5 ms·

Remember, programming is a branch of mathematics.

by amelius 2mo ago

ChrisGreenHeur 2mo ago
What’s the mathematical proof of this?
- IngoBlechschmid 2mo ago
  The Curry-Howard correspondence. For instance, in mathematics, we have A ⇒ A (every statement implies itself, for instance "if it rains, then it rains"); and analogously, in programming, we have the identity function of type A → A (which reads a value as input and outputs the same value). This is the tip of an enormous iceberg identifying, in a certain precise sense, proving with programming (and stating mathematical assertions with specifying the desired behavior of a program). However, programming is a bit more general than proving: Circular proofs are simply of no value, whereas looping programs can still be valuable. For instance, I for sure hope that the main loop of the browser I'm currently using to fill out this textbox does not prematurely stop.
  - mrob 2mo ago
    >we have the identity function of type A → A (which reads a value as input and outputs the same value) That only exists in theoretical computer science. In real computer programming, you always have some bounds to the value of A.
    - pdhborges 2mo ago
      I think it is time to repost Against Curry-Howard Mysticism (https://liamoc.net/forest/loc-000S/index.xml https://liamoc.net/forest/loc-000S/index.xml)
siva7 2mo ago
so is physics?
- abstractbill 2mo ago
  Theoretical physics, sure, ok. Not experimental physics though.
  - lioeters 2mo ago
    That's arguable.
    - goatlover 2mo ago
      The empirical part is not mathematical, in that you run experiments and get results.
  - brador 2mo ago
    That too. Statistics used to analyze results and turn them into conclusions.
    - Revanche1367 2mo ago
      As my mathematical statistics professor told us on the first day, “statistics is not mathematics.” It’s a good idea to remember: if a branch of the subject x is called “mathematical x,” then x in general is not totally mathematical and can be studied to some extent without mathematics.
nextaccountic 2mo ago
computer science, yes, 100% a branch of math programming is more like communicating to a computer to convince them to do some task. has always been like this, and this will not change
Llamamoe 2mo ago
In the same sense as pharmacology is a branch of physics. Technically, yes. Realistically the overlap is small and you don't need one for the other most of the time.
TheOtherHobbes 2mo ago
Programming is the mathematical equivalent of brick layers looking at architects and saying "I could do that."
- perching_aix 2mo ago
  Do architects lay bricks often? Wasn't aware.
- amelius 2mo ago
  Using GenAI, they certainly can.
- general1465 2mo ago
  Well I have often times see an architect creating a wild fantasy like structure and statistician with project manager saying, nope it is going to be another box due to actual physics and budget constraints.
sandworm101 2mo ago
>> programming is a branch of mathematics. I saw a cryptographer interviewed. She was maybe 20yo and was working onboard a US aircraft carrier. Installing and managing cryptographic systems does not make one a cryptographer. Doing math via computer programing also does not make one a mathematician any more than driving a car makes one a mechanic.
renyicircle 2mo ago
There's a difference between "branch of mathematics" and "can be modeled using mathematics".

Remember, programming is a branch of mathematics.

by amelius 2mo ago

Remember, programming is a branch of mathematics.

ChrisGreenHeur 2mo ago

What’s the mathematical proof of this?

IngoBlechschmid 2mo ago
The Curry-Howard correspondence. For instance, in mathematics, we have A ⇒ A (every statement implies itself, for instance "if it rains, then it rains"); and analogously, in programming, we have the identity function of type A → A (which reads a value as input and outputs the same value). This is the tip of an enormous iceberg identifying, in a certain precise sense, proving with programming (and stating mathematical assertions with specifying the desired behavior of a program). However, programming is a bit more general than proving: Circular proofs are simply of no value, whereas looping programs can still be valuable. For instance, I for sure hope that the main loop of the browser I'm currently using to fill out this textbox does not prematurely stop.
- mrob 2mo ago
  >we have the identity function of type A → A (which reads a value as input and outputs the same value) That only exists in theoretical computer science. In real computer programming, you always have some bounds to the value of A.
  - pdhborges 2mo ago
    I think it is time to repost Against Curry-Howard Mysticism (https://liamoc.net/forest/loc-000S/index.xml https://liamoc.net/forest/loc-000S/index.xml)

siva7 2mo ago

so is physics?

abstractbill 2mo ago
Theoretical physics, sure, ok. Not experimental physics though.
- lioeters 2mo ago
  That's arguable.
  - goatlover 2mo ago
    The empirical part is not mathematical, in that you run experiments and get results.
- brador 2mo ago
  That too. Statistics used to analyze results and turn them into conclusions.
  - Revanche1367 2mo ago
    As my mathematical statistics professor told us on the first day, “statistics is not mathematics.” It’s a good idea to remember: if a branch of the subject x is called “mathematical x,” then x in general is not totally mathematical and can be studied to some extent without mathematics.

nextaccountic 2mo ago

computer science, yes, 100% a branch of math programming is more like communicating to a computer to convince them to do some task. has always been like this, and this will not change

Llamamoe 2mo ago

In the same sense as pharmacology is a branch of physics. Technically, yes. Realistically the overlap is small and you don't need one for the other most of the time.

TheOtherHobbes 2mo ago

Programming is the mathematical equivalent of brick layers looking at architects and saying "I could do that."

perching_aix 2mo ago
Do architects lay bricks often? Wasn't aware.
amelius 2mo ago
Using GenAI, they certainly can.
general1465 2mo ago
Well I have often times see an architect creating a wild fantasy like structure and statistician with project manager saying, nope it is going to be another box due to actual physics and budget constraints.

sandworm101 2mo ago

>> programming is a branch of mathematics. I saw a cryptographer interviewed. She was maybe 20yo and was working onboard a US aircraft carrier. Installing and managing cryptographic systems does not make one a cryptographer. Doing math via computer programing also does not make one a mathematician any more than driving a car makes one a mechanic.

renyicircle 2mo ago

There's a difference between "branch of mathematics" and "can be modeled using mathematics".