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

[WWGD]

I just saw a short interview with Liam Neeson.
I didn't know he was into physics, he even did an explanation of an experiment, I guess he likes physics:

Physics of fighting hijackers in a plane?

 

[WWGD]

I wonder what the minimal algebraic conditions are in an algebrsic structure A for a polynomial in A[x] to have at least one solution. Algebraic closure is overkill, but finite stru tures like, e.g. Zn don't have the property.

 

[fresh_42]

If any polynomial has at least one solution then you get algebraic closure, since you can always divide off that zero and proceed with the rest. Otherwise $A$ shouldn't be Euclidean, esp. no PID. If you allow non integral domains for $A$ things get weird I guess.

 

[WWGD]

If any polynomial has at least one solution then you get algebraic closure, since you can always divide off that zero and proceed with the rest. Otherwise $A$ shouldn't be Euclidean, esp. no PID. If you allow non integral domains for $A$ things get weird I guess.

What do you do with , e.g., $(x+1)(x^2+1)$ over the Reals?

 

[fresh_42]

What do you do with , e.g., $(x+1)(x^2+1)$ over the Reals?

The point is, that you didn't pose any restrictions on the polynomials. So as long as you require that any polynomial splits, you get the entire package. The definitions in question are "normal and separable field extensions", but you didn't require a field. As I write this, I wonder what e.g. $\mathfrak{su}(n)[x]$ would look like.

 

[WWGD]

I understand, thanks, that I can always extend by an element of choice. But, short of knowing the structure in question is already an extension, is there a ready-made structure where this is guaranteed? Maybe not, don't see a reason for this to be the case.

 

[fresh_42]

... is there a ready-made structure where this is guaranteed?

Not sure what you mean by "this". There are universal objects or you can "tensor up" the scalars, e.g. from real to complex $-\otimes_\mathbb{R} \mathbb{C}$. Then there are (half) group algebras etc. An indeterminate attached to a structure is normally just a simple transcendental extension. Looking for zeros is asking for ideals.

But Galois theory is only one branch where those questions lead to. Others are algebraic geometry, complex analysis, K-theory, quadratic forms, elliptic curves or whatever. We need polynomials and their zeros even in linear algebra. Those damn things are everywhere.

 

[WWGD]

Kind of weird response:
" Let's open up a restaurant".
" All restaurants around here are already open!".

 

[Keith_McClary]

They pay "journalists" to take a small table of numbers and expand it into thousands of words like this:

...
Newfoundland reported no new cases of COVID-19 on Monday marking three full days without a new infection.

The province has tested 20,583 people for the virus so far, and 258 have recovered from infections.

According to health authorities, a total of three people have died as a result of COVID-19.

Neither the Northwest Territories or Nunavut reported new cases of COVID-19 on Monday.

So far, the Northwest Territories has not seen any COVID-19-related deaths, and has tested 2,859 people for the virus.

A total of five people have recovered from infections in the territory.
...

https://globalnews.ca/news/7171991/canada-coronavirus-infections-world-13-million/

And then they wonder why the traditional media are dying.

 

[BillTre]

I know an academic (in biology) who is unable to makes heads or tails out of a 2 x 3 excel table (?$%#@&?).
Putting it in words can be helpful to some people.

 

[WWGD]

Mi friend designed an app that uses a database and thinks he can avoid injection through login and permission restrictions only, without parametrizing queries. Doubt it will work out.

 

[Ibix]

I wonder what e.g. $\mathfrak{su}(n)[x]$ would look like.

Very bright. Use a filter.

 

[WWGD]

My sharpness in dealing with technical questions:
"Should we use discord ?"
" No, I prefer dat cord".

 

[Ibix]

Mi friend designed an app that uses a database and thinks he can avoid injection through login and permission restrictions only, without parametrizing queries. Doubt it will work out.

Looks like a job for little Bobby Tables.

 

[fresh_42]

My sharpness in dealing with technical questions:
"Should we use discord ?"
" No, I prefer dat cord".

Sharpies is a forbidden word.

 

[WWGD]

Very bright. Use a filter.

And SPF 5 or higher.

 

[WWGD]

Sharpies is a forbidden word.

Where? How about if I mention the Sharpies of Jehova? ( Stones already coming my way. I am outta here).

 

[Ibix]

How about if I mention the Sharpies of Jehova?

You are sentenced to have a false beard drawn on your face in permanent ink.

Nobody is to draw a beard on anybody, even if they do say Sharpies!

 

[fresh_42]

Romani ite domum!

 

[WWGD]

Romani ite domum!

Qued Era Demonstrandum ( Too lazy to look it up( I am on my phone). Something about Romans, I guess.)

 

[DrGreg]

Romani ite domum!

What have Monty Python ever done for us?

 

[Ibix]

Qued Era Demonstrandum ( Too lazy to look it up. Something about Romans, I guess.)

"Romans go home" - the correct version. Brian originally writes "Romanes eunt domus" which John Cleese translates as "People called Romans, they go, the 'ouse" before giving a lesson in Latin grammar at swordpoint.

 

[Ibix]

What have Monty Python ever done for us?

...well, there's the Dead Parrot sketch.

 

[WWGD]

"Romans go home" - the correct version. Brian originally writes "Romanes eunt domus" which John Cleese translates as "People called Romans, they go, the 'ouse" before giving a lesson in Latin grammar at swordpoint.

Domum arigato .

 

[Ibix]

Domum arigato .

Bitter schön

 

[fresh_42]

What have Monty Python ever done for us?

...well, there's the Dead Parrot sketch.

And not to forget the Ministry of Silly Walks.

 

[Ibix]

And not to forget the Ministry of Silly Walks.

But apart from the Dead Parrot, the Ministry of Silly Walks, Fish Slapping, the Black Knight, the Spanish Inquisition, Monsieur Creosote, and the Killing Joke, what have bloody Monty Python ever done for us?

 

[fresh_42]

But apart from the Dead Parrot, the Ministry of Silly Walks, Fish Slapping, the Black Knight, the Spanish Inquisition, Monsieur Creosote, and the Killing Joke, what have bloody Monty Python ever done for us?

The unladen swallow, Loretta.

 

[WWGD]

Want absurdity?
Just saw online images of protestors in front of a Starbucks:
We
Want
Just
Ice

And they're rioting just because they want ice? I like my drink cold, but I am not that hard core about it.

 

[DrGreg]

But apart from the Dead Parrot, the Ministry of Silly Walks, Fish Slapping, the Black Knight, the Spanish Inquisition, Monsieur Creosote, and the Killing Joke, what have bloody Monty Python ever done for us?

They made a three-sided album, The Monty Python Matching Tie and Handkerchief.

Spoiler: Three-sided??

When you played the second side of the vinyl disc, you would randomly hear one of two completely different sets of sketches. This would have come as a complete surprise to most listeners, as there was nothing on the label or sleeve to indicate what would happen. To add to the confusion, both sides of the disc were labelled "Side 1".

Spoiler: How was it done?

Two concentric spiral grooves, interleaved between each other, instead of the usual one.

 

[WWGD]

 

[WWGD]

 

[WWGD]

 

[BillTre]

But apart from the Dead Parrot, the Ministry of Silly Walks, Fish Slapping, the Black Knight, the Spanish Inquisition, Monsieur Creosote, and the Killing Joke, what have bloody Monty Python ever done for us?

The Galaxy Song:

 

[collinsmark]

They made a three-sided album, The Monty Python Matching Tie and Handkerchief.

Spoiler: Three-sided??

When you played the second side of the vinyl disc, you would randomly hear one of two completely different sets of sketches. This would have come as a complete surprise to most listeners, as there was nothing on the label or sleeve to indicate what would happen. To add to the confusion, both sides of the disc were labelled "Side 1".

Spoiler: How was it done?

Two concentric spiral grooves, interleaved between each other, instead of the usual one.

Yep.

Spoiler: Some more info on this

Skip to ~4:38 to see the Monty Python specific part.