An electron track observed in a cloud chamber only ‘looks’ like a path, but is really nothing more than a series of water droplets left in its wake.

I dabble with "paths" or contours all the time in complex analysis and find this statement valid but vapid. On a computer screen a path is just a sequence of points or pixels, or, more accurately, something identifying an underlying entity having no "body".

Thanks for the 1935 commentary. Husserl and I share an ancestral connection: Karl Weierstrass. Husserl was temporally close the great mathematician, while I am one of about 35,000 descendants. Husserl may have been at a point in mathematics with little to no precedents while triggering the ideas of manifolds and categories in math.

But the 1935 commentary is babble somehow critical of abstractions in math and science, IMO.

they show the empirical sciences what is hidden to them in their own naive assumptions. — Joshs

When and where would that be?

Also, why do you think 'quantum physics' has any more implications than (e.g.) 'miracles' or 'Euclidean geometry' for philosophical conceptions of 'reality'? :chin: — 180 Proof

Good point. Moving from Newtonian to quantum physics we are forced to replace the tool of ordinary language and analogies arising therefrom to "understand" or "picture" reality to a more sophisticated language, modern mathematics, wherein "real" accords more analogues with nature in its micro levels at least.

This "new" language demonstrates a preciseness the "old" language lacks.

As an old and probably extinct practitioner I have been able to glimpse things through mathematical descriptions that rival - surpass even - what I can describe using traditional language and analogies, although some would argue all of math is ultimately reducible to ordinary language. I suspect this is true.

Broglie-Bohm theory may connect "mathematical vision" with that encompassed prior to the mystics of QT. From a paper by G Hooft:

Discussions of the interpretation of quantum mechanics [1–20] seem to be confusing and endless. This author prefers to consider the mathematical equations that make the difference. Having the equations will make the discussion a lot more straightforward. Here, we reduce the theory of quantum mechanics to a mathematical language describing structures that may well evolve deterministically. The language itself is equally suitable for any system with classical or quantum evolution laws

Oh, have children both inside and outside of Israel been taught a Two State Solution is best? — jgill

You think one state solution is best? — ssu

I'm not advocating, only saying that IF a two-state solution is sought the journey starts with how children in the areas affected are taught. Young people have the energies to push hard for a cause.

The real dreadful thought is that if Bibi fucks this up, we actually could really have a two state solution: — ssu

Oh, have children both inside and outside of Israel been taught a Two State Solution is best?

Christianity promotes a regressive theory of disease — Art48

Tell that to These people.

I thought you and others might enjoy knowing that most physicists regard String Theorists and other specialists in unprovable/unfalsifiable theories as not really being "physicists", and actually being "mathematical philosophers". ;) — Jaded Scholar

As a retired mathematician, a "mathematical philosopher" resonates more as someone indulging in mathematical foundations - a topic at the heart of the subject, but one many if not most practitioners have little concern over.

I would classify that as metaphysical speculation. — Metaphysician Undercover

I agree.

I hope you stick around. Actual scientists are a rarity here, as are math people. The intersections of science and philosophy can be an entertaining circus. :cool:

My goodness, those are delightful ! :smile:

Do they know what they're voting for? Do they care? Do they understand? I think the answer is 'no' on all counts. — Wayfarer

I think you may be correct. Many might assume democracy has broken down and a Glorious Leader is the answer.

And without a hierarchy of moral values which only philosophy can provide, your own proposition itself, that "physicists have better things to do", is meaningless prattle. Such a proposition would require reams of support to justify it as sound. — Metaphysician Undercover

Point scored for philosophy. :up:

Very nice. I especially like the sense of motion in the water.

I think it's mainly because large numbers of Americans are nuts. — frank

Let's pretend the next presidential election has a financial criminal running against what many perceive to be a somewhat demented nitwit and his political cohort a lady who giggles a lot. How would you vote?

Perhaps you would ignore the figureheads and vote the liberal party. But, wait, that party has led to America being a "failed state", according to Britannica (lost control of its border). And it virtually overnight returned Afghanistan to the Middle Ages under the control of extremest religious zealots. Never mind that Suzy Orman states that 75% of Americans can't put their hands on $400 in an emergency. (She may or may not be right).

According to a survey conducted by Bankrate in early January, 56% of Americans are unable to cover an unexpected $1,000 bill with their savings1. This indicates that a significant percentage of American adults may have difficulty getting money in an emergency.

BingAI

I've had former academic colleagues who are "nuts", as you put it.

I think this thread shows that mathematics is insufficient for explaining the reality of physical existence. That's why we've developed philosophy. — Metaphysician Undercover

The philosophy is being done by the scientists, and some would call it speculation. Philosophical ideas seem to require ream after ream of supporting prattle. Physicists have better things to do. :cool:

A great song that I would recommend every philosopher,scientist,mathematician and witches [avoid?]

But "Inch Worm" is cute.

If Colorado does remove him, it will only martyr him more, and all for nothing, because Colorado wasn't going Trump anyway. — Hanover

Unless he gets a majority of votes nationwide. Then CO will, by legislative decree, add their support.

Don't count The Donald out. In an election in which a criminal runs against what many regard as a senile nitwit all bets are off.

Many thousands of years ago beer was the most popular beverage in Egypt, with pyramid workers getting paid their wages in beer. It was safer to drink than water from the Nile.

I imagine the Singularity (associated with Big Bang) not as a space-time object, but as the mathematical definition (e.g. program) of a Potential (not yet actual) universe — Gnomon

Well, in math a singularity is roughly where a function goes haywire, but your interpretation is interesting.

(Pure mathematics I have dabbled with suggests the origins of the universe might never have had a "beginning point" in time, and that - in this weird perspective - virtually anything might have set up a causal chain at any point in early enough time.)

In absence of anything/everything, speaking of perspectives doesn't make much sense... — jorndoe

Ditto for the thread IMO. There has been a failure for something to have arisen out of nothing.

The last bit of southern pride I recall before leaving the area for good was "GO BAMA !"

But when Charlayne Hunter Gault moved into a dorm room at the University of Georgia - I was in the USAF, far away, by then - a high school friend of mine wrote telling me about himself and perhaps a few others taking over a room or two on the same hall in order to protect her, not from fellow students or local rednecks, but state and local law enforcement.

Is there a general rule here? If not, then why does this work only for 6 digits or more specifically, — universeness

Sorry, I have neither the time nor interest to delve into this. I think number theory may be full of stuff like this, but I never even took a course in the subject. My general area was complex analysis, dealing with the limit concept in the complex plane.

Yesterday, upon my chair
I saw nothing that wasn't there
It wasn't there again today
I wish that nothing would go away!

Were I to sit upon my chair
Would nothing again be there?
Or lack of nothing be gone away?
A curious thing, what can I say? :cool:

I was also hoping you would explain the 6 digit trick, divided by the three primes, as to why it worked. — universeness

That one expression I presented shows it all. The dots are multiplication. When you write out abcabc, like 869869, what you are really expressing is [a(10^5)+b(10^4)+c(10^3)+a(10^2)+b(10^1)+c] , and dividing by 13, 11, and 7 is the same as dividing once by their product, 1001. (Since the product divides evenly, so will the factors of the product: 13, 11,7)

Factor out the expression in my original equation that is enclosed in parentheses and you are left with (10^3 + 1)/1001 = 1.

??

It is clear that the impossibility of creating a CAD system that can correctly draw square circles places no limits on what computers can do. — PL Olcott

Are you referring to Squaring the circle? Are you sure about your opening statement?

Computer programs can actually do this to any preassigned degree of accuracy. But using only a string compass available to the ancients and a straight edge is impossible in a finite period of time.

Transfinite numbers

Don't get lost in the labyrinth.

What about the interior of the empty set? — jgill

I thought this was meant as a counter-example — Ø implies everything

I was just tossing it out to get your opinion. Sorry for the confusion.

I was offering support for your position. — jgill

I don't see how. You seemed to offer a counter-example to my claim that absolute nothingness is impossible. — Ø implies everything

If someone were to say, "Well, empty space has nothing in it", I would say, "But it is inundated with various fields".

Absolute nothingness is most definitely impossible — Ø implies everything

But physically, there are fields everywhere inundating empty space. — jgill

That is self-contradictory. The space is not empty if there are fields in it. These kinds of retorts seem to rise from a confusion of exactly how absolute the absolute nothingness is. We are talking "about" the inexistence of anything definable and undefinable; the inexistence of absolutely everything. — Ø implies everything

I was offering support for your position. I'm old but not that senile. :roll:

However, I think you make an empty mountain out of a philosophical molehill.

Absolute nothingness is most definitely impossible — Ø implies everything

What about the interior of the empty set? Non-syntactically speaking. But physically, there are fields everywhere inundating empty space.

I think my argument can be simplified to this:

Absolute nothingness is impossible, but it would not be impossible if it were not for the existence of something. — Ø implies everything

Simplified? You're kidding. Convoluted, it appears to have philosophical substance. Does it really?

My first vote for president was JFK. I have never seen a presidential election like the upcoming one. The potential candidates are like Looney Tune characters. Please, third partiers, come forth!

Curious. I never came across "witness" in math before this thread. Mostly Foundations I suppose. But, loosely, it seems to be a sort of example. Normally, when a mathematician proves a conjecture they might demonstrate by citing an example to make it more "real". "Under certain circumstances there exist certain things of which the following is an example", etc.

While the robot's sources may well be impeccable, you can't prove it. — Vera Mont

True. But BingAI lists the internet sources, so you can go directly to them for verification. Though some might be shaky, as any search might show. What can you believe on the internet? On Wikipedia, for example, I have found advanced mathematics pages to be very accurate, but elementary pages not necessarily.

It's a big, ad-infested goldmine of knowledge - why restrict yourself to a chatty robot? — Vera Mont

Well, the chatty robot can do a lot of the searching for you and provide a quick answer.

A right-hand glove could be put on a left hand if it could be turned round in four-dimensional space. — plaque flag

That's a stretch. :cool:

But I like his conciseness.

I feel you. Did you ever look into the famous TLP ? — plaque flag

6.5 If a question can be put at all, then it can also be answered.

Incompleteness in mathematics puts a kink in this. Is "this and that" provable? Will "yes" or "no" always suffice?

Of course the 'now' itself is 'stretched' with anticatipation and memory, allowing me to appreciate music and understand a long sentence. Note that I constant expect expect expect, and that attention is drawn to violations of expectoration — plaque flag

Come on. Spit it out. :smile:

I think there's a 'good' discursive part of philosophy, some of it basically so creative as to be visionary. This or that person somehow cuts through the general confusion with just the right metaphor, just the right revelation of false necessity as mere contingency, opening up the space. — plaque flag

:up:

The problem, as I see it, is that then a revolutionary idea is drowned in a sea of words. Being a math guy and not a philosopher, to be concise is paramount (though some in my former profession violate that principle).

I was suddenly grabbed by the beauty of it. It is like granite or marble — plaque flag

I like that. I was a rock climber.

I'm assuming you also are 'speaking a language' in your work. You have the feeling (I hypothesize) that patterns are being revealed that aren't just computer-checkable patterns in dead symbols. — plaque flag

I love those symbols. They are an integral part of exploring an obscure path of conceptualization and discovery. It's all about exploration.

I'd wager that most of 'em would say not so much. — plaque flag

Yrs, but should I believe them? They simply don't seem to know — FrancisRay

But I'll save that for others who aren't satisfied with the relatively trivial (however difficult at times ) syntactical part. — plaque flag

I confess. In my own research I have never cared, being more concerned with the difficult trivia that goes on outside the hallowed halls of Foundations. For instance, I rarely came into contact with transfinite theory :cool: