this is a portal through which one can exert some control of elements of the subconscious, for the subconscious interprets sensory input.

The moment of coexistence of the breaking and unbrokenness is the actual breaking in unbrokenness. Physics and math have no ability to see it or describe it. — Corvus

Sure they do. A simple graph describes the aging of the glass, then, abruptly, there is a discontinuity when the glass breaks. Draw your own picture.

Now I see why fdrake retired as moderator.

Math can describe the motions and movements of objects in numbers and functions. But they are not time itself, is it? — Corvus

There is a continuity of existence that is mechanically measurable. A car sitting by the curb ages a bit over twenty four hours in a an approximation of an ideal or mathematical continuity. Unless, for instance, someone comes along and blows it up. Then there is a discontinuity of existence and the end of a mathematical parallel description. The Riemann integral concept in math analysis embodies the notion of addition of a sequence of temporal points, the distances between points shrinking to zero. When applied properly to dynamical systems that are analogous to physical change, predictions result.

The accuracy achieved is, of course, ultimately governed by Planck dimensions. So, whether Bergson's interval description of the atoms of time is cited or a "continuity" of points is described, is irrelevant.

I agree with everything you say. Latin used to be a high school course available to those students having aspirations in the medical areas, especially MD prep. That made sense. On the other hand, learning Greek could possibly lead to better understandings of ancient wisdom - which seems a bit superfluous in modern times. As a retired mathematician my familiarity with Greek didn't extend beyond a very useful alphabet.

Being perceived is not what it is for something to exist — Banno

A breathe of fresh air. A history over time exists whether it is recorded through human perception or not. Paleontologists discover this truth frequently.

For those who suspect math underpins the character of nature, then the passage of time might well be understood in mathematical rather than philosophical discourse. What does the limit concept say about time? In the ever expanding galaxy of mathematical subjects does time arise?

This is news to me. Hillsdale is a conservative college frequently cited in the more conservative news shows, and I have no problem with that. However most K12 schools are public, charter or non-charter, and where I live we hear little about Christian schools, although they exist here.

The boom of which you speak is the mouse's squeak, but loud, not weak. :cool:

↪jgill
What do you think about TREE(3)? — Arcane Sandwich

I think nothing of TREE(3). From my background in classical complex analysis it is merely notation without any connection to my area of interests. Just another of more than 30K math entries on Wikipedia.

One: It has multiple meanings. One such meaning is: It means "1".
Two: It means "2".
Three: It means "3". — Arcane Sandwich

Now I see why you seem infatuated with Graham's Number. I looked it up and found that it's the largest number associated with an actual mathematical problem (in Ramsey Theory). I also read of Knuth Arrows. New to me and a universe away from my mathematical interests. But whatever spins your wheels.

I see from your location on your info page you have followed Yogi's advice and have taken the fork in the road. Sorry to see the only moderator who is a mathematician leave that position. Fair sailing.

The problem with Time dilation is that it is another hypotheses i.e. possibility if you could fly in the speed of light. Could you fly in the speed of light? Could anyone? Even if you did, the result is not confirmed. It is a hypotheses — Corvus

https://en.wikipedia.org/wiki/Experimental_testing_of_time_dilation

I see nothing of substance in this philosophical discussion of time. But, if something can be physically manipulated and scientifically measured, I wager it exists. Time dilation does just that.

Do we think that DOGE will go after enormously expensive health care spending, which first and foremost is expensive because corporations make profit from it? — ssu

Interesting comment. I've wondered about our health care system, and this past year I have discovered how well it functions for senior citizens during the treatments of a broken leg and cancer at age 87, with complications. It's been one year since the fall shattering my right femur, then, in hospital, finding I had cancer elsewhere. I have a Medicare Advantage plan provided by my public employee's retirement program, and pay into it monthly, but my out of pocket charges were virtually minute.

A good friend recently had triple bypass surgery, and his surgeon told him that at the age of 82 had he lived in Ireland he would not have had surgery and would have been sent home to die.

More the dimensionality of thought than geometry. You might illustrate by describing an educational curriculum in elementary physics embodying your concepts.

:up:

It's very simple to show that infinite sets are not atl the same size — Janus

A misuse of the word "size".

Category theory would be the philosophers companion here, but uh... we haven't been trained in category theory in school or in the university. That is really something lacking! — ssu

This has come up before. There are categories in my own subject of complex analysis, but in order to work with them you need a solid background of complex analysis at the beginning grad level. Now set theory can start literally at the bottom and work up. I've mentioned before my intro to the Peano axioms and beginning at 0 and ending (at the end of the course) with exponential functions.

Category theory seems to be more a graduate school offering, whereas set theory can be presented at a much lower level. However, "New Math" of the 1960s and 1970s flopped when this was tried. Feynman was very critical of the effort.

. . . so one could describe the situation like mathematicians have outsourced the philosophical problem to set theorists — ssu

I like this. However, category theory - which includes categories of sets - an outgrowth of algebraic topology and what ever else of similar abstraction seem to have gotten into the game.

I was fortunate that the large state university I chose to get my PhD over half a century ago had a perfectly adequate but not elite math faculty, and I was able to do my research in a subject arising from classical complex analysis. Had I been confronted with category theory or a similar abstract topic I probably would have switched to computer science or electrical engineering.

Complex analysis, itself, has apparently moved up the inevitable steps of abstraction to the point that the arXive.org collections of papers on the subject are unreadable to me.

Classical mathematics doesn't need "infinity" as a sort of number with associated features. The limit concept works well. However, modern math defines the term(s) and goes into abstracta.

From the OP article:

My position is first that mathematics is an exercise in pure logic. It is not a human construct.

I'm not sure how to interpret this statement. If math is an exercise in pure logic and pure logic is a human construct, then so is math. So, is pure logic not a human construct?

Thanks for your reply. Very informative.

3) Philosophy is the Goddess of the Sciences — Arcane Sandwich

I checked with Copilot and AI agrees with you. (Well, it used to be - it hasn't provided much guidance in recent years, unless one means scientists who speculate)

That's the "level of dignity" that Foundations of Mathematics has. Now whose "fault" is that? Do professional mathematicians need to take the blame here, yes or no? — Arcane Sandwich

Only those relative few who have an interest in Foundations. :roll:

I have two apples. But I want to eat three — Arcane Sandwich

You apply Banach-Tarski to one apple, turning it into two the same size, then eat all three. But only if you have faith in the Axiom of Choice. If you do not you might raise the question on The Philosophy Forum. Abundant deep answers are found there.

"Years and Years" (2019) A British limited series that explores what might have arisen during and after Trump's first term. Excellent cast and intriguing story. Alternate history. HBO.

↪Corvus
What about Combinatorics, Group theory, Set theory, Boolean algebra etc.?
The world is exactly the way these disciplines describe. — EnPassant

So, the world has transfinite ordinal numbers. Or does it?

:clap:

This happens in mathematics as well. Long involved arguments get turned over to grad students and end up disappearing. Make it short and concise.

Numbers are fictions, and no fictions have causal efficacy. — Arcane Sandwich

Numbers don't exist as fictions, they exist as brain processes — Arcane Sandwich

So, numbers are fictions that don't exist as fictions. Does The Maltese Falcon exist as fiction?

Word games

Draw a circle on the X, Y axis with radius pi. All points on the circumference except 4 of them are irrational numbers. No others are rational, — EnPassant

Assuming you mean the ordered pairs of real numbers that identify points on the circumference have at least one member, x or y, irrational, what are those four points? x^2+y^2=pi^2.

Mathematics is the consideration of the properties of magnitude and multitude in the absence of any other properties — Count Timothy von Icarus

Hmmm . . . never thought of it that way.

Mazur's article on category theory introduces one to modern mathematics. Not necessarily mathematics as practiced by a great many professionals. As time passes levels of abstraction increase and the subject seems more and more like philosophy and less and less like calculus, for instance.

I'm suspicious of a process whereby students end up as variations of their professors. — Tom Storm

Sounds like a typical PhD program in mathematics. Occasionally a student flies off in an interesting exploration of their own. Usually knowledge advances incrementally.

This is logic's job. It is not limited to mathematics because mathematics is only one of the many formal domains of study, and the way that mathematicians progress in knowledge will not be identical to the way that other specialists progress in knowledge within their own field. — Leontiskos

This gives pause for thought. When I think of progress in math compared to progress in physics, say, the initial step of A to B requires speculation and experimentation, or with math, finding examples. In other words, one must posit the B. After that the mathematician works to logically connect A to B, while the physicist is perhaps more interested with finding counterexamples that would invalidate their theory.

Set theory is closely tied to logic, and lies in an area overlapping mathematics and philosophy. So one might ask whether Philosophy of Mathematics is a part of philosophy. I say it is, but others might disagree.

The notion that scientific laws and maths are contingent human artifacts rather than the product of some Platonic realm seems more intuitively correct to me. — Tom Storm

I agree.

But as an untheorized amateur, I would say that. — Tom Storm

We are all amateurs in this regard. Mathematicians rarely spend their time discussing or arguing the issue. It has so little to do with traditional math research. But times change for any human endeavor, and "modern" mathematics, category theory e.g., is an elevated and abstract perception of the way the subject has been for millennia and is possibly closer to the Platonic conundrum, although I can't see how.

And...does that mean I can't trust anything science says? — Darkneos

Of course not. Science works pretty damn well. If you were an astronaut would you distrust the science that got you to the moon and back? The proof is in the pudding.