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

[Astronuc]

Stumbled across a bit of trivia from a biographical note for George F Smoot,

My father had started a lumber business after the war to provide additional income. The business was successful, providing just enough for us to eke by. Then, a problem came up. In one of the stands of trees that my father purchased, a large, productive still was producing bootleg alcohol for this dry portion of the state. As soon as the tree cutting began, the group operating the still approached my father. They offered him cash not to cut the trees and expose their substantial operation. My father, at some personal risk, informed the police, and the trees were promptly impounded (no longer allowed to be cut for the saw mill) by the judge handling the case. He was apparently on the payroll of the illegal distillery operation as some police must have been. This caused an immediate financial crisis for us, as much of the saw mills/lumber company funds were tied up in trees, which were to be cut down and then milled to lumber and sold. Suddenly there was a shortage of trees to mill. Needless to say, our lumber company was soon in bankruptcy.

https://www.nobelprize.org/prizes/physics/2006/smoot/biographical/

 

[Borg]

Until recently, there were Smoot Lumber stores in the northern Virginia area. I've been there because they sold wood products that you couldn't find anywhere else. It appears that they were bought by another company but still have the Smoot name on the website. Seems to be quite a coincidence in names and trades.

 

[nuuskur]

Thesis complete. Defense in June. 4 years flew past quick

 

[WWGD]

Wonder if a topic for a Math thesis in the 15th century would be along the lines of ( in Latin)" On the solution set of x+1=2"

 

[WWGD]

Congratulations, @nuuskur . May you tell the general topic?

 

[nuuskur]

Congratulations, @nuuskur . May you tell the general topic?

Semigroups, categories, Morita equivalence.

 

[fresh_42]

Semigroups, categories, Morita equivalence.

And before you all start looking it up ...

https://ncatlab.org/nlab/show/Morita+equivalence

 

[Astronuc]

A large Navy research vessel that once belonged to late Microsoft billionaire Paul Allen tipped over — injuring 33 people — and is stuck at a 45 degree angle

https://www.yahoo.com/news/large-navy-research-vessel-once-214227909.html

The 3,000-ton ship was originally funded by Microsoft co-founder Paul Allen, who bought the then-offshore service vessel in 2016 and had it retrofitted to serve as an underwater research and exploration vessel. Allen hoped the boat would serve to scan the ocean's depths and locate historic shipwrecks and explore underwater ecosystems.

During its service years, the Petrel discovered several lost shipwrecks, including the USS Hornet and the USS Lexington, two significant US aircraft carriers that were sunk in World War II.

 

[fresh_42]

The first time someone did not use this misleading model of a balloon for our universe. He described it as a 3d-lattice instead where the points are the galaxies and the lines are all expanding. This is far better since every galaxy aka lattice point is the center of expansion. No more "center" was needed, and the big bang took place everywhere.

Why don't they still use this ballon metaphor?

 

[Tom.G]

Why don't they still use this ballon metaphor?

Who is going to do, or read, a Doctorate Thesis on a balloon?

 

[WWGD]

Doesn't @phinds include a balloon analogy in his posts?

 

[Ibix]

The first time someone did not use this misleading model of a balloon for our universe. He described it as a 3d-lattice instead where the points are the galaxies and the lines are all expanding. This is far better since every galaxy aka lattice point is the center of expansion. No more "center" was needed, and the big bang took place everywhere.

Why don't they still use this ballon metaphor?

You can draw the 2d version of such a grid on the surface of a balloon or on a flat sheet of rubber, which is a passable model for a spatial slice of the positive and zero spatial curvature FLRW spacetimes. I gather that a 2d Euclidean surface with constant negative curvature cannot be embedded in a 3d Euclidean space (or possibly it can be done but it intersects itself, I don't recall), so there's no great analogy for that.

The 3d grid you're imagining can only represent the curvature of the space in which it's embedded. That's either a flat Euclidean space or a spatial slice of our real spacetime, whatever that is.

While the latter is necessarily a correct model, it's probably not that helpful an analogy. It reminds me of an episode of the old radio comedy series The Goon Show where they travel to Paris. They decide to look at a map, which is followed by paper rustling sounds for about ten seconds, a pause, and then Peter Sellars' voice in the distance saying "Big, isn't it?" They have to take a taxi to meet up again.

 

[phinds]

Doesn't @phinds include a balloon analogy in his posts?

Yes

 

[dlgoff]

Now it's 33°F.

Well, it's a little warmer at 41 degrees. Still not what spring should be like. :(

 

[Klystron]

Well, it's a little warmer at 41 degrees. Still not what spring should be like. :(

Chilly here in the high desert at 58 degrees F.

I was heading outdoors to poolside to exercise prior to the anticipated 1 April opening of swim season, but decided to workout indoors until the cloud cover dissipates.

 

[dlgoff]

Chilly here in the high desert at 58 degrees F.

That IS chilly for where you're at.

 

[Klystron]

That IS chilly for where you're at.

Friends and neighbors told me at lunch this week that 2023 March has been the coldest in Las Vegas Valley in many decades. We locals wore sweaters and fleece -- equivalent to puffy parkas in colder climates -- over cotton layers and long pants. Even my friends from Nova Scotia felt chilly.

Our host suggested this cold Spring presages hotter-than-average Summer temperatures.

 

[dlgoff]

Our host suggested this cold Spring presages hotter-than-average Summer temperatures.

Bold by me.
That sounds good to me right now.

 

[WWGD]

Interesting question( not mine; from a Math undergrad) " If I hit the Real line at random. How do I know I will always hit a number? I replied that the standard ordering < " less than" is dense in itself, i.e., if there are x,y with x<y, then there will always be a z with x<z<y. But this is not fully convincing, because the same is the case for Rationals x',y', but Rationals have gaps. I mumbled something to the effect of " That's why it's called the continuum, Reals satisfy the Lub- Completeness property.

I meant to say, if you're given the Reals axiomatically, how would you tell the Real line is a valid model for them.

 

[gmax137]

Bold by me.
That sounds good to me right now.

Drove to Vegas yesterday from home near Reno. Saw a few snowflakes while in Red Rock Canyon this afternoon, that's a first.

 

[dlgoff]

Drove to Vegas yesterday from home near Reno. Saw a few snowflakes while in Red Rock Canyon this afternoon, that's a first.

My daughter who lives in Golden, Colorado told me it's been in the 30s and windy.

 

[Klystron]

Drove to Vegas yesterday from home near Reno. Saw a few snowflakes while in Red Rock Canyon this afternoon, that's a first.

I live a few miles south of Red Rock Canyon. Saw snow flurries outside several times this Winter. This year the snow melted once on the ground but a few inches accumulated late Feb 2019.

 

[Astronuc]

How a Fake Mountain Range Slowed Down Arctic Exploration

The 19th-century naval officer John Ross had a knack for seeing land where it wasn’t.
https://www.atlasobscura.com/articles/john-ross-arctic-mountain-fake

On August 31st, 1818, around 3 p.m., the Arctic explorer John Ross was called away from his dinner and onto the deck of the ship he commanded, the Isabella. Ross and his crew were moored in Baffin Bay, just south of Greenland, seeking a way through to the Arctic sea beyond. All day, they had been waiting for the fog to clear, so they could take a look around and try to find it.

Ross stepped out onto the deck and began scanning the horizon: ice, more ice, and, in between, an imposing set of peaks. “I distinctly saw the land, round the bottom of the bay, forming a connected chain of mountains with those which extended along the north and south sides,” he wrote soon after. There was, he concluded, no way through.

Some are born great; some achieve greatness; some have greatness thrust upon them. And some narrowly miss greatness, kept from it by a pesky propensity to imagine land where there is none.

I'm wondering if he saw an iceberg, which is a transient phenomenon. It eventually moves and/or melts.

 

[dlgoff]

How a Fake Mountain Range Slowed Down Arctic Exploration

The 19th-century naval officer John Ross had a knack for seeing land where it wasn’t.
https://www.atlasobscura.com/articles/john-ross-arctic-mountain-fakeI'm wondering if he saw an iceberg, which is a transient phenomenon. It eventually moves and/or melts.

... the Arctic explorer John Ross was called away from his dinner and onto the deck of the ship he commanded, the Isabella. ...

"Isabella was the imaginary friend of Clara Sutter, one of the children aboard the USS Enterprise-D."
See: https://memory-alpha.fandom.com/wiki/Isabella

 

[fresh_42]

Did you ever recognize that ordinary people get convenient finger positions while state guests and presidents have to use outfield positions with a stair?

 

[pinball1970]

Did you ever recognize that ordinary people get convenient finger positions while state guests and presidents have to use outfield positions with a stair?

Can you elucidate?

 

[fresh_42]

Can you elucidate?

 

[fresh_42]

I can't stop wondering ...

 

[Astronuc]

National Geographic, Yellowstone National Park - "One bug [bacterium] yielded a heat-friendly, DNA-copying enzyme that works at high temperatures. The enzyme led to PCR tests used today in everything from forensics and genetic testing to accurate COVID checks."

Apparently to read the article requires a subscription
https://www.nationalgeographic.com/magazine/article/yellowstone-national-parks-geothermals

 

[WWGD]

Wow, overheard high schoolers trying to solve an exam problem ( that had been marked as wrong ; exam had been returned to them), that did not seem too easy nor obvious: Worker A starts on the 5th of April and travels every 3rd day . Worker B starts on the 2nd of April and travels every 4th day. During what days , if any, in April will they both be traveling? This was,from what I gathered, a timed test. I could only tell it had to see with the LCM of 3 and 4. Yes, we need to find positive Integer solutions to 5+3k =2+4j. I fail to see a quick solution to it.

 

[berkeman]

5+3k =2+4j

I'm not sure why you need complex numbers to solve this...

 

[fresh_42]

Yes, we need to find positive Integer solutions to 5+3k =2+4j. I fail to see a quick solution to it.

That's $3k=4j.$ Where is the problem?

 

[WWGD]

That's $3k=4j.$ Where is the problem?

Not

 

[Ibix]

Yes, we need to find positive Integer solutions to 5+3k =2+4j.

RHS is even so 8+6k suffices for LHS. Thus the LHS can only be 14, 20 or 26, and the RHS isn't divisible by four. So the 14th and the 26th, surely?

 

[WWGD]

Not quite , k=4, j=3 is not a solution:
$5+12 \neq 2+12$

 

[WWGD]

That IS chilly for where you're at.

Santiago de Chilly?

 

[fresh_42]

\begin{align*}
5+3k &=2+4j \Longleftrightarrow 3+3k=4j \Longleftrightarrow 3(k+1)=4j \Longleftrightarrow 3k'=4j\\[6pt]
4\,|\,k'&\wedge 3\,|\,j \Longrightarrow k'=4n \wedge j=3m \Longrightarrow 12n=12m \Longrightarrow n=m\\[6pt]
5+3\cdot(4n-1)&=2+4\cdot 3n
\end{align*}

 

[WWGD]

I never said they were intrinsically difficult. I said that, for 14-15 year olds with limited Math skills, on time pressure, it's not an easy problem.

 

[fresh_42]

I never said they were intrinsically difficult. I said that, for 14-15 year olds with limited Math skills, on time pressure, it's not an easy problem.

Guess I misunderstood you.

 

[WWGD]

Guess I misunderstood you.

Neinert problemachkeit.

 

[Jarvis323]

Not quite , k=4, j=3 is not a solution:
$5+12 \neq 2+12$

2 + 3 + 3k = 4j + 2
3 + 3k = 4j
3(k+1)=4j

 

[fresh_42]

Neinert problemachkeit.

PF's first law: the easier the question the more posts, especially if it is answered in post #2.

 

[WWGD]

2 + 3 + 3k = 4j + 2
3 + 3k = 4j
3(k+1)=4j

But the point is this is for a timed test for high-school kids, i.e., 14-15 year olds.

 

[gmax137]

I would draw a 7x4 calendar grid and put As and Bs in the traveling days, probably take less than a minute.

 

[Rive]

I would draw a 7x4 calendar grid and put As and Bs in the traveling days, probably take less than a minute.

Way back in a competition we got a programming example around the same difficulty.
I just did something like you suggested and provided results in a minute or so. Then I just left (the whole idiotic competition too, by the way.)
The winner took arond half an hour and wrote some recursive self-calling whatever mess which provided the same results.

Even that time I had a strong expectations for textbook examples to have at least some sense.

 

[gmax137]

If the question asked for results April a year from now, then maybe the mathematical approach would be faster. Maybe...

 

[WWGD]

If the question asked for results April a year from now, then maybe the mathematical approach would be faster. Maybe...

You'd have to consider issues of leap years, etc. And you'd have to consider number of days each month if you wanted to know beyond April dates.

 

[Klystron]

Wow, overheard high schoolers trying to solve an exam problem ( that had been marked as wrong ; exam had been returned to them), that did not seem too easy nor obvious: Worker A starts on the 5th of April and travels every 3rd day . Worker B starts on the 2nd of April and travels every 4th day. During what days , if any, in April will they both be traveling? This was,from what I gathered, a timed test. I could only tell it had to see with the LCM of 3 and 4. Yes, we need to find positive Integer solutions to 5+3k =2+4j. I fail to see a quick solution to it.

I would draw a 7x4 calendar grid and put As and Bs in the traveling days, probably take less than a minute.

I suppose we can call this a matrix geometrical solution as opposed to algebraic?
Using @gmax137 's method:

Drew 7x4 grid on paper with pencil.
Labeled first column 1, 8, 15, 22, 29 for indexing. (not actually necessary)
Offset first A to square 5 and B to square 2,
Counted 3 squares from A and marked an "A" until end of grid.
Likewise for worker B counting by 4.

A and B meet on squares 14 and 26 meaning workers A and B both travel on 14 and 26 April.

Entire exercise including checking my work and reciting the mnemonic "Thirty days have November., April, ...", required <2 minutes. Less time than reading the posts.

Reminds me of using "Sieve of Eratosthenes" to find primes among first 100 natural numbers.

 

[gmax137]

Reminds me of using "Sieve of Eratosthenes"

Exactly my thought!

 

[WWGD]

Too easy. Do it using Roman numerals now.