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Author Topic: Random Stuff Part II  (Read 1217679 times)

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sudgy

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Re: Random Stuff Part II
« Reply #2075 on: November 26, 2014, 05:28:31 pm »
0

Can someone explain the math/science distinction you have in the States? Isn't Mathematics a science?

Mathematics is the study of manipulating abstract quantities, while science is the study of the universe through the scientific method.  I would say they are a lot different.
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Re: Random Stuff Part II
« Reply #2076 on: November 26, 2014, 05:30:11 pm »
+9

Can someone explain the math/science distinction you have in the States? Isn't Mathematics a science?

No problem:

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Re: Random Stuff Part II
« Reply #2077 on: November 26, 2014, 05:35:45 pm »
+1

I hate this xkcd comic so much, I can't even express it accurately into words. The French educative system worships at the altar of mathematics and it's just infuriating.

You know the guys that created the elaborate financial systems that led to the 2008 crisis* ? French people from prestigious schools (Polytechnique in particular) who thought everything and anything can be solved by maths.

* Not talking about the subprimes aspect of it, that's on you guys.
« Last Edit: November 26, 2014, 05:42:58 pm by Teproc »
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silverspawn

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Re: Random Stuff Part II
« Reply #2078 on: November 26, 2014, 05:37:38 pm »
+1

I hate this xkcd comic so much, I can't even express it accurately into words. The French educative system worships at the alter of mathematics and it's just infuriating.

You know the guys that created the elaborate financial systems that led to the 2008 crisis* ? French people from prestigious schools (Polytechnique in particular) who thought everything and anything can be solved by maths.

* Not talking about the subprimes aspect of it, that's on you guys.

the comic doesn't judge usefulness or importance though, just purity. Maybe it's misinterpreted, but I don't see anything wrong with it.

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Re: Random Stuff Part II
« Reply #2079 on: November 26, 2014, 05:38:54 pm »
+2

I hate this xkcd comic so much, I can't even express it accurately into words. The French educative system worships at the alter of mathematics and it's just infuriating.

You know the guys that created the elaborate financial systems that led to the 2008 crisis* ? French people from prestigious schools (Polytechnique in particular) who thought everything and anything can be solved by maths.

* Not talking about the subprimes aspect of it, that's on you guys.

Does that mean I won't get a "+1" from you? :(
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Re: Random Stuff Part II
« Reply #2080 on: November 26, 2014, 05:40:27 pm »
0

Oh yeah, maybe that wasn't clear : I'm not saying my haterd of that comic is justified, the guy is probably just making a joke, I'm saying it infuriates me because it's an attitude that is dominant here.
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Titandrake

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Re: Random Stuff Part II
« Reply #2081 on: November 26, 2014, 05:40:43 pm »
+3

To quote a pure math major I know, "Only math is legit. Computer science is bullshit. Applied math is slightly less bullshit."

More seriously, the core of math is coming up with useful definitions of what an object is, then proving properties that arise from this through logically consistent proofs that are impossible to dispute once properly understood, while science is about trying to model parts of the universe by coming up with theories that empirically match observations we can make about the universe. There's no longer a guarantee of logical consistency, and that's the main distinction. It's also why getting interested in anything after math can be kind of tricky...

Edit: When it comes to financial models, I don't think there exists a system that can provably generate value. If there was, it would be in ridiculously high demand. More accurately, there are reasonable underpinnings on which mathematics can operate on data generated by other means. For example, maybe we make lots of observations on different stock prices, and we assume it follows some distribution of values. Then math gives tools to manipulate that distribution and give useful information, but it's all still underpinned on the assumption that the distribution we use is correct/accurate enough. The 2008 crisis was caused in part because those assumptions weren't true.
« Last Edit: November 26, 2014, 05:45:07 pm by Titandrake »
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liopoil

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Re: Random Stuff Part II
« Reply #2082 on: November 26, 2014, 05:48:39 pm »
0

To quote a pure math major I know, "Only math is legit. Computer science is bullshit. Applied math is slightly less bullshit."

More seriously, the core of math is coming up with useful definitions of what an object is, then proving properties that arise from this through logically consistent proofs that are impossible to dispute once properly understood, while science is about trying to model parts of the universe by coming up with theories that empirically match observations we can make about the universe. There's no longer a guarantee of logical consistency, and that's the main distinction. It's also why getting interested in anything after math can be kind of tricky...
I like this definition much better than sudgy's. Definitions and making logical conclusions from definitions.

In regard to the last sentence... uh-oh...

Out of curiousity, what was the distinction between applied math and computer science that made applied math "slightly less bullshit"?
« Last Edit: November 26, 2014, 05:49:53 pm by liopoil »
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pacovf

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Re: Random Stuff Part II
« Reply #2083 on: November 26, 2014, 05:55:22 pm »
0

The vibe I am getting from this is that Maths is not considered a science because it is -pardon the speech- masturbatory in its nature, which I disagree with.
Mathematics don't exist in a vacuum, research is guided (loosely) by real life problems, whether in physics, criptography, computer science, what have you. There's not a clear cut distinction between some maths fields and theoretical physics, for example; it's not like the latter is super-super concerned about whether this particle can be observed or that spatial configuration can be interacted with. Respectively, statistical mathematics and probability are so much more in touch with reality.
So from the moment you have a continuum between maths and the "sciences", I am not sure the distinction isn't purely artificial.

EDIT: oh hey I am a jester now how fitting.
« Last Edit: November 26, 2014, 05:58:58 pm by pacovf »
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Re: Random Stuff Part II
« Reply #2084 on: November 26, 2014, 06:12:53 pm »
0

my favorite teacher in my old school taught us that there are two different types of scholarships. I'll call them "science" and "arts" although I'm not sure if that really fits. basically, everything that is based on nature is science, everything that's not is arts. He also said it's not a clear distinction, and there are people who claim that almost everything is science. For example, astronomy is clearly science, and astrology is probably arts. However, you could make the argument that even astrology is science because it's based on things in nature, and likewise, many scholarships that are widely considered arts are in fact science. He concluded that the only scholarship which is clearly not science is maths, because it is purely based on definitions. That always made sense to me.

The translation is iffy here though. In german, there are three terms:
Wissenschaft, which is translated science
Geisteswissenschaft, which literally means "science of the mind" and which I translated with arts, and
Naturwissenschaft, which literally means "science of nature" but which is used as a synonym for science.

So everything is called a science, it's just a question of what kind of science it is. The distinction in this case is between the latter two.

well anyway, I do think a distinction exists here. The English terms seem unfortunate though, because why should maths not be a science just because it's masturbatory. unless that's the kind of definition people have for science.

Titandrake

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Re: Random Stuff Part II
« Reply #2085 on: November 26, 2014, 06:21:31 pm »
0

Just so we're clear, I don't fully agree with that quote, although I do think there's an elegance in pure math that is hard to describe, and that elegance doesn't exist in other fields because there's complicated things like the real world in the way :P

There's definitely a sliding scale - I'd say that theoretical computer science and physics might as well be branches of math. The important distinction for me is "purity". I think a field of science is more pure if you can solve more problems by only logical thinking, or at least be able to make conjectures that are reasonably likely of being true because of a line of logical thinking you can create (for example, whatever people in string theory are doing right now. There's still not a way of showing that theory is correct, but that doesn't stop them from thinking through implications despite there being no real-world analogue to the work they are doing.)

Maths and Sciences are generally lumped together before college level education. I think that once you get into more advanced material, it makes more sense to differentiate subjects. You don't say Maths and Sciences, you say Math or Science. Then subdivide Science into Chemistry/Physics, and divide those further, and so on. I suppose that if you divide everything in small enough categories, some of those categories are going to start to look similar or overlap.

I think the reason he said that applied math was less bullshit is because all the methods you learn along the way are proven to work on any possible input values. The "bullshit" part is that it doesn't feel like you necessarily get an understanding of how this method may lead into other methods that give better approximations/results, and that's it's more interesting from a pure math perspective to operate on as abstract an object as possible. Something that approximates derivatives in the reals is kinda-boring, but something that generalizes a derivative to any collection of objects that allows addition + multiplication (aka a field) is more interesting, because it has more explanatory power.

TL;DR I got opinions man.
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GeoLib

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Re: Random Stuff Part II
« Reply #2086 on: November 26, 2014, 06:29:09 pm »
+1

I think people refer to math and science separately primarily because that's how it's generally understood in the language. I'm taking German right now, and my understanding is that Wissenschaft, which is translated to science, basically just means "knowledge creation" such that any academic is a Wissenschaflter. In English, people don't necessarily assume you're including math when you say "science," so you say both. That being said, math counts as natural science in my college curriculum.

I would say that math underpins science such that there is a lot of overlap between studying one or the other. However, math is not experimentally rooted, whereas science is. I can come up with a mathematical framework completely disconnected from reality and that's fine, but if your scientific theory doesn't actually predict anything about the way the world works it isn't much of a theory. However, people keep discovering that the weird artificial system mathematicians came up with is perfect for understanding some real-world problem. I was speaking with someone earlier today and he mentioned that when complex numbers were first invented, they were (with tongue firmly in cheek) lauded as having no practical applications, and then now of course they have a ton.

On the education discussion, I personally love doing in-class problems. I find it very frustrating when lecture is exclusively the teacher telling us things and much prefer to work things out myself when possible. Of course, the degree to which this is possible varies with the material. Probably my favorite class this semester is an algorithms course in which the professor has slides (where the different things appear one at a time), and the general format is that she explains what a problem is, usually with visual aids, and then challenges us to work in groups to figure out how to do it. Then we return to the full class and people offer up their suggestions and she works from however far we got to a full solution.
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eHalcyon

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Re: Random Stuff Part II
« Reply #2087 on: November 26, 2014, 06:29:34 pm »
+3

my favorite teacher...

My favourite teacher was my grade 3 teacher.  He was kind and funny, and he engaged with students using an in-class currency as a reward for various things.  Every Friday there would be a "store day" where a rotating group of students could bring in home-made crafts and treats to sell to the other students using the in-class currency.  There were regular contests where he would give us a category and then we would go home and make lists of things relating to that category.  We would earn currency based on how long our lists were.  I remember spending a couple hours trying to think of things related to astronomy for this.  It was really good for creative thinking.  At the end of the year, he brought in a bunch of random stuff and held an auction with everyone in the class.

I was stoked when I got him again for grade 4, but he disappeared halfway through the year.  We had a series of substitute teachers before getting a more permanent replacement.  I learned later on that he had been busted for illegal drug use.  I can't remember exactly what it was; I think it was marijuana and minors were involved.  Little 10 year old me was crushed.
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Dsell

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Re: Random Stuff Part II
« Reply #2088 on: November 26, 2014, 07:01:28 pm »
+2

random stuff

And we've come full circle! Good work, guys! Let's pack it up.



P.S. that sucks :(
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Re: Random Stuff Part II
« Reply #2089 on: November 26, 2014, 07:12:20 pm »
+1

random stuff

And we've come full circle! Good work, guys! Let's pack it up.



P.S. that sucks :(

It was not the greatest thing when I was a kid, but I got over it.  Life happens, and now I have a neat anecdote about it.

In Alberta, grade 7-9 is Jr. High (some other places have grades 6-8 as middle school, I think... it varies).  While elementary grades stick with one teacher in one room, Jr. High is when you start to move around to different teachers for different subjects.  We still stuck with the same classmates though, and we had a homeroom.

There was to be a school-wide canned food drive, with homerooms competing.  It was announced early, and the prize was a pizza party.  With such high stakes, there was no way we would play by the rules.  We began collecting food in advance, hiding our illegal goodwill in the cupboards beneath the desk "islands" (hexagonal stations with sinks and such; it was a science classroom).  We easily won.  The pizza was delicious.
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AHoppy

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Re: Random Stuff Part II
« Reply #2090 on: November 26, 2014, 07:17:36 pm »
+1

Re: Math/science discussion
I was in Engineering Math last semester (Basically a class that fills in the gaps from the math classes we took, so it took parts from classes like stats, and linear algebra because those aren't required courses). I remember my prof was teaching us about eigenvectors, and gave us the definition that it's the vector you multiply some vector by to get the same vector multiplied by some scalar (correct me if that's wrong... this is just from memory and wikipedia).  Well, some students of course didn't quite understand this definition, because as engineers, most of us require some kind of application in order to understand.  So he goes and shows us how you can use eigenvectors/eigenvalues to solve (I think it was) mass+spring oscillatory systems.  He told us a story about how he was at some kind of academic conference once, talking to a mathematician and telling him how he loved to teach his engineering students about eigenvectors by showing them how to solve mass+spring problems and how it helped them understand the concept.  To which the mathematician replied "Well then they don't really understand eigenvectors".  And this is my biggest beef with mathematicians in general: they seem to deny the practical use of what they are doing and are merely concerned with the theoretical and philosophical value in mathematics.  I know there are probably many who don't think that and I'm not saying I think mathematicians don't recognize applications, but it just doesn't feel right to tell me I don't understand something because I require some application of the concept.

TL;DR - eigenvectors

pacovf

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Re: Random Stuff Part II
« Reply #2091 on: November 26, 2014, 07:32:17 pm »
+1

Re: Math/science discussion
I was in Engineering Math last semester (Basically a class that fills in the gaps from the math classes we took, so it took parts from classes like stats, and linear algebra because those aren't required courses). I remember my prof was teaching us about eigenvectors, and gave us the definition that it's the vector you multiply some vector by to get the same vector multiplied by some scalar (correct me if that's wrong... this is just from memory and wikipedia).  Well, some students of course didn't quite understand this definition, because as engineers, most of us require some kind of application in order to understand.  So he goes and shows us how you can use eigenvectors/eigenvalues to solve (I think it was) mass+spring oscillatory systems.  He told us a story about how he was at some kind of academic conference once, talking to a mathematician and telling him how he loved to teach his engineering students about eigenvectors by showing them how to solve mass+spring problems and how it helped them understand the concept.  To which the mathematician replied "Well then they don't really understand eigenvectors".  And this is my biggest beef with mathematicians in general: they seem to deny the practical use of what they are doing and are merely concerned with the theoretical and philosophical value in mathematics.  I know there are probably many who don't think that and I'm not saying I think mathematicians don't recognize applications, but it just doesn't feel right to tell me I don't understand something because I require some application of the concept.

TL;DR - eigenvectors

For a given matrix A, an eigenvector V of eigenvalue (a number) λ is a vector such that:

A*V = λ*V


About the mathematician example, it's just like saying that people don't know how to use Windows just because they know how to Google stuff and open Word. It's not about the applications per se, I don't think there's nothing wrong about his opinion, but not being there, I can't say how much of a dick he was about it.
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Re: Random Stuff Part II
« Reply #2092 on: November 26, 2014, 07:56:58 pm »
+2

I would say that math underpins science such that there is a lot of overlap between studying one or the other. However, math is not experimentally rooted, whereas science is. I can come up with a mathematical framework completely disconnected from reality and that's fine, but if your scientific theory doesn't actually predict anything about the way the world works it isn't much of a theory. However, people keep discovering that the weird artificial system mathematicians came up with is perfect for understanding some real-world problem. I was speaking with someone earlier today and he mentioned that when complex numbers were first invented, they were (with tongue firmly in cheek) lauded as having no practical applications, and then now of course they have a ton.

I think you could argue that Math is experimentally rooted in a way. Everything is derived from an axiom system that we assume to be true based on our naive thinking and observation.
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Re: Random Stuff Part II
« Reply #2093 on: November 26, 2014, 07:57:48 pm »
+1

Re: Math/science discussion
I was in Engineering Math last semester (Basically a class that fills in the gaps from the math classes we took, so it took parts from classes like stats, and linear algebra because those aren't required courses). I remember my prof was teaching us about eigenvectors, and gave us the definition that it's the vector you multiply some vector by to get the same vector multiplied by some scalar (correct me if that's wrong... this is just from memory and wikipedia).  Well, some students of course didn't quite understand this definition, because as engineers, most of us require some kind of application in order to understand.  So he goes and shows us how you can use eigenvectors/eigenvalues to solve (I think it was) mass+spring oscillatory systems.  He told us a story about how he was at some kind of academic conference once, talking to a mathematician and telling him how he loved to teach his engineering students about eigenvectors by showing them how to solve mass+spring problems and how it helped them understand the concept.  To which the mathematician replied "Well then they don't really understand eigenvectors".  And this is my biggest beef with mathematicians in general: they seem to deny the practical use of what they are doing and are merely concerned with the theoretical and philosophical value in mathematics.  I know there are probably many who don't think that and I'm not saying I think mathematicians don't recognize applications, but it just doesn't feel right to tell me I don't understand something because I require some application of the concept.

TL;DR - eigenvectors

For a given matrix A, an eigenvector V of eigenvalue (a number) λ is a vector such that:

A*V = λ*V


About the mathematician example, it's just like saying that people don't know how to use Windows just because they know how to Google stuff and open Word. It's not about the applications per se, I don't think there's nothing wrong about his opinion, but not being there, I can't say how much of a dick he was about it.
True.  I wasn't there either, but that isn't quite the same... The person who understands what an eigenvector is completely doesn't mean they know how to use it to solve a spring+mass problem.  But is it better to understand everything about the concept "eigenvector", or to have a working knowledge of them, but be able to use them to solve real problems?  I don't know, it's mostly my bias as an engineer, but I'd say the latter.

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Re: Random Stuff Part II
« Reply #2094 on: November 26, 2014, 08:09:41 pm »
+2

It depends.

I read the mathematician's point as "engineers don't really understand what eigenvectors ARE", and the engineer point as "the mathematician doesn't understand what eigenvectors are USED for". I don't think either view is better than the other.

The engineer does have a disadvantage, in that he lacks a part of the picture, so if he encounters a problem in his reasoning, he can't be sure if he is the one that made a mistake, or if there's something in his understanding of whichever mathematical object that is only an approximation of the real thing.
I've had to explain some fairly basic stuff about linear algebra to some friends late in their engineering careers because their teachers never bothered to properly define some objects before using them. The problem here is the teacher, who made a bad call about what was and what wasn't required to be known to work effectively.
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Re: Random Stuff Part II
« Reply #2095 on: November 26, 2014, 08:16:14 pm »
+1

Next time someone goes off on a tangent about eigenvectors, just stand up, grab his papers from him, scream "Those are MY vectors!", and storm off. Or violently erase what he wrote from the blackboard if he's not writing it on something grabbable. 
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Re: Random Stuff Part II
« Reply #2096 on: November 26, 2014, 08:34:57 pm »
+1

Pure mathematicians care about applications too. It's just that those applications consist of applying math to other math. :P
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Re: Random Stuff Part II
« Reply #2097 on: November 26, 2014, 08:42:32 pm »
0

I am the math that cries.
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Re: Random Stuff Part II
« Reply #2098 on: November 26, 2014, 08:46:17 pm »
+9

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Re: Random Stuff Part II
« Reply #2099 on: November 26, 2014, 08:48:49 pm »
+5

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