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Alan
Posts: 2663
Joined: December 19th, 2001, 4:01 am
Location: California
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### Re: Philosophy of Mathematics

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.

Collector
Posts: 2562
Joined: August 21st, 2001, 12:37 pm
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### Re: Philosophy of Mathematics

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?

Marsden
Posts: 283
Joined: August 20th, 2001, 5:42 pm
Location: Maryland

### Re: Philosophy of Mathematics

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.

bearish
Posts: 4963
Joined: February 3rd, 2011, 2:19 pm

### Re: Philosophy of Mathematics

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.

trackstar
Posts: 3418
Joined: January 1st, 1970, 12:00 am

### Re: Philosophy of Mathematics

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.

Marsden
Posts: 283
Joined: August 20th, 2001, 5:42 pm
Location: Maryland

### Re: Philosophy of Mathematics

"eidal ... quiddital ... and archaeal."
Also second year courses at Hogwarts, if I'm not mistaken ...

Cuchulainn
Posts: 18065
Joined: July 16th, 2004, 7:38 am
Location: Lviv

### Re: Philosophy of Mathematics

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

https://www.rte.ie/lifestyle/living/202 ... -hamilton/
вот мой дорогой двоюродный брат

katastrofa
Posts: 7024
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Philosophy of Mathematics

"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

Cuchulainn
Posts: 18065
Joined: July 16th, 2004, 7:38 am
Location: Lviv

### Re: Philosophy of Mathematics

вот мой дорогой двоюродный брат

katastrofa
Posts: 7024
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Philosophy of Mathematics

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.