4 ms·

You are correct; you can learn what these things "are," but without at least some of the mathematics, it's going to be tough to fully grasp. And yes, mathemati

You are correct; you can learn what these things "are," but without at least some of the mathematics, it's going to be tough to fully grasp. And yes, mathematics is a language; it is the language for modelling the phenomena we experience in the world, including the non-physical (contracts, data / counting, etc.). I so, so, so wish that people were taught that mathematics is a language of relationships rather than one of rote numerical calculation. I think more people would stick with it. It's a shame, because the doors it opens are huge.

The_rationalist 7y ago
I don't quite understand how mathematics are more adapted to model the world than a programming language.
- caspper69 7y ago
  The short answer, they are not; The long(er) answer? Mathematics are more limited, and thus, at least on the surface, provide a more rigid model. Plus, we have about 4500 years worth of equations that we know to be accurate; not so true for C or any other programming language. Plus, we can model all the way down in mathematics, as it is more abstract in nature. The long(est) answer? It's turtles all the way down.
  - kd5bjo 7y ago
    > Mathematics are more limited The fundamental point of the Church-Turing thesis is to show that everything computers can do can be described by mathematics, so any programing language has either the same or less power than math. They are certainly easier to use for many problems, though. Additionally, Gödel showed that there are true statements that can be described but not proven by math, ao it can never be a perfect model of the real world.
    - progval 7y ago
      > Additionally, Gödel showed that there are true statements that can be described but not proven by math, ao it can never be a perfect model of the real world. I assume you are refering to Gödel's incompleteness theorems; but this is not what they "say". What they say is that any formal system powerful enough to contain basic arithmetic is either inconsistent (ie. it can both prove and disprove a particular theorem) or incomplete (ie. cannot either prove or disprove all theorems). If you take the ZF set theory, for example, it is incomplete, because some statements cannot be either proved or disproved within ZF, such as the Axiom of Choice (AC) or Zorn's Lemma. However, that doesn't imply that ZF cannot be "a perfect model of the real world", because the AC is irrelevant in a the real world, because the AC only applies to infinite sets, which do not exist in the real world.
    - The_rationalist 7y ago
      Gödel theorem does not say anything about the real world. Mathematics are a superset of physics as they allow to explain all possible universes not just our. I've yet to see one concrete statement that ZFC can't explain. There's a list of such statements on wiki if I remember well.
- mcguire 7y ago
  Short pithy answer: Exact real arithmetic is still an open research problem. Slightly longer answer: To the extent that they are formal languages, they both have the same ability to express things. More philosophical answer: Mathematics has a tradition of extension. Have a new idea you want to express as concisely as possible because you are going to be using it a lot? Grab a handful of Greek letters, symbols, funny fonts, and random other typography, and go to town. Outside of Lisp,[1] this flexibility is hard to do in most programming languages. [1] But inside a dog, it's too dark to read.

The_rationalist 7y ago

I don't quite understand how mathematics are more adapted to model the world than a programming language.

caspper69 7y ago
The short answer, they are not; The long(er) answer? Mathematics are more limited, and thus, at least on the surface, provide a more rigid model. Plus, we have about 4500 years worth of equations that we know to be accurate; not so true for C or any other programming language. Plus, we can model all the way down in mathematics, as it is more abstract in nature. The long(est) answer? It's turtles all the way down.
- kd5bjo 7y ago
  > Mathematics are more limited The fundamental point of the Church-Turing thesis is to show that everything computers can do can be described by mathematics, so any programing language has either the same or less power than math. They are certainly easier to use for many problems, though. Additionally, Gödel showed that there are true statements that can be described but not proven by math, ao it can never be a perfect model of the real world.
  - progval 7y ago
    > Additionally, Gödel showed that there are true statements that can be described but not proven by math, ao it can never be a perfect model of the real world. I assume you are refering to Gödel's incompleteness theorems; but this is not what they "say". What they say is that any formal system powerful enough to contain basic arithmetic is either inconsistent (ie. it can both prove and disprove a particular theorem) or incomplete (ie. cannot either prove or disprove all theorems). If you take the ZF set theory, for example, it is incomplete, because some statements cannot be either proved or disproved within ZF, such as the Axiom of Choice (AC) or Zorn's Lemma. However, that doesn't imply that ZF cannot be "a perfect model of the real world", because the AC is irrelevant in a the real world, because the AC only applies to infinite sets, which do not exist in the real world.
  - The_rationalist 7y ago
    Gödel theorem does not say anything about the real world. Mathematics are a superset of physics as they allow to explain all possible universes not just our. I've yet to see one concrete statement that ZFC can't explain. There's a list of such statements on wiki if I remember well.
mcguire 7y ago
Short pithy answer: Exact real arithmetic is still an open research problem. Slightly longer answer: To the extent that they are formal languages, they both have the same ability to express things. More philosophical answer: Mathematics has a tradition of extension. Have a new idea you want to express as concisely as possible because you are going to be using it a lot? Grab a handful of Greek letters, symbols, funny fonts, and random other typography, and go to town. Outside of Lisp,[1] this flexibility is hard to do in most programming languages. [1] But inside a dog, it's too dark to read.