201–210 of 256 posts
I can program just fine, write functions left and right, receive data, do something with it, return a result...
But in maths? Oh dear god no I couldn't write a math function on a piece of paper to save my life.
Someone recently pointed out the parallels and while I couldn't deny it, as it was plain as day... I never once considered it during all these years.
Kinda scary.
Earlier quoted context omitted.
> Mathematics and programming are not really all that related to each other I may be wrong but I believe the Curry-Howard correspondence disproves your claim. One can translate between the two and find that they are equivalent. The difficulty is that some programming languages are hard to model mathematically due to the way they were designed and implemented. Some, like Idris or Agda, make it easy to see the correspo…
Curry-Howard maps typical practical tasks on the programming side to completely useless make-work on the math side. Turning a customer's name and address into text to make a mailing label has to happen at some point, but you really don't need to go through all those steps to show that if customers exist, then strings exist.
There's an unpopular and somewhat seemingly contradictory opinion that I have regarding this, because this isn't the first time I've seen this topic brought up. Mathematics and programming are not really all that related to each other and I think there's an overemphasis on the importance of math in programming for 99% of applications. Sure, mathematical thinking can be useful, but it's only one type of logical thinki…
Mathematics and programming are strongly related more than most people think. http://www.norvig.com/spell-correct.html How did he solve it? Using probability theory and sets. It's not just games, cryptography, finance, signal processing, compression, optimization, and AI that require mathematics, tons of programming does most people just don't realize it and brute force their way to a solution. Lot's of real world pr…
There's an unpopular and somewhat seemingly contradictory opinion that I have regarding this, because this isn't the first time I've seen this topic brought up. Mathematics and programming are not really all that related to each other and I think there's an overemphasis on the importance of math in programming for 99% of applications. Sure, mathematical thinking can be useful, but it's only one type of logical thinki…
With respect, that tells us much more about you than about math or programming.
No Haskell expert, or formal methods expert, or complexity theory expert, would ever make a statement like that.
You may be right that math is quite a distance from day to day development, of course. (I don't think I'm being pedantic here, but perhaps.)
> it's only one type of logical thinking among many types which can be applied to programming.
What do you have in mind? Design patterns and software development practices, or something else?
Earlier quoted context omitted.
Ah, well, you just described the relative value of math in much the way I'd describe the relative value of... well, just about any intellectual pursuit. Same in philosophy. Or in law. Or in physics. A lot of people with particular interest in one area -- say, mathematics -- don't realize that much of what is important is much more generally applicable. It's not that these things are distinctly important for math. It'…
I see math as the language of thinking. Math doesn’t really have a domain beyond: how do we think, how do we know, and how do we communicate our knowledge. The progression of mathematics has been the systematic removal of domain. Numbers are widely applicable because they are very abstract and devoid of domain, and they are one of the least abstract things in mathematics. I agree with your gist, there are lots of thi…
And as programmers we work with mathematical objects called state spaces, that have vastly more than 100 dimensions.
That said one can easily be a competent programmer without having much formal mathematical knowledge much like one can easily be a competent ball player without knowing the differential calculus. However, just as modern ball players improve their games with computer aided mathematical analysis of their swings and so on, a programmer can improve the quality of his output by mathematical analysis, in particular via the use of the predicate calculus and its, in my opinion, most useful application of loop analysis.
Earlier quoted context omitted.
Writing a lot of code you later discard because it isn’t part of the final solution is like throwing clay on the table and then carving away the bits that don’t fit. Nobody criticizes the sculptor for the clay that ends up on the floor, and clay is heavy. We carve away bits, they have no mass and don’t need to be swept up, all we have to do is cut them away, revealing the final program.
This is not a useful analogy; it is more of an excuse for not trying to think things through. Would this be a reasonable analogy for building a bridge? If you don't have a reasonably detailed idea of what you want and how to achieve it, you are unlikely to get it. https://dilbert.com/strip/1991-9-6
Earlier quoted context omitted.
Logic is part of math, not the other way around. Basically the same goes for your "how it affects the web" since that becomes about directed graphs. On algorithms and data structures: do you actually evaluate their complexity if that's not about math? Math is everywhere.
I'm always mindful of complexity when designing algorithms but I would barely consider it math. It's not an exact science and you're hardly quantifying anything. Complexities are essentially just eyeballed approximations.
1. Are you aware that the complexity analysis isn't about being precise but about being able to predict the time for any given input given some sample? Since from my own experience, it's more of an analytical part and it's about calculations of worst case scenarios/computability of the process overall. Still, it has everything to do about actually predicting the exact values, with the grain of salt that the relativity of the method is.
2. Are you actually aware that the math isn't about being "precise" in the sense of numbers but about relationships between abstract entities? Ever heard something about category theory or pretty much anything related to the abstract algebra?
3. Is there anything else than math that helps abstraction in your opinion? For what I know, even mediocre understanding of abstract algebra helps a lot. Please note that this question is totally non-ironic, I'd really want to know.
How do I express my models of programs on paper that doesn't easily translate into math? I understand that the part of programs there you have a formula on beforehand (e.g., convert between Celsius and Fahrenheit) is easily expressed in a mathematical formula before implementing it. However, how should I express I/O? Often when I have a problem that isn't easily expressed in mathematical notation (albeit to my limite…
Author here. I would say that modeling the computational process in math is not typically helpful (you already have a formal programming language) you should model the real-world (or at least computer world) problem you are trying to solve. Carefully define operations and constraints, introduce abstractions for solving them, etc. Do you have an example of an I/O problem you have thought about that you would like me t…
The question I'm trying to ask is how I should express (part of) programs on paper using math when I don't see how they are related to math.
Example: How could I easily express a function that takes a string as input and outputs the string capitalized using math notation?
I understand that the problem you solve in the post should probably be put on paper first before you began writing any code.
My problem is to express programs in math when "calculate" isn't part of the problem description, like it is in the example in the blog post.
Edit: Changed example question.
I was surprised to learn that I really enjoy coding, whereas I rather dislike math. I feel like this article might resonate with some people, but not with me. > Programming languages are implementation tools, not thinking tools. They are strict formal languages invented to instruct machines in a human-friendly way. In contrast, thoughts are best expressed through a medium which is free and flexible. I don't find math…
Couldn't disagree with that more. That's a language of its own with a lot of extensions and variations introduced by the people involved. Basically any sound formal system (usually the talk's on rings) is viable, therefore math is indeed free and flexible. All you have is to escape the box of spoken language, the same thing as you'd do to learn a programming language if it's not "verbose" enough to make you think in phrases instead of the language in question.
Shake up your thinking about math: "Iconic Math" http://iconicmath.com/
Math-first programming: CQL - Categorical Query Language
> The open-source Categorical Query Language (CQL) and integrated development environment (IDE) performs data-related tasks — such as querying, combining, migrating, and evolving databases — using category theory, a branch of mathematics that has revolutionized several areas of computer science.
https://www.categoricaldata.net/
Thinking about physics math in computer language: "Structure and Interpretation of Classical Mechanics" by Gerald Jay Sussman and Jack Wisdom with Meinhard E. Mayer.
https://en.wikipedia.org/wiki/Structure_and_Interpretation_o...