49 Replies  6378 Views  Last Post: 17 July 2012  01:05 PM
#16
Re: Basic Stupidity
Posted 12 July 2012  09:08 PM
Although programming and computer science are obviously derived from mathematics, I don't think there's anything wrong with approaching computer science with a "learn (math) as you go" mindset. Most people can be very good in their mathrelated profession if they just know the stuff required for the SAT  namely algebra II and geometry. After a point (maybe higher than algebra II, correct me if I'm wrong, as I don't know how useful calculus is), learning more math is just superfluous.
A large portion of very advanced math is useless, really, unless you're a professor in some pretentious, impractical field where you get a buzz from writing arcane equations on a blackboard all day in hopes that some inferior being who probably makes $100,000 more than you sees you and your convoluted equations on the Science channel.
So don't feel bad about not knowing everything about math. It's certainly helpful, but overrated. Programming is logic, not calculus.
#17
Re: Basic Stupidity
Posted 13 July 2012  02:16 AM
So if you are afraid of becoming such a person then start learning right now. There are tons of materials you can use to learn so that is not a problem.
#18
Re: Basic Stupidity
Posted 13 July 2012  04:34 AM
The whole philosophy behind Khan Academy is, in my opinion, a great one
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I think they do great work and you sound like you could definitely benefit from checking out the site.
This post has been edited by Jstall: 13 July 2012  04:36 AM
#19
Re: Basic Stupidity
Posted 13 July 2012  06:51 AM
AVReidy, on 12 July 2012  11:08 PM, said:
Programming is logic, and logic is math. Calculus is not advanced math, calculus is one tool for analyzing equations and finding points in them. There's a lot to math that has little relation to calculus, and a lot of it is stuff you use every day, without knowing it.
#20
Re: Basic Stupidity
Posted 13 July 2012  07:42 AM
jon.kiparsky, on 13 July 2012  09:51 AM, said:
Yes.
jon.kiparsky, on 13 July 2012  09:51 AM, said:
No.
Math is so greedy. It sees an organized method of inquiry and immediately lays claim to entire disciplines that were doing perfectly fine with it. There are systems of logic considered mathematical and those that aren't. Simple reasoning is NOT math. And this is the "logic" that is required for programming.
Can logic be express in symbolic mathematical terms? Sure. However, this is not required to use logic.
#21
Re: Basic Stupidity
Posted 13 July 2012  08:55 AM
And it's on that basis that I claim, and maintain, that logic is essentially a branch of math.
Math is not fundamentally about numbers. Math is fundamentally about abstract reasoning in formal systems  this is why math includes plane geometry, which has no sense of numbers and only a formal system, and why it also includes numbers (which are derived from axioms, and not from the real world) and arithmetic, algebra, and calculus, which are tools for manipulating and talking about numbers, and why it also includes something like group theory, which is about combinations of operations on complex systems, and so forth. Logic, as a formal system, clearly falls into this bailiwick, ergo it is part of math.
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I agree with this. However, simple reasoning (aka "common sense") is not coextensive with logic. There is logic in simple reasoning, and there is simple reasoning in logic, but if you evaluate a problem with common sense, you can come up with conclusions that logic, formally speaking, will not allow. That is, you can "prove" things with common sense which you haven't yet proved logically. Sometimes this is useful  for example, if something is obviously the case and you don't bother to prove it logically, and you're correct, you can save a lot of time. Sometimes this is problematic, for example, when something is obviously the case and you don't bother to prove it and you're incorrect. But the two sorts of thinking can establish different conclusions from the same premises, so they're not the same thing.
As a programmer, simple reasoning is certainly useful, but that's not what said. If you're talking about logic, you're talking about math.
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There are plenty of organized methods of inquiry which are not mathematical in nature. They might use mathematical tools to do their, but math does not try to lay claim to them. Economics, cognitive science, linguistics, and computer "science" (engineering, really, as many people have pointed out) are some examples.
#22
Re: Basic Stupidity
Posted 13 July 2012  09:17 AM
Instead of saying, "logic is math", it could be better to say, "math describes logic, therefore math is a great asset when it comes to logic".
I'm a huge proponent of math, but really math is a tool. You use math for something, you use it for logic. So you wouldn't say "building is a hammer", it's "a hammer helps me build".
Though logic is kind of a tool as well. But logic is certainly a more abstract set of tools, which mathematical logic is a member of. So let's rephrase my analogy again... you wouldn't say "building tools are a hammer", it's "a hammer is a building tool".
This post has been edited by lordofduct: 13 July 2012  09:20 AM
#23
Re: Basic Stupidity
Posted 13 July 2012  09:22 AM
jon.kiparsky, on 13 July 2012  11:55 AM, said:
As you define it. Reason is rather a blanket term. Both formal and informal. It includes philosophy, logic, mathematics and most other thought systems. If you were to say "programming is reason" I'd be right there with you.
As you contrast logic to common sense, you appear to be describing, ironically, deductive reasoning. You know, my "simple reasoning." This is logic. This is not necessarily math.
You clearly disagree with that. That's fine. I prefer my logic in the philosophy section. You may look for it in mathematics. You'll find it in both places.
#24
Re: Basic Stupidity
Posted 13 July 2012  10:13 AM
If that's what you mean by logic, then yes, that is not a branch of mathematics. When I said "logic is math" I was speaking of a formal system for manipulating formal systems, and that is a branch of math. I don't know that I will be able to say anything more about that statement that isn't a variation on this theme.
I have no problem with using reasoning that is not captured in formal logic, in fact I do it all the time, as does everyone. I'm just saying it's not the same thing as logic  not that it's not good, or that it can't lead us to useful insights, or whatnot.
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I can't disagree with this, because it seems a transparent restatement of my previous claim. I'm not sure if that was intentional or not, but I'm pleased to find us in agreement, assuming we are.
#25
Re: Basic Stupidity
Posted 13 July 2012  10:19 AM
#26
Re: Basic Stupidity
Posted 13 July 2012  10:35 AM
I'm not as bent about is as this guy, but I'm kind of with him.
Pythagoras, one of the great contributors ( and crackpots ) of math would have probably called himself a philosopher. Modern mathematics often becomes the short hand for some very clever ideas. It's cool you can derive the short hand, but I find the ideas are often more approachable in the original. I like ideas.
#27
Re: Basic Stupidity
Posted 13 July 2012  10:41 AM
baavgai, on 13 July 2012  12:35 PM, said:
I wouldn't say that I'm boiling stuff down to math. I'm just drawing a line around abstract formal systems and saying "this stuff is mathy". Everything else can use math to solve their problems without being math, but if it's an abstract formal system, I will call it mathematical.
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The funny thing is, he's saying exactly the same thing that I'm saying, only he's much more upset about it. There's lots of ways to come up with reasons, and formal logic is one of them. It's useful in a very limited set of contexts, for solving certain sorts of problems which must have certain characteristics.
He's talking about other sorts of systems of thought. He wants, confusingly enough, to call them "logic", but that's okay. As long as we're able to clarify what we mean, there's no real basis for argument. And we can all just get along. (RIP, Rodney King)
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And Newton did "natural philosophy"....
This post has been edited by jon.kiparsky: 13 July 2012  10:46 AM
#28
Re: Basic Stupidity
Posted 13 July 2012  10:41 AM
math to logic is not a transitive comparison.
(math = logic) =/= (logic = math)
#29
Re: Basic Stupidity
Posted 13 July 2012  10:47 AM
#30
Re: Basic Stupidity
Posted 13 July 2012  10:48 AM
Newton was a true Renaissance man; he did everything.
