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I mean, at a certain point, you're just abstracting logical thinking in general and calling it "math". You can say the same about baking, working out your sched
by culi 4y ago
I mean, at a certain point, you're just abstracting logical thinking in general and calling it "math". You can say the same about baking, working out your schedule ahead of time so you can pick up your kids and have time to buy groceries, or trying to sort your playlist of non-album singles in a way so that you optimally position each song in a way that minimizes how jarring the switch from one track to the next is
I feel like the whole point of "math" is to abstract these natural patterns so we can like... write them down and investigate them further. We have a limited mental capacity so we abstract it into a syntax/system of meaning so that we can let the paper or the computer do some of the memory work for us.
If you're doing it in your head, sure that's a skill, but is it really math?
- burrows 4y agoDo you use “math” and “deductive reasoning” to refer to distinct activities?
- jfengel 4y agoDeduction is used in a lot more than just the classes labeled "mathematics". Which makes one question just to what degree the mathematics classes are even useful. Perhaps deductive reasoning could've been taught to do more useful things than factoring polynomials.
- nicoburns 4y agoPhilosophy (at least in the Analytic tradition) involves a lot of deductive reasoning about non-mathematical things (the main difference from maths being that in maths everyone mostly agrees on the foundations, where in philosophy a lot of the reasoning is conditional: IF you believe X, Y, Z, then Q is also true).
- burrows 4y agoWhat are “foundations”? Inference rules, axioms, language?
- nicoburns 4y agoI was referring to axioms when I used the term "foundations" above. Inference rules are largely agreed upon across both maths and philosophy (and they're the same ones in both disciplines).
- burrows 4y agoA tangential but related thought. I’ve heard people say things like, “The world is math”, but it never seemed particularly coherent to me. Sometimes I’d assume they meant, “Inference systems with mathematical languages make useful predictions about my empirical experience.” But now I’m favoring the interpretation that experience is purely formal/syntactic with no semantic component. There is no additional meaning beyond (or behind) appearance.
- kazinator 4y agoThere is a notion of meaning in that it encodes possibility. A situation with lots of future possibilities has meaning. A dead-end situation has little or no meaning: stagnation, death, ... If the formal/syntactic appearance is how leads to new possibilities involving more formal/syntactic appearances, then that is its meaning.
- burrows 4y agoAre you suggesting that some people hold the normative position, “One ought prefer situations with more possibilities to those with fewer, ceteris paribus.” But isn’t that just some hidden metaphysical structure? That is, it’s unavailable as formal appearance?
- deleted 4y ago[deleted]
- culi 4y agoCould you give an example of philosophers from the analytic tradition that actually build their arguments in an axiomatic way like many practices in mathematics try to? I feel like I've read more attacks on this very approach than actual examples of this approach (from both analytics folks and continental folks)
- trashtester 4y agoClassical logic is related to boolean logic, and has its uses. But a lot of real world "logic" (decision theory, etc) is statistical in nature, often with a big inductive component and often based on "axioms" that only approximate the real world. In other words, the field of Analytic Philosophy, when not using the proper amount of math and statistics (especially Bayesian statistics) tend to either lead to doubting everything (if they know what things they do not know) or drawing bad conclusions (if treating their axiomatic assumptions as absolute truths) They have similar problems with science, and maybe Physics in particular, because of the abstraction of modern physics. By interpreting statements made by some physicist too literally, they may (falsely) end up with conclusions that go way beyond the domain of validity of the original statement. Imho, Philosophy is fine as a side-project for people in academia, but I think philosphers who do not study math, science, psychology, etc at a level comparable to their philosophy work are at risk of ending up in lala-land. I would estimate that if someone studies only philosophy in college, they will reach a point after about 1 year where their knowledge of philosophy come to a point that requires more understanding of math, science etc than they had when they started. Kind of like a physicist that doesn't take college level math.
- burrows 4y agoWhat activity are you designating with the name “philosophy”?
- corrral 4y agoI've been programming since I was 14, and getting paid to do it since I was 15 (I know, not impressively young compared to some folks, but still). Approaching 40 now. It's never felt like math to me. If it did, I probably wouldn't be able to do it. I'm not especially good at math and feel damn near dyslexic when I try to read math-notation-heavy writing. Programming, meanwhile has always come easily and naturally. ... except the languages that try to look like math. Looking at you, Haskell. I get the concepts just fine, but I can't stand the style.
- culi 4y agoI think that's totally normal. Many (admittedly, sometimes dubious) studies have made the claim that a background in [linguistics | juggling | playing music | etc] is a better predictor of the likeliness that someone will turn out to be a good programmer than a background in math is As someone with a background in math, I think that makes total sense. I don't feel like there's any magic reason why practicing reasoning under (one of the many paradigms of) mathematics would automatically carry over to the type of reasoning you practice while programming any more than the previously mentioned exercises. The only times math has helped me is when the programming I'm doing straight up references mathematical concepts I've practiced with (matrices, group theory, etc). Which is a pretty uncommon occurrence in my current position. If you want your background in something else to help you with programming I think you'll have to put conscious effort into identifying and using the relevant abstractions and metaphors
- blip54321 4y agoA professor in college had two terms: microprogramming and macroprogramming. Microprogramming was the kind of thing where you're trying to, for example, cut down an assembly loop to run in 6 cycles rather than 8, design a numerical algorithm, an operating system scheduler, or similar. This is very mathematical in style of thinking. Macroprogramming is what happens when you write a database-backed web application, for example. It's much more linguistic. It's about understanding other people's code, writing your code to be understood, and gluing a lot of stuff together. Both have their place. Macroprogramming is taking over now, but I enjoy microprogramming more.
- deleted 4y ago[deleted]
- kazinator 4y agoUmm, no; I'm specifically referring to reasoning that a certain clump of symbols has the same meaning/effect as another one by linking semantics with symbol manipulation rules.
- quantified 4y ago-(-x) = x. It's not far off. Different in degree of quantity and type of symbols, not different in kind.
- Dylan16807 4y agoSure, if you solve it with symbol manipulation rules. That's definitely not the general case when I'm comparing two pieces of code to see if they do the same thing.
- coldtea 4y agoIt is, you just follow the rules in an ad-hoc way, and without having all of them formally in your mind.
- Dylan16807 4y agoI think you've now defined every kind of reasoning to be math. I don't think that's a good way to define it. But if we do define it that way, then saying "x is math" becomes a very weak and much less interesting statement.
- yellowapple 4y ago> If you're doing it in your head, sure that's a skill, but is it really math? Is it not? Adding numbers in my head is certainly math. Algebra in my head is certainly math. Why would it stop being math just because I'm doing it more abstractly?
- taeric 4y agoIf you role play in your head the setting of a table, you may be able to count the plates used. This does not imply that you must do the symbolic reasoning of this in an equation.
- pfortuny 4y agoThe problem with “maths” is its sublimation. Maths is just what we use to deal with quantities and shapes, abstracted from their matter. Whether it is using symbols, pebbles or categories, it is neither better nor worse. But they make people think that “maths” is just a terrible abstract construction.
- xphos 4y agoYeah I think you are hitting the on what I think is math reduction thinking. That formalized process of thinking is the esencse of what math is. It's quantitative instead of qualitative. Before math formalized those things it's all an eyeballing and impossible to convey without demonstrations. The simple form of that is for baking but if you gave someone an excel sheet and step by step instructions for building radio antennas they can do it because its been formalized. And this certainly transfers to programming because the writing of a program formalizes the recipe
- sicp-enjoyer 4y ago> It's quantitative instead of qualitative. Advanced math typically starts with logic and structures, not numbers. Even when they study numbers, they tend to be focusing on their qualitative properties: compactness, convexity, primeness, etc.
- coldtea 4y ago>I mean, at a certain point, you're just abstracting logical thinking in general and calling it "math". Which isn't that bad a thing to do. Many programmers could use more formal logical thinking (or, just, logical thinking to begin with). DailyWTF situations, which most of us have seen in our jobs, are often the case of non applying basic logical principles properly.