I keep coming back to the idea that to be successful in philosophy (as I see it) one needs a solid awareness of the tradition and how ideas have been explored thus far. — Tom Storm

How, then, is "success" measured?

Probably not by getting hundreds of posts on a thread one starts on TPF.

Space is real, and I don't think space bending is a metaphor. — Constance

Usually this expression is used in reference to spacetime and depends on a certain metric. Objects, however, become distorted by gravity and speed. Length contraction, etc.

What is a philosopher? One who contributes something new and of publishable quality to the realm of philosophy. Thus professional philosophers control the intellectual environment.

Then there is philosophical banter, enjoyed by millions.

We're desperately trying to find something that doesn't exist, because we simply cannot comprehend the confrontation with the fact, that the universe doesn't care whether or not we exist. Whatever you might say is the meaning of life, let it be happiness, power or serving some god, it will never satisfy the human desire for a meaningful meaning. — Carlikoff

I suppose some are prone to this level of existential anguish. Others find that one creates one's own meaningful life. One that will satisfy human desire.

So you don't have to look it up, from Wikipedia:

In a modern sense, a philosopher is an intellectual who contributes to one or more branches of philosophy, such as aesthetics, ethics, epistemology, philosophy of science, logic, metaphysics, social theory, philosophy of religion, and political philosophy. A philosopher may also be someone who has worked in the humanities or other sciences which over the centuries have split from philosophy, such as the arts, history, economics, sociology, psychology, linguistics, anthropology, theology, and politics.

As a retired mathematician, my profession is defined a bit more specifically, citing "using extensive knowledge of mathematics" to solve problems, etc.

Random vs logical? or random vs determined? Randomness is a logical concept. And logical is a human concept.

Is infinity necessary? Hell yes for mathematics!!! — ssu

You bet. :cool: As an abbreviation for certain statements. For example $\sum\limits_{k=1}^{\infty }{{{s}_{k}}}\lt\infty$

And you even get paid for it! — EugeneW

Not since I retired 22 years ago. :cry:

t strikes me that many (most? all?) so-called paradoxes are really just playing with language — T Clark

:up:

Does F(t) have a physical interpretation? It's a remarkable formula! — EugeneW

Go back and click on that second math note about extending the diagonal paradox. It occurs there. As far as something physical I don't know.

Depends on the context. You are driving with a passenger in a safe manner and a car runs a stop sign and hits you, killing your passenger. You have done nothing wrong. You confide in a close friend an embarrassing fact about a third person, expecting your friend to not reveal your comments, which they do to the third person and that third person commits suicide. You have done something wrong.

Kind of arrogant, no? I'm just saying that your claims are unbacked and waaay over the top. — noAxioms

One physicist to another, eh? The peanut gallery awaits eagerly. :chin:

Wave on the unit interval compresses to a line infinitely long.

Yes

I was asked to relate a bit of QP to (elementary) math, and the Schrodinger equation in a simple version resembles a fundamental relationship in elementary calculus. In this way the SE is related to continuous compounding. Weird, huh?

You've given more info on the physics part, which is admirable. I don't attempt to add physics I'm not familiar with.

I could be wrong, but doesn't . . . — EugeneW

Wave from circle

or, another interpretation

$F(t)=t+iCos\left( \left( \frac{{\hat{H}}}{h} \right)t \right)$

Just some rough analogies between elementary math and QP.

Absolute True Reality — Gnomon

Assuming there is such a thing.

The first proposed infinite measuring system, the natural numbers for example, would require a larger infinite measuring system, to measure it. — Metaphysician Undercover

(Power set)

Embedded in the rationals embedded in the reals. Not so much going bigger above than counting more points between natural numbers.

But your analysis is interesting.

When a recursive process gets you closer and closer to an answer the more you apply it, and this process goes on step by step with no ending stipulated, then this is all about "infinity" that is needed for most mathematics. $\infty$ is a convenient way of saying this.

Foundations and set theory, however, go a significant step beyond into transfinite pastures. Occasionally a result in other areas of math require a cow chip or two from these leas.

Are you referring to traveling analogue waves — universeness

The things that appear on oscilloscopes, old fashioned stuff.

As a maths expert, do you have anything to add that would aid my understanding of the difference between the terms wave /function/form/equation as they are used in maths compared to quantum physics? — universeness

In math a simple wave is a time-dependent vector field defined, say, on the complex plane as
$F\left( z,t \right)$. One can elaborate on this, but I don't think that will help. Fourier series, of course, are associated with waves. But the closest I've come in recent years to producing a wave-like result might be these notes: Wave tunnels to centroids, Compressed wave of infinite length.

Perhaps the most illuminating way to connect the easiest of math waves with QP is to take a look at the foundational equation of the subject, the Schrodinger equation. Recall from basic calculus the mathematical relationship describing the rate of change of something compared with the quantity of that something. This is fundamental to so so much. It says the instantaneous rate of change of a quantity is proportional to the existing quantity at that moment.

$\frac{d}{dt}Q(t)=KQ(t)$. Easily solved to $Q(t)=Q(0)\cdot {{e}^{Kt}}$

Compare this with the Schrodinger equation in simplest form:


$\frac{d}{dt}|\Psi (t)\rangle =-i\left( \frac{{\hat{H}}}{h} \right)|\Psi (t)\rangle$


Notice that the capital K if replaced by $-i\left( \frac{{\hat{H}}}{h} \right)$
gives
${{e}^{Kt}}={{e}^{-i\left( \frac{{\hat{H}}}{h} \right)t}}=Cos(\left( \frac{{\hat{H}}}{h} \right)t)-iSin(\left( \frac{{\hat{H}}}{h} \right)t)$


And this, as t=time progresses, can produce a wave in the complex plane.

My comments are heuristic and descriptive, avoiding complexities beyond my grasp.

Waveforms certainly exist in electronics, but in Quantum theory they may be in abstract spaces where collapse of wavefunctions occur. What is actually physically happening vs probability measures, etc. At least that's how I see it - and I'm probably off track.

Agent Smith is a lot brighter than he seems at times. Humor him. :roll:

Yes, there are thoughts. I think therefore I thought. :cool:

Name an actual infinity, prove it exists! It's a simple procedure — Agent Smith

You are the one who says there is no physical infinity. Prove your statement. :roll:

There are no actual infinities; there are no physical infinities — Agent Smith

Speculation presented as fact. A no no for philosophers.

mathematicians should abandon the use of infinity in making calculations in favor of a
more logically consistent alternative. . . . Fortunately, such a concept is available to us—a concept called indefiniteness — Gnomon

This is kind of a non-issue with most mathematicians. If you are a set theorist you probably like fiddling with various infinities, otherwise if you encounter an endless process you'll probably call it "unbounded".

A tired subject. :yawn:

Superposition is collapsed by a virtual photon. — EugeneW

Which sounds more abstract, even mystical, than most of mathematics. Are things really that bizarre in the quantum realm, or is a dramatic paradigm shift over the horizon, awaiting an Einstein? How much of the weirdness is due to limitations of experimental investigations?

Long, long ago I thought of majoring in physics, but found the concepts of mathematics were clearer to me.

Another way to say this is that if you start with a 0 (e.g., "nothing") and end up with a 1 (e.g., "something"), you can't do this unless somehow the 0 isn't really a 0 but is actually a 1 in disguise, even though it looks like 0 on the surface. — Roger

You might consider rethinking your analogies. :roll:

Is math invented or discovered? :
Mathematics is an intricate fusion of inventions and discoveries. Concepts are generally invented, and even though all the correct relations among them existed before their discovery, humans still chose which ones to study. ___Mario Livio, theoretical astrophysicist — Gnomon

I would alter this slightly by saying the correct relations among them come into existence when the concepts do. Then these are sought out.

In the context of this thread, is a zero-dimension point considered to be Real or Ideal, Physical or non-Physical? As a philosophical or mathematical thought-experiment, the notion of "nothing producing something" might be a valid ideal concept. But as a scientific observation it might be as unrealistic as a vacuum fluctuation popping a particle of matter into existence.

As I understand it, a Virtual Particle is equivalent to a dimensionless point — Gnomon

I would say a zdp is both real and ideal, but not physically real. As for vps, they are excitations of the underlying quantum fields, so perhaps zdps are as well.

It's all Greek to me. I just try to do the math. :cool:

The arrow fields are vector fields with arrows showing direction and magnitude when a point is moved by application of the underlying function. When the arrows point to a specific point, that is an attracting fixed point. When they go away from a point, it is a repelling fixed point. Short answer for a sophisticated set of ideas. The brown picture is an image generated by iterating each point a specific number of times and pixel coloring according to magnitude.

Pile of 2-stones sits on a red square. Close by, pile of 3-stones sits on a green square. Seeing pile-of-2-stones and pile-of-3-stones, would you give each pile the same label? — ucarr

I love these Einsteinian thought experiments ! :nerd:

That's so incoherent it's actually funny. — Metaphysician Undercover

:cool:

(you can see this happening in the first note I linked) :wink:

Nice imagery isn't it? That's the fairly simple geometric and projective aspects of MTs. The analytic aspect Is what I do. For example.

Why can't we understand time? It's a clock ticking or asymmetric motion based on symmetric motion. Time can't be reversed because it has a beginning. The beginning is caused by timeless motion. — EugeneW

Motion without time. You're on a roll!

I don't think the human brain is capable of "understanding" time. There are endless arguments about beginnings or eternities but its like a dog trying to understand calculus.

I can't see a parabole, as you write. — EugeneW

Here's a link to the short note. This is a technical subject and probably not appropriate for TPF. If there are other questions it's best if they come through messaging.

What's philosophical is the idea of a dimensionless point producing an offspring. This happens as the value of t goes from 0 to 1. Like b(t) = a(1+t).

Nice presentation on traditional bifurcations via DEs. Not relevant to the situation I describe which is a process of growing a second (and repelling) fixed point (FP) as a parabolic LFT (having a single attracting FP) morphs into a non-parabolic LFT (having two FPs). Thanks for posting it.

It's really a sort of unique but trivial way of progressing from F=r to defining a new fixed point, b. Bifurcation is usually meant to "split" one fixed point into two fixed points. A kind of "Adam's Rib" sort of thing. In this instance, the function in the background (not the function,F, seen here) is a parabolic linear fractional transformation. But enough mathematics. Thanks.

OK. You do see the difference between {5,2,4} and (5,2,4) or <5,2,4> don't you? In the latter two position is inferred.

Any set can be defined as a vector (a starting point but no limit) — SkyLeach

OK, take the set {5,2,4} and generate a vector space since this set can be defined as a vector.