Posted on 05/22/2020 2:44:42 PM PDT by DUMBGRUNT
It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway.
In the summer of 2018, at a conference on low-dimensional topology and geometry, Lisa Piccirillo heard about a nice little math problem. It seemed like a good testing ground for some techniques she had been developing as a graduate student at the University of Texas, Austin.
“I didn’t allow myself to work on it during the day,” she said, “because I didn’t consider it to be real math. I thought it was, like, my homework.”
Before the week was out, Piccirillo had an answer: The Conway knot is not “slice.” A few days later, she met with Cameron Gordon, a professor at UT Austin, and casually mentioned her solution.
“I said, ‘What?? That’s going to the Annals right now!’” Gordon said, referring to Annals of Mathematics, one of the discipline’s top journals.
“He started yelling, ‘Why aren’t you more excited?’” said Piccirillo, now a postdoctoral fellow at Brandeis University. “He sort of freaked out.”
“I don’t think she’d recognized what an old and famous problem this was,” Gordon said.
Piccirillo’s proof appeared in Annals of Mathematics in February. The paper, combined with her other work, has secured her a tenure-track job offer from the Massachusetts Institute of Technology that will begin on July 1, only 14 months after she finished her doctorate.
(Excerpt) Read more at quantamagazine.org ...
Well, I could tell her about party lines and rotary phones. Maybe even interest her in typewriters........As for my circle of friends, we’re till circling with nothing to do.......LOL!
What’s slice? It’s the umbrella term for two properties that this kind of mathematical knot can have. And a mathematical knot is a whole major field of study unto itself, inspired by regular knots that can exist in real life.
Imagine if you tied your shoelaces like usual, but the ends weren’t loose—instead, the laces form a circle. They’re classified by the number of crossings, counted anywhere the strand of the knot crosses itself as you do when you begin to tie any regular knot.
The results of these twisting math knots are one part Cat’s Cradle and one part M.C. Escher. And what they represent is just as abstract. The plain loop is called the unknot, and all true knots must pass a test of whether they can be untangled into an unknot.
https://www.popularmechanics.com/science/a32635156/conway-knot-problem-solved/
The article said Conway died of COVID-19 last month. That is a loss.
Conway’s Game of Life
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970.[1] It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. It is Turing complete and can simulate a universal constructor or any other Turing machine.
https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
Don’t you have to take into account the time you lose while the cop has you pulled over?
If you don’t know where I live you might never arrive. And if on the drive you travel 1/2 of the way, then 1/2 of the rest of the way, and 1/2 of the rest of the way...again you might never arrive. But let me know when you are coming and we’ll leave the light on
” And if on the drive you travel 1/2 of the way, then 1/2 of the rest of the way, and 1/2 of the rest of the way...again you might never arrive. “
Might never arrive, but Ol’Zeno and company worked this problem to death some years back.
Don’t you have to take into account the time you lose while the cop has you pulled over?
There’s a virus going around, so the cops are laying low.
Dear Lisa,
I think I love you.
- Reynoldo
I’ve never been good at tying knots. I would likely be terrible at such high level mathematical abstractions.
I’ve hardly ever seen someone who is so much smarter than they think they are. Usually most people think they’re smarter than they really are, not the other way around.
Yep, you guys are right. Tricky.
Just ask my wife, she will disabuse you of any incorrect assumptions.
And, she is in fact smart.
So you wonder how Grunt snagged such a smart one?
Well, for forty-some years she claims it was a mistake and one she would never repeat.
Infinity
Most folks who are smarter than they think they are have the expectation that what they know, (almost) anyone else can, too. If they can teach what they know to (almost) anyone, they are invaluable.
And the answer is …
Indeterminate, Infinity, Undefined… and WARP SPEED.
Lacking a WARP key/function on my calculator I’m unsure but clearly that would be VERY, very close.
Like with horseshoes and hand grenades, close is good enough. 90 is NOT close.
Math Problem Supposedly Almost Fooled Einstein
https://www.menshealth.com/trending-news/a30985688/math-puzzle-albert-einstein-max-wertheimer/
In 1934, psychologist Max Wertheimer sent a letter to his friend, the physicist Albert Einstein, with the following puzzle enclosed.
There’s an old car that needs to go up and down a hill. The hill is 1 mile going up, and 1 mile going down . Because the car is old, it can only average a speed of 15 mph during the ascent, but may be able to go faster during the descent.
The question is: how fast must the car be going downhill, in order for its speed to reach an average of 30 mph for the entire 2-mile journey?
At the time Einstein received the letter, he had already been honored with the Nobel Prize for Physics, and come up with his famous E = mc2 equation. So this should have been super simple for him to figure out, right? Apparently not. According to German psychologist Gerd Gigerenzer’s book Risk Savvy: How to Make Good Decisions, Einstein wrote that he didn’t see the “trick” until he had already calculated the answer...
The car in question is a Rolls Canardly and the laws of physics don't apply.
The Rolls Canardly rolls down the driveway but canardly drive back up.......
“The Rolls Canardly rolls down the driveway but canardly drive back up.......”
Keep working hard so as not to lose your day job.
No day job left bro so comedy is my specialty........
Einstein said, “If you can’t explain it in terms that a layman can understand, then you don’t really understand it.”
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