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Mathematical language is precise. Problem 1 of this problem sheet is expressed in precisely as many words and symbols as is required. You dont need any more la

by wayn3 10y ago

Mathematical language is precise. Problem 1 of this problem sheet is expressed in precisely as many words and symbols as is required. You dont need any more language to fully understand the problem. Any less, and the problem would not be correctly specified. That is the beauty of mathematics. The things you say are always falsifiable. When taking a math exam, you can not contest having "misunderstood the question". The question is precise. By saying you "misunderstood it", you acknowledge that you don't understand the topic well enough to pass the exam. There are no ambiguities in correctly expressed math. Whatever youre going to write down as your answer for problem 1a) is either correct or its not. No amount of arguing is going to change that. We don't need to write essays and we don't want to. We just apply what's been proven correct to solve new problems. If math problems were "communicated in more natural ways", they would be reduced to problems people are going to argue and reason about, like they do in a liberal arts class. If you don't want cough up the required rigor, just go do something different. Mathematics does not make amendments for the rigor impaired. If you want to study something math-y without all the rigorous proofs, physics is what you're looking for.

demonshalo 10y ago
> When taking a math exam, you can not contest having "misunderstood the question". The question is precise. By saying you "misunderstood it", you acknowledge that you don't understand the topic well enough to pass the exam. This right here is completely unfair and infuriating. Great mathematicians always find themselves taking the wrong turn and producing the wrong result(s) because they "misunderstood the question". Granted they learn form their mistake and revise and iterate until they get their theories and proofs right. But if they constantly fail, how could you then claim that they "don't understand the topic well enough". Are you telling me that Tao does not understand prime numbers well enough because he cannot solve for formula X? This is the 3rd post that I reply to that seem to illustrate my point. You are RIGHT about the nature of mathematical language. But you CANNOT appeal to the general public with that arrogant attitude. You cannot communicate using dense language and expect non-math people to relate or even care. Granted, you might not give a fuck about that. But that is counter productive because if you want more rigor in society you should introduce more people to math rather than having them being put-off by some elitist attitude. Once again, this is a M.SC. Exam so it should be this way. My issue is with math communication to the public in general, not this pdf specifically!
- wayn3 10y ago
  I don't expect non-math people to relate or even care. If you open a textbook on algebraic topology and you've never studied even the most mundane calculus, you won't understand anything. Somehow, this infuriates people. The same people would have no problem admitting that they should probably not read specialized literature on law that requires readers to have gone through 8 years of law school before they can make sense of the content. Mathematical literature is not meant for casuals. Its impossible to express advanced concepts concisely, in such a way that people who don't know the material can understand them. This is like asking someone for an explanation on how to walk and then throwing a fit when they reply with "well, place one foot on front of the other in such a way that you dont fall over". You don't expect them to discuss activation levels in skeletal musculature resulting from biochemical processes in the nervous system. But in Math, thats what you want. Clear and concise language that inspires and is fun AND fully describes the problem at the same time. Not going to happen.
  - demonshalo 10y ago
    You still don't get it... You are arguing against something I did not say!
    - wayn3 10y ago
      Theres no elitism in math. We just require you to write proof in such a way that it is actually a proof, and not just some idea you've had. In order to do that, you need to study math. Not because we are elitists but because you need to learn how to prove something. You need to learn the tools. The same way a mason expects you to learn his craft before he takes you seriously. If you don't have a clue about masonry, you can still semi reliably build a brickwall in your backyard. But not a cathedral. Obviously, you dont expect anyone to allow you to work on a cathedral. But you expect mathematicians to take your thoughts on math seriously. Its like a bootcamp idiot trying to piss all over a big software project. Just because they know how to vomit on a keyboard doesnt mean they get to make decisions.
      - 10y ago
exergy 10y ago
> If you don't want to cough up the required rigor... Forgive me, but this sounds absurdly elitist. Mathematics is not a subject reserved for a select set of chosen elite. It is a very necessary tool for almost every scientific endeavour. And this is a huge problem because people in those fields aren't just studying maths. Case in point, I'm a mechanical engineer. I have to study thermodynamics, materials, structural analysis, mechanics and on and on. In the midst of all this, I needed to learn advanced numerical methods, but was flummoxed because it was taught by a senior professor, to a class of mostly mathematicians, with an inordinately huge amount of effort placed towards proving things etc. and not much thought spared for us non-applied mathematicians. I once heard maths described as something like "a person sees a category of something that exhibit a certain behaviour and then abstracts away the specifics to be left with a set of "general principles" that let the something exhibit it's behaviour". Thing is, it sounds like you start from the specific and abstract towards the general, but it is taught as a general and I am left to my own devices when dealing with the specific. All for good reasons I'm sure, but then who is making a case for how we lesser mortals learn it? I was nearly in tears by the end of the course, convinced of my own stupidity and incompetence, because it was as if the class was communicating in their own language, and I (and other aerospace guys) were the village idiots who accidently made it in. It was only after I took it upon myself later to learn using a lot of youtubing, "maths for idiots" type backtracking that I was able to learn just enough.
- demonshalo 10y ago
  >I once heard maths described as something like "a person sees a category of something that exhibit a certain behaviour and then abstracts away the specifics to be left with a set of "general principles" that let the something exhibit it's behaviour". Thing is, it sounds like you start from the specific and abstract towards the general, but it is taught as a general and I am left to my own devices when dealing with the specific. You made my point far better than I ever could. When I am faced with a general abstraction I have to conceptualize it in terms that I understand (the specific). Yet when the general case is presented, very little is said about the specific so I have to grind for months until I can finally maybe understand what was being meant. All of that could have been prevented had the concept been communicated in a more friendly, yet still mathematical, manner. >All for good reasons I'm sure, but then who is making a case for how we lesser mortals learn it? I was nearly in tears by the end of the course, convinced of my own stupidity and incompetence, because it was as if the class was communicating in their own language, and I (and other aerospace guys) were the village idiots who accidently made it in. That's how I felt constantly in college and it is actually part of the the reason I dropped out. It almost felt as if this alienation is intentional. Which makes me somewhat sad!
nikofeyn 10y ago
> The things you say are always falsifiable. is that necessarily absolutely true? i myself would take a deep breath before making such a wide-sweeping claim. first thing that pops into my mind is the axiom of choice and also godel's work. i am sure there are a ton more examples. > There are no ambiguities in correctly expressed math. not accurate because define "correctly expressed". ambiguities absolutely exist in mathematics, though people do indeed seek to weed them out. but i think you are romanticising mathematics too much. it can be messy and confusing because even mathematicians can disagree what the right way to do mathematics is. and once you get into various models and approaches (e.g., set theory vs category theory, classical logic vs intuistic or constructive logic) this is made more apparent. take smooth infinitesimal analysis for example. it completely turns on its head what you know about differentiable functions because it chooses to work in a different logic and model than classical calculus and analysis. the amiguity is clear because which is correct? people need to relax when bible thumping their mathematical sermons. mathematics is not something etched in stone by the universe. it is very much an art as it is an application of logic and should not be treated as such an elitist subject.
- Smaug123 10y ago
  > > The things you say are always falsifiable. > is that necessarily absolutely true? i myself would take a deep breath before making such a wide-sweeping claim. first thing that pops into my mind is the axiom of choice and also godel's work. Broadly speaking, if things aren't falsifiable, they're either provably not falsifiable (so everyone knows that debating their truth isn't particularly fruitful, like the case of Choice), or they're precise but not provably unfalsifiable (Gödel might permit this, but we have never yet found a plausible example of such a statement), or they're imprecise (in which case they're recognised as being "not yet rigorous").
- wayn3 10y ago
  > is that necessarily absolutely true? i myself would take a deep breath before making such a wide-sweeping claim. first thing that pops into my mind is the axiom of choice and also godel's work. i am sure there are a ton more examples. thats kind of true, but axioms are not "results" of math, they are starting points. they are deliberate. although most mathematicians would argue that our set of axioms is "reasonable", we have just agreed to use them. that is true.
waynisarapist 10y ago
He is very comfortable with hurting science.

by wayn3 10y ago

demonshalo 10y ago

> When taking a math exam, you can not contest having "misunderstood the question". The question is precise. By saying you "misunderstood it", you acknowledge that you don't understand the topic well enough to pass the exam. This right here is completely unfair and infuriating. Great mathematicians always find themselves taking the wrong turn and producing the wrong result(s) because they "misunderstood the question". Granted they learn form their mistake and revise and iterate until they get their theories and proofs right. But if they constantly fail, how could you then claim that they "don't understand the topic well enough". Are you telling me that Tao does not understand prime numbers well enough because he cannot solve for formula X? This is the 3rd post that I reply to that seem to illustrate my point. You are RIGHT about the nature of mathematical language. But you CANNOT appeal to the general public with that arrogant attitude. You cannot communicate using dense language and expect non-math people to relate or even care. Granted, you might not give a fuck about that. But that is counter productive because if you want more rigor in society you should introduce more people to math rather than having them being put-off by some elitist attitude. Once again, this is a M.SC. Exam so it should be this way. My issue is with math communication to the public in general, not this pdf specifically!

wayn3 10y ago
I don't expect non-math people to relate or even care. If you open a textbook on algebraic topology and you've never studied even the most mundane calculus, you won't understand anything. Somehow, this infuriates people. The same people would have no problem admitting that they should probably not read specialized literature on law that requires readers to have gone through 8 years of law school before they can make sense of the content. Mathematical literature is not meant for casuals. Its impossible to express advanced concepts concisely, in such a way that people who don't know the material can understand them. This is like asking someone for an explanation on how to walk and then throwing a fit when they reply with "well, place one foot on front of the other in such a way that you dont fall over". You don't expect them to discuss activation levels in skeletal musculature resulting from biochemical processes in the nervous system. But in Math, thats what you want. Clear and concise language that inspires and is fun AND fully describes the problem at the same time. Not going to happen.
- demonshalo 10y ago
  You still don't get it... You are arguing against something I did not say!
  - wayn3 10y ago
    Theres no elitism in math. We just require you to write proof in such a way that it is actually a proof, and not just some idea you've had. In order to do that, you need to study math. Not because we are elitists but because you need to learn how to prove something. You need to learn the tools. The same way a mason expects you to learn his craft before he takes you seriously. If you don't have a clue about masonry, you can still semi reliably build a brickwall in your backyard. But not a cathedral. Obviously, you dont expect anyone to allow you to work on a cathedral. But you expect mathematicians to take your thoughts on math seriously. Its like a bootcamp idiot trying to piss all over a big software project. Just because they know how to vomit on a keyboard doesnt mean they get to make decisions.
    - 10y ago

exergy 10y ago

> If you don't want to cough up the required rigor... Forgive me, but this sounds absurdly elitist. Mathematics is not a subject reserved for a select set of chosen elite. It is a very necessary tool for almost every scientific endeavour. And this is a huge problem because people in those fields aren't just studying maths. Case in point, I'm a mechanical engineer. I have to study thermodynamics, materials, structural analysis, mechanics and on and on. In the midst of all this, I needed to learn advanced numerical methods, but was flummoxed because it was taught by a senior professor, to a class of mostly mathematicians, with an inordinately huge amount of effort placed towards proving things etc. and not much thought spared for us non-applied mathematicians. I once heard maths described as something like "a person sees a category of something that exhibit a certain behaviour and then abstracts away the specifics to be left with a set of "general principles" that let the something exhibit it's behaviour". Thing is, it sounds like you start from the specific and abstract towards the general, but it is taught as a general and I am left to my own devices when dealing with the specific. All for good reasons I'm sure, but then who is making a case for how we lesser mortals learn it? I was nearly in tears by the end of the course, convinced of my own stupidity and incompetence, because it was as if the class was communicating in their own language, and I (and other aerospace guys) were the village idiots who accidently made it in. It was only after I took it upon myself later to learn using a lot of youtubing, "maths for idiots" type backtracking that I was able to learn just enough.

demonshalo 10y ago
>I once heard maths described as something like "a person sees a category of something that exhibit a certain behaviour and then abstracts away the specifics to be left with a set of "general principles" that let the something exhibit it's behaviour". Thing is, it sounds like you start from the specific and abstract towards the general, but it is taught as a general and I am left to my own devices when dealing with the specific. You made my point far better than I ever could. When I am faced with a general abstraction I have to conceptualize it in terms that I understand (the specific). Yet when the general case is presented, very little is said about the specific so I have to grind for months until I can finally maybe understand what was being meant. All of that could have been prevented had the concept been communicated in a more friendly, yet still mathematical, manner. >All for good reasons I'm sure, but then who is making a case for how we lesser mortals learn it? I was nearly in tears by the end of the course, convinced of my own stupidity and incompetence, because it was as if the class was communicating in their own language, and I (and other aerospace guys) were the village idiots who accidently made it in. That's how I felt constantly in college and it is actually part of the the reason I dropped out. It almost felt as if this alienation is intentional. Which makes me somewhat sad!

nikofeyn 10y ago

> The things you say are always falsifiable. is that necessarily absolutely true? i myself would take a deep breath before making such a wide-sweeping claim. first thing that pops into my mind is the axiom of choice and also godel's work. i am sure there are a ton more examples. > There are no ambiguities in correctly expressed math. not accurate because define "correctly expressed". ambiguities absolutely exist in mathematics, though people do indeed seek to weed them out. but i think you are romanticising mathematics too much. it can be messy and confusing because even mathematicians can disagree what the right way to do mathematics is. and once you get into various models and approaches (e.g., set theory vs category theory, classical logic vs intuistic or constructive logic) this is made more apparent. take smooth infinitesimal analysis for example. it completely turns on its head what you know about differentiable functions because it chooses to work in a different logic and model than classical calculus and analysis. the amiguity is clear because which is correct? people need to relax when bible thumping their mathematical sermons. mathematics is not something etched in stone by the universe. it is very much an art as it is an application of logic and should not be treated as such an elitist subject.

Smaug123 10y ago
> > The things you say are always falsifiable. > is that necessarily absolutely true? i myself would take a deep breath before making such a wide-sweeping claim. first thing that pops into my mind is the axiom of choice and also godel's work. Broadly speaking, if things aren't falsifiable, they're either provably not falsifiable (so everyone knows that debating their truth isn't particularly fruitful, like the case of Choice), or they're precise but not provably unfalsifiable (Gödel might permit this, but we have never yet found a plausible example of such a statement), or they're imprecise (in which case they're recognised as being "not yet rigorous").
wayn3 10y ago
> is that necessarily absolutely true? i myself would take a deep breath before making such a wide-sweeping claim. first thing that pops into my mind is the axiom of choice and also godel's work. i am sure there are a ton more examples. thats kind of true, but axioms are not "results" of math, they are starting points. they are deliberate. although most mathematicians would argue that our set of axioms is "reasonable", we have just agreed to use them. that is true.

waynisarapist 10y ago

He is very comfortable with hurting science.