4 ms·

Do you think mathematical innovation is dominantly enabled by clever design?

dhosek 4y ago
Oh most definitely. Our conventional algebraic notation is only a few hundred years old. Things that we have children do in math class now were the domain of professionals 500 years ago. Imagine doing basic algebra without our familiar single-letter variables and the notation for addition, subtraction, multiplication and division you learned in grade school. Leibniz's notation opened up Calculus in ways that Newton's geometric analysis did not (which is why high school students are writing ∫x²dx and not doing a geometric analysis of that expression). This is also why programmers are looking for the bright shiny language that will let them express what they really mean in their code without ambiguity. I think that we might still be looking for the algebraic notation or Leibniz notation for programming that will make everything completely obvious and will make future generations look back at our C, Python, Rust, et al and marvel that we were able to do anything.
- platers 4y ago
  I wonder if mathematics would have been pioneered in Asia if they had arabic numerals instead of abacuses.
  - kevin_thibedeau 4y ago
    They had rod numerals.
- User23 4y ago
  Let’s not forget Robert Recorde’s[1] sign for equality, a pair of parallel horizontal line segments. He revolutionized notation. It’s hard to overstate the importance of the equation. [1] https://en.m.wikipedia.org/wiki/Robert_Recorde https://en.m.wikipedia.org/wiki/Robert_Recorde
  - mjd 4y ago
    https://blog.plover.com/math/recorde.html https://blog.plover.com/math/recorde.html
    - jciochon 4y ago
      Really cool post, thanks for sharing!
- galaxyLogic 4y ago
  APL? That's a very math-like notation if I recall.
  - Someone 4y ago
    Very math-like, yes, but most programming isn’t really math or rather, the requirements for the program aren’t, and that’s what you want to stay close to in the code.
    - TruffleLabs 4y ago
      APL was not originally a programming language (pardon the pun) but as a notation for array mathematics. https://en.wikipedia.org/wiki/APL_(programming_language) https://en.wikipedia.org/wiki/APL_(programming_language) "A mathematical notation for manipulating arrays was developed by Kenneth E. Iverson, starting in 1957 at Harvard University. In 1960, he began work for IBM where he developed this notation with Adin Falkoff and published it in his book A Programming Language in 1962." It didn't become an actual (usable) programming language until 1963.
- tekknolagi 4y ago
  I was reading a thread this morning that categorized programming languages into "lisps" and "fortrans" based on how much you were directing an abstract machine vs a real hardware machine and I think this is a similar idea
  - regularfry 4y ago
    I wonder where forths sit on that spectrum.
  - easrng 4y ago
    The thread: https://transmom.love/@elilla/108157666333644028 https://transmom.love/@elilla/108157666333644028
- breck 4y ago
  > I think that we might still be looking for the algebraic notation or Leibniz notation for programming that will make everything completely obvious and will make future generations look back at our C, Python, Rust, et al and marvel that we were able to do anything. I used to think this too, and spent years looking for that notation, but now I think I was wrong. I think any gains now from notational inventions will be dwarfed by further gains from scaling up neural nets. I think we've 'been living in Symbolia but now are in the age of Weightville.
mathematicaster 4y ago
In my opinion, "dominant" is too strong of a characterization.

Oh most definitely. Our conventional algebraic notation is only a few hundred years old. Things that we have children do in math class now were the domain of professionals 500 years ago. Imagine doing basic algebra without our familiar single-letter variables and the notation for addition, subtraction, multiplication and division you learned in grade school. Leibniz's notation opened up Calculus in ways that Newton's geometric analysis did not (which is why high school students are writing ∫x²dx and not doing a geometric analysis of that expression). This is also why programmers are looking for the bright shiny language that will let them express what they really mean in their code without ambiguity. I think that we might still be looking for the algebraic notation or Leibniz notation for programming that will make everything completely obvious and will make future generations look back at our C, Python, Rust, et al and marvel that we were able to do anything.

platers 4y ago
I wonder if mathematics would have been pioneered in Asia if they had arabic numerals instead of abacuses.
- kevin_thibedeau 4y ago
  They had rod numerals.
User23 4y ago
Let’s not forget Robert Recorde’s[1] sign for equality, a pair of parallel horizontal line segments. He revolutionized notation. It’s hard to overstate the importance of the equation. [1] https://en.m.wikipedia.org/wiki/Robert_Recorde https://en.m.wikipedia.org/wiki/Robert_Recorde
- mjd 4y ago
  https://blog.plover.com/math/recorde.html https://blog.plover.com/math/recorde.html
  - jciochon 4y ago
    Really cool post, thanks for sharing!
galaxyLogic 4y ago
APL? That's a very math-like notation if I recall.
- Someone 4y ago
  Very math-like, yes, but most programming isn’t really math or rather, the requirements for the program aren’t, and that’s what you want to stay close to in the code.
  - TruffleLabs 4y ago
    APL was not originally a programming language (pardon the pun) but as a notation for array mathematics. https://en.wikipedia.org/wiki/APL_(programming_language) https://en.wikipedia.org/wiki/APL_(programming_language) "A mathematical notation for manipulating arrays was developed by Kenneth E. Iverson, starting in 1957 at Harvard University. In 1960, he began work for IBM where he developed this notation with Adin Falkoff and published it in his book A Programming Language in 1962." It didn't become an actual (usable) programming language until 1963.
tekknolagi 4y ago
I was reading a thread this morning that categorized programming languages into "lisps" and "fortrans" based on how much you were directing an abstract machine vs a real hardware machine and I think this is a similar idea
- regularfry 4y ago
  I wonder where forths sit on that spectrum.
- easrng 4y ago
  The thread: https://transmom.love/@elilla/108157666333644028 https://transmom.love/@elilla/108157666333644028
breck 4y ago
> I think that we might still be looking for the algebraic notation or Leibniz notation for programming that will make everything completely obvious and will make future generations look back at our C, Python, Rust, et al and marvel that we were able to do anything. I used to think this too, and spent years looking for that notation, but now I think I was wrong. I think any gains now from notational inventions will be dwarfed by further gains from scaling up neural nets. I think we've 'been living in Symbolia but now are in the age of Weightville.

mathematicaster 4y ago

In my opinion, "dominant" is too strong of a characterization.