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June 7

Magnetic dipole for a proton?

The magnetic dipole of an electron seems to be a well established and understood concept, but is there any known equivalent for a proton? Byron Forbes (talk) 17:50, 7 June 2023 (UTC)

Protons, neutrons and electrons all have magnetic dipole moments, but the ones for protons and neutrons are about 1000 times smaller. So magnetic effects in materials are due primarily to the electrons. See https://www.physicsforums.com/threads/are-protons-neutrons-magnetic-do-they-have-north-and-south-poles.567358/ Philvoids (talk) 20:16, 7 June 2023 (UTC)

I would expect that most observable magnetic effects in materials are due to the orbital dipole moments of particles, not their spin moments, whereas I think the "magnetic dipole moment of the electron" refers to its spin moment. Happy to be corrected on either point. --Trovatore (talk) 21:38, 7 June 2023 (UTC)

Se also Nucleon magnetic moment. Ruslik_Zero 20:21, 7 June 2023 (UTC)

The fact that a neutron has a magnetic moment drives lots of chemistry students crazy if they've taken intro-physics. DMacks (talk) 15:32, 8 June 2023 (UTC)

There's a handy table here (although it doesn't match the section heading): Magnetic_moment#Elementary_particles. --Amble (talk) 21:34, 7 June 2023 (UTC)

Thanks to all for those replies. Byron Forbes (talk) 06:19, 8 June 2023 (UTC)

June 8

Expanding Universe and Relativity.

Did a little research on this and the main point I found is that when Einstein assumed the Lorentz transformation, he was totally oblivious to the expanding universe. So in other words, the concept of every point in space moving away from all others was not known to him. It was assumed that space was "still" and not moving relative to itself.

Had he known this, would he have thought that the idea of Relativity (the speed of light is the same to all observers) was a non workable idea?

Because an expanding universe seems to lead to the idea that any point generally in front of a photon will see that photon's speed as c - v and any point behind it will see its speed as c + v (where v is simply the relative velocity of a given point in space to the point the photon is at).

So the question is, how can Relativity possibly not be self violating with the notion of expanding space? Byron Forbes (talk) 06:35, 8 June 2023 (UTC)

See the top of this page 'We don't answer requests for opinions, predictions or debate.' This is a reference desk for an encyclopaedia. NadVolum (talk) 07:12, 8 June 2023 (UTC)

So where is my opinion, prediction or debate?

I have asked a simple question - an answer would be appreciated.

Censorship in the name of serving agendas is not what I'm looking for at all. If you don't like the implication of the question then that's your bad luck! Please take your combative attitude elsewhere! Byron Forbes (talk) 07:29, 8 June 2023 (UTC)

Please be civil. A question that begins "Had he known this, would he have thought" is clearly unanswerable. Shantavira|^{feed me} 09:05, 8 June 2023 (UTC)

You are on a mission to resurrect the concept of a luminiferous aether. I wish you the best of luck with that; only, do not use Wikipedia for the purpose. Wikipedia is not a forum for discussing or advocating any particular point of view, scientific or otherwise. This also applies to user pages and to the Reference desk.  --Lambiam 09:58, 8 June 2023 (UTC)

The question is simple - everything else is context.

And the question is, how does expanding space not violate the 2nd postulate. Who can direct me to info on that? Byron Forbes (talk) 16:25, 8 June 2023 (UTC)

For your photon scenario try Velocity-addition_formula#Special_relativity (use wisely). For everything else, read a book. --Wrongfilter (talk) 16:49, 8 June 2023 (UTC)

a velocity-addition formula is an equation that specifies how to combine the velocities of objects in a way that is consistent with the requirement that no object's speed can exceed the speed of light

So assume the theory to prove the theory?

I'm sorry, but I'm yet to be convinced that a photon at point B, that was just at point A a moment earlier, doesn't have a velocity of c + v where v is the relative velocity between A and B.

We know that the photon's velocity is c in B, and we know A travels away from B at v - the conclusion seems unavoidable to anyone but the religious followers of Relativity. Byron Forbes (talk) 17:21, 8 June 2023 (UTC)

I take "religious follower" as a personal insult. --Wrongfilter (talk) 17:27, 8 June 2023 (UTC)

The universe doesn't care whether you can be convinced about how it works or not. AndyTheGrump (talk)

Maybe hold a seance and ask Einstein yourself. ←Baseball Bugs ^{What's up, Doc?} carrots→ 11:21, 8 June 2023 (UTC)

• Davis, T. M.; Lineweaver, C. H (2004). "Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe". Publications of the Astronomical Society of Australia. Superluminal recession is a feature of all expanding cosmological models that are homogeneous and isotropic and therefore obey Hubble's law. This does not contradict special relativity because the superluminal motion does not occur in any observer's inertial frame. All observers measure light locally to be travelling at c and nothing ever overtakes a photon.
• Nussbaumer, Harry (2014). "Einstein's conversion from his static to an expanding universe". The European Physical Journal H.

Here’s a thought experiment. Suppose one sends a satellite in lower Earth orbit, with a high-precision clock, and a radio transmitter that regularly broadcasts the clock time to Earth. Suppose one stands on Earth, next to the same kind of high-precision clock, and monitors the difference between the Earth clock time and the satellite broadcast time.

Of course, that difference will increase with the distance between the satellite and the reception station, because light speed is not infinite, but that can be accounted for.

Relativity proponents predict that the satellite clock will run faster than the clock on Earth (i.e. "time is relative" and all that jazz); according to them, the time difference will increase over time by about 38μs/day. Of course, standard Galilean physics say the clock will run exactly as fast, and therefore no such trend will be observed.

Now, what would you say if this (purely hypothetical) experiment was done, and turned out to show a shifting trend exactly as relativity proponents suggest? Tigraan^{Click here for my talk page ("private" contact)} 15:59, 9 June 2023 (UTC)

Here's a hint: In 1955, Friedwardt Winterberg proposed a test of general relativity—detecting time slowing in a strong gravitational field using accurate atomic clocks placed in orbit inside artificial satellites. Special and general relativity predicted that the clocks on GPS satellites, as observed by those on Earth, run 38 microseconds faster per day than those on the Earth. The design of GPS corrects for this difference; because without doing so, GPS calculated positions would accumulate errors of up to 10 kilometers per day (6 mi/d). Philvoids (talk) 16:33, 9 June 2023 (UTC)

---

References

Wien displacement law and frequency

Since Wien's displacement law is a linear function "l=b/T" and a wavelength is linked to a frequency "l=C/f", by definition, how can we accept that the Wien's displacement law in frequency is different from "f=CT/b"? Malypaet (talk) 11:43, 8 June 2023 (UTC)

Let's start with Planck's_law#Correspondence_between_spectral_variable_forms, which shows how the spectral radiance in terms of wavelength, $B_{\lambda }(\lambda ,T)$, is related to the spectral radiance in terms for frequency, $B_{\nu }(\nu ,T)$ (the relation between the energy densities $u_{\lambda }$ and $u_{\nu }$ is the same). Note that it is not just a matter of replacing $\lambda$ and $\nu$ via $\lambda =c/\nu$; the wavelength interval has also to be transformed. Your calculation gives the maximum of $B_{\lambda }$, expressed as a frequency. Wien's law in frequency, however, gives the maximum of $B_{\nu }$, a different function with its maximum at a different place. --Wrongfilter (talk) 14:45, 8 June 2023 (UTC)

It's just a question of Cartesian logic. If there is a maximum for a certain wavelength, by the relation v=c/l then should also have the frequency for this same maximum. In the same place! Knowing that the only possible experimental verification measurement is on the wavelength, then translated into frequency, right? Malypaet (talk) 16:54, 8 June 2023 (UTC)

The difference is in measuring the amount of radiance in a frequency range versus a wavelength range. For the long wavelength radiation, it is concentrated into less frequency and spread over more wavelength. For short wavelengths, radiance is packed into less wavelength range, but more frequency range. SO this distorts the graphs so they are not the same, and maximums re different. Graeme Bartlett (talk) 23:36, 9 June 2023 (UTC)

Planck dλ/dv

Where Planck find this surprising equation :

dλ/dv=-c/dv²

?

When we speak about dv, is it with v+dv, or some other thing ?

Malypaet (talk) 17:06, 8 June 2023 (UTC)

Where did you find this surprising equation? It makes no sense, mathematically.  --Lambiam 22:13, 8 June 2023 (UTC)

I think you meant

${\frac {d\lambda }{d\nu }}=-{\frac {c}{\nu ^{2}}}.$

That is a Greek letter $\nu$, not a Latin letter v. Starting from $\lambda \nu =c,$ we have $d(\lambda \nu )=dc=0,$ since $c$ is constant. But also, by the product rule,

$d(\lambda \nu )=\lambda d\nu +\nu d\lambda ,$

so $cd\nu +\nu ^{2}d\lambda =\lambda \nu d\nu +\nu ^{2}d\lambda =\nu (\lambda d\nu +\nu d\lambda )=\nu d(\lambda \nu )=0,$ which means that $\nu ^{2}d\lambda =-cd\nu .$ Divide both sides by $\nu ^{2}d\nu$ and you are done.  --Lambiam 22:40, 8 June 2023 (UTC)

Thank's, that's great !

You helped me. Malypaet (talk) 06:41, 9 June 2023 (UTC)

Earth Circumnavigation Vertically

If money were no object, could modern technology build an aircraft that could circumnavigate the earth longitudinally (crossing both poles) without landing or mid-air refuelling? 24.72.82.173 (talk) 19:33, 8 June 2023 (UTC)

Why not? Non-stop non-refueled circumnavigations (non-polar) have happened after all. Ruslik_Zero 20:37, 8 June 2023 (UTC)

Circumnavigation along a meridian and its antipodal partner is a bit more challenging, since the aircraft cannot use the jet streams for assistance. Also, crossing both poles implies the length of the trajectory is at least 40,007.863 km (24,859.734 mi). Most aerial non-stop circumnavigations have fallen short of that. The length record for any non-stop non-refueled flight is held by Steve Fossetts 2006 circumnavigation in the GlobalFlyer, a flight of 41,466 kilometres (25,766 mi).  --Lambiam 23:15, 8 June 2023 (UTC)

The previous recordholder, of course, was the Rutan Voyager. According to Wikipedia, it flew 26,366 statute miles (42,432 km) on its non-stop, non-refueled circumnavigation but the FAI-certified record is only 40,212 km (which is 24,987 miles). What happened to the other 2,220 km? --142.112.221.43 (talk) 02:44, 9 June 2023 (UTC)

I'm not sure, but I remember having read something about it flying in a holding pattern for several hours before landing in order to burn off unused fuel -- might that be the reason for the discrepancy? 2601:646:9882:46E0:1CFE:39D7:62CF:ECBA (talk) 04:02, 9 June 2023 (UTC)

For an FAI circumnavigation diploma you do not have to cross the poles, but fly north of 75N and south of 75S and for a total distance of 34,000 km.[1] fiveby(zero) 13:00, 9 June 2023 (UTC)

June 9

Expanding universe and inertial frames of reference.

So the contemporary thinking is that space itself is expanding and the expansion is also accelerating.

So what are the implications for inertial FOR? If I choose any point in space, and thus all points around this point accelerate away from me isotropically, gravity aside, doesn't this mean that any given point in space is still an inertial FOR? Can it not be legitimately thought of as the classical "stationary FOR" for the purpose of most, if not all, physics calculations? Byron Forbes (talk) 05:56, 9 June 2023 (UTC)

Does our article Proper frame, usually called "comoving frame" in the context of the expanding universe, help to clear up some confusion? Just like an atlas with flat maps has only limited use in describing a spherical Earth, so do Euclidean frames of reference have only limited use in handling the reality of a curved spacetime.  --Lambiam 09:13, 9 June 2023 (UTC)

No.

My specific question here, is that due to any given point in space having all points around it accelerating away uniformly and isotropically, cannot any point be thus a legitimate inertial FOR? In fact, if we ignore gravity, then any given point can be thought of as the universal FOR. Byron Forbes (talk) 10:16, 9 June 2023 (UTC)

A single point cannot be a frame of reference. Any single point of space at a single point of time, i.e. a point in spacetime, can serve as the origin of a frame of reference.  --Lambiam 13:21, 9 June 2023 (UTC)

I believe you are exactly wrong.

If you think about this, all physics problems are solved by points in space. They are typically thought of as belonging to a "frame", but that is ultimately irrelevant because they are entirely able to define their "frame" all on their own.

For example, typical physics problems involve length, which is, of course, a measure between 2 "points" that may or may not be in the same FOR.

Any point in space is a self defining FOR. What other points around it are doing is irrelevant in terms of its specific FOR. Points around it may or may not be a part of the same FOR. But in an expanding universe, that is NEVER the case anyway!

Again, I will argue that any given point in space, assuming the region is generally not accelerating, is an inertial FOR. Especially in the case where all points around it behave uniformly and isotropically, as is the case with expanding space. Byron Forbes (talk) 05:17, 10 June 2023 (UTC)

I am not sure that you understand the concept of a frame of reference. The statement that "all physics problems are solved by points in space" is utterly devoid of meaning. The concept of spatial distance between two points in spacetime requires a common frame of reference. Any point in spacetime admits a continuum of possible frames of reference. The Minkowski metric of special relativity, which can be generalized to a Lorentzian metric in general relativity, does not require a specific frame of reference, but it is not a measure of spatial distance. To use it for that, you again need to choose a specific frame of reference.  --Lambiam 07:38, 10 June 2023 (UTC)

So are you saying that a "point" cannot be a FOR because it has no dimensions? Byron Forbes (talk) 07:51, 10 June 2023 (UTC)

Points and coordinate systems belong to different categories. A language cannot be an airplane, not because languages do not have wings, but because languages are not physical objects. A point cannot be a frame of reference, not because it has no dimensions, but because a point is not a system assigning values to other points.  --Lambiam 14:26, 10 June 2023 (UTC)

A typical FOR is a plane, which is merely a collection of points. I fail to see how any point in any FOR isn't a FOR itself.

Are you aware where I'm headed with this ------> proof that cosmological red shift is a violation of CoE? Is that what you're defending or do you really believe a point cannot be a FOR? :) Byron Forbes (talk) 05:04, 11 June 2023 (UTC)

Lambiam is correct for a point can serve as an origin or a point of reference and not as a metric of a metric space. Prior to SR, all distances are invariant in all reference frames and one can apply a Galilean transformation. However Einstein's spacetime dispenses with that, of course, but that does not mean it cannot be resurrected. Modocc (talk) 20:16, 10 June 2023 (UTC)

EM waves and photons.

I think everyone is well aware of the lovely diagrams we have for the above mentioned - beautiful blue and red sinusoidal waves perpendicular to one another and propagation, and in phase, right?

This notion normally comes from an antenna which produces E dipoles via AC current. So when the dipole is at a max so is the E field, but there is zero current and the B field (Ampere's Circuital Law) = 0.

So how do we get in phase E and B fields as per the lovely diagrams?

I have seen it said that the generated E field magically produces the B field, but that would be a curl and still not in phase anyway, right? Because when the E field is at a max, its rate of change = 0 and thus no B field, curl or otherwise, is being produced.

What am I not seeing here? Could someone please point me to some information that can clean me up on this issue? TIA. Byron Forbes (talk) 07:31, 9 June 2023 (UTC)

The Maxwell–Faraday equation $\operatorname {curl} ~\mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}$ relates the spatial variation in the electric field to the temporal variation in the magnetic field.  --Lambiam 09:06, 9 June 2023 (UTC)

Sorry, but I'm failing to see how a curl E field plays any role in a resultant perpendicular field.

An explanation I just saw was that due to the changing E field of the E dipole, you get a curl B field. But this happens when the current = 0. As the current increases, we get a curl B field then due to current, so such an explanation has an eternal curl B field. Byron Forbes (talk) 10:04, 9 June 2023 (UTC)

When the curl operator is applied to a field, the change in the operand in any plane produces a vector component that is orthogonal (perpendicular) to that plane.  --Lambiam 13:29, 9 June 2023 (UTC) Yes. Here is a link to Curl_(mathematics). Philvoids (talk) 16:00, 9 June 2023 (UTC)

Not sure what you're getting at here. If you are referring to a curl E field produced by the curl B field (from the antenna) then you get E fields also in and against the direction of propagation - i.e. you get a mess.

Let me re iterate the obvious error here.

It is assumed, wrongly, that when the E dipole in the antenna is maximised, that this then produces a changing E field (with a max rate of change), thus producing a curl B. So this has the B and E fields maximised at the same time. The mistake here is that curl B fields are produced by moving charges, not changing voltages. This is a widely misunderstood thing. The curl B field has no interest in electron acceleration or how much voltage might be being applied to it - it is only concerned with charge speed and the rate of dipole change, especially relevant in a wire due to electron movement relative to nuclei.

But it is also clear that the current = 0 at this time and thus no curl B field (Ampere) is produced by that. But now the E dipole starts to collapse, current rises and so does the curl B field (Ampere), so this means that one curl B field is dropping off and the other one (Ampere) is increasing, resulting in an eternal Curl B field.

This is simply wrong. Maxwell got it wrong and the world is yet to fix it!

This is very basic stuff. Byron Forbes (talk) 06:01, 10 June 2023 (UTC)

I can't follow this. You stated that you failed to see how a curl E field plays any role in a resultant perpendicular field. I pointed out that curl E, being the field resulting from the spatial variation in E, is componentwise perpendicular to the variation. If that is not what you failed to see, it might help if you used the language of mathematics, such as commonly used by physicists to communicate ideas, to make your questions less ambiguous. X plays a role in Y if they co-occur in some law of physics, unless Y denotes a constant.  --Lambiam 07:21, 10 June 2023 (UTC)

So you're deliberately avoiding the essence of this?

How do you explain the eternal curl B field? First, apparently produced by the changing dipole when current = 0, and then, 1/4 of the AC phase later, legitimately produced by Ampere's Law due to max current?

Is there some Law I don't know about that goes something like "The Law of ignoring Ampere's Circuital Law"? Byron Forbes (talk) 08:04, 10 June 2023 (UTC)

................or let me try this.

When the B field is at a max its rate of change = 0 ---------> curl E = 0

When the E field is at a max its rate of change = 0 ---------> curl B = 0

In no universe do you get in phase fields, even taking the curl mess out of consideration. Byron Forbes (talk) 10:41, 10 June 2023 (UTC)

curl B = 0 does not imply B = 0. --Wrongfilter (talk) 10:44, 10 June 2023 (UTC)

So where do the B and E fields come from? Byron Forbes (talk) 11:05, 10 June 2023 (UTC)

If you want to see how confused the world is on this, go and take a look on youtube.

There are lecturers portraying this in utterly ludicrous ways with glaring mistakes. One of them has the + and - charges of an antenna's dipole passing each other at the middle and says the current = 0 at that time! It's as though he is trying to trick us by having the + and - cancel each other resulting in 0 current (LOL). It is simply mind boggling! Byron Forbes (talk) 11:19, 10 June 2023 (UTC)

Btw, could someone tell me if referring to a Youtube video is against the rules without providing a specific link? Byron Forbes (talk) 11:22, 10 June 2023 (UTC)

It's OK to provide Youtube links on this desk. Modocc (talk) 20:21, 10 June 2023 (UTC)

Tried that - they got knocked back. Actually, the link somehow got changed to "Youtu.be" which is blacklisted (shrugs) Byron Forbes (talk) 02:13, 11 June 2023 (UTC)

https://www.youtube.com/watch?v=bwreHReBH2A&t=411s

See anything wrong here? Check out 6:52 - could he possibly be just making a simple mistake like this?Byron Forbes (talk) 02:23, 11 June 2023 (UTC)

"So where do the B and E fields come from?" These fields are two components of the electromagnetic field, which has a value at every point in spacetime. The electromagnetic field has been an aspect of the universe since space and time began, just like the gravitational field. It is everywhere, and where there is an electromagnetic field, there is also an electric field and a magnetic field. They are everywhere. Where did these fields come from? That is a good question, which might be answered if we knew where the universe came from. Who ordered it? Why is there anything at all?  --Lambiam 14:02, 10 June 2023 (UTC)

It's hard to believe you're not dodging the subject.

My question is simple - how do you get perpendicular, in sync E and B fields for EM waves and photons?

If anyone could start from the beginning and walk us through that it would be greatly appreciated. Might want to have a look at this brilliant attempt for reference! https://www.youtube.com/watch?v=bwreHReBH2A&t=411s Byron Forbes (talk) 02:19, 11 June 2023 (UTC)

Is there a probability consideration with an infinite number of possibilities?

Is there a case in the field of probability theory in which there are an infinite number of possible outcomes?
Normally there are only finitely many outputs, even if there are very very many outputs.
Is there a case of infinite possibilities, for example in quantum physics? 2A02:8071:60A0:92E0:9B9B:C02B:F5CC:22D1 (talk) 09:20, 9 June 2023 (UTC)

I can't help but think that if you allowed an infinite number of outcomes, the probability of any specific outcome is one over infinity, which is absolutely zero. So, no outcome is possible. 97.82.165.112 (talk) 11:12, 9 June 2023 (UTC)

An impossible event has a probability of 0, but the converse is not necessarily true; see note 1 in our article on Probability.  --Lambiam 13:16, 9 June 2023 (UTC)

There are at least two ways this can be done.

A random selection from a continuous distribution, such as the real numbers in the interval [0,1], gives an example where the probability of any specific value is zero, even though every event will produce a value in the range.

Alternatively, set up a probability distribution over an infinite number of discrete values, such as selecting natural numbers n (integers from 1 upwards) where the probability of n p(n) = (1/n) - (1/(n+1)). This gives a total probability of 1, and assigns every outcome n a non-zero probability, eg p(1) = 1/2, p(2) = 1/6 and so on.

(This really belongs on the Mathematics ref desk.) -- Verbarson  ^talk_edits 12:00, 9 June 2023 (UTC)

Mathematics has no problem dealing with continuous probability distributions, such as the standard normal distribution and the standard uniform distribution. This requires an approach to dealing with arbitrarily, even infinitesimally small quantities in a rigorous way. This cannot be done for physical systems; the laws of physics (including quantum physics) as we know them break down at the Planck scale.  --Lambiam 13:10, 9 June 2023 (UTC)

I see two problems: (1) Bertrand paradox (2) the problem with mesure of sets with cardinality like IR. 2A02:8071:60A0:92E0:9B9B:C02B:F5CC:22D1 (talk) 13:37, 9 June 2023 (UTC)

What are the as-yet undiscovered trailing decimal digits of transcendental numbers such as π and e? Philvoids (talk) 14:54, 9 June 2023 (UTC)

0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. (All the right numbers, not necessarily in the right order.) -- Verbarson  ^talk_edits 15:34, 9 June 2023 (UTC)

How much space do you need to type the right number (with the right digits in the right order)? Philvoids (talk) 16:53, 9 June 2023 (UTC)

There is no proof that any of the digits in the not yet computed parts of the decimal expansion of π is a digit 7.  --Lambiam 07:08, 10 June 2023 (UTC)

Mathematicians generally believe that the decimal expansion of π contains every finite sequence of digits. Philvoids (talk) 18:16, 10 June 2023 (UTC)

The Poisson distribution is an example of a discrete probability distribution that has an infinite number of possible values, the nonnegative integers 0, 1, 2, etc. Each value ≥ 0 has a finite probability greater than zero. This distribution often comes up in many fields of science. --Amble (talk) 16:13, 9 June 2023 (UTC)

An even simpler example is the number of times one needs to flip a fair coin before heads comes up. Even if you have flipped the coin 999 times, and each time tails came up, there is no guarantee heads will come up the next time. The probability is only 50%, also after 999999 tries, or 999999999 tries. So any positive integer is a possibility. The distribution is the (shifted) geometric distribution of mean 2.  --Lambiam 14:17, 10 June 2023 (UTC)

Of course. Pick an integer randomly. Theres 0.5 probability it is even, 1/3 that it divides by 3 without reminder etc.

Zarnivop (talk) 20:31, 10 June 2023 (UTC)

You have to specify the procedure how the integer is picked "randomly". If you ask all your friends to pick an integer randomly, I bet none will pick an integer that is greater than googolplex. Yet almost all integers are greater than googolplex.  --Lambiam 21:31, 10 June 2023 (UTC)

I always tell my students that all natural numbers are small - after all, for any given number there are only finitely many smaller ones, but an infinity of larger ones ;-). --Stephan Schulz (talk) 09:22, 11 June 2023 (UTC)

If you roll an infinite-sided die infinitely many times, the odds of ever rolling infinity are exactly 1-1/e, which is slightly worse than two out of three.  Card Zero  (talk) 21:29, 10 June 2023 (UTC)

While the odds of rolling an $n$ in $n$ tries on an $n$-sided die equals $1-\left({\frac {n-1}{n}}\right)^{n},$ and $\lim _{n\to \infty }1-\left({\frac {n-1}{n}}\right)^{n}=1-e^{{-}1},$ I think that the statement about rolling an infinite-sided die has no mathematical meaning.  --Lambiam 21:39, 10 June 2023 (UTC)

It is written that a million-to-one chance crops up nine times out of ten. -- Verbarson  ^talk_edits 21:45, 10 June 2023 (UTC)

What is the mechanism of action of Basil in mildly reducing blood pressure?

The only food I know that works for some people around the world (and worked for me personally) in mildly reducing blood pressure is the Basil plant.

Dietary supplements containing high concentrations of dried Basil leaves are also being sold and marketed as mildly reducing blood pressure.

If indeed I am correct and basil plant eaten raw (or maybe also dried) significantly but mildly reduce blood pressure, what is the mechanism of action?

Thanks. 2A10:8012:17:CDC6:E886:F0E4:683B:2264 (talk) 14:12, 9 June 2023 (UTC)

Basil contains eugenol, a plant-based antioxidant that may help reduce blood pressure by acting as a natural calcium channel blocker.^[2] It also contains hexane, that reduces levels of circulating catecholamines and diminishing vascular resistance.[3] The effects were temporary, lasting two minutes before returning to normal.^[4] More details here. --136.54.99.98 (talk) 16:18, 9 June 2023 (UTC)

I'm reluctant to answer this question since it seems to be getting awfully close to medical advice given what the OP has said. But I would note that basil when consumed as a dietary supplement should probably be treated fairly different from basil consumed as part of food. Basil is generally used as a herb which a number of people find pleasant. If basil is used in food, this may change the types of food consumed or at least may change some aspects of the food such as the amount of salt (or other sources of sodium) added. These changes could be the source of any change in blood pressure rather than anything to do with the basil itself. (These sort of confounding factors are one of the reasons attributing any observed health change to some specific part of the diet is generally very complicated.) Nil Einne (talk) 13:34, 10 June 2023 (UTC)

Comparing improvements in task performance

The improvements in task performance by AI models on benchmarks tend to be reported in recent papers as percentual correctness increases. Suppose two teams are reporting on their work. Team A reports an increase from 64% correct to 80% correct, which is reported as an improvement of 25% (0.80/0.64 = 1.25). Not bad. Team B reports an increase from 40% correct to 60% correct, which is reported as an improvement of 50%, so that should be even more impressive. But you can also present this as, for Team A, a decrease from 36% wrong to 20% wrong, reducing the wrong responses by 44%, whereas Team B achieved a decrease from 60% wrong to 40% wrong, reducing the wrong responses by only 33%. Are there publications that discuss the methodology of comparing such improvements?  --Lambiam 21:02, 9 June 2023 (UTC)

On the precarious assumption that every answer can be classed unambiguously as "right" or "wrong", a method can be used similar to the test for telepathy done using Zener cards (five groups each of five like cards). Each card contains an image of either a circle, cross, square, star or wavy line. The 25 cards are shuffled. The subject is then asked to give the identity of each card. A score of 10 correct out of 25 indicates some form of telepathy and higher scores show higher ability. Philvoids (talk) 21:57, 9 June 2023 (UTC)

Interpret "wrong" as "not correct". The question is not about assigning scores, but about comparing improvements of what in the Zener card test would be different subjects. If Alice scored on the average 16 last week but this week 20, while Bob scored 10 last week but now 15, both showing impressive improvements, which of the two had the more impressive improvement?  --Lambiam 06:52, 10 June 2023 (UTC)

Cardrew is more impressed by Bob's improvement than Alice's improvement because Bob got off to a weak start while Alice obviously entered as the stronger player from whom relatively more should be expected, and that expectation should rightfully be quantified in Handicapping as implemented with the mathematical precision that fairness demands in many competitive sports ^{* * * * *} . Dolores is most impressed by Alice's achievement of the highest score yet seen and she protests at the Misogyny revealed in this, yet again, rampant barefaced attempt by Patriarchy to devalue and belittle downtrodden Alice because of her gender. My friends Dolores and Cardrew are so upset by your divisive scenario that exploits unsourced information about two living persons A---- and B-- that we may have to call on Edward, whose qualifications in Impressionism are often demonstrated at parties, to resolve your question about perceived impressions that can only be answered in the realm of Subjectivity. Philvoids (talk) 16:23, 10 June 2023 (UTC)

The question was actually not about your eminently qualified friends and their perceived impressions, but about the existence of publications that discuss the methodology of making such comparisons. That may include publications that give the advice, "Don't even try."  --Lambiam 17:26, 10 June 2023 (UTC)

Hahaha yes this is a very real question for schools where they want to say how improved a child is by a teachers tuition, and it affects the schools ratings for parents and can influence the amount of money they get, see for example [5][6],[7]. And their answer? It depends! I'll be intersted if you get a good answr! NadVolum (talk) 17:44, 10 June 2023 (UTC)

“An Extensive Comparative Analysis of Chatbot Technologies” This paper compares three chatbots: chatGPT, Google BARD, and Microsoft Bing in natural language processing, machine learning, and user experience. “Comparative Analysis of Chatbots” This paper analyzes and compares the total accuracy score of eight chatbots based on the answers provided by them to a set of predefined questions. Future directions for chatbot research: an interdisciplinary research agenda. Philvoids (talk) 18:40, 10 June 2023 (UTC)

The paper compares accuracy scores; it does not compare improvements.  --Lambiam 21:53, 10 June 2023 (UTC)

Methodology does matter and their scores are a statistical sample subject to all kinds of caveats, such as being very small as is, but for comparison purposes this question falls under effect size. Skimming the article I found this observation "Since rather large probabilities of passing were used, there is a large difference between relative risk and odds ratio. Had failure (a smaller probability) been used as the event (rather than passing), the difference between the two measures of effect size would not be so great." Modocc (talk) 22:46, 10 June 2023 (UTC)

Thank you, that is extremely relevant. Clearly, there are a plethora of metrics to choose from. There are statistical handbooks that give practical methodological advice regarding the choice of an appropriate test from the plethora of statistical tests. One might hope for a text giving practical methodological advice to researchers who need to choose an appropriate metric for comparing effect sizes.  --Lambiam 10:48, 11 June 2023 (UTC)

June 10

Curl B fields and electric plates.

Let's say we have 2 electric plates hooked up to an AC power supply. Let's say we can turn on the power in such a manner that we get a changing E field between the plates but no electrons jumping from plate to plate (not sure if this is possible but we'll make it a thought experiment in any case).

Does the changing E field between the plates produce a curl B field? I point out here that there is no moving charges here, just a changing E field. In reality, of course, it would be very hard to determine the difference between any curl B fields produced by the rest of the circuitry, but let's see what people have to say anyway or if someone can point me to a known experiment of this type. Byron Forbes (talk) 06:43, 10 June 2023 (UTC)

The curl of a magnetic field at any given point is equal to the current density vector at that point. No current, no curl.  --Lambiam 06:58, 10 June 2023 (UTC)

I'm a bit puzzled why you would say that. The vacuum Maxwell equation without current density still reads $\nabla \times \mathbf {B} =\mu _{0}\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}$; this cannot be solved in isolation, of course, since Maxwell's equations are coupled and need to be solved together. In the case of the parallel-plate capacitor, it will emit a pulse of electromagnetic radiation while being charged. The detailed shape and frequency spectrum of that will depend on the details of how the capacitor is charged. --Wrongfilter (talk) 14:53, 10 June 2023 (UTC)

You are right. Many sources just state a "differential form" of Ampère's law that ignores the electric displacement field, like here equation 2.43 for $\mathbf {H} ,$ and I copied that without looking further. The fluxion of that field should be added.  --Lambiam 17:18, 10 June 2023 (UTC)

I disagree.

I think curl B fields are produced only in the presence of charged particles and not by a raw E field. Maxwell makes a clear distinction here that this is a displacement current and also alludes to electric dipoles.

Current in a wire represents rising and falling E dipoles due to electron motion relative to nuclei.

Also, to consider a string of electrons moved past a point, such a situation also creates a virtual dipole rising and falling as the field at that point changes. Indeed, 1 electron on its own can do likewise.

I was almost going to mention that the explanation on the "Maxwell's Equations" page was "daring" and "bold" since it refers to mere "electric fields" on numerous occasions. :)

Having said this, it is basically impossible, I presume, to have a changing E field without moving charged particles being involved. I believe they are inseparable things. Byron Forbes (talk) 05:40, 11 June 2023 (UTC)

.................and, come to think of it, I see what's happened here.

For a photon to "work" far from charged particles, we must have a raw E field generating a raw B field, etc, etc, of course. We wouldn't want any evil aether particles around and required, now would we? :) Byron Forbes (talk) 05:51, 11 June 2023 (UTC)

Perhaps you should take your crusade against the developments in physics since 1850 to a different forum.  --Lambiam 10:30, 11 June 2023 (UTC)

LOL - that hit a nerve, didn't it?

And here is where I got the reminder, right here on Wikipedia on this page https://en.wikipedia.org/wiki/Maxwell%27s_equations, under the heading Ampère's law with Maxwell's addition, 2nd paragraph -

Maxwell's addition to Ampère's law is important because the laws of Ampère and Gauss must otherwise be adjusted for static fields.[clarification needed] As a consequence, it predicts that a rotating magnetic field occurs with a changing electric field. A further consequence is the existence of self-sustaining electromagnetic waves which travel through empty space.

Good old Relativity people assuming theory to prove theory and adjusting everything to line up with their theory. Changing fields mean there are local, moving charged particles - this not being the case is unlikely in the extreme!

Not that I suggest any famous scientist ought to be treated as a god, but I think it is clear here that Maxwell specifically did not mean a mere, raw E field! Byron Forbes (talk) 13:33, 11 June 2023 (UTC)

Thank you.

And, FWIW, I agree. Byron Forbes (talk) 10:21, 10 June 2023 (UTC)

See displacement current (if you have not already found that article), which directly addresses the question of current in capacitors. catslash (talk) 18:17, 10 June 2023 (UTC)

Maximum depths of a theoretical ocean

How deep could a theoretical water ocean be before it starts forming ice under the pressure of the water above? Also, how would that change for arbitrary values of temperature/gravity/salinity? Is it even reasonable to assume a constant temperature/salinity (or gravity even?) for the entire depth? I've no clue how to even begin calculating this from an assumption of an infinite plane of ocean, and googling hasn't been helpful either. I'd appreciate any pointers. ― Synpath 17:38, 10 June 2023 (UTC)

OK, skipping the chatbot response... it sounds like what you're looking for is some sort of equation for the freezing point of water at a given pressure and salinity; an equation for pressure at a given depth; and possibly equations for the interactions of salinity and pressure, and salinity and depth? I don't have that information, nor do I know where to find it, but maybe someone else does. -- Avocado (talk) 16:10, 11 June 2023 (UTC)

I ended up calculating a ~100 km depth from a 1 m² column of water and seeing it matched an answer below I suppose its close enough to correct. The notion of Brine rejection was useful in that it lead me to these two papers: [8] and [9] where the first has some nice visuals of it for high pressure ice phases (Fig. 1 and Fig. 3) and the second has a phase diagram based on water LiCl solutions (Fig. 1) where the phase boundary between liquid and Ice VI is roughly in the same order of magnitude as for pure water. So, while salinity would increase the final depth it won't be doubling it or anything assuming the sodium hydration shell radius doesn't change things much. ― Synpath 18:37, 11 June 2023 (UTC)

Warning: This statement by Bing chatbot may contain unverified speculation.
The following discussion has been closed. Please do not modify it.
One of the most fascinating phenomena in the deep ocean is the formation of ice crystals under high pressure. The water at the bottom of the ocean is very cold, close to freezing point, but it does not freeze because of the dissolved salts and minerals. However, when the pressure increases due to the weight of the water above, some of these dissolved substances are squeezed out of the water molecules, making them more pure and less dense. This allows them to form ice crystals, called ice VII, that have a different structure than normal ice. These crystals can float up to the surface, creating a layer of slushy ice under the water.

Do not rely on the statement above. Philvoids (talk) 19:18, 10 June 2023 (UTC)

Take into account that from a certain depth, the mantle heat will melt water under higher pressure. The water phase diagram you already used will help to determine if water is liquid at a combination of pressure and temperature.

Zarnivop (talk) 20:27, 10 June 2023 (UTC)

In Earth gravity, the pressure increases about 10⁴ Pa/m. At a pressure of about 10⁹ Pa ice VI will begin to form. That means that the ocean can be about 100 km deep. With more gravity, it will be shallower; with higher temperature, it will be deeper; with higher salinity, it will be deeper too. But it will be on that order of magnitude. BTW, amazing what kind of rubbish that chatbot can make up. I at least know that I know nothing. PiusImpavidus (talk) 23:33, 10 June 2023 (UTC)

Impossible to answer for a real ocean by calculation alone. For water it depends on the temperature and salinity at a given depth. At 20 deg C and 0% salinity the pressure would have to be 10000 atmospheres, so 100 km down, roughly. If colder, less, if salty, more. Greglocock (talk) 23:59, 10 June 2023 (UTC)

I am sceptical of the chatbot's notion that water pressure can "squeeze....dissolved substances out of water molecules". This seems applicable to Desalination of seawater but the only technologies known for this are Distillation or Reverse osmosis through a Semipermeable membrane. Philvoids (talk) 00:45, 11 June 2023 (UTC)

To the notion of dissolved substances being somehow squeezed out... where would they go? ←Baseball Bugs ^{What's up, Doc?} carrots→ 04:47, 11 June 2023 (UTC)

The unstated implication is that a gradient of gradually rising concentration would arise in the water column, so they would effectively be gradually transferred upwards, but I agree that the entire premise is at best questionable and unverified, although the chatbot (which merely strings together words associated in its corpus within grammatical constraints) may have got them from somewhere. {The poster formerly known as 87.81.230.195} 90.221.195.5 (talk) 07:47, 11 June 2023 (UTC)

Hmmm... So, given the premise that the salt would rise, how would that salt have gotten to the bottom of the ocean in the first place? ←Baseball Bugs ^{What's up, Doc?} carrots→ 08:15, 11 June 2023 (UTC)

With freezing the water crystalizes and rejected salt creates a denser brine that is forced out of pockets called brine cells. The brine sinks and the purer ice floats. See Brine rejection. Modocc (talk) 08:19, 11 June 2023 (UTC)

See, this is the problem I raised on the Talk page. We're earnestly discussing the possible correctness of a vaguely plausible-sounding passage assembled by a chatbot because it didn't cite a source (and if it had it might have cited a fake one). To avoid this sort of thing becoming a huge time-sink, I propose we henceforth ignore all chatbot-generated contributions to Ref desk answer threads. {The poster formerly known as 87.81.230.195} 90.221.195.5 (talk) 14:22, 11 June 2023 (UTC)

You may have ignored the warning. There is also an obvious red flag in the chatbot's Weasel worded introduction "One of the most fascinating phenomena..." But supposing you saw the chatbot statement without its first sentence, how do you propose handling it? Ernest fact-checking is urgently called for as our best human reaction now that chatbots are flourishing and may even co-opt the chant WE'RE QUEER, WE'RE HERE, GET USED TO IT! Philvoids (talk) 16:39, 11 June 2023 (UTC)

References

June 12

Century years (June 4)

• Transferred from Miscellaneous desk as this appears to be an astronomical question

The relevant Tabor lecture appears to be this one [10]. The arguments appear to have been adequately answered in the response to the second of 90.221's posts of 19:16, 7 June 2023. 80.47.0.234 (talk) 12:57, 12 June 2023 (UTC)

I don't see a question. The earlier discussion is archived here.  --Lambiam 06:19, 13 June 2023 (UTC)

Has anyone ever come up with a plausible explanation for how Pokeballs could work in the real world?

Question as topic. Just for fun. I know there have been people written about how one might plausibly make a light saber or how a Star Trek phaser might work. Iloveparrots (talk) 15:02, 12 June 2023 (UTC)

• HOW WOULD A POKEMON POKEBALL WORK IN REAL LIFE?. Alansplodge (talk) 17:39, 12 June 2023 (UTC)

What about that inconvenient complication known as the Heisenberg uncertainty principle??? 2601:646:9882:46E0:6998:C31A:9514:BAA4 (talk) 02:23, 13 June 2023 (UTC)

So for the moment I think your best bet is to use VR goggles. On a quick search I see there is a game PokeQuest VR being developed. NadVolum (talk) 20:03, 12 June 2023 (UTC)

June 13

Edgware Road

So, let's say an outer rail service is just coming in from Kensington and will terminate at Edgware Road -- will it (normally) stop on Track 1 or Track 3? If on Track 1, then how will it reverse without disrupting other outer rail trains coming in from Hammersmith (especially since, according to a (possibly outdated) schedule, there's one coming in from Hammersmith and going on toward King's Cross just 1 minute after the terminating service from Kensington)? Also, once the train reverses and goes around the inner rail, after it comes in from King's Cross, will it (normally) stop on Track 3 or Track 4 before continuing to Hammersmith? And last but not least, if I remember the layout of the Praed Street junction rightly, trains departing for Hammersmith from Track 4 must cross over both the Kensington-bound track of the Circle Line (which becomes Track 3 in the station) and the District Line track (Track 2) -- how do they avoid delays due to this? 2601:646:9882:46E0:6998:C31A:9514:BAA4 (talk) 02:53, 13 June 2023 (UTC)

Courtesy link: Edgware Road tube station (Circle, District and Hammersmith & City lines). --142.112.221.43 (talk) 03:23, 13 June 2023 (UTC)

This is a big problem for the tube trains, you can't have two going in different directions along the same tube - they have to be disassembled at the end of the line and transported back by lorry ;-) Sorry having looked at it I don't know. NadVolum (talk) 08:54, 13 June 2023 (UTC)

Surely you can just run it up an escalator? ;-) Alansplodge (talk) 15:18, 13 June 2023 (UTC)

I'm not locally familiar, but I found this map. Apparently, trains leaving westbound from track 1 can't move to the left-hand track. All London Underground trains run on the left (a few exceptions involve grade-separated crossings), so trains terminating at Edgeware road and returning to Kensington must use tracks 2 and 3. I assume one is for District line trains, the other for Circle line trains. A train leaving for Kensington from track 2 or 3 doesn't interfere with trains coming in from Hammersmith on track 1.

Assuming tracks 2 and 3 are for trains for Kensington, it makes most sense if trains for Hammersmith use track 4. The line from Edgeware Road to Praed Street junction appears to be simply double track, so all trains leaving westbound have to be merged onto one track. A bigger problem is that trains for Hammersmith have to weave through those from Kensington.

It looks like the track layout at Edgeware Road was designed such that any one of the tracks can be taken out of service without blocking any of the routes served, although capacity would be reduced. PiusImpavidus (talk) 09:09, 13 June 2023 (UTC)

I was on Edgware Road station on Sunday, when there was no service between Edgware Road and Hammersmith. Trains coming from the east would cross to platform 1 where they would dwell before setting off eastwards again. The signage is "platform 1 eastbound". I've never known trains going east leave from any other platform - it's difficult to see how they could because platforms 2 and 3 are for Circle and District line trains completing their journey having passed through Paddington (that's the Praed Street station - there's another one near Bishop's Bridge Road for trains going to and from Hammersmith). When these trains leave they go back the way they came. If you're going Paddington (Bishop's Bridge Road) and stations to Hammersmith platform 4 is the place for you. 2A00:23C6:2417:3101:CD7D:9961:DB38:71A (talk) 11:28, 13 June 2023 (UTC)

Track layout map here. Alansplodge (talk) 15:18, 13 June 2023 (UTC)

I forwarded the original query to Clive Feather, who answered as follows. (I haven't compared his answers to the ones above.)

So, let's say an outer rail service is just coming in from Kensington and will terminate at Edgware Road -- will it (normally) stop on Track 1 or Track 3?

It will use platform 2, though it could in principle use platform 3.

The normal platform use is:

1. Trains towards Baker Street
2. Circle trains from Kensington terminating and returning to Kensington
3. District trains from Kensington terminating and returning to Kensington
4. Trains directly towards Hammersmith

If on Track 1, then how will it reverse without disrupting other outer rail trains coming in from Hammersmith...

There is no practical way for it to reverse in platform 1.

In principle a train could shunt forward into the running tunnels, then back into platform 2 or 3, but that would be incredibly disruptive.

Also, once the train reverses and goes around the inner rail, after it comes in from King's Cross, will it (normally) stop on Track 3 or Track 4 before continuing to Hammersmith?

It will normally use platform 4, though it could use platform 3 if there is disruption.

...trains departing for Hammersmith from Track 4 must cross over both the Kensington-bound track of the Circle Line (which becomes Track 3 in the station) and the District Line track (Track 2)

No, that's not how it works.

The four platform tracks converge into two tracks just west of the station. The outer rail connects to platforms 1 to 3; the inner rail to platforms 2 to 4. This is done by a scissors crossover between the platform 2 and 3 tracks immediately west of the station, then 1 & 2 merging and 3 & 4 merging west of that.

Then, a short distance further west, there is a simple double junction and westbound Hammersmith trains will cross over the outer rail from Kensington.

So the platform 4 track doesn't "cross" either the platform 3 or 2 tracks. Rather, the three converge into one before splitting into Hammersmith and Kensington options. Similarly, eastbound, the two lines merge into one before splitting into platform 1, 2, and 3 tracks.

how do they avoid delays due to this?

Careful timetabling.

(Clive's answers posted with his permission.) --142.112.221.43 (talk) 16:06, 13 June 2023 (UTC)

Which all matches with the track layout map linked above. PiusImpavidus (talk) 18:01, 13 June 2023 (UTC)

Just a note that the map was linked twice, at 09:09 and 15:18 yesterday. The second link has a zoom button but the first link is already enlarged. 2A00:23C6:2417:3101:DC52:6F3C:C31E:314A (talk) 14:02, 14 June 2023 (UTC)

Are the most recent artifactual definitions of kg and meter still made of the best kg/meterstick substance known to man?

Well best to be the one national kilograms and metersticks aim for. Sagittarian Milky Way (talk) 03:55, 13 June 2023 (UTC)

The current definitions are not artifactual. The most recent artifactual definition of the kilogram is embodied in Le Grand K, manufactured in 1879. It was fashioned of a 90% platinum and 10% iridium alloy. The same alloy was used for the most recent artifactual definition of the metre, the International Prototype Metre, manufactured between 1886 and 1899. I don't know how to compare it with potential other substances (92% adamantium and 8% unobtanium?) for goodness. A search for "meterstick substance" did not turn up promising results.  --Lambiam 06:09, 13 June 2023 (UTC)

I know the kg and meter are no longer the mass and length of physical objects by definition. I was wondering if they'd still use platinum with about 10% iridium if the objects were being built today or if they've realized something better is possible some time in the last 124+ years. Maybe some other platinum-group metal alloy? Or a 1 kilogram diamond? (it would have to be artificial as the largest uncut natural diamond ever was only a pound and a third). Would the kilo be spherical instead of cylinderical to minimize surface area? ~~~~ Sagittarian Milky Way (talk) 17:04, 13 June 2023 (UTC)

If you define what the properties are you want to optimize for, the question might, perhaps, become answerable or at least researchable. (: Obviously, clay is better, as it is a hell of a lot cheaper. :)  --Lambiam 20:39, 13 June 2023 (UTC)

Double Slit Experiment.

As we know, multiple single photons can be fired through 2 slits to form interference patterns as can electrons and small particles.

I believe there is no explanation for this - it is merely observed.

Has anyone ever suggested that a diffraction contour pattern is obviously formed on either side of the slits by the multitude of photons in a given room, all of whom diffract as we see from single photon diffraction? And thus, their energy/momentum can be imparted to electrons and small particles, thus creating the illusion that the particles themselves are diffracting? Byron Forbes (talk) 16:58, 13 June 2023 (UTC)

I don't follow what you're saying but the diffraction pattern is formed exactly the same even if the light intensity is so low that only a single photon at most will be in the experiment at a time. SO multitudes has nothing to do with it. NadVolum (talk) 17:07, 13 June 2023 (UTC)

Clarification: every single photon hits one and only one point. However, if you test photon by photon the pattern will emerge, as more photons will hit where the wave function superposition is positive, and vice versa.

Also, it's not exactly true to say that it is not explained. The Copenhagen interpretation is that the wave function collapses upon measurement (though what consists a measurement is not well defined), and the pilot wave interpretation explains it as the probability the wave function that directs the photon is more likely to lead it to certain areas and less to others.

Zarnivop (talk) 17:48, 13 June 2023 (UTC)

No physicist has suggested this, because it does not make sense.  --Lambiam 20:34, 13 June 2023 (UTC)

June 14

Pregnancy

Technically, how long after giving birth can a girl get pregnant again? 2001:B07:6442:8903:D478:83BE:7BFE:74E3 (talk) 16:03, 14 June 2023 (UTC)