What is the newest installment of 'Random Thoughts' on Physics Forums?

[WWGD]

I've now applied. Just waiting to see if my application is accepted.

Good luck, keep us posted. I suggest if you have a clear, specific idea of your research topic you can start looking for someone to work with and save yourself a lot of time in completing your thesis. Others here that know more physics than I ( which is just about everyonr here) may be able to guide you in that regard.

 

[BillTre]

Using "a" or "an" before before another word, as I understand it, is determined (usually) by whether or not the following word starts with a vowel.
"An" goes before vowels, "a" goes before consonants (in the first position of letters in the following word).

Abbreviating of a word starting with an "m" makes an abbreviation (M), which would be spoken as "em" (beginning with a vowel).

Should it get the "an"?
Sounds better that way to me.

What's that relationship between the words called?

 

[WWGD]

Using "a" or "an" before before another word, as I understand it, is determined (usually) by whether or not the following word starts with a vowel.
"An" goes before vowels, "a" goes before consonants (in the first position of letters in the following word).

Abbreviating of a word starting with an "m" makes an abbreviation (M), which would be spoken as "em" (beginning with a vowel).

Should it get the "an"?
Sounds better that way to me.

What's that relationship between the words called?

Not sure. But I do remember this guy who would keep saying the likes of , "A hour" and " A accident" despite others suggesting he do otherwise.

 

[WWGD]

If auto ( in)correct is at the cutting edge of A.I, there should be no fear of machines rebelling and taking over any time soon.

 

[DrGreg]

Using "a" or "an" before before another word, as I understand it, is determined (usually) by whether or not the following word starts with a vowel.
"An" goes before vowels, "a" goes before consonants (in the first position of letters in the following word).

Abbreviating of a word starting with an "m" makes an abbreviation (M), which would be spoken as "em" (beginning with a vowel).

Should it get the "an"?
Sounds better that way to me.

It's based on how you pronounce it, not how you spell it. So, yes it is "an em".

Words that begin with "h" can go either way because some pronounce the "h" ("a historic victory") and some don't ("an historic victory"); either is acceptable.

 

[fresh_42]

Is it correct that there is a difference between an umbrella and a unique solution, despite the vowel?

 

[hmmm27]

IIRC, acronyms sposeta be pronounced as if the words are out in full, ie: "He has a MBA".

That could be just in writing, though. Doesn't make much sense for speech.

"h" is just a pain to figure out. Latest decision on my end is "an historical", but "a history"

"unique" is pronounced "you neek" (in English, well... American English), so "a".

 

[WWGD]

Jenner is doing an add for the Armani (S)Exchange.

 

[WWGD]

Is it correct that there is a difference between an umbrella and a unique solution, despite the vowel?

Umbrella and unique solutions ?

 

[Ibix]

If auto ( in)correct is at the cutting edge of A.I, there should be no fear of machines rebelling and taking over any time soon.

Any Tim's son, however, should probably keep his head down.

 

[Astronuc]

It appears from the last paragraph that there was evidence of 'the crack' from May 2019. It's not clear to me at present, if they are saying the crack was partial or fully through the beam. If it was clear that there was a crack, then there was a complete failure in the inspection process that allowed continued operation of the bridge in that condition.

Kayaker's photos show crack in closed I-40 bridge in 2016
https://news.yahoo.com/kayakers-photos-show-crack-closed-171326461.html

MEMPHIS, Tenn. (AP) — Photos taken by a Mississippi River kayaker about five years before a crack was found in the Interstate 40 bridge linking Tennessee and Arkansas appear to show the fracture that led transportation officials to close the span indefinitely last week.

Arkansas transportation officials said they cannot confirm or refute what’s shown in the 2016 photos, which raise questions about how early the crack appeared.

Photos from drone footage of 2019 show the crack partially through the beam. It seemingly started at the bottom and propagated upward. From the length of the crack in 2019, some length of crack should have been there in 2016. The bending in the beam ahead of the crack would increase as the crack lengthened.

The first image shows the crack from 2019, already about 80-85% of the way through the beam. The other two are from 2021 showing the crack when discovered. The third image shows a slight lateral displacement.

 

[dlgoff]

I suggest if you have a clear, specific idea of your research topic you can start looking for someone to work with

I have and I have. Thanks.

 

[WWGD]

Confusing-enough, Python's Linear Algebra contains...Modules.

 

[Ibix]

Confusing-enough, Python's Linear Algebra contains...Modules.

lambda f: c/f

It's the lambda lambda.

 

[fresh_42]

Confusing-enough, Python's Linear Algebra contains...Modules.

By the way modules. I tried to figure out the English term for the sum of simple submodules, which in German is Sockel. It turned out to be socle. Now is this a loanword and who borrowed from whom, or is it a parallel development from some medieval word?

 

[WWGD]

lambda f: c/f

It's the lambda lambda.

Lambada? You're out of Sync, Ibix.

 

[WWGD]

By the way modules. I tried to figure out the English term for the sum of simple submodules, which in German is Sockel. It turned out to be socle. Now is this a loanword and who borrowed from whom, or is it a parallel development from some medieval word?

Ask Ibix, it seems to see with the Lambada Calculus.

 

[WWGD]

By the way modules. I tried to figure out the English term for the sum of simple submodules, which in German is Sockel. It turned out to be socle. Now is this a loanword and who borrowed from whom, or is it a parallel development from some medieval word?

Socle? Never heard of it.

Maybe you misheard? It happens to me often with British English: Maca singing " Do me a Weber (favor; W pronounced as a V), let them in" *, or " Eastern boys and Western Girls"instead of " East End Boys and West End girls".

*They used to play it all the time on the radio in a recent job

 

[DrGreg]

Socle? Never heard of it.

I hadn't either, but Wikipedia has: Socle (mathematics)

 

[fresh_42]

Socle? Never heard of it.

The German word is very common, in its meaning of the pedestal where statues are placed upon, not the submodule.

 

[Ibix]

The German word is very common, in its meaning of the pedestal where statues are placed upon, not the submodule.

I'd call that a plinth, if I didn't call it the thingy a statue stands on. I'd never heard socle as far as I'm aware. The English etymology is here, from Latin indirectly. I suspect German got it the same way.

 

[fresh_42]

I'd call that a plinth, if I didn't call it the thingy a statue stands on. I'd never heard socle as far as I'm aware. The English etymology is here, from Latin indirectly. I suspect German got it the same way.

This sounds as if a German mathematician named the submodule Sockel and the English word socle was taken from that rather than the other way around.

Sockel is used for anything on the ground when something else is above it. E.g. this is a 'Sockelleiste', or figurative: to put someone on a 'Sockel'.

I assume that it is of the same origin as socks ('Socken').

 

[Ibix]

this is a 'Sockelleiste',

That's a skirting board in English.

I don't really understand what a mathematical socle does - could it be seen as a supporting entity for a larger or more general construction? If so, someone probably borrowed the architectural term

 

[fresh_42]

That's a skirting board in English.

I don't really understand what a mathematical socle does - could it be seen as a supporting entity for a larger or more general construction? If so, someone probably borrowed the architectural term

The other two descriptions are more telling:
- the biggest semisimple submodule
- the intersection of all great (large? big?) submodules

It is a bit of a core, but bigger than just $\{0\}$. It has nice functorial properties, so it makes sense to define it.

 

[jbriggs444]

That's a skirting board in English.

In the U.S. the term I am most familiar with would be "baseboard".

(also called skirting board, skirting, wainscoting, mopboard, floor molding, or base molding)

 

[Ibix]

In the U.S. the term I am most familiar with would be "baseboard".

Fair enough. It's a skirting board everywhere in the UK as far as I'm aware, although I've heard wainscoting from time to time. I've never heard it called a socle, anyway.

 

[etotheipi]

I wonder if there will ever be commercially available tiny black hole pellets that you could just throw at people and it sucks them up. Some things to consider would be manufacturing the black hole pellets in situ, keeping them stable before ejection and the mechanism of the absorption on impact. Also I don't know how the resulting body would interact with the Earth. But anyway I think black holes can eventually be weaponised.

 

[Frigus]

I wonder if there will ever be commercially available tiny black hole pellets that you could just throw at people and it sucks them up. Some things to consider would be manufacturing the black hole pellets in situ, keeping them stable before ejection and the mechanism of the absorption on impact. Also I don't know how the resulting body would interact with the Earth. But anyway I think black holes can eventually be weaponised.

Guns almost give the same result, so I don't think we need that.

 

[etotheipi]

Actually, does anyone know if there are more exotic shapes that black holes can take other than just the boring spherically symmetric one? Like frisbee-shaped or boomerang-shaped would be neat, but maybe those shapes would arise as some modes of a certain oscillation. How do you find the possible vibrational modes of a black hole?...

 

[Ibix]

Actually, does anyone know if there are more exotic shapes that black holes can take other than just the boring spherically symmetric one?

"Black holes have no hair". They radiate gravitational waves and very rapidly sink into a state completely characterised by mass, angular momentum, and charge. So you can have weird shapes (e.g. during a merger - you can find LIGO-authored animations online) but only transiently.

 

[Keith_McClary]

Wonder if anyone knows how to find the vibrational modes of a black hole

Black holes have no hair.

A 10kg hole has a lifetime of $10^{-13}$s.

Hawking radiation calculator ​

 

[WWGD]

If they mass produce them , some people will surely get sucked into buying them.

 

[collinsmark]

I wonder if there will ever be commercially available tiny black hole pellets that you could just throw at people and it sucks them up. Some things to consider would be manufacturing the black hole pellets in situ, keeping them stable before ejection and the mechanism of the absorption on impact. Also I don't know how the resulting body would interact with the Earth. But anyway I think black holes can eventually be weaponised.

Ignoring the question of how one would go about "throwing" such a thing, there's a bigger problem that any black hole with the mass of mere pellet would almost instantly, after the moment of creation, explode rather cataclysmically due to Hawking radiation. It wouldn't be sucking anything in; rather it would be blowing things apart.

 

[etotheipi]

What does it mean "no hair"? I guess you don't mean actual hair, because I'm pretty sure there's no keratin in a black hole...

Ignoring the question of how one would go about "throwing" such a thing, there's a bigger problem that any black hole with the mass of mere pellet would almost instantly, after the moment of creation, explode rather cataclysmicly due to Hawking radiation. It wouldn't be sucking anything it; rather it would be blowing things apart.

I did not study at all this phenomenon of Hawking radiation yet, because first it is necessary to study the Bogoliubov transformations. So I take your word for this. But why will this process be violent, I was under the impression Hawking radiation was a slow process?

 

[WWGD]

I did not study at all this phenomenon of Hawking radiation yet, because first it is necessary to study the Bogoliubov transformations. So I take your word for this. But why will this process be violent, I was under the impression Hawking radiation was a slow process?

I believe it is the Sponge Bogoliubuv transformation.

 

[collinsmark]

I did not study at all this phenomenon of Hawking radiation yet, because first it is necessary to study the Bogoliubov transformations. So I take your word for this. But why will this process be violent, I was under the impression Hawking radiation was a slow process?

It's very, very slow for stellar mass black holes or larger. But for hypothetical black holes with masses on the order of a human (tens or even hundreds of kilograms) it's very fast -- more akin to a thermonuclear weapon's energy discharge type of fast.

 

[Ibix]

What does it mean "no hair"? I guess you don't mean actual hair, because I'm pretty sure there's no keratin in a black hole...

Well they don't have actual hair either. But there are "no hair" theorems showing that black holes have no identifying characteristics beyond mass, angular momentum and charge. They radiate everything else away in extremely short time. Ask Peter for details...

 

[Ibix]

But why will this process be violent, I was under the impression Hawking radiation was a slow process?

I don't know much either, but I do know that the temperature of the radiation scales inversely with mass, so small black holes radiate more, becoming smaller so radiating yet more. Positive feedback.

 

[etotheipi]

These are all Komar integrals yes? So the no hair theorem is to say this is a maximal set of independent Komar integrals that fully characterise the black hole, is that correct? But I do not see the connection to hair

It's very, very slow for stellar mass black holes or larger. But for hypothetical black holes with masses on the order of a human (tens or even hundreds of kilograms) it's very fast -- more akin to a thermonuclear weapon's energy discharge type of fast.

Ah okay, yes I see in the textbook the relation $\tau \sim M^3$

 

[Ibix]

It's very, very slow for stellar mass black holes or larger.

In fact, their Hawking temperature is below the CMB temperature, so even an isolated black hole will net absorb energy and increase in mass and will continue to do so for a long time until the CMB has cooled.

These are all Komar integrals yes? So the no hair theorem is to say this is a maximal set of independent Komar integrals that fully characterise the black hole, is that correct?

Probably. You're reaching the point where I know facts but don't know the reasoning. Talk to Peter...

But I do not see the connection to hair

I don't know the origin of the expression, but that's what they're called.

 

[Frabjous]

What does it mean "no hair"? I guess you don't mean actual hair, because I'm pretty sure there's no keratin in a black hole...

https://en.wikipedia.org/wiki/No-hair_theorem which according to the page should not be confused with the hairy ball theorem

 

[WWGD]

These are all Komar integrals yes? So the no hair theorem is to say this is a maximal set of independent Komar integrals that fully characterise the black hole, is that correct? But I do not see the connection to hair

Ah okay, yes I see in the textbook the relation $\tau \sim M^3$

What does the relationship mean? What do $\tau, M^3$ stand for?

 

[etotheipi]

It is the complete decay time estimated from Stefan's Law; at rest the energy of the black hole equals its mass $E=M$, meanwhile the area of the event horizon $A \propto M^2$ and as @Ibix mentioned in #7139 $T \propto 1/M$ (which reflects the funny thing that black holes have negative heat capacities...). So overall $dM/dt \propto -AT^4 \propto -1/M^2$ so crudely $\tau \sim M^3$ upon integrating

 

[WWGD]

Hey, if you can't find a place to park your mini cooper, I can put it in my back pack.

 

[Frabjous]

Hey, if you can't find a place to park your mini cooper, I can put it in my back pack.

Will it make it through airport screening?

 

[WWGD]

Will it make it through airport screening?

Maybe, if I remove the 25 cops inside first ;).

 

[WWGD]

Kind if interesting. I play this free online Sudoku puzzle. This is the distribution of the winning times

 

[WWGD]

I guess this distribution implies only people who become good play the game often enough, which seems like a reasonable interpretation of the distribution of winning times.

 

[collinsmark]

A couple of years ago I wrote a sudoku solver program for kicks and giggles (it was written in C#). I'm pretty proud of it (given that I wrote it just for fun). I'm not very speedy at sudoku puzzles myself, but my program is. It starts by using the same techniques that humans would use to solve sudoku puzzles. Then -- and only if it is unable to make progress -- does it fall back onto a brute-force method that involves recursion.

It can solve just about any valid puzzle I can throw at it, such as those you would find in a newspaper, in a matter of milliseconds (Edit: it also checks if the puzzle is valid and if it has one and only one unique solution). It takes just over half a second to solve Arto Inkala's puzzle, perhaps the hardest sudoku puzzle ever made.

int[] testArray04 = new int[]  // Hardest ever, perhaps, 21 clues Also called Arto Inkala's puzzle
            {
                8, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 3, 6, 0, 0, 0, 0, 0,
                0, 7, 0, 0, 9, 0, 2, 0, 0,
                0, 5, 0, 0, 0, 7, 0, 0, 0,
                0, 0, 0, 0, 4, 5, 7, 0, 0,
                0, 0, 0, 1, 0, 0, 0, 3, 0,
                0, 0, 1, 0, 0, 0, 0, 6, 8,
                0, 0, 8, 5, 0, 0, 0, 1, 0,
                0, 9, 0, 0, 0, 0, 4, 0, 0
            };

I've been neglecting it because I still need to write a user interface for it, and user interfaces are boring.

 

[etotheipi]

I don't know the origin of the expression, but that's what they're called.

Apparently if the black hole uses Pantene shampoo and conditioner then it's all okay
Black holes have a lush head of ‘soft hair’

At least I think that's the main point Prof Hawking was trying to make...