graycat

67 ms·

571.
by graycat 4y ago
That's the first case of rigged I ever saw. For your "pre-Hilbert" space, I never saw that either but likely my guess at what you mean would be correct. Can go ahead and take the completion (maybe the same as what used to
572.
by graycat 4y ago
Congratulations on typing ΔpΔx=ℏ, Whenever I see that in a physics video on YouTube, one more such outrage and it's back to a Marilyn Monroe movie. Same for a book on quantum mechanics. If they have an application of Parseval's t
573.
by graycat 4y ago
Yes, the set of reals, as in the usual construction, is the only complete Archimedean ordered field . And some amazing properties are (with my TeX markup) in John C.\ Oxtoby, {\it Measure and Category:\ \ A Survey of the Analogies between
574.
by graycat 4y ago
> You are still presenting a mix out of climate denial myths and lies. Would be glad to see with credible evidence that the examples were either "myths" or "lies". > Global warming didn't "go away",
575.
by graycat 4y ago
Thanks for the clarification. I never heard of rigged in either math or physics. I've tried to understand quantum mechanics, but apparently I keep getting YouTube MIT lectures and books that make a mess out of the subject. E.g., th
576.
by graycat 4y ago
There is both Fourier series and the Fourier transform. For each, need to establish that they exist. Then will usually want to know that the inverse transform DOES approximate the original function. Details are in 4 books by W. Rudin. O
577.
by graycat 4y ago
There is both Fourier series and the Fourier transform. For each, need to establish that they exist. Then will usually want to know that the inverse transform DOES approximate the original function. Details are in 4 books by W. Rudin. O
578.
by graycat 4y ago
The set of real numbers is commonly defined and their properties established in a first course in abstract algebra. Model theory is not required. Axiomatic set theory is not even required. Hilbert space? A complete inner product space wh
579.
by graycat 4y ago
Here we see another problem, the use of random . At the level of Kolmogorov, Loeve, Breiman, Neveu, Cinlar, Karr, etc., we use random only in random variable . We define random variable carefully but never say what random by itself
580.
by graycat 4y ago
When physicists talk math concepts, e.g., probability densities, differentiability, continuity, probability, inner products, Fourier transforms, solutions to differential equations, unitary transformations, etc. they are talking math. They
581.
by graycat 4y ago
I put in a qualification: > ... the usual assumption in the physics is that the math ... Soooo, you got into the physics. I avoided getting into the physics. E.g., when Newton wrote out his second law or Maxwell wrote out his equations
582.
by graycat 4y ago
Of course, the space was not made explicit. With R the set of real numbers, the usual assumption in the physics is that the math is done in R^3 with the usual inner product, norm, metric, and topology.
583.
by graycat 4y ago
> identically zero everywhere. Not a probability density.
584.
by graycat 4y ago
Take one cubic inch. Let the probability the particle is in that cubic inch be p. Then take integer n >= 2 / p cubic inches. Then the probability that the particle is in those n cubic inches is np >= 2 > 1 greater than 1, a
585.
by graycat 4y ago
Sorry, Feynman, whatever else he did, on probability he gets a grade of flat F. Here is why: In his book Lectures on Physics he states that a particle of unknown location has a probability density uniform over all of space. No it doesn
586.
by graycat 4y ago
Yes, CO2 is a greenhouse gas. I gave the reference to its absorption spectrum. From that, it causes some warming . And that is "very basic and confirmed physics". But that alone is, for practice, meaningless. Instead, the
587.
by graycat 4y ago
Motivation? Minimization is a large and old problem. In physics, some problems can be solved by noting that energy, momentum are conserved and maybe also minimized or action is minimized. In operations research, minimization is a centra
588.
by graycat 4y ago
Yes, I saw that article. But I was surprised it didn't mention Plateau's problem, that is, with the minimization in soap bubbles, as at https://encyclopediaofmath.org/wiki/Plateau_problem or F. Almgren as in
589.
by graycat 4y ago
As I argued, as has been made clear for years, the UN and its IPCC are political and not scientific. As I mentioned, one of their main goals is to arrange big bucks transfers from rich nations to poor ones. In particular, the many predicti
590.
by graycat 4y ago
If you have some credible evidence that human sources of CO2 have caused, are causing, or will cause significant warming, then trot it out. I've been waiting for such evidence for years. By now you have a big problem: We have had in r
591.
by graycat 4y ago
> Humanity has increased the CO2 content in the atmosphere by 50%. Within 200 years, most in the last 50. Which already has caused a significant warming, which is very well documented. There is plenty of rock solid science behind this
592.
by graycat 4y ago
Yes, I salute all those who are perfect and apologize again for all my shortcomings!
593.
by graycat 4y ago
Yes, but you don't know how pretty she was, and how sweet and feminine, etc. otherwise!! Also, no one understands love, in particular, you don't. I'm not nearly the first man to stay in love for life!
594.
by graycat 4y ago
You are correct about thermometers -- we are really good at measuring temperatures. Early in my career I was at the NBS, now NIST, and our lab routinely measured temperatures to within 0.01 C. And, right, global warming needs to be evalua
595.
by graycat 4y ago
> No I am 100% correct. FMVSS requires stability control. So, we have the DOT, Department of Transportation, the NHTSA, National Highway Traffic Safety Administration, and the FMVSS, the Federal Motor Vehicle Safety Standards. Then at h
596.
by graycat 4y ago
Can we also measure warming with accurate thermometers?
597.
by graycat 4y ago
A LOT of things are vulnerable to EMPs! Sooooo, US military vehicles don't use computer controlled fuel and ignition in the engines??? Hmm ...!
598.
by graycat 4y ago
I'm all for computer controlled engine fuel and ignition, but otherwise I don't want computers in my car. I was happy with my 1987 Chevy S-10 Blazer until the oil pan rusted out due to winter road salt. Then I upgraded to a 2001
599.
by graycat 4y ago
WOW. Good grief. The article https://electronics-sourcing.com/2022/05/04/how-many-chips-a... has: "By 2020, electronics now comprise 40% of the car’s cost," WOW. Looks like a golden opportunity o
600.
by graycat 4y ago
The article has "A car from the 2020s with thousands of microchips ..." "Thousands"? Uh, I confess: That's where I stopped reading!

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