3 ms·

I have no idea why, but I love alternate number systems (p-adics, surreals, base -2, split-complex, etc.). This one is playful. Anyone know where to find a rig

by sblom 5y ago

I have no idea why, but I love alternate number systems (p-adics, surreals, base -2, split-complex, etc.). This one is playful. Anyone know where to find a rigorous maths treatment for it?

oh_sigh 5y ago
Uh...isn't this just binary?
- whatshisface 5y ago
  It's binary in "fully reduced" form, what's interesting are the graphical rules for addition, multiplication and reduction. (They correspond to things you can do with the expanded algebraic representation of a base-2 number, Sum a_k 2^k, but that's a necessary prerequisite for such a number system to work. After all, a way of writing numbers that did not ultimately correspond to the existing ways of writing numbers would be wrong.)
- progre 5y ago
  For addition I can see the binary addition at work. The ding "carries" if it get put in a ring that already has a ding by getting its own ring etc... For multiplication I just WAT
  - whatshisface 5y ago
    Take a couple expanded algebraic representations of base-2 numbers: 1×2 + 1×4 + 0×8 + 1×16, 1×8 and substitute the second for every 1 in the first, 8×2 + 8×4 + 0×8 + 8×16 then finally un-distribute, (1×8)(1×2 + 1×4 + 0×8 + 1×16) and that's why putting small copies of the second number in the place of every "ding" in the first number results in multiplication.
    - progre 5y ago
      Oh yeah, thanks!
- tromp 5y ago
  It's binary with the central dot/ding being the leading 1 and then toward the right a ring is 0 a ring,ding is 1 The ring represents a doubling of its contents. The special case for the leading bit could be avoided by always having an innermost empty ring. That would also give you a better (i.e. visible) representation for 0. The addition rule ensures that you always have exactly 1 leading 0.
  - whatshisface 5y ago
    It's not binary because all of the intermediate results shown during the videos are also valid numbers. It's actually an (upside down so as not to spoil it for anyone) ˙ǝuo ɟo uoıʇıppɐ ʇuǝsǝɹdǝɹ sʇop ǝɥʇ puɐ 'oʍʇ ʎq pǝıןdıʇןnɯ sʇuǝʇuoɔ ǝɥʇ ɥʇıʍ sısǝɥʇuǝɹɐd ʇuǝsǝɹdǝɹ sǝןɔɹıɔ ǝɹǝɥʍ uoıssǝɹdxǝ ɔıʇǝɯɥʇıɹ∀
    - taejo 5y ago
      From the article: > The rings must be nested. The innermost ring must have a ding. No region can have more than one ding. Those are the only rules. According to these rules the intermediate results are not valid numbers
JoeyBananas 5y ago
I don't think there's anything resembling a unifying theory of alternative number systems. But it's a fun topic for sure.

by sblom 5y ago

I have no idea why, but I love alternate number systems (p-adics, surreals, base -2, split-complex, etc.). This one is playful. Anyone know where to find a rigorous maths treatment for it?

oh_sigh 5y ago

Uh...isn't this just binary?

whatshisface 5y ago
It's binary in "fully reduced" form, what's interesting are the graphical rules for addition, multiplication and reduction. (They correspond to things you can do with the expanded algebraic representation of a base-2 number, Sum a_k 2^k, but that's a necessary prerequisite for such a number system to work. After all, a way of writing numbers that did not ultimately correspond to the existing ways of writing numbers would be wrong.)
progre 5y ago
For addition I can see the binary addition at work. The ding "carries" if it get put in a ring that already has a ding by getting its own ring etc... For multiplication I just WAT
- whatshisface 5y ago
  Take a couple expanded algebraic representations of base-2 numbers: 1×2 + 1×4 + 0×8 + 1×16, 1×8 and substitute the second for every 1 in the first, 8×2 + 8×4 + 0×8 + 8×16 then finally un-distribute, (1×8)(1×2 + 1×4 + 0×8 + 1×16) and that's why putting small copies of the second number in the place of every "ding" in the first number results in multiplication.
  - progre 5y ago
    Oh yeah, thanks!
tromp 5y ago
It's binary with the central dot/ding being the leading 1 and then toward the right a ring is 0 a ring,ding is 1 The ring represents a doubling of its contents. The special case for the leading bit could be avoided by always having an innermost empty ring. That would also give you a better (i.e. visible) representation for 0. The addition rule ensures that you always have exactly 1 leading 0.
- whatshisface 5y ago
  It's not binary because all of the intermediate results shown during the videos are also valid numbers. It's actually an (upside down so as not to spoil it for anyone) ˙ǝuo ɟo uoıʇıppɐ ʇuǝsǝɹdǝɹ sʇop ǝɥʇ puɐ 'oʍʇ ʎq pǝıןdıʇןnɯ sʇuǝʇuoɔ ǝɥʇ ɥʇıʍ sısǝɥʇuǝɹɐd ʇuǝsǝɹdǝɹ sǝןɔɹıɔ ǝɹǝɥʍ uoıssǝɹdxǝ ɔıʇǝɯɥʇıɹ∀
  - taejo 5y ago
    From the article: > The rings must be nested. The innermost ring must have a ding. No region can have more than one ding. Those are the only rules. According to these rules the intermediate results are not valid numbers

JoeyBananas 5y ago

I don't think there's anything resembling a unifying theory of alternative number systems. But it's a fun topic for sure.