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> Almost every popular tool or technique we use has a clear and direct lineage from math I don't think that's true. It's very often the other way around.

by neolog 6y ago

amw-zero 6y ago
My example was the relational model of data, which is literally a mathematical model of data storage. Other ones I can think of off the top of my head: - the DOM (an applied tree which is a graph) - everything to do with programming language construction (compilers and interpreters use graph theory extensively) - testing (permutations and combinations) - static analysis (including eslint) - abstracting logic with functions Can you think of anything that isn’t directly derived from some math concept?
- SkyMarshal 6y ago
  You might enjoy this letter by Edward Dijkstra on why Americans sometimes don't realize the mathematical basis of programming: https://www.cs.utexas.edu/users/EWD/transcriptions/EWD06xx/EWD611.html https://www.cs.utexas.edu/users/EWD/transcriptions/EWD06xx/E... Excerpt: "The first series of machines —that of the singletons— was mainly developed in the USA shortly after the World War II, while a ruined continental Europe had neither the technology, nor the money, to start building computers: the only thing we could do was thinking about them. Therefore it is not surprising that many US Departments of Computer Science are offsprings of Departments of Electrical Engineering, whereas those in Europe started (later) from Departments of Mathematics (of which they are often still a part). This different heritage still colours the departments, and could provide an acceptable explanation that in the USA Computing Science is viewed more operationally than in Europe."
  - pyuser583 6y ago
    I’m pretty sure it precedes WWII. Compare the work of scientists like Alan Turing with the pre-war work of Claude Shannon/Vannevar Bush. Turing was a mathematician focused on theoretical problems. Shannon and Bush spent several years building analog computers at MIT. I think the difference was the way electronics and telecommunications established themselves as academic disciplines in America. America was training tons of electrical engineers, but surprisingly few mathematicians, as early as the mid 19th century. Look at schools like MIT - what the UK equivalent? Oxbridge is known for Classics, PPE, and Maths. There’s no “institutes of technology.”
    - danielheath 6y ago
      > Turing was a mathematician focused on theoretical problems. The famous theoretical problems of fire-control systems for anti-aircraft weapons and wartime code-breaking.
  - amw-zero 6y ago
    That’s such an interesting perspective. I’d expect nothing less of Djikstra!
- bordercases 6y ago
  A part of the inefficiency is that business-logic oriented applications (a) often use stateful object models to organize their code and services, which are (b) extremely difficult to reason about mathematically, both due to the pseudo-mathematical nature of mutable state, and due to no canonical formal representation of what an "object" is mathematically, nor what an "object" ought to be in software engineering. The situation may be improving: more programming is moving over to the functional style which at the very least gets you algebraic concepts like combinators as the method for code reuse, and types + monoids as formal stand-ins for objects. In other words programming moves towards math when it makes functions really functions. Category Theory and Linear Logic also provide models for data-transformation locales (objects) as well as resource consumption (mutation); but they are still heavyweight formalisms which have yet to make full penetration towards applications which quite frankly might not need them to do useful work.
  - amw-zero 6y ago
    What makes state hard to reason about mathematically? TLA+ has a very formal definition of state and time that can be model checked or used for proofs. I think the reason that this is such a common statement is exactly because people don’t even know that state can be reasoned about mathematically, they just assume that it can’t be. The biggest thing that TLA+ showed me is that there’s no difference between functional and imperative programming from an algorithm standpoint. You can implement the exact same algorithm in both paradigms, and while the functional one has no explicit state, it can have a tremendous amount of implicit state. Recursion where a new state parameter is passed as argument to the next call is just as difficult to reason about as mutable state, it’s just less efficient from a processor standpoint.
    - bordercases 6y ago
      I have no experience using TLA+, just secondhand knowledge, so you might very well be right. From my understanding, everything I said is true when restricted to classical logic. Otherwise, there are multiple approaches to objects and time, all of which are non-classical logics, and so are not commonly taught nor have they yet been embedded in many languages. TLA+ has been getting more traction, which might signal some kind of convergence since I last looked into it? I guess Rust would be another example where state is checked against using ownership signals, which uses non-classical concepts. Defending myself against the second claim, yes these algorithms have implicit state because the machines we're operating on are fundamentally stateful. But that's meant to be abstracted away at the language level and left for the interpreter/compiler to resolve. This still leaves problems for how to modularize code at the domain layer using functional idioms, which primarily express behavior over properties. OOP can be restricted in a way which makes this simple to bridge towards using the Actor model but that's still a step away from habitually structuring your code using modules monoids and combinators. TLA+ doesn't quite address this, since (IIRC) you don't implement your final system in TLA+.
- neolog 6y ago
  None of those is derived from a math concept. Math was applied to them after they were developed.
  - amw-zero 6y ago
    How did we come up with the concept of a function in a programming language before considering math? Everything I listed is an example of applying math to a problem. The math came first.
hyperpallium2 6y ago
Apart from relational algebra, two big ones are regular expressions and diff (longest common subsequence). However, you're saying vice versa: Almost all math we use has a clear and direct lineage from a popular tool or technique. There's something to this - many of the well-known theorems and algorithms for regular expressions started with Ken Thompson, though of course he used Kleene algebra. And for relational algebra in this submission, there's almost no mathematics, just a set of tuples... and make an algebra around it. That's why Codd's paper has hardly any references, he pretty much made it all up, to solve a practical problems he saw (unnecessary rewriting of code). Though he was a mathematician, so... The limits of knowledge, of what can be proven, is to do with "computability" - sure sounds like a prpgrammer thing! So maybe you have something there...

> Almost every popular tool or technique we use has a clear and direct lineage from math I don't think that's true. It's very often the other way around.

by neolog 6y ago

> Almost every popular tool or technique we use has a clear and direct lineage from math I don't think that's true. It's very often the other way around.

amw-zero 6y ago

My example was the relational model of data, which is literally a mathematical model of data storage. Other ones I can think of off the top of my head: - the DOM (an applied tree which is a graph) - everything to do with programming language construction (compilers and interpreters use graph theory extensively) - testing (permutations and combinations) - static analysis (including eslint) - abstracting logic with functions Can you think of anything that isn’t directly derived from some math concept?

SkyMarshal 6y ago
You might enjoy this letter by Edward Dijkstra on why Americans sometimes don't realize the mathematical basis of programming: https://www.cs.utexas.edu/users/EWD/transcriptions/EWD06xx/EWD611.html https://www.cs.utexas.edu/users/EWD/transcriptions/EWD06xx/E... Excerpt: "The first series of machines —that of the singletons— was mainly developed in the USA shortly after the World War II, while a ruined continental Europe had neither the technology, nor the money, to start building computers: the only thing we could do was thinking about them. Therefore it is not surprising that many US Departments of Computer Science are offsprings of Departments of Electrical Engineering, whereas those in Europe started (later) from Departments of Mathematics (of which they are often still a part). This different heritage still colours the departments, and could provide an acceptable explanation that in the USA Computing Science is viewed more operationally than in Europe."
- pyuser583 6y ago
  I’m pretty sure it precedes WWII. Compare the work of scientists like Alan Turing with the pre-war work of Claude Shannon/Vannevar Bush. Turing was a mathematician focused on theoretical problems. Shannon and Bush spent several years building analog computers at MIT. I think the difference was the way electronics and telecommunications established themselves as academic disciplines in America. America was training tons of electrical engineers, but surprisingly few mathematicians, as early as the mid 19th century. Look at schools like MIT - what the UK equivalent? Oxbridge is known for Classics, PPE, and Maths. There’s no “institutes of technology.”
  - danielheath 6y ago
    > Turing was a mathematician focused on theoretical problems. The famous theoretical problems of fire-control systems for anti-aircraft weapons and wartime code-breaking.
- amw-zero 6y ago
  That’s such an interesting perspective. I’d expect nothing less of Djikstra!
bordercases 6y ago
A part of the inefficiency is that business-logic oriented applications (a) often use stateful object models to organize their code and services, which are (b) extremely difficult to reason about mathematically, both due to the pseudo-mathematical nature of mutable state, and due to no canonical formal representation of what an "object" is mathematically, nor what an "object" ought to be in software engineering. The situation may be improving: more programming is moving over to the functional style which at the very least gets you algebraic concepts like combinators as the method for code reuse, and types + monoids as formal stand-ins for objects. In other words programming moves towards math when it makes functions really functions. Category Theory and Linear Logic also provide models for data-transformation locales (objects) as well as resource consumption (mutation); but they are still heavyweight formalisms which have yet to make full penetration towards applications which quite frankly might not need them to do useful work.
- amw-zero 6y ago
  What makes state hard to reason about mathematically? TLA+ has a very formal definition of state and time that can be model checked or used for proofs. I think the reason that this is such a common statement is exactly because people don’t even know that state can be reasoned about mathematically, they just assume that it can’t be. The biggest thing that TLA+ showed me is that there’s no difference between functional and imperative programming from an algorithm standpoint. You can implement the exact same algorithm in both paradigms, and while the functional one has no explicit state, it can have a tremendous amount of implicit state. Recursion where a new state parameter is passed as argument to the next call is just as difficult to reason about as mutable state, it’s just less efficient from a processor standpoint.
  - bordercases 6y ago
    I have no experience using TLA+, just secondhand knowledge, so you might very well be right. From my understanding, everything I said is true when restricted to classical logic. Otherwise, there are multiple approaches to objects and time, all of which are non-classical logics, and so are not commonly taught nor have they yet been embedded in many languages. TLA+ has been getting more traction, which might signal some kind of convergence since I last looked into it? I guess Rust would be another example where state is checked against using ownership signals, which uses non-classical concepts. Defending myself against the second claim, yes these algorithms have implicit state because the machines we're operating on are fundamentally stateful. But that's meant to be abstracted away at the language level and left for the interpreter/compiler to resolve. This still leaves problems for how to modularize code at the domain layer using functional idioms, which primarily express behavior over properties. OOP can be restricted in a way which makes this simple to bridge towards using the Actor model but that's still a step away from habitually structuring your code using modules monoids and combinators. TLA+ doesn't quite address this, since (IIRC) you don't implement your final system in TLA+.
neolog 6y ago
None of those is derived from a math concept. Math was applied to them after they were developed.
- amw-zero 6y ago
  How did we come up with the concept of a function in a programming language before considering math? Everything I listed is an example of applying math to a problem. The math came first.

hyperpallium2 6y ago

Apart from relational algebra, two big ones are regular expressions and diff (longest common subsequence). However, you're saying vice versa: Almost all math we use has a clear and direct lineage from a popular tool or technique. There's something to this - many of the well-known theorems and algorithms for regular expressions started with Ken Thompson, though of course he used Kleene algebra. And for relational algebra in this submission, there's almost no mathematics, just a set of tuples... and make an algebra around it. That's why Codd's paper has hardly any references, he pretty much made it all up, to solve a practical problems he saw (unnecessary rewriting of code). Though he was a mathematician, so... The limits of knowledge, of what can be proven, is to do with "computability" - sure sounds like a prpgrammer thing! So maybe you have something there...