If you use the search words 'Does expansion create new space' on sites such a quora, physics stack exchange etc. You get many many viewpoints . . . — universeness

It's hard to discern on TPF if a poster really knows what they are talking about, especially topics in physics. I think Haglund does have a graduate degree, and Kenosha Kid has a PhD. There may be one or two more. But a lack of in-depth studies of QM or general relativity is not a deterrent to posting a seemingly knowledgeable and well written statement on the subject. And if you go to a source like Wikipedia you might find confusing arguments and counter-arguments among experts in the talk sections.

One member here suggested a metric used in GR and when I read it on Wiki I could not tell whether a crucial term meant proper time or spacetime. And guess what, neither could a few of the "experts" speaking out in the general TALK discussion. Another instance was my attempt to find out what measure was appropriate for Feynman's path integral. In the article itself its just a brief hand wave, and when I asked about it in TALK I got no response. After a while I deleted my question.

My view is that space does not bend and surely, not break. The immaterial does not bend or stretch, etc. — val p miranda

It does look that way, doesn't it? Confusion arises when 4D spacetime is introduced with a different metric, and said to curve, etc. But space itself does seem to show signs of curvature. Beyond me.

This expansion involves neither space nor objects in space "moving" in a traditional sense

The distance between objects changes in some sense.

Lagrangians (excuses for the term used on this forum) — Haglund

Kinetic energy minus potential energy? Or that functional used in path integrals? The term comes up over and over it seems.

Perhaps jgill would comment on the maths argument used above. — universeness

The arithmetic of infinities is a subject of axiomatic set theory. IMHO little to do with the real physical world. Others would disagree. As for the "expansion" of space, Wikipedia says it best:

The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time.[1] It is an intrinsic expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. This expansion involves neither space nor objects in space "moving" in a traditional sense, but rather it is the metric (which governs the size and geometry of spacetime itself) that changes in scale. As the spatial part of the universe's spacetime metric increases in scale, objects become more distant from one another at ever-increasing speeds.

(Wiki)

Those who have experimented with psychedelics often describe a sensation of connectedness with objects around them, things like rocks, trees, or rivers. Sometimes the "connectedness" is more literal, as high doses of psychedelic drugs like LSD may cause users to believe the walls are talking to them.

[Eric Schank, SALON] :chin:

So it is wrong to assert that the same shape is to some degree flat, and to some degree curved. — Metaphysician Undercover

Well, there are different metrics involved, but I can see your point. My first grad course in math in 1962 was differential geometry, and it was a puzzling experience, a topic I never found use for in all the intervening years. My view of this issue these days is very superficial: the difference between an ant crawling across the surface of a large sphere and recognizing another dimension above, and an ant somehow embedded and crawling in the same surface and finding it 2-dimensional. Pretty shallow. :roll:

Did you invent those contours eating each other? — Haglund

Just examples of little interest apart from the imagery.

The world is in too much chaos right now to get anything of substance done about climate change. Best to start adapting. For example, the Colorado river supplies water to about 65 million people downstream. And predictions indicate less and less flow. Arizona is already discussing piping in ocean water and desalinizing it. What will Las Vegas do? Desalinization on a large scale takes lots of energy, and hydroelectric is forecast to diminish.

You said a thing is flat to the degree that it's not curved, and a thing is curved to the degree that it's not flat — Metaphysician Undercover

Theorema egregium.

The "remarkable", and surprising, feature of this theorem is that although the definition of the Gaussian curvature of a surface S in R3 certainly depends on the way in which the surface is located in space, the end result, the Gaussian curvature itself, is determined by the intrinsic metric of the surface without any further reference to the ambient space: it is an intrinsic invariant

(Wiki)

Did residues and contour integration, etc. but this seems new. Or is it a normal thing in the field. Did you turn it into a visual? — Haglund

Coupled Differential Equations

There is a tremendous amount of complex variable theory that is not covered in a typical course (which I taught a number of times). I got into my specialty over a half century ago via complex valued continued fractions, which led to a general study of infinite compositions of complex functions.

Yes, I extracted the visuals.

At your level you are basically learning about tools and preparation. It has nothing to do with mathematics — I like sushi

In fact, as fundamental tools it has everything to do with mathematics. The algebra and trigonometry and perhaps basic calculus you learn is useful throughout the incredibly diverse realm of mathematics.

G'nite my friend. :yawn:

Did you succeed with that Victorian cross (no offense!)? — Haglund

Not more than a fraction of a second. It awaited a smaller, stronger body.

If self creation is coherent, then there can be nothing and then something.
That isn't something from nothing. That's nothing and then something. The cause of teh [the] something is not the nothing, but the something itself. — Bartricks

Moments of clarity like this make a mockery of claims that all that is worthwhile has been mined from philosophy. :chin:

What's a toity world? Well, it's just a device to make clearer what a toity truth is. — Bartricks

It's refreshing that, having assumed all avenues of original philosophical exploration had been traveled, something novel and appealing bubbles up from spilled beer at the local bar. :strong:

I guess it pales in the face of your accident about 35 years ago... — Haglund

Sadly that's the strongest part of my body now. :worry:

↪jgill
Looks very Mayan! Perhaps its just the combination of color and the swirling motif. — Agent Smith

Hidden within those intricate folds are the secrets of the universe.

Well, maybe not. :sad:

Not so. He was an officer on the front lines, decorated several times. — jgill

Thanks. I did not know that. — god must be atheist

I knew Lester Germer slightly, as a famous physicist (wave/particle duality) but more as a fellow rock climber. My impression of him grew considerably when I found he had been a fighter pilot in WWI. A multi-dimensional person.

That was more Kripke — Banno

In Philosophical Investigations §201a Wittgenstein explicitly states the rule-following paradox: "This was our paradox: no course of action could be determined by a rule, because any course of action can be made out to accord with the rule"

Yes, the bizarre addition example.

He was a complete fuck-up. — god must be atheist

Not so. He was an officer on the front lines, decorated several times.

(But I kind of agree regarding his wondrous rule-following paradox.)

Begin with a number between 0 and 1 in the first cell. Next cell = previous cell x (1 - previous cell) x some constant between 2 and 4. — Cuthbert

Sound like elementary cellular automata, championed by Wolfram some time ago. I've written programs that show a constant sort of development, then a jump to a weird line or something. Wolfram thought he had come upon a hugely important concept, writing a book with over a thousand pages. I, like most other readers, gave up after a few hundred pages.

Somehow they seem to eat each other. Raw sex in the complex plane... — Haglund

Like Pac-Men. My friend, you need to get out of the house more often. :wink:

But I often find the talk pages on Wikipedia more informative than the articles themselves, especially on philosophical subjects — magritte

I do also. In this case [mathematical physics] the talk section makes one's head spin!

Where that presents difficulties, is that there is no provision in most people's minds for things to exist in different ways — Wayfarer

If things were not bizarre enough: Rydberg polaritons

I'm tied to my home for a still few weeks — Haglund

You live in Shanghai ? :smile:

So philosophy's not your cup of tea — frank

More a form of entertainment. :cool:

Have a good evening — frank

You too. :smile:

Laplace's demon has been upgraded with the latest software by David Chalmers — frank

The guy who believes rocks have feelings?

I've often wondered how the aether affects ectoplasm.

Wiki:

Laplace's demon was based on the premise of reversibility and classical mechanics; however, Ulanowicz points out that many thermodynamic processes are irreversible.

Gotta move up to the 21st century, buddy.

Random numbers are generated by a deterministic system. In a computer it's a quartz oscillator — frank

Suppose my random number comes from an observation of unpredictable minute changes in atmospheric pressure?

Have you written some background on the maths involved? — Banno

Lots of notes/articles as a hobby. Here's an example: Woven Contours

I've written all my computer programs in BASIC.

You have an algorithm that, once begun, leads to an outcome - thus determined. But halfway through the algorithm is a step requiring the input of a random integer between 0 and 9. Is the outcome determined? Random? Both? Neither?

Can you zoom in like in those colored fractal zoomings (where the colors represent a rate of convergence, if Im not mistaken)? — Haglund

It's not a fractal, but sometimes one can focus on a spot and enlarge it and find additional intricacies. Iterations are done at pixel levels with light shades when the modulus is great and dark shades when it is small. Very simple.

↪jgill
Impressive. This is yours? — Banno

Yes, I've done lots of unpredictable images. Look at my icon on TPF. Here's another I call Reproductive Universe:

Here is a non-chaotic image arising from an iteration process that involves differing functions rather than a single function. Its' beautiful intricacies might possibly be predictable were an attempt made to do so, but it would take a significant effort. This is a dynamical system in C that rewards its inventor. I call it Dream of Gold.

To Mathematicians

Is Chaos Theory (math) an admission that the calculations involved are too complex for humans and current top-of-the-line supercomputers (extremely difficult to predict) or is the claim that there's true randomness (unpredictability). — Agent Smith

The computer calculations define the dynamical system in C (complex plane). Iteration of a function carries an initial point in C to a new position - usually not the same position unless the original point is a fixed point of the function. When there is a condition in which two points very close to one another diverge dramatically and relatively unpredictably under iteration the system may be chaotic (under other circumstances fractals might appear). This might occur everywhere on a set S in C, or on a part of S. This is the simplest version of chaos theory. Draw your own conclusions. :cool:

Calculus, complex numbers and chaos theory were developed to cope with the ineffectiveness of current maths to deal with emerging problems in physics — Cuthbert

Not entirely true. Complex numbers arose in the study of roots of polynomial equations, more pure math than physics.

It’s simple: you can’t step even once because, as soon as you touch the water, one instant later it is not anymore the same you touched initially, because it is flowing. — Angelo Cannata

The word "same" means persistence over a span of time in this case. The instant (t=0) your toe touches the flowing water all is frozen in time. Think of a photo taken at that instant. For t>0 the word same comes into play. This becomes an argument of time as instances vs time as periods. Think Einstein vs Bergson (1922).

It is similar to Zeno’s paradox of the arrow, but the opposite way. — Angelo Cannata

Nice point.

Mathematical physics are dynamical systems where anything that is mathematically possible is also physically possible until the theory is shown to violate some physical law. — magritte

Not really: Mathematical physics. A person engaged in this pursuit seeks mathematical ideas and procedures that might illuminate aspects of physics. Sometimes new math is developed in this quest, but there are over 26K separate topics in mathematics on Wikipedia so there is a wealth of material one might search for applications in physics. Also, mathematical physicists attempt to put foundations in place to prove certain math procedures in physics - like renormalizations and path integrals - are mathematically sound. Dynamical systems, a very specific area of mathematics, sometimes are referred to as classical mathematical physics.

Your position sounds similar to the ancient philosopher Cratylus, "you cannot step in the same river once." — Jackson

Sure you can. But not twice. :roll:

A minor point, but when a mathematician explores a possible theorem, searching for a hypothesis that will guarantee a certain outcome, he does so over a period of time. But when he finds such a starting point, the conclusion instantly exists. A implies B involves no time component. Is this true of cause and effect in the physical world? Hitting the ball with your bat is certainly cause and effect, possible only during an interval of time.

Here's the first article I've seen that discusses the possibility of determining whether alternate universes might exist. It still seems a reach.

In mathematics, a dynamical system might proceed to evolve along alternate paths at points of bifurcation. But what happens in math may be mere fiction in the physical world.