"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.

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.