Ask HN: Why doesn't math look like a programming language?

miauw62 · 148 points · Posted at 12:13:20 on May 20, 2022 · (Permalink)

The only thing stopping math from being more accessible is that it is literally impossible for normal people to understand what ∑ means. Thats the only thing.

[deleted] · 83 points · Posted at 12:33:48 on May 20, 2022 · (Permalink)

It's short for ∑nd your career

RepresentativeNo6029 · 47 points · Posted at 14:18:57 on May 20, 2022 · (Permalink)

Only if you’re poor. Rich kids get another math without such shit and look where it takes them

/uj math does tend to introduce more single letter variables and suffix/prefixes than needed. They have no scoping so everything has to be a unique global variable. Very quickly it becomes unreadable.

irqlnotdispatchlevel · 114 points · Posted at 15:49:06 on May 20, 2022 · (Permalink)

It also does not have:

Zero-cost abstractions
Move semantics
Guaranteed memory safety
Threads without data races
Trait-based generics
Pattern matching
Type inference
Minimal runtime
Efficient C bindings

RepresentativeNo6029 · 17 points · Posted at 15:52:45 on May 20, 2022 · (Permalink)

Cost? It’s const you immoral ghoul

FluxFlu · 4 points · Posted at 21:22:13 on May 21, 2022 · (Permalink)

Math 100% has type inference. Well, like 78% at least.

elmusfire · 5 points · Posted at 05:39:23 on May 21, 2022 · (Permalink)

Mathematics totally has zero-cost abstractions.

irqlnotdispatchlevel · 12 points · Posted at 06:13:40 on May 21, 2022 · (Permalink)*

It costed my a lot of bad grades, so no, it doesn't.

[deleted] · 28 points · Posted at 17:40:58 on May 20, 2022 · (Permalink)

lol no royal road to math

/uj Look, just yesterday I wrote this comment in a student's test:

“In a double integral, the outer limits of integration cannot depend on the inner variable of integration. Just like when, given two nested loops, the outer loop's range cannot be defined using the inner loop's index.”

(Yes, he is a software engineering student.) What's this if not a variable scope issue?

RepresentativeNo6029 · 12 points · Posted at 17:49:38 on May 20, 2022 · (Permalink)

/uj it most certainly is. Maybe integrals need to be indented like python ;)

Honestly I’ve had multi dimensional integrals before and keeping track of the boundaries of the thing you are integrating is kinda non trivial. You kinda have to repeatedly shout at yourself mentally to not forget it

n3f4s · 1 points · Posted at 09:40:36 on May 21, 2022 · (Permalink)

Significant whitespace in math seem horrible to write by hand

fp_weenie · 24 points · Posted at 14:56:48 on May 20, 2022 · (Permalink)

They have no scoping so everything has to be a unique global variable. Very quickly it becomes unreadable.

ok wagie

doomvox · 6 points · Posted at 15:28:32 on May 20, 2022 · (Permalink)

But it fits better on a blackboard, which is the name of my new language.

lambda-male · 111 points · Posted at 12:34:38 on May 20, 2022 · (Permalink)

This but unir-

Why do we still use symbols like ∑ instead of just writing it inline like sum()

uhh not like this

duckbill_principate · 52 points · Posted at 20:46:44 on May 20, 2022 · (Permalink)*

yeah, really should be InternalFrameInternalMathFrameBeanContextServiceProviderFunctorsClassMethodWrapper.DiscreteSum

rafgro · 65 points · Posted at 13:49:54 on May 20, 2022 · (Permalink)

Why doesn't human language look like a programming language? I want to speak in monads and generics

fp_weenie · 35 points · Posted at 14:57:22 on May 20, 2022 · (Permalink)

generics

careful, if mathematicians could sort an array they might become unpragmatic immediately

doomvox · 18 points · Posted at 15:31:28 on May 20, 2022 · (Permalink)

Why doesn't human language look like a programming language?

That's an excellent question. We all know that the mathematical elegance embedded in languages such as lisp map perfectly to human consciousness-- just ask any language designer in the CS department.

chayleaf · 3 points · Posted at 15:01:29 on May 20, 2022 · (Permalink)

there's plenty of generics, that is, suffixes/prefixes that you can attach to many different words... although it's debatable as to whether it's parametric or just value polymorphism

materialdesigner · 3 points · Posted at 22:06:51 on May 20, 2022 · (Permalink)

Well if you think about verb moods and tenses moods are monads with a custom composition operator across tenses.

NiceTerm · 2 points · Posted at 23:46:04 on May 20, 2022 · (Permalink)

Apply.Always $ Comparisons.currentTenseEquals Meaning Obvious

NiceTerm · 59 points · Posted at 12:05:43 on May 20, 2022 · (Permalink)

I ask this question, but in reverse.

grapesmoker · 11 points · Posted at 12:23:53 on May 20, 2022 · (Permalink)

mathematica tho

Althorion · 17 points · Posted at 14:29:06 on May 20, 2022 · (Permalink)

Or APL.

BufferUnderpants · 41 points · Posted at 17:31:06 on May 20, 2022 · (Permalink)*

Gatekeeping, plain and simple.

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RepresentativeNo6029 · 13 points · Posted at 17:54:09 on May 20, 2022 · (Permalink)

Do you also cater to code artisans?

BufferUnderpants · 11 points · Posted at 17:58:06 on May 20, 2022 · (Permalink)

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kuzux · 7 points · Posted at 20:19:17 on May 20, 2022 · (Permalink)

Wouldn't it be better to end math and democratize gatekeeping?

BufferUnderpants · 6 points · Posted at 20:28:51 on May 20, 2022 · (Permalink)

We'll pivot to that ~~once we pull the rug on the crypto "project"~~ should this project not prosper, as to share our learnings with the community.

doomvox · 5 points · Posted at 18:36:10 on May 20, 2022 · (Permalink)

How long will it take me to become a clear?

BufferUnderpants · 5 points · Posted at 19:27:12 on May 20, 2022 · (Permalink)*

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sohang-3112 · 28 points · Posted at 12:55:07 on May 20, 2022 · (Permalink)

You can do this in reverse - make programming more like math notation by using APL.

doomvox · 3 points · Posted at 15:29:26 on May 20, 2022 · (Permalink)

Don't you mean prolog?

sohang-3112 · 8 points · Posted at 15:54:38 on May 20, 2022 · (Permalink)

No, I mentioned APL because like maths, is very concise. Also, its creator, Ken Iverson, originally created it as a better math notation.

doomvox · 7 points · Posted at 17:17:08 on May 20, 2022 · (Permalink)

But if you want to make it more like math, and not just cargo cult the notation, you need to build it around Assertions of Truth, and get away from that assignment operator stuff.

fp_weenie · 16 points · Posted at 14:55:13 on May 20, 2022 · (Permalink)

If only Alexander Groethendieck had been as pragmatic as Rob Pike. Then his work might have had influence.

RepresentativeNo6029 · 11 points · Posted at 15:04:23 on May 20, 2022 · (Permalink)

Inspired by Pike’s merger of the for and while loops, Mathematics is happy to announce the merger of Cantor’s two infinities.

No one shall banish us from the paradise Pike has built us

doomvox · 8 points · Posted at 18:32:55 on May 20, 2022 · (Permalink)*

By the way:

https://docs.raku.org/language/optut

 sub prefix:<Σ>( *@number-list ) {
     [+] @number-list
 }

 say Σ (13, 16, 1); # OUTPUT: 30

Real programming languages let you go just as far up the sigmoid curve as you want.

Goheeca · 3 points · Posted at 16:16:10 on May 21, 2022 · (Permalink)

package Sigma;

use Filter::Util::Call;

sub import {
  my $type = @_;
  my $not_preambled = 1;
  my $not_appendixed = 1;
  filter_add(
    sub {
      my $status;
      if ($not_preambled) {
        $_ = q[use List::Util qw(sum); use feature qw(say);];
        $not_preambled = 0;
        $status = 1;
      } elsif (($status = filter_read()) > 0) {
        s/Σ/sum/g;
      } elsif ($status == 0 && $not_appendixed) {
        $_ = q[say q(Fuck Perl 6; All my homies hate Perl 6.);];
        $status = 1;
        $not_appendixed = 0;
      }
      $status;
    }
  );
}

1;

Usage:

use FindBin;
use lib $FindBin::Bin;
use Sigma;

say Σ (13, 16, 1);

zamlz-o_O · 7 points · Posted at 21:07:19 on May 20, 2022 · (Permalink)*

I once created a human language that was more mathematical in nature. We were able to describe numerous concepts in very few syllables. The throughput of communication was super human, and a few of my fellow compatriots got good enought to use the language in conversation with each other. Unfortunately, the human is not ready for that level of communication, we ended up all getting seizures and are practically brain dead in the hospital now. I now waste away my life browsing reddit from the hospital room incapable of much else.

Goheeca · 5 points · Posted at 14:55:30 on May 21, 2022 · (Permalink)

I, too, have forked Ithkuil.

Goheeca · 5 points · Posted at 16:35:35 on May 20, 2022 · (Permalink)

It does and it's HoTT.

doomvox · 6 points · Posted at 15:27:14 on May 20, 2022 · (Permalink)*

And why hasn't Math become a programming language? The equal sign is used to assert an absolute eternal truth? Pfft. How often do you run into those?

dixego · 1 points · Posted at 18:56:15 on May 26, 2022 · (Permalink)

Lol no homotopy type theory

ProfessorSexyTime · 3 points · Posted at 20:00:22 on May 20, 2022 · (Permalink)

Those damn ancient Greeks and their squiggly symbols. If only they knew about the wonders of programming, like Go.

[deleted] · 3 points · Posted at 23:43:28 on May 20, 2022 · (Permalink)

/uj I think everyone has this idea at one point in their career.

cuminme69420 · 3 points · Posted at 02:13:42 on May 21, 2022 · (Permalink)

Ask HN: Why doesn't the Kama Sutra look like a programming language?

RepresentativeNo6029 · 10 points · Posted at 14:08:18 on May 20, 2022 · (Permalink)

/uj you can’t possibly dispute the unergonomic-ness and unmaintainability of math. Homotopy Type Theory was developed for this reason!

/rj math of course is simultaneously the most fundamental of all thoughts and encompasses all thought. the way math has been handed to us is THE math and we shall pass on tricky integration problems till eternity. btw, how dare you?

[deleted] · 20 points · Posted at 14:10:05 on May 20, 2022 · (Permalink)*

[deleted]

avdnl · 18 points · Posted at 14:14:23 on May 20, 2022 · (Permalink)

More grad level I'd think. Or maybe I just went to a shit undergrad

doomvox · 9 points · Posted at 15:33:06 on May 20, 2022 · (Permalink)

Or maybe I just went to a shit undergrad

But aren't they all?

You can have profs who can teach, or profs who care about their careers, never the twain.

RepresentativeNo6029 · 10 points · Posted at 14:13:36 on May 20, 2022 · (Permalink)

Just FYI: copilot will replace all of us. I mean it can literally code better than me. It must be super intelligent

fp_weenie · 14 points · Posted at 14:57:38 on May 20, 2022 · (Permalink)

unmaintainability of math

ok wagie

VariationDistinct330 · 3 points · Posted at 15:45:44 on May 20, 2022 · (Permalink)

Sir/Madam, it appears you have scaled the ivory tower, floated off past architecture astronaut orbit and are now breathing pure number theory in the idiot savant orbit.

Will you come down? Your mom is calling you for dinner

/uj I reject infix operators, even if they're in maths. Maths is just wrong then

ConcernedInScythe · 9 points · Posted at 21:37:35 on May 20, 2022 · (Permalink)

i've seen what it takes to prove very basic results in homotopy in HTT and if you think it's more 'ergonomic' than normal maths you're hitting the dependent types way too hard

RepresentativeNo6029 · 3 points · Posted at 01:33:58 on May 21, 2022 · (Permalink)

Lol no explicit unjerk

/uj I used HoTT as an example of an attempt by a serious mathematician to tackle this challenge. I’m not saying they were successful. It’s an open question

[deleted] · 4 points · Posted at 14:10:47 on May 20, 2022 · (Permalink)

[deleted]

doomvox · 11 points · Posted at 15:34:32 on May 20, 2022 · (Permalink)

I'm sorry, I can't bring myself to vote this down. I should write a bot that responds to every comment with this line.