But when you approach these problems, Zeno's paradoxes for example, and the irrationality of pi and the square root of 2, with the attitude that these problems have already been solved, you do not look at them as real problems — Metaphysician Undercover

What makes these "problems" unsolved and real? :chin:

But when you approach these problems, Zeno's paradoxes for example, and the irrationality of pi and the square root of 2, with the attitude that these problems have already been solved, you do not look at them as real problems — Metaphysician Undercover

Work-arounds were in existence 3,600 years ago and have improved over the eras since. And, yes, 2,600 years ago there was considerable dismay among the ancients. You have confirmed what is seen frequently here that when one turns philosophical on an issue one goes back in time to see what the Greeks had to say, and to join them across the ages in their despair.

I would think intuitionism might appeal to you. But even there the obvious imperfections are swept into a corner and allowed to exist.

Out of curiosity, are you an old guy like me, middle aged, or a "youngster"?

Just filling in space until JS reappears. :cool:

I am not a mother, but I was "Mr. Mom" back when this was either a joke or something seen as suspicious or wrong. — Fooloso4

For darn sure women's lib changed my experience of being a woman. I crashed from being a Mother Goddess to "just a housewife". — Athena

I supported Womens' Lib and that resulted in me becoming "Mr. Mom" - a single parent - for a while. But life moved on in unexpected but welcome ways.

Don't look back. Something might be gaining on you.

I think I have mentioned before, but I wrote a Wikipedia page on an obscure mathematical topic a few years ago. Recently, when I asked chat about that topic it replied with the first paragraph verbatim from Wiki. I guess I was flattered, but it is a low priority math topic. :cool:

As noted, I've used ChatGPT since day one, it's become very much part of my day-to-day. — Wayfarer

I use the Bing version of AI chat, but it's been disappointing. On some historical issues it simply reprints paragraphs from Wikipedia. Two days ago I asked about a fatal accident that had occurred in a nearby community, and it came back apologetically with no results. I then Googled the accident and it came up on top of the first page.

Moreover, one of the reasons for modern mathematics no longer being merged with the field of physics is that - as I also mentioned previously - assumptions and value judgements about physicality or "reality" are outside the field of mathematics, which is now primarily directed with finding and fleshing out any and every mathematical system we can think of — Jaded Scholar

Some time back on this forum I mentioned that October of 1958 when I started a postgraduate curriculum for the USAF at the U of Chicago I found that the mathematics department would no longer offer courses to the physics department, the latter offering all physics math courses. The rift went beyond the obvious differences in notation and symbolism (which I find annoying and distracting) and probably had something to do with differing attitudes about proofs. And the foundational stuff about mathematical systems.

I am an old guy, and when I go to one of 26K pages on math on Wikipedia I'm not sure what is being discussed. Even most of modern complex analysis seems foreign.

I enjoyed reading your rebuttal to MU. Amusing and entertaining, unlike so much on the forum that rehashes and compares what classical philosophers had to say.

Born in Alabama. Naturalized Coloradan. High Prairie.

What happens when an observation is made is that those probabilities ‘collapse’ into a precise measurement. — Wayfarer

An analogy I've used before is that a differential equation (like the Schrodinger equation) may have a multitude of solutions, one of which suits the experiment being performed. Upon measurement one of these is determined to be be correct. No "collapse". But my analogy may be incorrect.

.there’s no mention of the word ‘fractal’ anywhere in it. I don’t think it supports the argument you’re making — Wayfarer

Pop science usage seems to be anything that is wiggly and is wiggly upon magnification. Mandelbrot's creation carefully derived in the complex plane is another matter. Maybe other pop usages as well.

No evidence our cells are intelligent?!!! — ken2esq

OK, this guy is legit. A lot depends on how intelligence is defined, at least for me. Do cells think as well?

The Levin Lab:
We work at the intersection of developmental biology, computer science, and cognitive science. Our goal is to understand degrees of intelligence at multiple scales of biological, artificial, and hybrid systems; we use these insights to develop interventions in regenerative medicine.

In high school in the 1950s in Atlanta I had a course in civics. Is that what you were talking about? Also world history. But emphasis was on science and math. I was a major in high school ROTC, and our Army officer in charge, a captain, was an alcoholic. Baby steps toward a Military Industrial Complex?

The fractal nature of our biology doesn't quite work the same way. — Vaskane

Thanks. I learned something.

Abstract

Fractal geometry allows structures to be quantitatively characterized in geometric terms even if their form is not even or regular, because fractal geometry deals with the geometry of hierarchies and random processes. The hypothesis is explored that fractal geometry serves as a design principle in biological organisms. The internal membrane surface of cells, or the inner lung surface, are difficult to describe in terms of classical geometry, but they are found to show properties describable by fractal geometry, at least sectionwise and within certain bounds set by deterministic design properties. Concepts of fractal geometry are most useful in characterizing the structure of branching trees, such as those found in pulmonary airways and in blood vessels. This explains how the large internal gas exchange surface of the lung can be homogeneously and efficiently ventilated and perfused at low energetic cost. It is concluded that to consider fractal geometry as a biological design principle is heuristically most productive and provides insights into possibilities of efficient genetic programming of biological form.

https://pubmed.ncbi.nlm.nih.gov/1767856/

"Fractal" in this environment would imply intelligence at each level would be the the same - if magnified it would be what we normally call intelligence - and if intelligence implies consciousness, then our cells are conscious in the same way we are. There is no evidence of this.

Your other threads I looked at seemed for me too long. A few paragraphs and some of us here drift off. Maybe be more concise.

Do you not think that we truly are, as Carl Sagan suggested, in the title of his first episode of the series COSMOS, 'on the shores of the cosmic ocean?' — universeness

Eloquent.

a singularity represents a transition point where our theories (or maybe just our current system of mathematics, or both) stop working and, as far as we can tell, no longer describe reality. — Jaded Scholar

The essential singularity of complex analysis would seem strange enough it might provide some clues about how math diverges from reality in a spectacular way and how our ideas of reality could shift. Particularly since the exponential function is fundamental in physics. Just idle thoughts. Good you are around.

Man, you have really gotten into this stuff !! I admire your tenacity and ability to digest material that spooks me. :smile:

led to a new school of study into the way that Art promotes knowledge and understanding. — Saskia

Sounds a little like the Waldorf School which goes back to 1919. Or Spacial Dynamics, a more recent attempt to combine movement and art into all aspects of learning. An old friend of mine was instrumental in bringing this to America.

But then can there ever be huge enough event to cause significant change? And conversely, how many little events add up to the kind of intransigent determinism you are proposing? — schopenhauer1

Perhaps the rise of Alexander the Great, or the Atomic Age. I would speculate lots of instances.

Your second question is a good one. Actually, the Atomic Age and the resulting societal changes came about through incremental incidents over a period of time, one researcher at a time. Well, sort of.

What does it mean for mathematical structures to be "real"? — schopenhauer1

From the perspective of a mathematician, I would say examples exist. Not necessarily physical. If a function is "real" (not a real function) examples within mathematics must exist.

Physics? Well, we will see . . .

Another possibility which l reject is that we’ll get to the core, and arrive at the most fundamental laws and complete physics — Sirius

Agree.

Was the Kennedy assassination the thing that most pushed the nascent radical change that occurred in the 60s? — schopenhauer1

No. From my perspective at the time, social movements were on their way.

I think of Lem's rebuttal of the Butterfly Theories of history; his Ergodic Theory of history tells us that, in the passages of civilizations, were we to travel back in time and change an incident that from our advanced perspective might well have changed a huge part of the way history evolved, we would be disappointed at how little would have been altered. No Hitler? Someone else would have popped up. JFK surviving assassination? Not much difference in how society developed.

( On the other hand I have a personal acquaintance with the butterfly notion: how a tiny act can affect how a certain future (millions) perform something they enjoy doing. )

it's so easy to be shuffled into the category of "I don't know but I know it when I see it" — Jaded Scholar

Along with its bed mate? :cool:

When I say "t=0" in this case, I'm using it as a shorthand for the much more difficult-to-characterise hypothetical boundary where our mathematical models interpolate the existence of spacetime itself, as we know it, to exist on this side, and to not be able to exist on the other side — Jaded Scholar

I have never thought of boundaries of spacetime. Since both space and time are in essence metaphysical concepts through which we nevertheless function, the idea of "boundaries" might refer mostly to mathematical models. The Big Bang being possibly an exception. MU has argued before about the notion of a point in time, and his arguments are similar to those of Peter Lynds, who denies the existence of such points in favor of duration or intervals, somewhat like Bergson.

In Physics, we get mathematical results that can be called "unphysical", but I don't recall any such qualification given a single time in my Complex Theory lectures. — Jaded Scholar

That's something for me to chew on. Fifty years ago I wrote a paper concerning limits of infinite compositions of Mobius transformations. There was a strong connection with analytic continued fractions, and these can be used somewhere in physics. Later, I found that such expansions might be accelerated or analytically continued through fixed points. If you think infinite compositions of complex functions theory might find a niche in physics, let me know!

But I think we should assume that there are limits on what mathematics we can imagine, — Jaded Scholar

Perhaps. But ArXiv.org receives hundreds of original math papers each day, every day. 26,000 math topics in Wikipedia. However, applications to the "real" world is another matter. I never went that direction.

For the graph f := (x,y) — Sirius

What is f=(x,y)? A function is a certain kind of collection of ordered pairs. I suspect you are tacking on a vertical line segment to link the two end points.

We define miracle as an event — Sirius

At the very outset, what evidence do you have that a single miracle has occurred? Tales of miracles are simply stories.

My aim is to broaden the definition of "nature" and "laws of nature" to include any irregular event ( Fire not burning wood , Walking on water ) as a possibility in nature by introducing meta-laws which preside over what we commonly regard as the laws of nature. — Sirius

How can one "broaden" the definition of nature without requiring repetitions of miraculous events? And when the first such event cannot be verified where can one go?

Nevertheless, interesting idea.

What this will do is subject any possible claim of miracles to science ( physics and mathematics primarily ) — Sirius

Gee, thanks. If things weren't complicated enough already with the pseudo-miracle of entanglement.

To give an analogy, in mathematics we can assign values to a function where it's not continuous — Sirius

( f(x)=0 if x<1 and f(x)=1 if x>=1 is already defined at the critical point. Can you cure this sick function?)

Vietnam was a direct result of Kennedy not pulling American advisory forces that were already there. He died before he was (probably) going to do that. LBJ immediately escalated.. So the result can be seen as very directly. — schopenhauer1

I like to think JFK, had he been president in 1964 would have taken a more thoughtful and nuanced approach to the Gulf of Tonkin incidents. I suspect he would not have accelerated USA involvement in Vietnam like his successor did.

What role did JFK play in the cultural bloom of the 1960s? — BC

I voted for him. And in 1961 he extended my tour of duty in the USAF for a year because of the construction of the Berlin Wall. This delayed my entrance to grad school but I wasn't really distressed. My impression of the early 1960s is the glamour of the inhabitants of the White House had a substantial effect on American society. But so much else was happening. My wife and I sang Kumbaya with Joan Baez at Stillman College in Alabama and attended civil rights demonstrations. And I watched Lee Harvey be assassinated live on TV. And around the campfires in the Climbers Campground in the Tetons drugs appeared and occasionally things got out of control. I resigned my commission as captain in the Reserves, preferring to focus on family and future rather than the insanity of Vietnam. I can't forget Huntley-Brinkley each evening giving the numbers of Americans killed or wounded that day.

So, are there any members of this forum who fought in that conflict?

Firstly, I don't know how one can believe something just for its potential utility. — Tom Storm

Good point. Can one will ones' self into a belief? Possibly in politics.

I was tempted to say anything running over ten pages.

But then I recalled Wile's proof of Fermat's last theorem.

I have popcorn ceilings, too. Never think about it. Big deal.

I try to always have a math project I can explore - one that no one else has worked on. That makes my leisure attitude pleasing, no matter what the outcome. Math tends to be a very competitive activity.

Nice cats.

I am a retired mathematician and my learning style has always required examples. If I try to understand a math concept I need to see it in action.

(I had an acquaintance who did a PhD thesis on a particular set of functions, but when asked on an oral exam to produce even one of those functions discovered their set of functions was the empty set.) :worry:

Dennett is nonsense here, IMO. What is needed is a member of this forum who has multiple personality disorder to speak up. Or possibly this condition only magnifies the "problem" of personality.

We are pre-conditioned genetically and then further conditioned by our environments.

In a meditative state some time back I shifted to another personality briefly. It's an experience ineffable and lasting.

Do you think that if a human travelled at light speed ( I know that human 'mass' currently makes that impossible) then the human would not age? — universeness

Now, that's a nice thought experiment. There would be no concept of time, and aging requires the existence of time it seems to me. This takes one back to a previous thread on change and time: does a physical change require a passage of time? For our little scamp, the photon, one has to ask if it changes other than position?

Attention physicists. Chime in if you are in the house. :cool:

Time doesn't exist for a freely moving photon. But when they are slowed down to a snail's pace time catches up.

Look at what has happened in Argentina where a populist Libertarian arose out of nowhere to take the presidency. True, they had 143% inflation last month. He has started a movement to eliminate public works and move to the private sector. He and Donald might well get along.

I can't imagine Joe and Kamala for another four years. But stranger things have happened.

I imagine Biden sqeaks out another win, despite his age — Mikie

A lot will depend upon Trump calming his rhetoric and presenting himself as the more energetic and middle of the road candidate. Stranger things have happened.

Start writing a book, young man.

The greatest threat to humanity is the collapse of the economy. — unenlightened

:up:

Logically, he would go directly diagonally across the field. Being tired he decides not to exercise his free will as to another path. I don't get it.

A few years ago, I heard from a girl who is a mathematician - that the sunset doesn't have any poetical nor artistic vibe, and it is a concept of astronomy. — javi2541997

Please don't assume mathematicians are like this in general. Among then you will find musicians and artists. We are not bean counters. :cool:

The Republicans of the Blue state of Colorado had a Centennial Celebration Dinner and did a poll on presidential candidates. Trump won in a landslide.

His re-election as president may trigger all sorts of PTSD. Be prepared.