dV/dh=A is not abstract. If you measure a change in depth, then dV=Adh gives the corresponding change in volume. — jgill


So d = depth? A variable is not abstract? — ucarr

Language of calculus. dV means "change in V", etc.

Is this an example of the difference between an abstract idea (equation) and its everyday expression as a physical event? — ucarr

dV/dh=A is not abstract. If you measure a change in depth, then dV=Adh gives the corresponding change in volume.

Suppose it were possible for that change in h to happen instantly. Then so would the change in V. That would be unrealistic, however.

↪ucarr
I don't see what "time" and "cause & effect" have to do with one another. IIRC, the equations of QFT lack time variables — 180 Proof

A good point. However, much of Q-theory presupposes spacetime in one or another metric framework. When you see d^4 in a formula that probably indicates space and time. But all of that is way beyond me.

A simple example: You have a cylindrical container having base area, A. The volume of liquid in the container is given by V=hA, where h is the depth of the liquid. A causal change in V is the result of draining the liquid to a lower value of h. dV/dh =A, which gives a change of V corresponding to a change of h. No time is involved in the equation, only change. But if h=h(t), then dV/dt=(dh/dt)A, and we have change associated with a passage of time.

I usually think of change as taking place over an interval of time.

he parachutist jumps from the airplane at ten thousand feet and plummets to earth at the speed of acceleration due to gravity.

What’s causing precise acceleration? — ucarr

It's nit-picking, but starting your lengthy presentation with an inaccurate statement can distract from your argument. The falling parachutist does not fall at a rate determined purely by gravity - air resistance must be taken into account and this slows the fall. Such an effect is frequently calculated as proportional to the square of the velocity when close to the ground, if I remember correctly.

We see now that cause and effect the logical conjunction: a⇒b morphs into
a⇒b−t⇒a⇔bn. — ucarr

???

Well, at least you get a minimum of one reply this time around. :cool:

I suspect that people with a high level of personal confidence, self-efficacy, agency, and so on are less likely to seek social shelter in conservative groups — BC

Possibly, but there are those in the immigrant community who are industrious and eager to succeed and choose the Republican Party because it tends to remove governmental restrictions on business growth.

As for wisdom in old age, I am as old or older than anyone here I suspect, and I find that I value patience more than when young.

I fear trying to correct a climate trajectory is a bit of a joke unless all on Earth work together diligently, taking away the comforts of civilized society. Not likely.

Sell your beachfront property while you can. I understand prices are going up in some places. Go figure.

The point is that we do yet fully understand nature — Art48

An understatement of significant proportions. :roll:

, ,

Oh well, and here I was trying to follow an important dictum of philosophical dialogue I have learned of on TPF: Wrong, but interesting. :smile:

Reinforcements from several different sources helps.

But look at the Ukraine/Russia War. How many Russian soldiers have died. One source may say 100,000, another source may say 36,000, and a third source may say 1,567.

Don't believe any of them.

I drive to Walmart to pick up my wife. She will either be standing at the door we agreed upon, or she will not (still shopping). When I get there, there she is - and the wave function has collapsed. Until I get there I do not know. She resides in that mystical state of superposition, being both there and not there. But I have calculated the probability and it has come out .7 in favor of her standing there and .3 her not.

Partial differential equations model quantum "realities". When you solve the equation there may be several possible solutions - that's just mathematics. Linear combinations of those solutions are also solutions. Until you actually perform the measurements you don't know which is correct. So, in the math, there is nothing weird going on. Mathematics is not a perfect model in would seem.

I was thinking more along the lines of infinite causation chains and original causes. Sorry to interrupt.

If the world is eternal then there can be no prior potentiality or actuality or prime mover — Fooloso4

From a certain mathematical perspective this is arguable.

I’d argue that being is the precondition for consciousness — Mikie

:up: If being is interpreted as existence I agree. If being is the nature of a person, I might argue that that essence must involve consciousness.

I bet that memory came back to you at the moment when you're not feeling well or your mind was pre-occupied — L'éléphant

Indeed it did. I'm 86 and things I haven't thought of in years come back to irritate. :meh:

But so do good things. :smile:

All water under the bridge — Wayfarer

And this could be a topic of discussion all by itself. It's interesting that a small incident that occurred years ago can pop up in our minds when we deliberately relegated it to "water under the bridge" - or so we thought. This happened to me last week when a casual remark made by a high school classmate seventy years ago popped into my thoughts. It's partly the evoked emotion caused by the incident that fixes it firmly in the subconscious, available for re-annoying. :sad:

Not commenting on your remark, Wayfarer. It just brought the topic to mind.

The mathematical axioms assume a continuity which is infinitely divisible. However, it can be demonstrated in theory (Pythagoras and Zeno), that these axioms will inevitably lead to problems in application. The conclusion we can draw, or which I would say we ought to draw, is that this idea, of infinite divisibility, is just an ideal which does not truly represent the nature of reality. — Metaphysician Undercover

I'm not sure what "problems in application" you refer to since in most applications - if not all - one works with rational or computable numbers. I can pretty much guarantee that Feynman's path integral is a computational problem.

However, you have written a compelling philosophical case for quanta time and space. I don't know about the set theory axioms that should be replaced. Beyond my sphere of interests. Wikipedia says this:

In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra. The choice of that algebra still varies from theory to theory. As a result of this change some variables that are usually continuous may become discrete. Often only such discrete variables are called "quantized"; usage varies.

and

Physical spacetime is a quantum spacetime when in quantum mechanics position and momentum variables x , p x,p are already noncommutative, obey the Heisenberg uncertainty principle, and are continuous. Because of the Heisenberg uncertainty relations, greater energy is needed to probe smaller distances. Ultimately, according to gravity theory, the probing particles form black holes that destroy what was to be measured. The process cannot be repeated, so it cannot be counted as a measurement. This limited measurability led many to expect that our usual picture of continuous commutative spacetime breaks down at Planck scale distances, if not sooner.

It's a very technical subject that bears a slight resemblance to "not turtles all the way down".

I was not comparing our knowledge of Computing Science, I was suggesting my love of Computing Science was probably comparable with your love or Pantagruel's love of mathematics. — universeness

Whoops. Sorry. My fault. :yikes:

Y= The town is entirely flooded by the river. X=River Drive is flooded. Go figure.

An impressive vocabulary. :smile:

(Oh, forgot. What Aristotle thought about something.)

:up: :lol:

I rather see it like this: — schopenhauer1

And that's why you're not a climber. You should try it. Might lead to an existential breakthrough. Can't hurt (since death is admirable).

Look how doing it has built your climber's muscles! His self-esteem is surging. Look on the bright side! :smile:

But isn't mountain climbing the perfect metaphor for getting nowhere? :grin: — schopenhauer1

Rather, getting to the edge of nowhere. Big difference. :cool:

The idea of death as the greatest consolation and escape, and which is always at hand, penetrates me with even greater force

(Zapffe)

And yet he lived to the ripe old age of 90. Also, he was a noted climber, so his existential search was not unfruitful.

I do think I could claim an equivalent relationship with computers as you or jgill — universeness

You are way above me, my friend. I never got over an infatuation with BASIC, merely dabbling in Fortran, C++, etc. Look at my icon. This little guy materialized after a magnification of well over 1,000X from a program I wrote on certain dynamical systems. :cool:

I honestly still do not get your point — L'éléphant

Me neither. Perhaps it's simply that we are born without meaning of existence somehow programmed into our brains, and yet a need for it, and must constantly deal with the burden of creating meaning in our lives. This, apparently, is suffering we must endure. Why doesn't society give us money so we can go live under a bridge and snort drugs? Why must we be born into such a fix? :roll:

Intuitively, Smooth infinitesimal analysis can be interpreted as describing a world in which lines are made out of infinitesimally small segments, not out of points. These segments can be thought of as being long enough to have a definite direction, but not long enough to be curved.

Until we take notice of the reality of how space and time are actually quantized in real discrete units, these attempts, such as limits and infinitesimals, will remain ideals of theory which do not adequately represent the quanta of reality. — Metaphysician Undercover

Perhaps space and time are not "actually quantized in real discrete units".

To find meaning in what one does or is, regardless of the degree of volition giving rise to the doing or being. As an example, you might be in the Army and be assigned to a hospital ward to assist with the disabled. At first you find this task upsetting, possibly revolting in some instances, but as time passes you have a change of heart and find deep meaning in your work.

Another example, you are young, casting about for a purpose in life, and an older friend gives you an amateur artist's kit while you are recovering from an injury. You find you have a natural talent and love what you've discovered, making it the vital theme of your life from then on.

In both examples meaning arises and is embraced. Once it is triggered, you are hooked.

That is to say, why we start any endeavor or project (or choose to continue with it or end it) is shaped continually by a deliberative act to do so — schopenhauer1

is it moral to cross that boundary intentionally, or to be entertained by real life conflict? — Benj96

Shadenfreude is one aspect.

Truth table

Restrict the philpapers results to metaphysicians in the target group of academic philosophers - 372 respondents - and the number who advocate idealism goes up to almost 7%! The number advocating realism rises to 84%.

Make of this what you will — Banno

I love it when philosophers dabble in statistics. It's fun to visualize a group of academics sitting around a coffee table in the philosophy faculty lounge tossing numbers at each other. One says, "Hey, that's wrong - but in an interesting way". :cool:

I see from my readings here that my thinking needs modulation by your robust brand of optimism. — ucarr

:rofl: .

Our challenge as physicists is to discover this elegant way and the infinity-free equations describing it — Infinity Is a Beautiful Concept – And It’s Ruining Physics - Max Tegmark

Lots of mathematicians don't use the infinity symbol except in a limit sense. The idea of some entity called infinity existing doesn't normally crop up in classical analysis, for example. Tegmark cites the expression $\frac{\infty }{\infty }$, but elementary calculus shows ways around that (in very elementary settings), stating the expression is meaningless. If I were to say $\underset{n\to \infty }{\mathop{\lim }}\,f(n)=\infty$, I only mean that as n increases so does the function, with no upper bound. I don't mean it ultimately ends up at a magical point at infinity.

All this is very simple. I've read that Hilbert spaces used in QM must be infinite in order to preserve continuity and completeness in some circumstances. But there are ways of dealing with these concepts in constructive mathematics. I suspect the noise made by math foundationalists regarding cardinalities and "squeezing in" numbers in R by forcing and such things might make physicists uneasy - if they even care. I don't. :cool:

His last participation was about a year ago. He had made some comment about pursuing a "Pot of Gold" with his guitar. :cool:

Since axioms are produced by mathematicians who practise pure mathematics, and those people who apply mathematics have a choice as to which axioms are used, it would appear like we ought not use axioms like these, which necessitate that aspects of reality will be unintelligible to us. Instead, we ought to look for axioms which would render all of reality as intelligible. — Metaphysician Undercover

Those who apply mathematics normally are not deeply conversant with its axiomatic structure. Most mathematicians - in the pure realm - are not either. It's dreadful stuff, but some treasure it. :cool:

There was a member here, active a couple years ago, I can't remember the name, but a self-proclaimed physicist who was big on this time reversal stuff. — Metaphysician Undercover

@Kenosha Kid. He was a Q-physicist who left the profession to play his guitar, as he explained to me. He liked Transactional physics.

Brian May is an example.

:up:

However,

The hard problem really boils down to "What is it like to be another conscious being?" — Philosophim

this doesn't seem quite correct. One could argue that someone with MPD experiences just that. But, you might say, they shift from one to the other, so being in one state at a time. I would even question that assertion. I have actually had a meditative experience in which I was able to be myself and another simultaneously for a few brief moments. No, I'm not crazy. As a matter of fact whenever we talk to ourselves we indulge very slightly in this experience. But I'm setting up a strawman here, so I'll leave it.

Don't know how large a leap that is — TiredThinker

The truth table for that statement has him taking no chances.

Yes. You did mention him. I found some of his papers on researchgate.net, to which I also belong. This guy is older than me!! How can that be?

I'm not conversant with his areas of expertise and that is usually a substantial impediment in mathematics. But I appreciate you pointing him out. :smile:

This Article is intriguing. At first I thought they had found a way to reverse time in the quantum world, but rather they rejuvenated a photon, taking it back to a previous state.

The mathematics involved is probably linear (much is in the quantum world), since most non-linear systems are not reversible. Who knows? :chin:

as jgill says, many maths educators are not the least interested in the philosophical question. — Wayfarer

I must admit that in my old age one philosophical issue does interest me: where does the set of potentials created by a "new" concept or discovery reside? And what triggers actualization in the arena of mathematical knowledge? My mathematical interests have always been in infinite compositions, and I see a structure therein that might model this process. :cool:

Looks like it could be 1/2. I used to teach stuff like this many years ago, but haven't indulged since. Could be 1/3 I guess. If you draw a diagram of paths possible, only one is favorable, with probability =1/2. @fdrake could step in here with clarifying comments. :cool: