-
Posts
289 -
Joined
-
Last visited
Duality's Achievements
Reformed Changeling (13/23)
10.7k
Brohooves Received
Single Status Update
-
teach me to not be scared of the very big numbers and the funny symbols and the very small numbers and the Greek letters
-
Numbers and symbols aren't any scarier than people define them to be. I have several fabulous fear-eliminators that might work for you.
For very big and very small numbers, the Riemann sphere works wonders to free you from terror once you've grasped how it works:
This is a model of the complex plane (the combination of a real axis and an imaginary axis, where i is the imaginary unit is the square root of negative one).
While this plane is normally represented as a flat surface, adding a single point at infinity allows for it to be curled up into a sphere. In this model of the complex plane, infinity is considered 'close to very large numbers' in the exact same sense that zero is 'close to very small numbers', and, by the same token, completely signless, so 'positive' infinity equals 'negative' infinity in the same sense that 'negative' zero equals 'positive' zero.
Another thing that makes this a very elegant model is that the 1, -1, i, -i line may be set precisely at the equator of the sphere. This is the case because there are exactly as many numbers between 0 and 1 as there are between 1 and infinity. There are an infinity of numbers between 0 and 1 and there are an infinity of numbers between 1 and infinity, and those two infinities are strictly equal to one another (there are infinities that aren't equal to each other, but that's a matter I don't know how to make less scary).
In summary, all the very big numbers and all the very small numbers can fit onto a simple hollow sphere that fits in your palm - much less scary.
Now, as for Greek letters, there's a great shirt you can buy here that has every single Greek letter on it plus an integrated label for each letter detailing all the mathematical and physical quantities they're commonly used to signify. Far less terror-inducing when you can wear them on a nifty T-shirt.
Finally, 'funny symbols'. The thing to remember about funny symbols is that some brainy boffin decades ago formally and officially chose to condense all the intricate and detailed meaning of a ludicrously involved mathematical concept into a weird squiggly line. They drew the weird squiggly line, matched it up with a bunch of other boffins' weird squiggly lines, and declared their pet collections of weird squiggly lines to be 'advancements in mathematics'.
All mathematicians are basically Pokemon trainers but with weird squiggly lines instead of magic animals.
Is this satisfactory teaching for the smartfrosty?
-