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Alan
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Re: Philosophy of Mathematics

December 17th, 2021, 4:35 pm

square root of probability any interpretation? 
In quantum mechanics, it's (roughly) the wave function: [$]|\psi(x)|^2 dx = p(x) \, dx[$], where [$]p(x)[$] is a pdf. 
 
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Collector
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Re: Philosophy of Mathematics

December 17th, 2021, 7:20 pm

square root of probability any interpretation? 
In quantum mechanics, it's (roughly) the wave function: [$]|\psi(x)|^2 dx = p(x) \, dx[$], where [$]p(x)[$] is a pdf. 
unfortunately these probabilities are not satisfactory, not even according to Prince Louis-Victor Pierre Raymond de Broglie :
He lived long and kept a sharp mind, the French wine?
 
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Marsden
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Re: Philosophy of Mathematics

December 18th, 2021, 2:45 pm

Probability is just a number, the units cancel out: two beans red out of ten beans total means 20% probability of picking a red bean.

But there's no beans about the 20%.

So the square root of probability is just a number, too.
 
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bearish
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Re: Philosophy of Mathematics

December 18th, 2021, 6:07 pm

If you know that the probability of the joint occurrence of two iid random variables is p, then [$] \sqrt{p} [$] is the probability of the occurrence of each.
 
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trackstar
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Re: Philosophy of Mathematics

January 28th, 2022, 2:47 am

Found this book in a university ghost town a few days ago - empty streets, but plenty of coffee and books available in the stores that were open.

Synthetic Philosophy of Contemporary Mathematics - Fernando Zalamea

From one of the reviews: "Three different approaches to Mathematics are outlined, which the author calls eidal (transfusions of form: very much pure Mathematics, including mathematics of mathematics), quiddital (transfusions of the real, mathematics based in physics), and archaeal (decantations of the Universal)."

 So far, reminiscent of Badiou. If you read and enjoyed The Blank Swan (Elie Ayache), this is worth a look.
 
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Marsden
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Re: Philosophy of Mathematics

January 28th, 2022, 5:55 pm

"eidal ... quiddital ... and archaeal."
Also second year courses at Hogwarts, if I'm not mistaken ...
 
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Cuchulainn
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Re: Philosophy of Mathematics

November 17th, 2022, 3:31 pm

Future Island: The impressive legacy of Dublin astronomer William Rowan Hamilton

https://www.rte.ie/lifestyle/living/202 ... -hamilton/
 
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katastrofa
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Re: Philosophy of Mathematics

November 17th, 2022, 5:45 pm

"profiling the work of Irish scientists Hamilton and Tyndall, who have left profound legacies."

I love Tyndall! I have blue eyes thanks to his scattering! (Not to beneath the dignity of my mother - I was conceived within marriage.)

Like a sky :-) https://www.iflscience.com/blue-eyes-ap ... ason-45949
 
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Cuchulainn
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Re: Philosophy of Mathematics

November 17th, 2022, 6:06 pm

 
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katastrofa
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Re: Philosophy of Mathematics

November 17th, 2022, 6:19 pm

I confirm based on my curriculum: he's allover physics - or everywhere between simple mechanical systems and higher level quantum mechanics. The mathematics that can describe the chaos of celestial bodies.
 
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Cuchulainn
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Re: Philosophy of Mathematics

February 25th, 2023, 9:49 am

Who put the "h" in Crank Nicolson?

https://en.wikipedia.org/wiki/Phyllis_Nicolson
 
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Cuchulainn
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Re: Philosophy of Mathematics

June 13th, 2023, 8:18 pm

Image
 
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Cuchulainn
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Re: Philosophy of Mathematics

August 29th, 2023, 6:23 pm

 
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Cuchulainn
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Re: Philosophy of Mathematics

February 6th, 2024, 8:46 pm

Image
 
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Cuchulainn
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Re: Philosophy of Mathematics

March 4th, 2024, 11:42 am

To prove the existence of a mathematical object that can be viewed as a maximal element in some partially ordered set in some way, one can try proving the existence of such an object by assuming there is no maximal element and using transfinite induction and the assumptions of the situation to get a contradiction. Zorn's lemma tidies up the conditions a situation needs to satisfy in order for such an argument to work and enables mathematicians to not have to repeat the transfinite induction argument by hand each time, but just check the conditions of Zorn's lemma.
If you are building a mathematical object in stages and find that (i) you have not finished even after infinitely many stages, and (ii) there seems to be nothing to stop you continuing to build, then Zorn’s lemma may well be able to help you.
— William Timothy Gowers, "How to use Zorn’s lemma"[7]