Recognizing stupidity as endemic to the human condition was my initial existential crisis — 180 Proof

Years ago a French mathematician I knew made the statement, "The one thing I cannot forgive is stupidity".

I disagreed. A stupid move by an intelligent person, yes. Innate stupidity, no.

It's just that I wanted to know if scientific calculations invovling infinities could be tamed in a manner of speaking. — Agent Smith

Renormalizations :roll:

Look at how the subject of identity is handled in formal logic, philosophical logic, mathematical logic, set theory, and mathematics. Those clear up a lot of questions (though there are still some philosophical questions that arise). — TonesInDeepFreeze

Precisely. In ordinary math we have an identity (valid for all or most values) and conditional equation (valid for a select set of values). 2(x+1)=2x+2 and 2(x+1)=3. Rough definitions.

So, in the sense you put it here, a bounded backward iteration with no end to the number of iterative steps would be what is traditionally called an actual infinite and unbounded potential — Bob Ross

It's simply a process that's unbounded. In math an actual infinite potential (I've never heard it called that - but I don't live in that mathematical world) is vague unless it corresponds to a cardinality. Tones-in-a-deep-freeze could go into this in a much more rigorous way.

However, just to clarify, I am not defining an infinite nor bounded/unbounded infinities in that manner, but I could see them as less precise examples — Bob Ross

I would have guessed more precise. Give me an example from the real world of what you are talking about.

↪jgill

Although I understand the point pertaining to the dispute amongst mathematicians over "potential" vs "actual" infinities, I am not sure how that objection relates to my essay. If you could please provide further elaboration, then that would be much appreciated. — Bob Ross

There's no significant dispute that I know of. Most of us not in foundations or set theory are not concerned with "actual" infinity. I assume what you are talking about is moving backward through causation chains with no recognizable beginnings. Like backward iteration in which there is no end to the number of iterative steps, but the process is either bounded or unbounded.

Quite a few mathematicians don't go beyond "potential" infinity. We're not all like Buzz Lightyear.

Suppose there was an upper bound to the Lorentz factor, $\gamma \lt M$.


Then the free variable v would also be bounded below c, which, in theory and thus computation, it is not:


$0\lt v \lt c \sqrt{1-\frac{1}{{{M}^{2}}}} \lt c$

How does intuition work in math? — Agent Smith

As it does in everyday life. But that is not the meaning of intuitionism in the philosophy of math.

Is there a finite number (Nmax) such that no calculations ever in physics will exceed that number? — Agent Smith

Calculations in physics. The Lorentz factor is unbounded.

Agent Smith is poking at us. He is much more intelligent than he seems.

Did you ever cross paths with Eugene Gendlin, who arrived at U. of C. in 1963? — Joshs

Afraid I was gone by then. But reading about him I can see a connection with what Mihály made his life's work. Was there a common school of thought there about that time? Incidentally, about that time the physics department started teaching all the math courses for its majors. Must have been a bit of ill will between physics and math departments.

There's always the temptation to overstate one's case in philosophy. — Banno

:clap:

This thread seems a little ridiculous. Call then laws or rules or whatever. They work, and I suppose the question is whether they will always work.

And the point is relevant to Trump whose lying still appears to suit the Republicans and their base, — Tom Storm

Not really. He has split the GOP, and now I think I saw a poll indicating at least 50% of them are more or less anti-Trump. But it's a sad state of affairs.

Indeed, once science turns its attention to subjectivity and consciousness, to experience as it is lived, then it cannot do without phenomenology, which thus needs to be recognized and cultivated as an indispensable partner to the experimental sciences of mind and life — Joshs

I'm a little skeptical of a "science of mind".

Phenomenologists reject the concept of objective research.

(Wiki)

However, this thread has made me aware of a new kind of mathematics supporting cognitive science,
Denotational Mathematics, created by a gentleman named Wang. It seems so peripheral that it doesn't even have a Wikipedia page (24,000 math topics do). It could be classified as a form of abstract alegbra, which has become a kind of jumbled mess IMO.

“Having studied physics, philosophy, and mathematics, [Arthur] Fine graduated from the University of Chicago in 1958 with a Bachelor of Science in mathematics. — Joshs

I was there at that time. I missed knowing Fine, but I did go climbing with Mihály Csíkszentmihályi, who later wrote extensively about a subject I discussed occasionally with him: "flow" in human activities. In particular, in gymnastics and climbing.

Ok, here’s some contrivance for you: — Joshs

It's not surprising these are in the general area of cognitive sciences, a more or less scientific discipline that combines aspects of philosophy with subjects like artificial intelligence and linguistics. Although neuroscience is in this grouping, the models relating to it are not biologically compatible.

I'd rather see Max Tegmark's speculations mentioned. When you throw philosophy in with traditional science the primary question is one of competence: Does philosophy of science require a considerable depth of knowledge in that scientific discipline?

Nobody has ever proposed a theory to explain everything — Cuthbert

Alexandre, an occasional poster on TPF, presented a paper that began with the encoding of every fact in the universe. That would be a big step towards a ToE.

On the whole the history of philosophy runs in parallel with the history of science , so if one progresses, the other must also. They are joined at the hip. — Joshs

Assume for a moment that science is a huge ocean liner moving slowly through a deep sea. Where do you see philosophy in this picture?

Curious what @Fooloso4 and @Manuel have to say. :chin:

Is there a finite number (Nmax) such that no calculations ever in physics will exceed that number? — Agent Smith

From special relativity, the Lorentz factor is unbounded as v approaches c.

$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$

There appears to be progress in the philosophy of mathematics, but I try to avoid it. :cool:

Because of the synchrony produced by extreme variability in density contours, coherence tends to endogenously occur . . . — Enrique

I'll get back to you after consulting my copy of Schaum's Outline of Quantum Mechanics.

I think Roger Penrose suggested a cyclic universe of multiple big bangs? Was that chaos theory? — TiredThinker

No. Chaos theory is a mathematical subject in dynamical systems in which slight variations at the beginning of a specified time period produce chaotic or unpredictable results.

Which means the climate-denying, election fraud-believing, Trump-worshipping, spineless corporate servants take back Congress —and nearly nothing gets done until 2024, when things could go even worse — Xtrix

Yes. J.P. Morgan analysts say there is the possibility of gas going up to $15 a gallon here in the US. Guess which party gets the most votes regardless of who are the candidates?

Science is advancing. This is very obvious. But is philosophy? — Alkis Piskas

That's a tough question. I think there are at least three forum members who post here who have doctoral degrees in philosophy (perhaps more), so one might assume the ball is in their court.

1. No calculation ever would exceed that number — Agent Smith

Sure, just fix whatever large number you wish and round off to that number. But you might make a mess of computations that follow. In physics renormalizations work in various settings.

Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Nikolay Bogolyubov and Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through "effective" descriptions. All scales are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each. Wilson clarified which variables of a system are crucial and which are redundant.

Wiki

That said, I was hoping to find a number such that

1. No calculation ever would exceed that number — Agent Smith

Why is it I think you are not serious? :smile:

in a universe that's finite — Agent Smith

Your supposition may not be valid. But entertaining idea.

Just as mathematics is the language of the quantum world, it's probably the language of any sort of world beyond the Big Bang, or the ends of time, and it's a language that evolves. It may be a hopeless task to try to gain philosophical knowledge that interprets these worlds in the contexts of our reality.

As you are far more a philosopher than me, I cannot argue the issue. :cool:

Without explaining nature, from what are predictions of "happenings in nature" deduced?

Philosophy might attempt to explain phenomena ...

Do you have an example of "a philosophical explain of phenomena" in mind? :chin: — 180 Proof

The obvious one, quantum mechanics. Predictions are highly if not entirely mathematical, many stemming from Schrödinger's equation, given here in stripped down form to demonstrate how it's solutions are wavelike (phasor). This concerns "particles" that are not little bowing balls:

$\frac{d\Psi }{dt}=iC\Psi (t)\text{ }\Rightarrow \text{ }\Psi (t)=K{{e}^{iCt}}=K\left( \cos (Ct)+i\sin (Ct) \right)$

This is not a physical wave. Very little explaining from nature there. That's left to (mostly) physicists who try to humanize what's happening with philosophical speculations:

Interpretations of QM

Yes, ontological vs epistemological and all is a subject for philosophers of physics.

Like a pointer that points to a state of disarray. — kudos

Imagine this comment coinciding with me misreading "drugs" as "dogs"? :chin:

Serendipity

Science explains nature (i.e. transformations of phenomena, facts-of-the-matter, states-of-affairs) with testable models and philosophy interprets – describes, infers – the conceptual ramifications (i.e. presuppositions, implications, extrapolations) of science, no? — 180 Proof

I would say that rather than explain nature, science develops models, mathematical or otherwise, that predict happenings in nature. Philosophy might attempt to explain phenomena in more day-to-day, less technical ways. Both are most successful if done by scientists, themselves. Carl Sagan, for instance.

The founding fathers were wary of the common man’s ability to vote and wanted to protect citizens from the “tyranny of the majority.” — Paulm12

Here in Colorado the citizens voted to give up our individual votes for president (electors) to whomever wins the nation-wide majority. There are conditions, of course. If a number of other states follow suite this will come into play. Hence an effort to revert to this "tyranny". This result surprised me.

And? — Jackson

You are approaching my level of succinctness on this forum. But I stay a step ahead by not posting.

Is this related to Kant? — Gregory

It Kant be.

T(x) ≔ x is true (definition) — Michael

Looks like you've defined a fixed point of some function. But I doubt that is what you mean?

Just as an ocean is one water that IS many waves, Existence Itself is one permanent substance that IS many impermanent forms — Relinquish

Pleasant observation. :chin:

Having had many experiences in the Art of Dreaming years ago, I recall the first thing I thought of when I was first successful was, "Now I understand how religion really started!"

Shamans, prophets, and others capitalized on this variant of consciousness to establish what later became organized religion - far, far removed from its origins.

Just my thoughts on the subject. It may be hard to understand unless you've had the experience. And the experience, of course, may establish a trajectory of thought that is possibly incorrect!

Which makes it even more distressing that, in a post-appearance interview, Bowers said that if Trump were to stand in 2024, he'd vote for him! — Wayfarer

After watching Biden as president it's a reverse Sophie's choice I fear.

American Republicanism really is a brain-eating virus or profound cognitive disorder, a symptom of a society that is literally destroying itself. — Wayfarer

We'll keep that in mind.

It's unfortunate this kind of language is used for this purpose. Heisenberg and Bohr cautioned against thinking of this as a physical process or having a "picture" view of what was going on. But then there are several interpretations of what's going on. Its so easy to let one's imagination follow a kind of mental animation.