Newton's third law. You push and it pushes back. But who pushes first?

That's Kaku's mind resonating. :smile:

Also, unlikely that the holy spirit is into men. — T Clark

Dunno... Looking at some internet sites for boys only this can be called into question.



Maria
Madame Wu
Lise Meitner
Jeane d'Arc
Barbarella
Grandma Moses
Mata Hari

vs.

Magda Goebbels
Cleopatra
Bloody Mary
Maria
Xantippe
Pandora

Society has suppressed them. It wants them to fulfill stereotypical roles. Why they comply?

Wait & watch. :ok: — Agent Smith

It's not enough just to watch. The models of weather are not models of climate. If the model predicts a 3 degree increase in temperature that temperature will rise! Some thinking before commenting is welcome. Only words won't do.

This forum is an insult to philosophy — peoplearesmart

But it allows for rational discussion and beneficial growth of ideas.

What does this mean, to produce a reflection of a vector? You refer to a "mirror", but surely no one holds a mirror to a vector field. What kind of material might be used to create such a reflection? I ask because it's possible that the weird reflection properties you refer to, are a product of the method employed to create the reflection. — Metaphysician Undercover

You actually mirror the vector in a mirror, like a straight arrow. In curved spacetime the vector becomes an object with variable length..You inverse one of the components, in a suitable base. Sometimes front to back, when the mirror is perpendicular to the arrow, sometimes, the length direction, when the mirror is parallel. The velocity vector stays the same, so vXB doesn't change if you turn B around (which is a reflection).
Neutrinos change tò non-observed neutrinos in the mirror. It is claimed they actually exist, but that's a myth I don't believe. In a mirror universe right-handed anti-neutrinos might exist. An idea I think is right, but which will stay a myth some time.

I must admit, I do not understand "complex numbers". Wikipedia tells me that complex numbers are a combination of real numbers with imaginary numbers. But I apprehend imaginary numbers as logically incompatible with real numbers, each having a different meaning for zero, so any such proposed union would result in some degree of unintelligibility. — Metaphysician Undercover

The complex plane combines real with imaginaries. There are a zillion interpretations, but the best way for me is that imaginary numbers and rotation in the plane are connected, like so-called quaternions can represent rotations in 3d space. A multiplication by e^(iq) rotates the number in this plane by q radials. Every wavefunction is connected to complex numbers. You can add them like 2d vectors and their difference gives interference. The length of the squared number gives a probability density. Or probabilities in the case of discrete variables.

This is the part which really throws me. How does a physicist dealing with fields distinguish between potential and kinetic energy? — Metaphysician Undercover

That, in fact, perplexes me too (it was one of these bot thoughts...). Kinetic energy is true energy of particles moving. The massless gauge fields (I don't think there are truly massive ones like the W and Z) contain potential energy only. To become actual when a matter particle (non-gauge particle) absorbs it. We observe that kinetic energies of matter particles, change. So we posit a compensating energy (like a compensating A-field to keep the Lagrangian the same (one could have started from a Hamiltonian). We can globally gauge this A field without changing E and B. like we can globally gauge a potential energy. This doesn't make the total potential energy (which curves spacetime!) unspecified though, as it's connected with global phase rotations that doesn't change the physics. In the Böhm-Aharonov effect the reality of the A-field and global rotations is observed. Only E and B were supposed to be the real existing fields, which were mathematically reduced from A. Gauging E and B globally affects the physics. Gauging A not necessarily, for a specific gauge function. You can even have an A-field without charges, like in the BA effect there is no E or B field but there is an A-field present.
Which was first, the matter fields or the gauge fields? Well, you need a matter field to generate a gauge field, but you need gauge fields to excite particle pairs from the vacuum. Or, in QFT jargon, to excite a matter vacuum bubble, a closed propagator line, by means of two real photons. But the real photons are in fact long-lived virtual ones, connected to other electrons by a real propagator, like all real electrons are coupled with an anti-part somewhere in spacetime, so electrons are part of real but long lived quantum bubbles of electrons and positrons (here I diverge from the establishment!).

How can potential energy be real energy? Why do two separated equal charges have a higher pot. energy than two close by? The particles have kin. energy, move away, after which their kin. energy is reduced and pot. energy increased? The PE goes in the virtual A-field, but how? Strange indeed. But the virtual A-field (which encodes stationary A and B fields, virtual photons, while the changing ones are the real A field, real photons) just does because we impose it.

I think that would be fine. There's been plenty of discussions before about the nature of the continuum. Just try and keep it away from the mathematical equivalent of pseudoscience — fdrake

The "point" is that constructing a continuum out of points seems like a pseudoscience to me. The fact that the line, plane or volume have the same cardinality is because of the attempt to reduce them to points. I'll give it a try later.

It occurs to me, that only a bot could do that in just a few days. — Metaphysician Undercover

Haha! Hi there! Great questions! The bot will reflect while walking the dog... :wink:

If there is no first moment then that doesn't imply there is no second. Each second moment needs a predecessor. Which can be a first moment. But as a moment needs a predecessor, there can't be a first moment. So the universe has to be infinite. We call the first moment first because we can't see its preceding moment. I can see a rabbit making droppings. Apparently out of nothing. Coming to realize the drops emerge from the rabbit's interns seems like a revelation. Same for every first moment.

//edit// because universals are just that - they are universal. They're not peculiar to the human intellect, or they wouldn't be universal, as a matter of definition.// — Wayfarer

Most universals are created. Only after the fact they are called universals. It depends on the people if they are valued or not. Correct me if I'm wrong.

A person can hold the believe that the door is closed and claim it while the door is closed.
Her neural network will differ from the people who rightly believe and claim that the door is open. What is rightly believing? Depends on what you call the right neural network for believing something is the case.
Humans here are reduced to NN. You can just as well ask the people without looking at their NN.

I am saying that unmasked healthy people protect vulnerable people from getting infected by being in close proximity with them — Roger Gregoire

Then viruses have to be there in the first place. The man can take them away by sucking them up or attract them to his skin. But the increased volume in the room (of his body) will increase the virus density around the lady. The man can't inhale enough of them to keep up. You can open the door. This will keep the virus density the same. So the man entering has to keep the door open, though initially the virus density around the lady will increase. Increasing the risk. This is obviously not happening with one mosquito.

So. The man enters naked, leaves the door open, and walks to our girlfriend. The number of viruses around the lady increases. Then he starts to suck viruses away from grandma and blow the air to the door. But what's the balance? It's better to let him enter masked, because he might bring in new viruses. Increasing the risk. The risk is not as easily assessed like you do. If he wears a mask he can suck though. Best of both worlds. No emission, only diversion, after initial increase.

What if I asked the question, as a new thread, if the continuum can be broken in parts? It's maybe a math question. Maybe not. It will not alter the essence though of this thread, which is life-related.

confidently throwing around specialist terminology. — SophistiCat

That's exactly what I not do. I question it. That's all. I have been given no satisfactory answer though. Jgill came close. But the bijection he prescribes is discontinuous and suffers from the same problem as the number of points on the interval [0.1, 0.999999....). You just can't make points touch, or break the continuum up in points. How many points lay between 0.1 and 0.999999...? Do all these numbers constitute the continuous interval [0.1-0.99999...)? (What is continuous? Undivided.) You can assign natural number to each of these numbers. Is a number left out, by the diagonal argument? If so, isn't that a new natural number, contradicting that you left one out?

That's exactly what I have done. And didn't agree with. But it's clear now. Thanks to my opponent. I don't agree with him though.

Take the square {(x,y):0<x<1,0<y<1} and map it one-to-one to the line {r:0<r<1) by using the procedure implied by the simple example (.329576914..., .925318623...) <-> .39229537168961243...

You can figure it out if you stay off the Xmas grog long enough. Although you are a smart physicist and may be pulling our legs. You and Agent Smith can work this out. It cropped up in the course I used to teach in Intro to Real Analysis.

Hence, there are exactly the same "number" of points in the (section of) the plane and on the unit interval. Same cardinality.
5h — jgill

Yes. I get that. Still... something is nagging. If I map all naturals on [0.1-0.999999] (there you go...) what do I leave out? [0-0.1] seems to contain more numbers than [0.1-0.99999...]:

0.01-0,0999999...
0.001-0.009999...
0.0001-0.00099999...
.
.
.


Which is absurd. Still... On each of the intervals (including [0.1-0.99999...]) you can map the set N directly. Can you break up a continuous interval, like [0.1-1], up in real points? Like 0.1, 0.2, 0.3,...,0.91, 0.92,...,0.110, 0.111,...,0.1222, 0.1223,..., 0.2111, 0.2112,..., 0.24444, 0.24445, ...0,2023432, 0.2023433, ..., 0.655555, 0.655556,.......,0.999999999999....

Every cardinal is contained once. Or is one left out? The diagonal? But how can that be? Say that number is 1000000023432500876.... Isn't that contained in N? But not in R?

If so, can you represent x by 0.5878900... and y by 0.197867....(to name two arbitraries) to map on r?

Or is continuum just continuum, no matter the dimension? No points attached?

The bijection between R and RxR is not continuous.

masterbation feels great — Miller

Now that feeling comes close to a mathematical contemplation.

Computers play music. — jgill

But the pattern of sound coming from them can't be caught into a superposition of sines. Unless the music consists out of sine waves in the first place. Can an arbitrary piece of music be Fourier transformed? Only short pieces, not? Short pieces compared to the wavelength. Music pulses.

Okay:

0.1 connects with 1
0.2 connects with 2
0.3 connects with 3
.
.
.
0.14 with 14
0.15 with 15
.
.
0.53 with 53
0.54 with 54
.
.
0.768 with 768
0.769 with 769
.
.
0.99998 with 99998
.
.
ad 0.9999999999......

Do I have to list all N numbers?

Do you mean to suggest that there is a 1-1 function from N onto 0? — TonesInDeepFreeze

No. I mean: why can't N be mapped onto 0.1-1 (or 0.1-0.9999999999.....). I use every member of N one time.

Okay, last time. Between 0.1 and 0.99999.... you use all numbers of N; 1,2,3,....9999999..... Are there more numbers?

It's a 1-1 map!

Strangely enough, you need more numbers between 0 and 0.1.

The diagonol proof doesn’t apply here. I was thinkiñg that too. The interval I talk about is 0.1 to 1. Not zero to 1.

By the way, you claimed that I have no sense of humor — TonesInDeepFreeze

I was a bit angry when I wrote that! Forget it! I don't even know you!

There is a 1-1 function from N onto [0.1-1] (the interval from 0.1 to 1). Isn't there?

Well, like duh. They go on the galactic birthday cake. All, umm, 13 billion of them. Not sure who gets to blow out the candles tho. . . . . — EricH

The intergalactic blow job...eeeehhh... galactic lightning struck fan. When the galactic black hole shitty hits it. Paaaarty time... Let's do the Webb....

I told you. You don't have proof of it. You only think you do. — TonesInDeepFreeze

But where am I wrong in my proof? Cannot N be mapped onto 0.1-1? You ñeed N numbers for that: 1-99999999.... What number do I leave out here? Or do I leave numbers out between 0.1-0.9999999....?

In thinking that the fact that in your own mind you imagine that it must be so implies a mathematical proof. — TonesInDeepFreeze

I mean, where am I wrong if I say that N^3 can be mapped on R?

I think it's the continuum that confuses me, and its break-up into (onto?) its parts. I think the break-up of a square into lines is the same as a line into points. But maybe the break-up of a square into points is the same as a line into points.

Then I bet you really would not like Banach-Tarski. — TonesInDeepFreeze

In fact, I like that theorem!

There is no map from N^3 onto R. — TonesInDeepFreeze

You can map N to all reals between 0.1 and 0.999999...
You can do this N times (for all smaller decimals). You can do this for all N size one intervals. Where am I wrong?

You have not shown any dogmatism by my. Nor any exclusion other than of ignorant confusion and misinformation. — TonesInDeepFreeze

Yeah, you are right about that! Sorry that I called you dogmatic and exclusionary! You certainly got me interested in this aleph topic! As a physicist I find it difficult to believe that the number of points on a line is the same as on a plane or in a volume. The number of directions are different though. Or not even that?

Just now, and in the other thread that was deleted yesterday — TonesInDeepFreeze

On the contrary. I even told you I contradict myself in previous posts. I never told you to consider other posts. Anyhow... I'm truly tired and my beloved has awoken. Damned! 7 hours about infinities.. I'm off to bed. Gonna contemplate about mr. Gill's procedure. It was fun! :smile:

That is, there are real numbers not mapped to. — TonesInDeepFreeze

You don't need the diagonal proof to realize that. Every real number can be mapped from N^3. Every real number can be reached from N^3. N^3 can be mapped onto R.

I wrote:

Well, the point made is that a pair of numbers (x,y)...

You keep resorting to saying that I must consider the rest of what you posted. — TonesInDeepFreeze

Where did I do that?

It is the crank, not the mathematician who is dogmatic and exclusionary. — TonesInDeepFreeze

It's you who is the crank. You are exclusionary and dogmatic. And you have no sense of humor. Sense of rigor, maybe. Jgill knew to convince me (well, almost...) in one comment. But he's a real mathematician.

Cantor diagonal set

The diagonal proof shows that any map from N to R is not onto R. That is, there are real numbers not mapped to.
28m — TonesInDeepFreeze

That's not what the proof is about. It just shows that [0-1]is uncountable. Every time you think you counted a new number shows up. After infinity.

Take the square {(x,y):0<x<1,0<y<1} and map it one-to-one to the line {r:0<r<1) by using the procedure implied by the simple example (.329576914..., .925318623...) <-> .39229537168961243... — jgill

Sounds good mr. Gill. Almost convincing. But you construct a new number from the both. Giving them both different decimal places. The diagonal proof of Cantor says you leave numbers out. Infinitely many. (same for (.0329576914..., .0925318623...).

That is not a real number, you understand, right?
11m — TonesInDeepFreeze

It's a pair of numbers. You must quote the whole line I wrote.

Name one. — TonesInDeepFreeze

Well, the point made is that a pair of numbers (x,y) say (0.678567..., 0,98678...) is contained in a single number 0.65456456.... The infinite number behind the 0 should contain both the infinites behind the 0 of x and y. This is not so.

L

You could ask for more details about the proof mentioned by jgill and about the proof in the Quora thread. — TonesInDeepFreeze

The point is that the proof in quora is incorrect. It's making use of decimal expansions also but overlooks the majority of them.

I was thinking about the "from nothing" part. Since there is no time passing in the lack of anything called 'Nothing', it's not like there was 'Nothing' and then there was something; so, I'd claim that the something that is always there is what banged. — PoeticUniverse

It could be that a new bang awaits behind us. If the universe expands because it does so on a 4d space. When the present universe has accelerated into infinity, a new 3d bang can bang at the 4d singularity behind us.

And you desperately need one if you are not to remain mired in your terrible confusions. — TonesInDeepFreeze

Well... I don't take it too seriously... You are probably right. Still, I can't see how R and RxR can have the same cardinality. There are just inf^3 times as many points in RxR as there are in R.

There you go what? I am the first to say that one has to use great caution trying to pick up math on the Internet. There are some excellent Internet sources, but usually the best approach is in books. I recommended the Internet to you only because I know you wouldn't bother to read a proper book on this subject. — TonesInDeepFreeze

There are a lot of good books indeed. Thanks for the references. I prefer the math use in physics though. And the alephity of the continuum has implications for particles moving in it. That's why I think the aleph of the volume is different from the line and plane. I have booked a hotel for us... Just kidding! Gnight!