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> Anyone who is serious about learning data science will read this book and will not shy away from learning math. The problem is not math. The problem is the w

> Anyone who is serious about learning data science will read this book and will not shy away from learning math. The problem is not math. The problem is the way math is explained. Most books do not go into the intuition and are very dry. People generally shy away due to the dryness of the material, not the content.

yummyfajitas 10y ago
One of the major points that this book is trying to convey is that your intuition is wrong. You need to burn it down, learn the formalism, and maybe develop new intuition based on that. Even then you need to recognize that intuition can be wrong. An N-dimensional vector space is not like R^3. A monad is not like a burrito, and >>= is not like chipotle forgetting to put chicken in your burrito, opening it up, adding chicken and wrapping in a new tortilla. Math is a new thing rather than the same old thing with new syntax. It needs to be understood on it's own terms. If you are serious you'll learn it.
- throw_away_777 10y ago
  I agree with your sentiment that math is important, but it is also true that math is not taught well. Just briefly glancing at chapter 2 the first part, the author presents the law of large numbers out of the blue, then just goes on to present proofs of it. There is no clear discussion of why this law is important, when you can use it and so on. If you contrast how wikipedia explains it: > In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed. This book: > If one generates random points in d-dimensional space using a Gaussian to generate coordinates, the distance between all pairs of points will be essentially the same when d is large. The reason is that the square of the distance between two points y and z ...
  - denzil_correa 10y ago
    I always get a eerie feeling for people who excessively stress on formalism. It almost goes to the point where I feel they wouldn't want to share their knowledge or intuition.
    - yummyfajitas 10y ago
      Clearly the guys who wrote the only comprehensive introduction to a topic don't want to share their knowledge.
      - denzil_correa 10y ago
        The previous comment was not directed towards the authors of this book.
    - BigJeffeRonaldo 10y ago
      They are trying to help you get a correct intuition. If you have never approached things this way, there are almost certainly very large holes in your understanding. Not to say that everyone needs to be formal all the time, but you need to sometimes.
      - denzil_correa 10y ago
        > If you have never approached things this way, there are almost certainly very large holes in your understanding. When anyone tells me that X is the ONLY way to do it, almost exclusively I have found them wrong - beyond data science. Formalism is a means of communication, not the end. You can always communicate ideas without formalism. FYI, I am a Ph.D Computer Science and a practicing Data Scientist for many years now.
    - BigJeffeRonaldo 10y ago
      They are trying to help you get a correct intuition. If you have never approached things this way, there are almost certainly very large holes in your understanding. Not to say that everyone needs to be formal all the time, but you need to sometimes.
- denzil_correa 10y ago
  You are essentially saying - the way I think of math is how it should be learned. Sorry but if you're serious, you will find a way to explain your mathematical intuition. The problem is detailed in this wonderful essay by Paul Lockdhart https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....
  - yequalsx 10y ago
    We can explain mathematical intuition. We just can't explain it as quickly or in as interesting way as you seem to want. Here's a simple concept: all polynomials with coefficients in a number system (field) have a solution (possibly in a larger field). Do you know how hard it is to convey what exactly this means and what the consequences are? I like Lockhart's essay. It resonates with me. However, I don't see his ideas being useful in terms of learning advanced topics. At some point one has to get their hands dirty and slog through the material. Intuition will come with experience.
    - denzil_correa 10y ago
      > Do you know how hard it is to convey what exactly this means and what the consequences are? I never said it is easy. > Intuition will come with experience. And this experience that some people have already reached should be shared, not limited to a select coterie of people.
      - yequalsx 10y ago
        It is shared. It's just that everyone has to go through to mental work to truly understand. It takes me a semester to convince my students that 3x+5x=8x and that this is true because of the distributive property. And this is why ax+2x = (a+2)x. And the reason we can't simplify further is because our language does not have a word for (a+2) but it does have a word for (3+5). But I know that after a semester of teaching this most still don't actually understand the distributive property. It takes a lot of effort on the part of students for the concept to click.
throw_away_777 10y ago
Most math textbooks focus too much on proofs, as does this book. Data science is a broad field, but for most use cases formal proofs are not really needed. I would prefer a text that focuses on examples and how/when to apply the theorems, rather than here is a theorem and here is a proof. Oh and here is another theorem and here is another proof. That isn't to say proofs are not important, but the focus of data science is usually on applied statistics.
- catnaroek 10y ago
  If you understand a mathematical theory, then you should be able to figure out on your own when that theory is applicable and how to apply it. So I can't help but read your comment as “I don't want to have to learn”.
  - throw_away_777 10y ago
    You are being condescending and over simplifying the issues, try to not rush to judgment. I have spent a lot of work and time learning how to apply machine learning, so your comment was offensive and wrong. Applying mathematical theory is not just a matter of understanding the theory - in the real world there are a whole lot of reasons why you won't be able to apply the theory, even if you understand it perfectly. You will always have to make assumptions and approximations. I like learning, but I prefer learning for a purpose. Proofs don't really give you a practical understanding of the theory.
    - catnaroek 10y ago
      > You will always have to make assumptions and approximations. The ability to determine when an approximation is good enough comes from a solid understanding of the underlying theory. For example, we understand that special relativity doesn't invalidate classical mechanics, because, in the limit, as speeds and energies become arbitrarily small, their predictions coincide. But, if all you have is a bunch of computational recipes, even the tiniest unexpected thing renders you unable to solve problems. Anyway, I'm not saying that examples of applications are a bad thing. But proofs are indispensable. Even for “intuitive” people, proofs are necessary confirmation that their calculations will match their intuitions.

yummyfajitas 10y ago

One of the major points that this book is trying to convey is that your intuition is wrong. You need to burn it down, learn the formalism, and maybe develop new intuition based on that. Even then you need to recognize that intuition can be wrong. An N-dimensional vector space is not like R^3. A monad is not like a burrito, and >>= is not like chipotle forgetting to put chicken in your burrito, opening it up, adding chicken and wrapping in a new tortilla. Math is a new thing rather than the same old thing with new syntax. It needs to be understood on it's own terms. If you are serious you'll learn it.

throw_away_777 10y ago
I agree with your sentiment that math is important, but it is also true that math is not taught well. Just briefly glancing at chapter 2 the first part, the author presents the law of large numbers out of the blue, then just goes on to present proofs of it. There is no clear discussion of why this law is important, when you can use it and so on. If you contrast how wikipedia explains it: > In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed. This book: > If one generates random points in d-dimensional space using a Gaussian to generate coordinates, the distance between all pairs of points will be essentially the same when d is large. The reason is that the square of the distance between two points y and z ...
- denzil_correa 10y ago
  I always get a eerie feeling for people who excessively stress on formalism. It almost goes to the point where I feel they wouldn't want to share their knowledge or intuition.
  - yummyfajitas 10y ago
    Clearly the guys who wrote the only comprehensive introduction to a topic don't want to share their knowledge.
    - denzil_correa 10y ago
      The previous comment was not directed towards the authors of this book.
  - BigJeffeRonaldo 10y ago
    They are trying to help you get a correct intuition. If you have never approached things this way, there are almost certainly very large holes in your understanding. Not to say that everyone needs to be formal all the time, but you need to sometimes.
    - denzil_correa 10y ago
      > If you have never approached things this way, there are almost certainly very large holes in your understanding. When anyone tells me that X is the ONLY way to do it, almost exclusively I have found them wrong - beyond data science. Formalism is a means of communication, not the end. You can always communicate ideas without formalism. FYI, I am a Ph.D Computer Science and a practicing Data Scientist for many years now.
  - BigJeffeRonaldo 10y ago
    They are trying to help you get a correct intuition. If you have never approached things this way, there are almost certainly very large holes in your understanding. Not to say that everyone needs to be formal all the time, but you need to sometimes.
denzil_correa 10y ago
You are essentially saying - the way I think of math is how it should be learned. Sorry but if you're serious, you will find a way to explain your mathematical intuition. The problem is detailed in this wonderful essay by Paul Lockdhart https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....
- yequalsx 10y ago
  We can explain mathematical intuition. We just can't explain it as quickly or in as interesting way as you seem to want. Here's a simple concept: all polynomials with coefficients in a number system (field) have a solution (possibly in a larger field). Do you know how hard it is to convey what exactly this means and what the consequences are? I like Lockhart's essay. It resonates with me. However, I don't see his ideas being useful in terms of learning advanced topics. At some point one has to get their hands dirty and slog through the material. Intuition will come with experience.
  - denzil_correa 10y ago
    > Do you know how hard it is to convey what exactly this means and what the consequences are? I never said it is easy. > Intuition will come with experience. And this experience that some people have already reached should be shared, not limited to a select coterie of people.
    - yequalsx 10y ago
      It is shared. It's just that everyone has to go through to mental work to truly understand. It takes me a semester to convince my students that 3x+5x=8x and that this is true because of the distributive property. And this is why ax+2x = (a+2)x. And the reason we can't simplify further is because our language does not have a word for (a+2) but it does have a word for (3+5). But I know that after a semester of teaching this most still don't actually understand the distributive property. It takes a lot of effort on the part of students for the concept to click.

throw_away_777 10y ago

Most math textbooks focus too much on proofs, as does this book. Data science is a broad field, but for most use cases formal proofs are not really needed. I would prefer a text that focuses on examples and how/when to apply the theorems, rather than here is a theorem and here is a proof. Oh and here is another theorem and here is another proof. That isn't to say proofs are not important, but the focus of data science is usually on applied statistics.

catnaroek 10y ago
If you understand a mathematical theory, then you should be able to figure out on your own when that theory is applicable and how to apply it. So I can't help but read your comment as “I don't want to have to learn”.
- throw_away_777 10y ago
  You are being condescending and over simplifying the issues, try to not rush to judgment. I have spent a lot of work and time learning how to apply machine learning, so your comment was offensive and wrong. Applying mathematical theory is not just a matter of understanding the theory - in the real world there are a whole lot of reasons why you won't be able to apply the theory, even if you understand it perfectly. You will always have to make assumptions and approximations. I like learning, but I prefer learning for a purpose. Proofs don't really give you a practical understanding of the theory.
  - catnaroek 10y ago
    > You will always have to make assumptions and approximations. The ability to determine when an approximation is good enough comes from a solid understanding of the underlying theory. For example, we understand that special relativity doesn't invalidate classical mechanics, because, in the limit, as speeds and energies become arbitrarily small, their predictions coincide. But, if all you have is a bunch of computational recipes, even the tiniest unexpected thing renders you unable to solve problems. Anyway, I'm not saying that examples of applications are a bad thing. But proofs are indispensable. Even for “intuitive” people, proofs are necessary confirmation that their calculations will match their intuitions.