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

[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...

 

[WWGD]

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.

Did you feed it the needed " Boundary Conditions" for a problem to be well-defined in the sense of having a unique solution or does it implicitly know them ( or does it stop with a message if it cannot)?

 

[WWGD]

I remember a post here a while back about the properties of sudokus when viewed as ( square) matrices. Interesting But don't remember much detail from it.

 

[Ibix]

idk

View attachment 283533

"Maybe she's born with it, maybe it's curved spacetime"?

 

[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.

Did you feed it the needed " Boundary Conditions" for a problem to be well-defined in the sense of having a unique solution or does it implicitly know them ( or does it stop with a message if it cannot)?

It figures it out if the solution is unique or not on the fly. I'll walk through the logic here.

Firstly, note that If you can solve a sudoku puzzle without making any "guesses," solving the puzzle with logic alone, then it follows that the resulting solution is unique. That's because each individual cell was found such that it must contain one and only one specific number; any other number would cause an inconsistency. And if the whole sudoku table is solved in this way, then the solution must be unique, because any deviation whatsoever would have caused an inconsistency somewhere along the way.

That said, really, really hard sudoku puzzles sometimes require guessing. That's where the program's recursion comes into play. If the solver finds itself unable to make progress with logic alone, it will start guessing. It does this by picking one of the unknown cells, filling it in with a guess, and feeding that into a new instance of the solver, but this time with the cell filled in with the guess (hence the recursion).

But it doesn't end with a single guess for the cell in question. It guesses all possibilities. For example, if by logic alone, the program narrows down a cell to be one of three possibilities, it will check [i.e., "guess"] all three possibilities. If more than one of those possibilities results in a valid solution for the puzzle, then the solution is not unique.

The recursion is quite useful here. Any child instance of the solver might discover that the puzzle has a non-unique solution, not the just the guess for that initial cell. A non-unique-solution flag along with any unique solutions are passed back to the calling method, even if that method happens to be another instance of the solver.

If at the end, after checking all guesses and following all logical possibilities, there is one and only one valid solution, that solution is deemed unique.

(On a side note, solving a sudoku puzzle is one of the few examples in my experience where recursion is not only convenient, but quite possibly essential.)

 

[WWGD]

It figures it out if the solution is unique or not on the fly. I'll walk through the logic here.

Firstly, note that If you can solve a sudoku puzzle without making any "guesses," solving the puzzle with logic alone, then it follows that the resulting solution is unique. That's because each individual cell was found such that it must contain one and only one specific number; any other number would cause an inconsistency. And if the whole sudoku table is solved in this way, then the solution must be unique, because any deviation whatsoever would have caused an inconsistency somewhere along the way.

That said, really, really hard sudoku puzzles sometimes require guessing. That's where the program's recursion comes into play. If the solver finds itself unable to make progress with logic alone, it will start guessing. It does this by picking one of the unknown cells, filling it in with a guess, and feeding that into a new instance of the solver, but this time with the cell filled in with the guess (hence the recursion).

But it doesn't end with a single guess for the cell in question. It guesses all possibilities. For example, if by logic alone, the program narrows down a cell to be one of three possibilities, it will check [i.e., "guess"] all three possibilities. If more than one of those possibilities results in a valid solution for the puzzle, then the solution is not unique.

The recursion is quite useful here. Any child instance of the solver might discover that the puzzle has a non-unique solution, not the just the guess for that initial cell. A non-unique-solution flag along with any unique solutions are passed back to the calling method, even if that method happens to be another instance of the solver.

If at the end, after checking all guesses and following all logical possibilities, there is one and only one valid solution, that solution is deemed unique.

(On a side note, solving a sudoku puzzle is one of the few examples in my experience where recursion is not only convenient, but quite possibly essential.)

Yes, I always thought it was an interesting question wether recursion is necessary. It seems I can solve a certain class of problems. I tried small scale to to use unsupervised learning to see if I can classify those problems that I have trouble with, but just a small project. I thought of recursion more in the sense that a Sudoku with x "unsolved" 1x1 squares can be dealt with in terms of one with x-1or fewer solved squares.

 

[WWGD]

Still trying to figure out why my PC becomes dusty as if I had left it open overnight in the #$% Sahara, while I leave it inside a case when I am not using it.

 

[Rive]

As an engineer, I still need somebody to translate standards to useful information.
Is there such a sub-class for engineering that 'lawyer-engineer', or something?

 

[atyy]

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?...

https://arxiv.org/abs/hep-th/0701035

 

[WWGD]

I fail to understand the use of bias in linear regression as the intersect with the x-axis. It doesn't seem to match the expression E(p)-p; E(p) is the expected value of p.

 

[WWGD]

As an engineer, I still need somebody to translate standards to useful information.
Is there such a sub-class for engineering that 'lawyer-engineer', or something?

Maybe try our engineering forums here? If they don't know themselves they may be better able to refer you to someone who does.

 

[WWGD]

Sorry to my Libertarian ( " Big L") friends . Visit any unmoderated site and read the tons of posts that quickly degenerate into " But your a looser to".

 

[Rive]

Our IT department just raised a new recommendation for passwords due security concerns: needs to be awful long, with numbers and capitals.
This became the first password for I had to spend a sticky note.

Congratulations, IT security.

 

[Borg]

No need for a sticky note.

 

[Frabjous]

No need for a sticky note.

We have to change our passwords every 90 day, so after a couple of years, your system is also difficult to remember.

 

[Borg]

I have to keep track of dozens of 14+ length passwords for my work that require numbers, letters and special characters and also change frequently. It's not a lot of fun sometimes but it beats the hell out of getting hacked because of poor security.

 

[WWGD]

But somehow ATM cards only require a 4-digit code; no special characters , not even letters, just 4 digits, so a chance of 1 in 10000.

 

[Borg]

That's a form of two factor authentication because you also have to have the ATM card.

 

[WWGD]

That's a form of two factor authentication because you also have to have the ATM card.

Can't you do online transactions using the ATM card alone. Besides, what if your wallet is lost or stolen?

 

[Borg]

What exactly do you insert your ATM card into when you're online?

The ATM card is one half and the pin is the second half of the authentication process. This is similar to when a website doesn't recognize your computer (i.e. no previous cookie) and wants to email or text a short code to a known email or phone tied to your account. In this case, the original username and password is similar to the ATM card that's used at the bank.
https://en.wikipedia.org/wiki/Security_token#Loss_and_theft

 

[WWGD]

I understand. I meant if you lose your ( physical) ATM card. I assume you're temporarily blocked from the system after 3-4 failed password guesses. But maybe you can retry a few days later? Maybe 1 chance in 1500 is still a good bet for ATM card holders. I assume tougher privacy would put a dent in the economy if more people were kept from accessing their money by being locked out of their ATM.

And, related, is there any value to RF ( Radio Frequency) protectors for credit cards?