That's a populist view. Mathematicians of the C30 and Eternity will remember John Conway for Monstrous Moonshine. 47x 59x 71 = 196883! The dimensions of space in which the biggest group lives. All is symmetry in Physics and Mathematics. And the number 12 seems to play a huge part in our Universe. Give or take the unit 1.Slow down Steve! I can only handle one mathematician at a time!
Interesting that Conway was best known for his late 1960s invention of the 'Game of Life'.
Conway's Game of Life - Wikipedia
With every symmetry comes a conservation law. Emmy Noether proved that.
Here's an interesting thing. We are accustomed to thinking that planets conserve energy and angular momentum in orbit. But actually another conservation law is at work: Laplace–Runge–Lenz vector - Wikipedia.
Seems the mistake we make is in not regarding this as a Four-dimensional problem.
This speculative John Baez article gives a wholly different approach to the evolution and pattern of our Universe: Planets in the Fourth Dimension | Azimuth
And what is particularly impressive, it translates to good old Quantum Mechanics too: gravitational
BTW, don't waste time on "Spooky Action at a Distance." Just plain wrong. 😱
Add 1 and you've got a baker's dozen!
You're still giving me information overload, Steve. I can't keep up when you're talking nineteen to the dozen!
I've been waiting all my life for a working, economically viable HOT fusion reactor.
This gets into numerology, which is way off topic!
Actually, if I was a betting man, I'd invest far more money in G.H. Hardy's or Ramunajan's Numerology than any other field! 😀
Numerology is considered an outsider in Mathematics. I have frequently been considered a crackpot for my affection for the Koide Formula.
TBH, I do find the Cabibbo Angle very difficult. Hard to find a physical interpretation..
But if you ask me, I'd go for 1728 or 1729 every time. 🙂
Numerology is considered an outsider in Mathematics. I have frequently been considered a crackpot for my affection for the Koide Formula.
TBH, I do find the Cabibbo Angle very difficult. Hard to find a physical interpretation..
But if you ask me, I'd go for 1728 or 1729 every time. 🙂
The ITER project involves 35 countries and, right now, it is constructing a huge test reactor in Southern France. It is hoped that the ITER Tokamak will eventually produce 500MW of fusion power for 50MW of input heating power. The plan is to have the first plasma produced by 2025, but it is unlikely that a working fusion plant will be up and running before 2050. Machine
The hands on a three handed clock are exactly coincident at only 12 AM/PM. Can you do the simple proof?
What is the Universe expanding into?
The answer is: in consciousness.
To understand the answer to this question you must understand that the nature of reality is idealism instead of materialism; the physical world we live in is the representation of consciousness.
Consciousness in not in your head or brain; ALL is (in) 1 consciousness.
Bernardo Kastrup can tell you more.
//edit: uni-verse = 1 verse (song)
The answer is: in consciousness.
To understand the answer to this question you must understand that the nature of reality is idealism instead of materialism; the physical world we live in is the representation of consciousness.
Consciousness in not in your head or brain; ALL is (in) 1 consciousness.
Bernardo Kastrup can tell you more.
//edit: uni-verse = 1 verse (song)
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The universe gives not a toss about the number twelve
For as we into this vast realm further delve
We find that with the universe God does not play dice
Anymore that a true Scotsman would have whisky with ice
So dear friends, let’s ponder this point with great care
Of reality, conscious, truth we remain as humans only just aware
For as we into this vast realm further delve
We find that with the universe God does not play dice
Anymore that a true Scotsman would have whisky with ice
So dear friends, let’s ponder this point with great care
Of reality, conscious, truth we remain as humans only just aware
I don't think I need to, since it is quite observable. Something to do with clock or modulo (12) and modulo (60) arithmetic. Gauss (Residue classes...) and Fermat (Little Theorem...) were pretty good at this stuff. But not my strength. It's a bit like John Kreskovsky's algebraic approach to loudspeakers. I can do algebra, but generally prefer geometry and graphs. 😱
While we have time on our hands, it is an excellent idea to read Leonhard Euler.
Laplace said:
E352 is particularly recommended, being a precursor of the Riemann Hypothesis: Student Translations of Euler's Mathematics
Interestingly, the sum of the alternating Euler Zeta(2) function is Pi squared/12. The sum of the series 1+2+3+4...is in some sense -1/12.
So don't tell me 12 is insignificant! 😀
It's a subtle problem, boswald.
I don't think this is elegant in any way, but we know the three hands line up every 12 hours at 12 o'clock.
The hour and minute hands line up 11 times in those 12 hours. About 5 past one, 10 past two etc...
The minute and the second hands line up in 59 places.
11 and 59 are both prime, and hence relatively prime, so can have no common point on the circle except the origin at 12 o'clock.
Not one of my best... I could do with refreshing on clock arithmetic. 😱
But it does suggest why in group theory (which often is based round clock arithemetic) the answer is often plus or minus one from what you might expect. 😎
Along the way I found out that 3599 has prime factors of 59 and 61. But didn't need to use it.
I don't think this is elegant in any way, but we know the three hands line up every 12 hours at 12 o'clock.
The hour and minute hands line up 11 times in those 12 hours. About 5 past one, 10 past two etc...
The minute and the second hands line up in 59 places.
11 and 59 are both prime, and hence relatively prime, so can have no common point on the circle except the origin at 12 o'clock.
Not one of my best... I could do with refreshing on clock arithmetic. 😱
But it does suggest why in group theory (which often is based round clock arithemetic) the answer is often plus or minus one from what you might expect. 😎
Along the way I found out that 3599 has prime factors of 59 and 61. But didn't need to use it.
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Not being able to understand Steve's explanation, I cheated and searched the internet to find a mathematician! 🙂
During an hour, the hour arm proceeds [FONT=MathJax_Main]360[/FONT][FONT=MathJax_Main]/[/FONT][FONT=MathJax_Main]12 [/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main] 30 [/FONT]degrees. During a minute, the minute arm proceeds [FONT=MathJax_Main]360[/FONT][FONT=MathJax_Main]/[/FONT][FONT=MathJax_Main]60 [/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main] 6[/FONT] degrees. Hence, when it is [FONT=MathJax_Math]h[/FONT] hours and [FONT=MathJax_Math]m[/FONT] minutes (where [FONT=MathJax_Math]m[/FONT] is allowed to be non-integer so as to incorporate all smaller units of time like second, milliseconds, etc.; but [FONT=MathJax_Math]h[/FONT] must be an integer), the hour and minute arms are aligned when:
30 (h + m/60) = 6 m
There was more to follow, but at that point I lost the will to live!
[FONT=MathJax_Main].[/FONT]
During an hour, the hour arm proceeds [FONT=MathJax_Main]360[/FONT][FONT=MathJax_Main]/[/FONT][FONT=MathJax_Main]12 [/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main] 30 [/FONT]degrees. During a minute, the minute arm proceeds [FONT=MathJax_Main]360[/FONT][FONT=MathJax_Main]/[/FONT][FONT=MathJax_Main]60 [/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main] 6[/FONT] degrees. Hence, when it is [FONT=MathJax_Math]h[/FONT] hours and [FONT=MathJax_Math]m[/FONT] minutes (where [FONT=MathJax_Math]m[/FONT] is allowed to be non-integer so as to incorporate all smaller units of time like second, milliseconds, etc.; but [FONT=MathJax_Math]h[/FONT] must be an integer), the hour and minute arms are aligned when:
30 (h + m/60) = 6 m
There was more to follow, but at that point I lost the will to live!
[FONT=MathJax_Main].[/FONT]
I explained it badly, being a bit new to me too... 😱
It's a symmetry and geometry problem, if you want to solve it that way, like this all-pass butterworth filter constructed around a 6 sided hexagon:
The surprise is the symmetries are not 12 and 60 as I expected, but 11 and 59.
There is an 11 sided Regular Polygon describing where the hour and minute hand (roughly) meet.
01:05, 02:11, 03:16, 04:23, 05:28, 06:33, 07:38, 08:45, 09:51, 10:55, 11:60 (=12:00)
Point is there are 11! 😱
There is a 59 sided polygon where the minutes and seconds meet. Same idea.
11 and 59 have no common factor, so the corners or vertices never overlap except at 12 o'clock.
If it was 11 and 44, the hands would overlap at all 11 main points. But that would be 45 seconds in the minute and would be a different sort of clock.
My sister used to have a wristwatch with 12 radial coloured slices on the face and a single hour hand. She said it gave you a whole new concept of time.
When I asked her what the time was, she said "A Quarter to Blue!" 😀
It's a symmetry and geometry problem, if you want to solve it that way, like this all-pass butterworth filter constructed around a 6 sided hexagon:
The surprise is the symmetries are not 12 and 60 as I expected, but 11 and 59.
There is an 11 sided Regular Polygon describing where the hour and minute hand (roughly) meet.
01:05, 02:11, 03:16, 04:23, 05:28, 06:33, 07:38, 08:45, 09:51, 10:55, 11:60 (=12:00)
Point is there are 11! 😱
There is a 59 sided polygon where the minutes and seconds meet. Same idea.
11 and 59 have no common factor, so the corners or vertices never overlap except at 12 o'clock.
If it was 11 and 44, the hands would overlap at all 11 main points. But that would be 45 seconds in the minute and would be a different sort of clock.
My sister used to have a wristwatch with 12 radial coloured slices on the face and a single hour hand. She said it gave you a whole new concept of time.
When I asked her what the time was, she said "A Quarter to Blue!" 😀
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You pass! I can't forget that problem because it was in a scholarship contest. The U of Wisconsin gave high school teachers 3 sets of 4 problems to hand to students they think might solve them. The catch was you didn't get the next set if you didn't solve the last one. I did the first and never heard back assuming I missed 1 or more of the 4. Just before graduation my teacher said that I got the first 4 correct but he never bothered to open the letter till it was too late. It was actually a nice chunk of 1967 dollars.
You might be right. But where we might reconcile is in in using an 11-fold symmetry in an a 12-dimensional space! Some of this group theory stuff is way beyond my pay-grade! 😱
I was quite touched by scott wurcer's experience. It reminded me of Evariste Galois. Most of his papers got lost. Dead by 21!
Other bright flames that burned out too soon in Mathematics were Abel and Ramanujan.
Me, I just missed out on the Nobel Physics Prize for the Quantum Hall Effect. Trouble was we couldn't even see the cold liquid Helium pouring over the Indium Antimonide semiconductor in the Bedford College physics lab. So gave up and retreated to the bar! 😱
But I don't care. Just plain old Quantum Mechanics. I knew that stuff anyway! 🙂
Now, if you ask me, the guy at the forefront of Maths and Physics right now is Edward Witten.
Interestingly, what he does isn't actually all that hard. 1 squared plus 2 squared... all the way up to 24 squared = 70 squared. This comes out as the Leech Lattice in 24 dimensions. Leech lattice - Wikipedia
But my interest continues to be the alternating Euler Zeta(2) function aka E352: http://users.rowan.edu/~nguyen/euler/index.html
It has a physical interpretation as electric charges reflected in parallel mirrors. I just got to figure out the details! 😎
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