In the 83 years I've been alive, the "perfect candidate" has not appeared...although there have been some good candidates and good winners.

Biden, no matter his many faults, will be a marked improvement over Trump. But even Mickey Mouse would be a marked improvement over Trump. — Frank Apisa

You and I, at 83, can barely remember FDR - who along with Washington and Lincoln top the list IMO.

I'm not so certain Biden will be a huge improvement over Trump. He will certainly be a more traditional president. We will probably have the opportunity to find out. :chin:

Please have a little patience, I think we might be getting somewhere soon. — Punshhh

Of course. :cool:

You are familiar with mathematics. By what principle would you say 10 is "higher", meaning a greater value, than 2? — Metaphysician Undercover

The "Looking at one's hands" principle. :smile:

OK. Forgive the intrusion. I was curious about first-hand knowledge of the topic being discussed. In other philosophical areas, like panpsychism, this is not a consideration. For several years I belonged to a forum in which a lengthy thread dealt with various aspects of mind. One participant had practiced Zen for thirty years, and we had some interesting conversations about his epiphanies and how they might have related to brain activity.

From SEP:In the wide sense, let us say that a ‘mystical experience,’ is: A (purportedly) super sense-perceptual or sub sense-perceptual experience granting acquaintance of realities or states of affairs that are of a kind not accessible by way of sense perception, somatosensory modalities, or standard introspection.

This definition is more inclusive than one positing some aspect of the divine. Have either of you had such a "mystical experience"? If so, please describe them. How did you enter into the mental states that led to revelations beyond normal sensory or introspective means? Did you meditate? Was there an epiphany at some point, an astounding and memorable moment?

Philosophizing about such internal adventures seems so remote from actually having them. Like discussing Citizen Kane without having seen the film.

I don't mean to be rude, but this is an area of which I have had some limited first hand knowledge, and so I see the disparity between participation and external ruminations. If all you wish is to speculate and discuss the analytic parameters of mysticism, then I beg your pardon, please continue.

Surreals by any other name are just an infinitesimals? — tim wood

No. I'm old enough that I knew Leibniz, and am familiar only with his basic ideas about infinitesimals. Surreals by Conway are much more elaborate. One can teach a calculus course using only the basic elements of infinitesimals. IMO the surreals are for set theorists and philosophers. Purer mathematics than anything I've done. The real and complex numbers are challenging enough for me!

The finite number line is a fiction. It may be useful for some things, but to insist that it is somehow 'real' and try to make meaningful inferences from that is meaningless. — A Seagull

I'll pass that on to my colleagues. What a bitter disappointment. :sad:

In mathematics one learns the concept underlying a symbol, then develops a skill for manipulating it. I once read of a prominent mathematician saying that the most valuable competency he had acquired was how to mechanically manipulate elementary calculus as if without thinking.

1:A natural spiritual need. The human propensity to look to a divine agency. — Punshhh

IMO wrong from the outset. The divine is not required.

Forgive me for being blunt, but this conversation is like two guys throwing frisbees in a meadow discussing how to pilot an SR-71 Blackbird. Are either of you serious mystics? If so, I will humbly retreat. :worry:

It's funny how ubiquitous the delta function still is in physical and engineering mathematics, and yet it is completely non-kosher from the point of view of standard analysis — SophistiCat

One way to make it kosher is to consider it a generalized function. I never worked with those either.

https://en.wikipedia.org/wiki/Generalized_function

So just where are, what are, the surreals? — tim wood

On the finite number line, infinitesimals are everywhere and nowhere. If r is an infinitesimal then 2+r lies to the right of 2 but to the left of any real number greater than 2. Your job, Tim, should you accept the assignment, is to find it and neutralize it! If you fail we will disavow any knowledge of it. :worry:

Is it not more accurate to say that some surcomplex numbers are surreals, or that there is a complex extension of the surreals? — Pfhorrest

Picky, picky, picky! :smile:

In over fifty years of complex analysis mathematics I don't think I ever really thought of these critters.

The Dirac Delta function (0 everywhere except at x=0, there infinite) can be thought of in terms of infinitesimals, here in terms of alpha:

$\int F(x)\delta_\alpha(x) = F(0)$

Surreal numbers are on the number line, unlike complex numbers, which are not. That is, surreal numbers are not complex numbers — tim wood

Every real number is a complex number, but not vice-versa. There are certain types of surreal numbers that are complex: s = a+bi , where a and b are infinitesimals:

Wiki: A surcomplex number is a number of the form a+bi, where a and b are surreal numbers and i is the square root of −1.[9][10] The surcomplex numbers form an algebraically closed field (except for being a proper class), isomorphic to the algebraic closure of the field generated by extending the rational numbers by a proper class of algebraically independent transcendental elements. Up to field isomorphism, this fact characterizes the field of surcomplex numbers within any fixed set theory.

You guys are going down a rabbit hole here. :nerd:

The concept of infinitesimals goes back at least to Leibniz and Newton. Modern day non-standard analysis incorporates these ideas in a legitimate mathematical model. One can prove basic theorems in calculus using infinitesimals, and there have been textbooks that have done that. I once considered teaching an experimental calculus course this way but decided against it. I have heard that for some students calculus is more understandable taught in this non-standard way. I view infinitesimals as metaphysical entities that have achieved a kind of actuality.

The set theory aspects are something else, and seem to appeal to philosophers. Have at it! :cool:

Banach-Tarski is merely the result of bad grammar? :roll:

Maybe by "grammar" you mean math here, and the AOC is "bad grammar"

B-T depends upon the Axiom of Choice. This shows how "dangerous" it is to simply add new axioms to ZF. One would think that AOC is obvious and of little consequence, but not so. It takes one away from the world in which we actually live and plunks us down in another universe.

For a more palatable paradox, there is Braess' Paradox (which has been employed in a number of major cities):

For each point of a road network, let there be given the number of cars starting from it and the destination of the cars. Under these conditions, one wishes to estimate the distribution of traffic flow. Whether one street is preferable to another depends not only on the quality of the road, but also on the density of the flow. If every driver takes the path that looks most favourable to them, the resultant running times need not be minimal. Furthermore, it is indicated by an example that an extension of the road network may cause a redistribution of the traffic that results in longer individual running times

You can create the number line with the null set. Let {0} = the null set:

{0}
{0}{0}
{0}{0}{0}
{0}{0}{0}{0}...etc

= 1, 2, 3, 4...: — EnPassant

And then come the fractions . . .

I read that Søren Kierkegaard self-published his books. So don't discard this idea. :smile:

But if they're to be resolved, it must be in and on the ground from which they came . . . — tim wood

One of the weirdest is Banach-Tarski, and that one arises if one assumes the Axiom of Choice. Discard the AOC and it goes away. Another, the Diagonal Paradox, is simply a matter of perspective and magnification.

Physics without math is Philosophy — Gnomon

Possibly. But in the quantum world much of the physics is the math. For example, a virtual particle may simply be a mathematical entity, an yet amateur philosophers may refer to these things popping in and out of physical existence.

I recently read of Feynman's lectures at Cal Tech back in the 1960s. Even there, with very bright physics students, most were unable to understand his attempts at explanation. A few followed the math and comprehended his ideas, but the majority were left in a state of confusion. When he first presented his "sum of all paths" formulation to an audience consisting of prominent physicists, very few initially comprehended what he was saying.

Physics without math is philosophy - if the philosopher is a physicist. That's my opinion, but I'm sure others here will disagree. That's OK. :cool:

Mathematics, properly understood, is the theory of everything. — Syamsu

:cool:

Perhaps the best overall model is that of a quantum wave. — A Seagull

Not quite the same as particle or interference wave. It's more a mathematical device for predicting certain quantum properties.

In mathematics it's easy to find examples of a passage of time with no change, as well as a change at an instant. Is that possible in the physical world? :chin:

A number line is an irrational conflation . . . that's why the idea creates so many problems — Metaphysician Undercover

It makes doing mathematics like walking across a minefield! :fear:

From NOVA online:

One of the missions of the Large Hadron Collider (LHC), the behemoth accelerator straddling the French-Swiss border, has been to test the possibility of unseen extra dimensions . Since the discovery of the Higgs Boson in 2012, completing the Standard Model of particle physics, the idea of looking at such extensions has become more central.

To establish the existence of extra dimensions with the LHC, there are three major avenues of attack. The first involves finding echo versions of existing particles, called Kaluza-Klein states. These would be like the known particles in all respects, except more massive, like overtones in music. At a proton-proton collision energy of 7 trillion electron volts, searches have been made for Kaluza-Klein gravitons, Kaluza-Klein gluons and others, so far to no avail.

Physicists are also using the LHC to search for evidence of gravitons seeping into higher dimensions. Such signals of otherwise unexplained missing energy would have to be sifted from enormous numbers of collision events, carefully ruling out a plethora of more mundane possibilities, such as escaped neutrinos.

Evidence for extra dimensions could also show up at the LHC in the form of microscopic black holes, predicted by certain higher dimensional theories. Famously, before the LHC opened, alarmists raised a fear of such objects destroying the Earth, despite calculations showing they would harmlessly decay within a tiny fraction of a second. Despite the hopes and warnings, miniature black holes have yet to be detected among the collision data of LHC experiments.

Currently, the LHC is switched off and being revamped in preparation for cranking up its collision energy almost twice as high as the previous run. In 2015 it is expected to reopen and collide protons at 13 trillion electron volts, offering the possibility of producing more massive particles and more unusual events. The upgrade will offer a greater chance to detect evidence of extra dimensions.

Where is time in a changless world? — prothero

A photo exists in a changeless environment and freezes time, but examining the photo involves time's passage. Do you really think that a changeless world could exist beyond the confines of a philosophical argument? Could there be places in deep space where there is zero change? And is change dependent upon an observer? We would see a ship approaching a black hole as slowing to a stop, but those on the ship would perceive normal movement.

Our days runnith over with confirmation bias.

See, here it is, the desire to know, right here at the base of mysticism — Metaphysician Undercover

I agree there is the desire to know what may be lying beyond everyday reality, to experience something beyond the normal world. Teresa of Ávila had the burning desire to know Jesus. A Zen student might want to know the truth about one's "I" . But too great a desire may very well be a hindrance to knowledge.

Nice presentation.

A little like the riddle, What is it that has quadrupedal movement, roams grasslands, prone to human domestication, gets hungry, etc etc ?

Would you say this set is NP-complete? — tim wood

Create an algorithm to list all the penguins. Then take the complement in the Universal Set.

This crops up in the Wiki article Talk section:

"Non random probabilistic flow of information in the Planckian order of magnitude"

Whereas, in the article: "In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object"

Not sure a random physicist could do much better than this.

Yet I am sure that a set that contains itself can be defined - I'm just not clever enough to think of it — tim wood

X={X}

:roll:

"...and among mathematicians only a small fraction are working in or at least interested in foundations." How true!

In the article in Wikipedia:

In 1923, Ludwig Wittgenstein proposed to "dispose" of Russell's paradox as follows: The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself.

In practice this is nonsense as well, IMO, although in some abstract sense it may have weight. In iteration the first application is f(f(z)). So the outer f acts upon a function value and not on the function itself. Fractals arise from these processes. Perhaps f(f) makes less sense. If F is a functional, then neither F(F(z(t))) nor F(F) is normally well-defined.

Matter is empty, so energy fills it up. — Braindead

Goes to show that physics can be both speculative and poetic. :smile:

Wasn't something being proposed about creative writing Baden ? Is that to be limited to Fiction ? — Amity

Obviously not, reading posts in this forum. :smirk:

{a} is a subset of A and A is a subset of X therefore {a} is a subset of X — EnPassant

{A} is a subset of X, not A. Ask fdrake or fishfry to explain this stuff to you. I'm done.

When I write a dynamical systems program to obtain an image, I determine the image. When the program runs, it causes the image to appear. — jgill

This doesn't sound like a very useful program that only displays one image - the one you determined. Computer programs are useful when they can be applied to create various images for different people based on the input from different users. The programmer doesn't necessarily know what images the program will generate because they are aren't aware of all the different kinds of input from different users. We can try to guess, but we can't account for every instance, which is why programs can have bugs. — Harry Hindu

What does "useful" have to do with this example? In fact, the programs I write have a number of different input parameters that I alter frequently to obtain new imagery. I don't design these programs for anyone but myself. But I am so happy you attempt to educate me, explaining why programs may have bugs. I feel so stupid. :yikes:

{a} is in X (because {a} is in A, B, C,...) — EnPassant

No, {a} is not "in" A,B,C,...

IMO this stuff is not worth the effort.

Set A = {a, w}
Set B = {a, x}
Set C = {a, y}

Set X = the set of sets that have {a} as an element. — EnPassant

None of them do. They have "a" as an element. D={{a},z} does.

This stuff is deleterious to mental health. :scream:

I am having some trouble thinking of any well-defined set that does contain itself. Help? — tim wood

x={x}

Nonsense, however.

Set theory can drive a person nuts. :worry:

5). Reversability. Almost all mechanism of physics are reversible and work equally well backwards as forwards. — Benj96

The formulae that involve a time variable seem to have this property. But keep in mind they merely describe phenomena and are not themselves phenomena. The reversibility might just be a quirk of the mathematics. A real physicist should comment. :chin:

When I write a dynamical systems program to obtain an image, I determine the image. When the program runs, it causes the image to appear. Sorry this is such a trite example. :worry: