Duality

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Duality last won the day on October 8 2017

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About Duality

  • Rank
    Butterfly
  • Birthday

My Little Pony: Friendship is Magic

  • Best Pony
    Chancellor Neighsay
  • Best Pony Race
    Pegasus

Profile Information

  • Gender
    Male
  • Location
    On average, about 149,608,900km from the centre of the sun.
  • Personal Motto
    "I prefer to make up my own quotes and attribute them to very smart people, so that I can use them to win arguments" ~ Albert Einstein
  • Interests
    - Engineering (particularly civil, structural, and water management),
    - Physics,
    - Mathematics,
    - Formal logic,
    - Adorable things (especially ponies, cats, bunnies, and grey ducks),
    - Collecting/accumulating various aesthetically pleasing oddments,
    - Collecting/accumulating various interesting antique miscellanies,
    - Collecting/accumulating various second-hand dictionaries/thesauri,
    - Collecting/accumulating various nifty and often archaic vocabillularary words,
    - Finding and categorising various forms of genetically mutated daisies,
    - Making things up on the spot (intellectual ad-libbing is my forte),
    - Owl City, Pentatonix, & chipper chiptune music,
    - Reading Sir Terry Pratchett & Brandon Sanderson novels,
    - Reading C.S. Lewis' classic theology books,
    - Lego (great for modelling simple engineering problems),
    - Minecraft,
    - 8-bit games,
    - Irony,
    - Being interesting.

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Single Status Update

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  1. teach me to not be scared of the very big numbers and the funny symbols and the very small numbers and the Greek letters

    1. Duality

      Duality

      Numbers and symbols aren't any scarier than people define them to be. I have several fabulous fear-eliminators that might work for you. :mlp_proud:

       

      For very big and very small numbers, the Riemann sphere works wonders to free you from terror once you've grasped how it works:

      Image result for riemann sphere

      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. :mlp_yeehaa:

       

      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. :-D

       

      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. :ticking:

       

      Is this satisfactory teaching for the smartfrosty?

    2. Frostgage

      Frostgage

      oh wow you put so much effort into my trash post ;-; <3

    3. Duality

      Duality

      it can't have been a trash post if it put a happy smile that big on my face <3