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To be fair, if math did have version numbers, we could abandon a lot of hideous notational cruft / symbol overloading, and use tau instead of pi. Math notation

To be fair, if math did have version numbers, we could abandon a lot of hideous notational cruft / symbol overloading, and use tau instead of pi. Math notation is arguably considerably worse than perl -- can you imagine if perl practically required a convention of single-letter variable names everywhere? What modern language designer would make it so placing two variable names right next to each other denotes multiplication? Sheer insanity. Consider how vastly more accessible programming has become from 1950 until the present. Imagine if math had undergone a similar transition.

hansvm 1y ago
If the compiler forbade syntactic ambiguity from implicit multiplication and had a sensible LSP allowing it to be rendered nicely, I don't think that'd be such a bad thing. Depending on the task at hand you might prefer composition or some other operation, but when reducing character count allows the pattern recognition part of our brain to see the actual structure at hand instead of wading through character soup it makes understanding code much easier.
- 0xDEAFBEAD 1y ago
  Yep, this explains why the APL programming language was so ridiculously successful.
tyg13 1y ago
What in the Hacker News in this comment? Mathematical notation evolved to its modern state over centuries. It's optimized heavily for its purpose. Version numbers? You're being facetious, right?
- 0xDEAFBEAD 1y ago
  >evolved Yes, it evolved. It wasn't designed. >Version numbers? Without version numbers, it has to be backwards-compatible, making it difficult to remove cruft. What would programming be like if all the code you wrote needed to work as IBM mainframe assembly? Tau is a good case study. Everyone seems to agree tau is better than pi. How much adoption has it seen? Is this what "heavy optimization" looks like? It took hundreds of years for Arabic numerals to replace Roman numerals in Europe. A medieval mathematician could have truthfully said: "We've been using Roman numerals for hundreds of years; they work fine." That would've been stockholm syndrome. I get the same sense from your comment. Take a deep breath and watch this video: https://www.youtube.com/watch?v=KgzQuE1pR1w https://www.youtube.com/watch?v=KgzQuE1pR1w >You're being facetious, right? I'm being provocative. Not facetious. "Strong opinions, weakly held."
  - Someone 1y ago
    > Without version numbers, it has to be backwards-compatible If there’s one thing that mathematical notation is NOT, it’s backwards compatible. Fields happily reuse symbols from other fields with slightly or even completely different meanings. https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbo... has lots of examples, for example ÷ (division sign) Widely used for denoting division in Anglophone countries, it is no longer in common use in mathematics and its use is "not recommended". In some countries, it can indicate subtraction. ~ (tilde) 1. Between two numbers, either it is used instead of ≈ to mean "approximatively equal", or it means "has the same order of magnitude as". 2. Denotes the asymptotic equivalence of two functions or sequences. 3. Often used for denoting other types of similarity, for example, matrix similarity or similarity of geometric shapes. 4. Standard notation for an equivalence relation. 5. In probability and statistics, may specify the probability distribution of a random variable. For example, X∼N(0,1) means that the distribution of the random variable X is standard normal. 6. Notation for proportionality. See also ∝ for a less ambiguous symbol. Individual mathematicians even are known to have broken backwards compatibility. https://en.wikipedia.org/wiki/History_of_mathematical_notation#Euler_and_prime_notations https://en.wikipedia.org/wiki/History_of_mathematical_notati... * Euler used i to represent the square root of negative one (√-1) although he earlier used it as an infinite number* Even simple definitions have changed over time, for example: - how numbers are written - is zero a number? - is one a number? - is one a prime number?
    - 9rx 1y ago
      > Fields happily reuse symbols from other fields with slightly or even completely different meanings. Symbol reuse doesn't imply a break in backwards compatibility. As you suggest with "other fields", context allows determining how the symbols are used. It is quite common in all types of languages to reuse symbols for different purposes, relying on context to identify what purpose is in force. Backwards incompatibility tells that something from the past can no longer be used with modern methods. Mathematical notation from long ago doesn't much look like what we're familiar with today, but we can still make use of it. It wasn't rendered inoperable by modern notation.
deleted 1y ago
[deleted]
vovavili 1y ago
Math personally "clicked" to me when I started to use Python and R for mathematical operations instead of the conventional arcane notation. I did make me wonder why we insist on forcing kids and young adults to struggle through particularly counter-intuitive ways to express mathematical concepts just because of historical baggage, and I am glad to hear now that I am not the only one who thinks this way.

hansvm 1y ago

If the compiler forbade syntactic ambiguity from implicit multiplication and had a sensible LSP allowing it to be rendered nicely, I don't think that'd be such a bad thing. Depending on the task at hand you might prefer composition or some other operation, but when reducing character count allows the pattern recognition part of our brain to see the actual structure at hand instead of wading through character soup it makes understanding code much easier.

0xDEAFBEAD 1y ago
Yep, this explains why the APL programming language was so ridiculously successful.

tyg13 1y ago

What in the Hacker News in this comment? Mathematical notation evolved to its modern state over centuries. It's optimized heavily for its purpose. Version numbers? You're being facetious, right?

0xDEAFBEAD 1y ago
>evolved Yes, it evolved. It wasn't designed. >Version numbers? Without version numbers, it has to be backwards-compatible, making it difficult to remove cruft. What would programming be like if all the code you wrote needed to work as IBM mainframe assembly? Tau is a good case study. Everyone seems to agree tau is better than pi. How much adoption has it seen? Is this what "heavy optimization" looks like? It took hundreds of years for Arabic numerals to replace Roman numerals in Europe. A medieval mathematician could have truthfully said: "We've been using Roman numerals for hundreds of years; they work fine." That would've been stockholm syndrome. I get the same sense from your comment. Take a deep breath and watch this video: https://www.youtube.com/watch?v=KgzQuE1pR1w https://www.youtube.com/watch?v=KgzQuE1pR1w >You're being facetious, right? I'm being provocative. Not facetious. "Strong opinions, weakly held."
- Someone 1y ago
  > Without version numbers, it has to be backwards-compatible If there’s one thing that mathematical notation is NOT, it’s backwards compatible. Fields happily reuse symbols from other fields with slightly or even completely different meanings. https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbo... has lots of examples, for example ÷ (division sign) Widely used for denoting division in Anglophone countries, it is no longer in common use in mathematics and its use is "not recommended". In some countries, it can indicate subtraction. ~ (tilde) 1. Between two numbers, either it is used instead of ≈ to mean "approximatively equal", or it means "has the same order of magnitude as". 2. Denotes the asymptotic equivalence of two functions or sequences. 3. Often used for denoting other types of similarity, for example, matrix similarity or similarity of geometric shapes. 4. Standard notation for an equivalence relation. 5. In probability and statistics, may specify the probability distribution of a random variable. For example, X∼N(0,1) means that the distribution of the random variable X is standard normal. 6. Notation for proportionality. See also ∝ for a less ambiguous symbol. Individual mathematicians even are known to have broken backwards compatibility. https://en.wikipedia.org/wiki/History_of_mathematical_notation#Euler_and_prime_notations https://en.wikipedia.org/wiki/History_of_mathematical_notati... * Euler used i to represent the square root of negative one (√-1) although he earlier used it as an infinite number* Even simple definitions have changed over time, for example: - how numbers are written - is zero a number? - is one a number? - is one a prime number?
  - 9rx 1y ago
    > Fields happily reuse symbols from other fields with slightly or even completely different meanings. Symbol reuse doesn't imply a break in backwards compatibility. As you suggest with "other fields", context allows determining how the symbols are used. It is quite common in all types of languages to reuse symbols for different purposes, relying on context to identify what purpose is in force. Backwards incompatibility tells that something from the past can no longer be used with modern methods. Mathematical notation from long ago doesn't much look like what we're familiar with today, but we can still make use of it. It wasn't rendered inoperable by modern notation.

deleted 1y ago

[deleted]

vovavili 1y ago

Math personally "clicked" to me when I started to use Python and R for mathematical operations instead of the conventional arcane notation. I did make me wonder why we insist on forcing kids and young adults to struggle through particularly counter-intuitive ways to express mathematical concepts just because of historical baggage, and I am glad to hear now that I am not the only one who thinks this way.