I’m not ready for this, but I wish I was: Post’s theorem.
Post’s theorem
Reply
Category Archives: Mathematics
“Categories for the Working Hacker” by Philip Wadler
An intro to category theory: “Categories for the Working Hacker” by Philip Wadler.
Math binge
Some fun math videos:
- How To Count Past Infinity
- The Banach–Tarski Paradox
- Numberphile v. Math: the truth about 1+2+3+…=-1/12
And some fun math articles:
The Circle
I did some creative writing, inspired by a new friend: The Circle.
3Blue1Brown
Learned about a YouTube channel that runs math videos: 3Blue1Brown. The channel is here.
More books!
I’ve got a kickass collection of old engineering books:
The Secret to Raising Smart Kids
I’m reading Proofs: A Long-Form Mathematics Textbook and it referred me to this article: The Secret to Raising Smart Kids. It’s an interesting read.
The book has a website, over here: https://longformmath.com/
Orders of magnitude
I wanted to get some intuition for what made a bigger difference: adding an extra item to a set, or having an extra order of magnitude of items in a set. So I created this spreadsheet and discovered that an extra order of magnitude smashes an extra item in the set.
In the spreadsheet the parameters are ‘x’, which is the size of the base set (called Set A), and ‘i’, which is the number of extra items to add into the second set (called Set B).
If you make x = 10 and i = 90 you break even, Set A and Set B grow at the same rate.
If you make x = 10 and i = 1 it’s no contest, Set A gets much bigger much faster.
Period and Frequency
I made a thing.
Oh, wait. I made it better.
These charts show how period, frequency, and the speed of light are related to each other, in scientific and compact units.
Period is measured in seconds, frequency is measures in Hertz (cycles per second), and the distance of light travelled during one period is measured in meters (it is also known as the wavelength). The equation for wavelength is:
λ = c / ν
Where λ is the wavelength in meters, c is the speed of light in meters per second, and ν is the frequency of the wave in Hertz (cycles per second).
Wavelengths between 400 nanometers (nm) for violet light to 700 nm for red light are the visible component of the electromagnetic spectrum. The frequency of red light, on the low end of the visible spectrum, is about 430 terahertz (THz); whereas violet light, on the high end of the visible spectrum, is around 750 THz.
Sets
Stolen from here.
LaTeX like this:
\begin{table}[H]
\caption{Number Sets}
\label{tab:email}
\begin{tabular}{cl}
\midrule
$\mathbb{N}$ & Natural Integers \\
$\mathbb{Z}$ & Relative Integers \\
$\mathbb{D}$ & Decimal Numbers \\
$\mathbb{Q}$ & Rational Numbers \\
$\mathbb{R}$ & Real Numbers \\
$\mathbb{I}$ & Pure Imaginary Numbers \\
$\mathbb{C}$ & Complex Numbers \\
\midrule
\end{tabular}
\end{table}
$\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}$