Post II: Tangents

Tangent I: Reflections on My Last Post

I was reflecting on the cool and original reference to Dr. Strangelove Or: How I Learned to Stop Worrying and Love the Bomb in my last title when I realized a coincidence that might have actually made it seem clever. When I was five years old I was big into Club Penguin, a sort of visual chat room for kids with mini-games, and, being the coolest kid, my main account name was Dr. Math.

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Proof

So henceforth I shall consider the previous title to be: Dr. Math Or: How I Learned to Stop Worrying and Love Math. It works better, but is still disappointing.

This shines light on my interest in math since a young age, though I sort of lost interest a few years later, and didn’t come back to it until recently.

I would also like to point out that my ramblings about how people often don’t see that math is more than just arithmetic is not some unique thought of my own. I’m sure every mathematician knows this same truth.

Tangent II: Numbers

You can see that I am using roman numerals to index the tangents and it’s because I am tired of these:

0123456789

Please get new ones. And while you’re at it change these too:

abcdefghijklmnopqrstuvwxyz

And on that same note I would like to bring up bases. You may be familiar with the everyday base ten system, the digits of which are written above, but something a lot of people don’t realize is how arbitrary it is. Besides the fact that we have ten fingers and it’s just what we’ve always used, there’s really no basis for why we use them. And indeed the metric measuring system is based on base ten and therefor arbitrary as well. So for those not in the know I would like to bring to your attention the base 12 system, otherwise known as duodecimal or dozenal. Not only does it have two pretty new digits:

7c81137e75
source

12 is also one of the early superior highly composite numbers, which means it has more divisors and is better for representing common fractions e.g. ⅓ in decimal is 0.333333… but in dozenal it’s 0;4. Also to count on your fingers in dozenal simply count the pads of your fingers with your thumbs.

I have joined The Dozenal Society and so should everyone. Though base 12 is interesting and slightly better than base 10, still, the farther along you go in the sequence of highly composite numbers the better. The Babylonians used a base 60 system, which is still seen in our units of time. But then there’s still the problem of having more and more symbols to keep track of, so no matter what base we choose it’s still arbitrary. I dream of one day having a perfect representation of numbers.

Tangent III: Khan Academy

Whether you love or hate Sal Khan’s voice and explanations I still think it’s a great resource for self teaching. However, whenever I see this big grid:

 

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The gaps are from new exercises they added since I last did it 😥

I get the urge to fill it up. So of course I start at the bottom: with elementary school math and filling all those up without ever learning anything new…

Tangent IV: Progress

I haven’t made any particular dents in the great barrier to mathematical knowledge since last time, mostly due to school robbing me of any ambition I have left, though I am still going slow and steady. I started Professor Leonard’s Calculus II course, and I spend a lot of my free time watching math related YouTube videos and random math lessons. I forget to save most of these but here are some [‘()’s are links to source]:

  • A really good linear algebra lesson ()
  • A short blog post that combines math with my interest in all things language: mathematical typesetting, particularly LaTeX. A bit of which I used in my last blog post ()
  • A nice Calculus summary ()
  • And a quite silly mathematical overview video, which has some very profound points, and also “The Map of Mathematistan” ()
  • I started reading the Introduction to Mathematical Philosophy by Bertrand Russel, one of the greatest logicians of the 20th century. It is the “abridged” companion book to The Principia Mathematica, an incredibly famous book that influenced great work such as Gödel’s Incompleteness Theorem and ZFC, and famously took hundreds of pages to prove that 1+1=2. This one talks about the meaning of numbers and the most “simple (using ‘simple’ in a logical sense) (2).”

If… there be mathematicians to whom these definitions and discussions seem to be an elaboration and complication of the simple, it may be well to remind them from the side of philosophy that here, as elsewhere, apparent simplicity may conceal a complexity which it is the business of somebody, whether philosopher or mathematician, or, like the author of this volume, both in one, to unravel (vi).

parts of mathematics ()

Tangent V: The Struggle

I also began the book Concrete Mathematics, a rather serious math textbook by some of the best computer scientists of the late 20th century.  Though I could generally grasp the concepts, I struggled immensely with some simple demonstrations of the inductive step. I’m not sure what my experience with induction will look like with some real math, though I know it is probably a weak area that I will want to improve.

This leads me to my final point. Though I’m pretty good at being a computer and understanding mathematical concepts that are already discovered. I’m not so confident in my ability to do real mathematics: making discoveries. Indeed, mathematics is so vast knowing all of it that is known in one lifetime is, to my despair, simply out of reach. The best mathematicians are those who likely don’t know all that much outside of their field (unless you’re Terry Tao). I don’t think I’ll ever make any significant advancements in mathematics in my lifetime, but I don’t care, my goal is simply to know and love mathematics as much as I can.

 

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