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Category Archives: math
The History of Planet Vulcan
For decades I have been fascinated by 19th century celestial mechanics. This book is about one of my favorite stories from that field.
Highlights from The Hunt for Vulcan: . . . And How Albert Einstein Destroyed a Planet, Discovered Relativity, and Deciphered the Universe, by Thomas Levenson
My First Peek at Renormalization
I have vaguely known about renormalization since the 1970’s, but had never seriously studied it. Out of curiosity I watched Renormalization and envelopes on YouTube Thursday evening. This was the final lecture of the Asymptotics and perturbation methods course by Prof. Steven Strogatz of Cornell University. I had watched the first two lectures of the course, but none of the others until this one. Fortunately, there were relatively few explicit dependencies on them, so I was able to follow this quite well. Here is the description:
Continue readingVector and Matrix Algebra Tutorial
Vector and Matrix Algebra is a short tutorial from Complexity Explorer. It is really quite elementary. I took a formal course in Linear Algebra long ago, and have reviewed the basics a couple times since then. I wanted to see if I still understand those basics. The answer is that I do: I had no trouble at all with the material.
Continue readingSignificant Figures
I found this post on Facebook: Why is it important to know so many digits of pi?.
My comment:
As someone who started computing with log tables and slide rules, the first question I ask is how many significant digits do the other variables in your calculation have? The smallest such number tells you how many digits of pi you need. With electronic devices there is no harm in using more in your calculation, as many as your device has, but do not let that give you a false idea of the precision of your result.
I learned about significant figures in my high school chemistry in 1967-68. (Thank you, Mr. Wheeler!). Use of appropriate significant figures, also from a chemistry class, clearly explains the concept and its use in practice.
I only first saw Star Trek (TOS) after high school, in reruns. Thanks to that chemistry class I gag every time I hear Mr. Spock reporting some calculation to an absurd number of decimal places. His input data could not possibly be that precise!
Calculating a limit
Today I saw this problem on Medium: Compute the limit
Followed by “Pause the article and attempt a solution now.” (Don’t cheat and look ahead)
So I did. I do not really like factorials, so I immediately thought of Stirling’s approximation:
ln n! ≃ n ln n – n as n → ∞
and all of the n‘s cancelled, leaving the result 1/e. I then looked at the author’s solution. My answer was correct, but he used a completely different approach, as you can see. I posted my solution, and got a nice complement from him.
This is Thanksgiving day in the USA. I am thankful that my calculus skills are still pretty good decades after my last formal course in that or any related field .
Statistics Hell
You hate statistics, you despise maths, you stain your pants at the mention of sphericity. Normal people love these things, but you, barrel of number-fearing sputum that you are, are terrified. Afraid for your worthless life you leapt pathetically to the internet for guidance. A freak spark of lightening hit your house sending a bolt of electricity through your computer. Sparks flew like tendrils from the screen, fusing with your face and sucking your head and body into the number vortex that is statistics hell. Your crime is evacuating your bowels at the mention of a t-test, your punishment is eternity in statistics hell. I am the gatekeeper, the evil ruler of this world of numbers. Although you might confuse me for a human full of empathy and compassion for those taking their first wobbly steps through this horrific world of equations, underneath my skin I am numbers without a soul.
Update in 2021. The author of this gem was Andy Field. Alas, he has removed this particular page from his web site https://www.discoveringstatistics.com/
From Hilbert Space to Dilbert Space, and beyond 