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Why is it that I find these questions always posed in a way that is MEANT TO make me NOT understand them? Granted, math is not my topic. However, I am intereste

Why is it that I find these questions always posed in a way that is MEANT TO make me NOT understand them? Granted, math is not my topic. However, I am interested and want to learn. I don't mean to be a dick, but I just simply find it frustrating that the goal of most mathematicians is to pose some question/conjecture in as few sentences as humanly possible. It really grinds my gears how interesting problems are always abstracted behind confusing vertical specific language. Even when reading a Wikipedia article about some cool problem, you get hit in the face with some abstraction that makes most problems seem far more complicated than they actually are. This is probably not a view shared by many here, but if math problems were to be communicated in more natural ways, far more people would be interested in the sciences. Just my 2 cents! Ps. I understand that this is an M.SC. exam. I am talking about math in general, not this pdf!

yiyus 10y ago
I do not agree this is the case. Can you give an example? How would you express these questions "in more natural ways"? (alternatively, feel free to point me to some example with other questions)
sytelus 10y ago
The issue is that even a little bit of non-technical language can cause loss of precision. A regular person would love if the technical language was watered down and sprinkled with colorful analogies but this is not often helpful to actually attack the problem. The problems in OP link builds on large pyramid of concepts and abstractions all the way starting from numbers. There is no way out than to walk through this hierarchy of concepts one at a time for many years to finally gain understanding of the problem. Sugar coated explanations might make you feel good but don't actually help work on it.
- demonshalo 10y ago
  I understand that and agree 100%. However, what I was trying to say is that for a non-technical person who is trying to understand a concept rather than solving a problem, accuracy is not the main concern. Sometimes you just need to understand the line of reasoning "roughly speaking". and as I said at the end, I understand that this is a set of M.SC. exam question and my issue is not with this pdf specifically. Take the problem of Integer Factorization, something that I have personally been fascinated by for years. The problem is so ridiculously simple that a 5 year old could understand it. With that said, google for a few wikipedia articles and see the notation and the way it is presented. The non-mathematician does not care about difference of squares or triangular numbers or what.have.you. It seems to be the case that mathematicians are unable to talk about math without requiring the person they are talking to to have extensive knowledge of the topic. That's IMO why Carl Sagan and Feynman were so great. They could take complex problems and reduce them (read communicate) in a good way that most could understand and reason about without needing to traverse the entirety of the knowledge pyramid. Similarly, that is what Numberphile does so well.
  - blahblah3 10y ago
    My suggestion would be to slow down when reading math or about math. Let's take Wikipedia's integer factorization for example: https://en.wikipedia.org/wiki/Integer_factorization https://en.wikipedia.org/wiki/Integer_factorization First paragraph is: "In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these integers are further restricted to prime numbers, the process is called prime factorization." This is a clear and precise statement of the problem. There are some key words that one might need to look up which takes time, but that's what I mean by slowing down.
    - demonshalo 10y ago
      Be kind and do this for me: Think of yourself as Sara, an average person in society. Put yourself in her shoes. Now click on the following link and scroll down for a bit. https://en.wikipedia.org/wiki/Factorization https://en.wikipedia.org/wiki/Factorization Scroll as slowly as you want/can. Tell me, do you think that this is a good way to communicate to Sara why this problem is of importance? or even better, do you think Sara will ever give a shit if all she can see is that? If you want to promote a more scientifically literate society, you should not try to render every single person into a scientists. Rather, try introducing scientific thinking into people's every day lives. The only way that will happen is if those who know the sciences learn to communicate better with the rest of us and help us get it into our daily lives. can you see where I am coming from? I am not annoyed by math or my ignorance toward the topic. I am trying my best to combat it. But the problem I often encounter is that those who know/can rarely speak the same language as those who cannot. Khan Academy grew big because he knew how to communicate, more people should be like him imo.
      - sammoth 10y ago
        All your examples of the problem you are talking about are from Wikipedia, but you give multiple examples in your posts of explanations of maths done the right way. Feynman, Khan Academy, Project Euler. So I guess some maths related text is written one way and some is written another way?
slurry 10y ago
I don't know, I was able to understand the initial problem statements, and even a bit of the numbered sub-problems, and I'm a trained classicist pig-ignorant in math.
umanwizard 10y ago
What do you think could be stated better? I studied math (I.e., I'm the target audience of this) and the problem statements were perfectly clear to me (although I don't remember how to solve most of the stuff) There really isn't a shortcut to math. I can tell you what to read in order to understand these questions, but it might take you a few years.
- demonshalo 10y ago
  > it might take you a few years. My complaint was not about these questions. These are M.Sc. exam questions and it should take you years of study to undertand and be able to solve them. My complain was about math communication in general. It shouldn't take me years of study to understand a question on a basic level. I gave the example of prime factorization earlier but you can think of how most math problems are communicated to the general public. A great example to illustrate my point is Project Euler. The way problems are communicated on PE is vastly different than the way they are communicated by professors, wikipedia or most other outlets. Every problem there starts with an introduction followed by a set of assumptions and a posed problem to be solved. It is far more friendly and inviting of a way to communicate math problems to the general public!
  - empath75 10y ago
    It doesn't take years of study. Those are mostly fairly basic linear algebra and calculus questions. You could learn enough to understand the basics by watching some khan academy videos.
    - umanwizard 10y ago
      You're assuming a solid understanding of pre-calculus math. It might well take 2+ years for people with no exposure to proofs, or who have a weak foundation in elementary algebra.
QuantumRoar 10y ago
The questions are actually pretty clear. The problem is that you lack a general understanding of mathematical concepts and therefore you don't know what to do with it. But that's fine and that's actually what the exam is for, i.e. only those may pass who understand these things. >This is probably not a view shared by many here, but if math problems were to be communicated in more natural ways, far more people would be interested in the sciences. I would argue the opposite. If more problems could be as well posed as mathematical problems, we wouldn't have people bullshitting their way through arguments that are in dire need of some scientifical rigor (see climate science, psychology, and other disciplines that are too complex to isolate phenomena completely). You can't handwave your way through a math exam and you shouldn't be able to do it in other fields of science.
- demonshalo 10y ago
  > I would argue the opposite. If more problems could be as well posed as mathematical problems, we wouldn't have people bullshitting their way through arguments that are in dire need of some scientifical rigor (see climate science, psychology, and other disciplines that are too complex to isolate phenomena completely). You can't handwave your way through a math exam and you shouldn't be able to do it in other fields of science. Amen. I have been saying that for years. But I think you misunderstood my original post. I am all for 100% scientific rigidity and less bullshit in society. But what you seem to classify as "clear" is not-so-clear to others. It's actually about how condensed the information is in each question. In order to unpack those questions, you need years of experience within that field in order to get anywhere. I bet you anything that each one of these questions could be posed in a different, yet still mathematical, manner that would make most non-mathy people (such as myself) at least understand the gist of what is being asked. But that is not something mathematicians are interested in. Which is what I was trying to say.
  - tankenmate 10y ago
    The issue is that each provable discovery in mathematics is named; it has to have a unique name. These discoveries are exact with at least one proof for their validity and for their limitations and assumptions; all that information is tied up in a name, say for example eigenvalues. These proofs are built on top of previous proofs (which of course are named as well), names and phrases built upon each other. So this ever growing collection of proofs and names is an accretion (or in our moments of grander hubris a pyramid). What you are asking for is the tip of the pyramid (with its wonderful view) without the stones below, in effect what you are asking for is magic, a stone floating in the air with nothing to support it.
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!
kbart 10y ago
We don't do math in human language for the same reason we don't write computer programs in human language: it's ambiguous and hard to define abstract objects using it. Only abstraction enables us to operate higher level, non-trivial problems.
- ashark 10y ago
  I just wish Math followed programming best-practices on commenting, variable naming, and including tests and their expected output. Bonus for IDE-like tools that can instantly tell me the type of a symbol or show me the expanded version of an operation.
  - kbart 10y ago
    Matlab then?
  - tnecniv 10y ago
    I agree, maybe because I learned to program way before I got into rigorous math. I really wish the community standardized notation more.
VerbatimVeritas 10y ago
I am in complete agreement. I've done a fair amount of teaching, which is to say I was employed to communicate information, such that someone else (from a fairly random selection sample) could and would remember it well enough to actually use the information productively. I have done this so much that I feel poorly abou tleaving the last paragraph as it is, given that I know there is most certainly a way to find a more parsimonious way to express what I am saying, and I think that is the trust of why mathematical language (and the language in wikis, or APIs, for example) is succinct to the point of absurdity. Everyone is striving for what's called maximum information density, communicating as much data with as few words as possible, and they do so in the jargon of their respective fields of interest. The problem is, those that are not specialized in that field cannot decipher the language well enough to gain anything of use from their efforts at being succinct. Quite the contrary, the field of potential interest becomes even less appealing for having appeared so mentally taxing to parse. Reddit has this ELI5 idea, which I think stems from Denzel Washington's character in the movie "Philadelphia" (Mr. Washington plays an attorney defending an AIDS patient who has been unduly fired) saying "Explain it to me like I'm five years old", to get people to reduce their use of jargon and get to the heart of the matter. Needless to say, the point I am making is that it is one of the great intangibles to be able to communicate one's self effectively, and in my experience is only done well when the communicator understands the level of interest and/or understanding of the communicatee, and can adjust their vocabulary "filter" accordingly. I think math is particularly tough in this regard because of the amount of time that goes into understanding topics that might be complex for an untrained observer (like an Eigen value, for instance, which are critical for a basic understanding of linear regression).
- demonshalo 10y ago
  > Everyone is striving for what's called maximum information density, communicating as much data with as few words as possible, and they do so in the jargon of their respective fields of interest. The problem is, those that are not specialized in that field cannot decipher the language well enough to gain anything of use from their efforts at being succinct. Quite the contrary, the field of potential interest becomes even less appealing for having appeared so mentally taxing to parse. That sums up my frustration perfectly. When talking to the general public, information density is your enemy not your friend. I have been trying to get mathematicians to understand that for years but they almost unanimously actively refuse to do so. I can list the reasons as to why I believe they refuse to do so but one thing is clear in my mind: you don't understand a concept unless you can ELI5. For an expert to be able to dive into a dick measurement competition with his PhD friends about who can use the most fancy jargon possible is of no use to society. I just wish more people in the sciences could understand that!
hackermailman 10y ago
What you need is a book on how to solve problems using a strategy, like the first few chapters of 'The Art and Craft of Problem Solving' by Zeitz and 'How to Solve it' by Polya. The Zeitz book specifically refers to the issues in abstract word problems and strategies for understanding them. 'Introduction to Mathematical Reasoning' by Eccles was another great book to explain the meaning of mathematical statements and how to think like a mathematician. If you read some of those, and want to learn more math, start with functional programming in SML since it naturally leads to understanding proof by induction https://existentialtype.wordpress.com/2011/03/21/the-dog-that-didnt-bark/ https://existentialtype.wordpress.com/2011/03/21/the-dog-tha...
tnecniv 10y ago
> This is probably not a view shared by many here, but if math problems were to be communicated in more natural ways, far more people would be interested in the sciences. To the mathematician, this is the most natural way. Sparse, simple, down to business. Providing extra information can be confusing (if I tell you some random facts, you might be worried that your answers aren't using them at all) and the last thing you want to read on the exam is a page of problem motivation. I think you are asking for too much out of a post like this. These problems are really constructed just to test you. The techniques you use to solve them will be important ones that they want to see that you have mastered, but the problems themselves are not really that meaningful.
Jach 10y ago
"We don't do science for the general public. We do it for each other. Good day." -- Renato Dalbecco, complete text of interview with H F Judson I assume the same applies to mathematics. I can sympathize with the frustration, but at the same time there's frustration from the other end. It takes a very skilled person who can at once describe something with enough detail to be understood by their peers and also be able to describe the same thing with enough preamble to cover and make clear where any obvious inference level gaps are for a layman. You simply cannot understand factorization (to use the example you've given before) without first understanding several things prior. For general literature, it is better to assume readers have the prerequisites and write for them. When there is confusion people can always do their own study and dive down the definition/link chain themselves. For literature aimed at a beginner of the subject matter, it makes sense to be more verbose and search for other analogies, but you still need to start at some base level and build inferences from there. Start too low, and it takes years, start too high, and it's inaccessible on its own. I remember some math concepts became a lot clearer to me when I realized how I could express them as computer programs, but it wasn't something any of my math teachers ever pointed out. It would have been helpful if they had. Still, having understood the concepts in the new way, I would rather use their mathematical formulation every time as there is no ambiguity and less room for error. Math is beautiful in that it doesn't really care what your internal representations are, in fact most people probably have widely different internal representations (Feynman's story about his friend who counts by visualizing instead of vocalizing comes to mind: https://www.youtube.com/watch?list=PLE80C041156D48764&v=Cj4y0EUlU-Y https://www.youtube.com/watch?list=PLE80C041156D48764&v=Cj4y...) so it's better to be precise independent of internal representation than to always burden yourself with some preferred internal representation that you use for metaphors.

yiyus 10y ago

I do not agree this is the case. Can you give an example? How would you express these questions "in more natural ways"? (alternatively, feel free to point me to some example with other questions)

sytelus 10y ago

The issue is that even a little bit of non-technical language can cause loss of precision. A regular person would love if the technical language was watered down and sprinkled with colorful analogies but this is not often helpful to actually attack the problem. The problems in OP link builds on large pyramid of concepts and abstractions all the way starting from numbers. There is no way out than to walk through this hierarchy of concepts one at a time for many years to finally gain understanding of the problem. Sugar coated explanations might make you feel good but don't actually help work on it.

demonshalo 10y ago
I understand that and agree 100%. However, what I was trying to say is that for a non-technical person who is trying to understand a concept rather than solving a problem, accuracy is not the main concern. Sometimes you just need to understand the line of reasoning "roughly speaking". and as I said at the end, I understand that this is a set of M.SC. exam question and my issue is not with this pdf specifically. Take the problem of Integer Factorization, something that I have personally been fascinated by for years. The problem is so ridiculously simple that a 5 year old could understand it. With that said, google for a few wikipedia articles and see the notation and the way it is presented. The non-mathematician does not care about difference of squares or triangular numbers or what.have.you. It seems to be the case that mathematicians are unable to talk about math without requiring the person they are talking to to have extensive knowledge of the topic. That's IMO why Carl Sagan and Feynman were so great. They could take complex problems and reduce them (read communicate) in a good way that most could understand and reason about without needing to traverse the entirety of the knowledge pyramid. Similarly, that is what Numberphile does so well.
- blahblah3 10y ago
  My suggestion would be to slow down when reading math or about math. Let's take Wikipedia's integer factorization for example: https://en.wikipedia.org/wiki/Integer_factorization https://en.wikipedia.org/wiki/Integer_factorization First paragraph is: "In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these integers are further restricted to prime numbers, the process is called prime factorization." This is a clear and precise statement of the problem. There are some key words that one might need to look up which takes time, but that's what I mean by slowing down.
  - demonshalo 10y ago
    Be kind and do this for me: Think of yourself as Sara, an average person in society. Put yourself in her shoes. Now click on the following link and scroll down for a bit. https://en.wikipedia.org/wiki/Factorization https://en.wikipedia.org/wiki/Factorization Scroll as slowly as you want/can. Tell me, do you think that this is a good way to communicate to Sara why this problem is of importance? or even better, do you think Sara will ever give a shit if all she can see is that? If you want to promote a more scientifically literate society, you should not try to render every single person into a scientists. Rather, try introducing scientific thinking into people's every day lives. The only way that will happen is if those who know the sciences learn to communicate better with the rest of us and help us get it into our daily lives. can you see where I am coming from? I am not annoyed by math or my ignorance toward the topic. I am trying my best to combat it. But the problem I often encounter is that those who know/can rarely speak the same language as those who cannot. Khan Academy grew big because he knew how to communicate, more people should be like him imo.
    - sammoth 10y ago
      All your examples of the problem you are talking about are from Wikipedia, but you give multiple examples in your posts of explanations of maths done the right way. Feynman, Khan Academy, Project Euler. So I guess some maths related text is written one way and some is written another way?

slurry 10y ago

I don't know, I was able to understand the initial problem statements, and even a bit of the numbered sub-problems, and I'm a trained classicist pig-ignorant in math.

umanwizard 10y ago

What do you think could be stated better? I studied math (I.e., I'm the target audience of this) and the problem statements were perfectly clear to me (although I don't remember how to solve most of the stuff) There really isn't a shortcut to math. I can tell you what to read in order to understand these questions, but it might take you a few years.

demonshalo 10y ago
> it might take you a few years. My complaint was not about these questions. These are M.Sc. exam questions and it should take you years of study to undertand and be able to solve them. My complain was about math communication in general. It shouldn't take me years of study to understand a question on a basic level. I gave the example of prime factorization earlier but you can think of how most math problems are communicated to the general public. A great example to illustrate my point is Project Euler. The way problems are communicated on PE is vastly different than the way they are communicated by professors, wikipedia or most other outlets. Every problem there starts with an introduction followed by a set of assumptions and a posed problem to be solved. It is far more friendly and inviting of a way to communicate math problems to the general public!
- empath75 10y ago
  It doesn't take years of study. Those are mostly fairly basic linear algebra and calculus questions. You could learn enough to understand the basics by watching some khan academy videos.
  - umanwizard 10y ago
    You're assuming a solid understanding of pre-calculus math. It might well take 2+ years for people with no exposure to proofs, or who have a weak foundation in elementary algebra.

QuantumRoar 10y ago

The questions are actually pretty clear. The problem is that you lack a general understanding of mathematical concepts and therefore you don't know what to do with it. But that's fine and that's actually what the exam is for, i.e. only those may pass who understand these things. >This is probably not a view shared by many here, but if math problems were to be communicated in more natural ways, far more people would be interested in the sciences. I would argue the opposite. If more problems could be as well posed as mathematical problems, we wouldn't have people bullshitting their way through arguments that are in dire need of some scientifical rigor (see climate science, psychology, and other disciplines that are too complex to isolate phenomena completely). You can't handwave your way through a math exam and you shouldn't be able to do it in other fields of science.

demonshalo 10y ago
> I would argue the opposite. If more problems could be as well posed as mathematical problems, we wouldn't have people bullshitting their way through arguments that are in dire need of some scientifical rigor (see climate science, psychology, and other disciplines that are too complex to isolate phenomena completely). You can't handwave your way through a math exam and you shouldn't be able to do it in other fields of science. Amen. I have been saying that for years. But I think you misunderstood my original post. I am all for 100% scientific rigidity and less bullshit in society. But what you seem to classify as "clear" is not-so-clear to others. It's actually about how condensed the information is in each question. In order to unpack those questions, you need years of experience within that field in order to get anywhere. I bet you anything that each one of these questions could be posed in a different, yet still mathematical, manner that would make most non-mathy people (such as myself) at least understand the gist of what is being asked. But that is not something mathematicians are interested in. Which is what I was trying to say.
- tankenmate 10y ago
  The issue is that each provable discovery in mathematics is named; it has to have a unique name. These discoveries are exact with at least one proof for their validity and for their limitations and assumptions; all that information is tied up in a name, say for example eigenvalues. These proofs are built on top of previous proofs (which of course are named as well), names and phrases built upon each other. So this ever growing collection of proofs and names is an accretion (or in our moments of grander hubris a pyramid). What you are asking for is the tip of the pyramid (with its wonderful view) without the stones below, in effect what you are asking for is magic, a stone floating in the air with nothing to support it.

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!

kbart 10y ago

We don't do math in human language for the same reason we don't write computer programs in human language: it's ambiguous and hard to define abstract objects using it. Only abstraction enables us to operate higher level, non-trivial problems.

ashark 10y ago
I just wish Math followed programming best-practices on commenting, variable naming, and including tests and their expected output. Bonus for IDE-like tools that can instantly tell me the type of a symbol or show me the expanded version of an operation.
- kbart 10y ago
  Matlab then?
- tnecniv 10y ago
  I agree, maybe because I learned to program way before I got into rigorous math. I really wish the community standardized notation more.

VerbatimVeritas 10y ago

I am in complete agreement. I've done a fair amount of teaching, which is to say I was employed to communicate information, such that someone else (from a fairly random selection sample) could and would remember it well enough to actually use the information productively. I have done this so much that I feel poorly abou tleaving the last paragraph as it is, given that I know there is most certainly a way to find a more parsimonious way to express what I am saying, and I think that is the trust of why mathematical language (and the language in wikis, or APIs, for example) is succinct to the point of absurdity. Everyone is striving for what's called maximum information density, communicating as much data with as few words as possible, and they do so in the jargon of their respective fields of interest. The problem is, those that are not specialized in that field cannot decipher the language well enough to gain anything of use from their efforts at being succinct. Quite the contrary, the field of potential interest becomes even less appealing for having appeared so mentally taxing to parse. Reddit has this ELI5 idea, which I think stems from Denzel Washington's character in the movie "Philadelphia" (Mr. Washington plays an attorney defending an AIDS patient who has been unduly fired) saying "Explain it to me like I'm five years old", to get people to reduce their use of jargon and get to the heart of the matter. Needless to say, the point I am making is that it is one of the great intangibles to be able to communicate one's self effectively, and in my experience is only done well when the communicator understands the level of interest and/or understanding of the communicatee, and can adjust their vocabulary "filter" accordingly. I think math is particularly tough in this regard because of the amount of time that goes into understanding topics that might be complex for an untrained observer (like an Eigen value, for instance, which are critical for a basic understanding of linear regression).

demonshalo 10y ago
> Everyone is striving for what's called maximum information density, communicating as much data with as few words as possible, and they do so in the jargon of their respective fields of interest. The problem is, those that are not specialized in that field cannot decipher the language well enough to gain anything of use from their efforts at being succinct. Quite the contrary, the field of potential interest becomes even less appealing for having appeared so mentally taxing to parse. That sums up my frustration perfectly. When talking to the general public, information density is your enemy not your friend. I have been trying to get mathematicians to understand that for years but they almost unanimously actively refuse to do so. I can list the reasons as to why I believe they refuse to do so but one thing is clear in my mind: you don't understand a concept unless you can ELI5. For an expert to be able to dive into a dick measurement competition with his PhD friends about who can use the most fancy jargon possible is of no use to society. I just wish more people in the sciences could understand that!

hackermailman 10y ago

What you need is a book on how to solve problems using a strategy, like the first few chapters of 'The Art and Craft of Problem Solving' by Zeitz and 'How to Solve it' by Polya. The Zeitz book specifically refers to the issues in abstract word problems and strategies for understanding them. 'Introduction to Mathematical Reasoning' by Eccles was another great book to explain the meaning of mathematical statements and how to think like a mathematician. If you read some of those, and want to learn more math, start with functional programming in SML since it naturally leads to understanding proof by induction https://existentialtype.wordpress.com/2011/03/21/the-dog-that-didnt-bark/ https://existentialtype.wordpress.com/2011/03/21/the-dog-tha...

tnecniv 10y ago

> This is probably not a view shared by many here, but if math problems were to be communicated in more natural ways, far more people would be interested in the sciences. To the mathematician, this is the most natural way. Sparse, simple, down to business. Providing extra information can be confusing (if I tell you some random facts, you might be worried that your answers aren't using them at all) and the last thing you want to read on the exam is a page of problem motivation. I think you are asking for too much out of a post like this. These problems are really constructed just to test you. The techniques you use to solve them will be important ones that they want to see that you have mastered, but the problems themselves are not really that meaningful.

Jach 10y ago

"We don't do science for the general public. We do it for each other. Good day." -- Renato Dalbecco, complete text of interview with H F Judson I assume the same applies to mathematics. I can sympathize with the frustration, but at the same time there's frustration from the other end. It takes a very skilled person who can at once describe something with enough detail to be understood by their peers and also be able to describe the same thing with enough preamble to cover and make clear where any obvious inference level gaps are for a layman. You simply cannot understand factorization (to use the example you've given before) without first understanding several things prior. For general literature, it is better to assume readers have the prerequisites and write for them. When there is confusion people can always do their own study and dive down the definition/link chain themselves. For literature aimed at a beginner of the subject matter, it makes sense to be more verbose and search for other analogies, but you still need to start at some base level and build inferences from there. Start too low, and it takes years, start too high, and it's inaccessible on its own. I remember some math concepts became a lot clearer to me when I realized how I could express them as computer programs, but it wasn't something any of my math teachers ever pointed out. It would have been helpful if they had. Still, having understood the concepts in the new way, I would rather use their mathematical formulation every time as there is no ambiguity and less room for error. Math is beautiful in that it doesn't really care what your internal representations are, in fact most people probably have widely different internal representations (Feynman's story about his friend who counts by visualizing instead of vocalizing comes to mind: https://www.youtube.com/watch?list=PLE80C041156D48764&v=Cj4y0EUlU-Y https://www.youtube.com/watch?list=PLE80C041156D48764&v=Cj4y...) so it's better to be precise independent of internal representation than to always burden yourself with some preferred internal representation that you use for metaphors.