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Street-Fighting Math: Educated Guessing and Opportunistic Problem Solving (2010) [pdf]

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Re: Street-Fighting Math: Educated Guessing and Opportunistic Problem Solving (2010) [pdf]

#21

Post by arglebarnacle »

dpflan wrote: post #5

I feel this was a response to this recent submission as perhaps an example of a math text that is less traditional? (Could be interesting to look at the discussion and see how this text holds up?) Why do many math books have so much detail and so little enlightenment? (2010) > https://news.ycombinator.com/item?id=14338411

It's an interesting comparison to be sure, but I'm not sure Street-Fighting Math has a lot to offer graduate-level pure math texts (the subject of that post).

I own and love the book, and did a lot of pure math in my math undergrad degree. But SFM is closer to the tradition of Martin Gardner's long-running "Mathematical Games" column in Scientific American than real higher pure math education.

I think that's because it hinges on giving you tools to "hack" problems in physics, geometry and calculus that leverage intuition about quantities and space. There are branches of pure math where this matters a lot, but frankly it's not going to help you learn about Lie groups or category theory. It's not clear to me that the style and approach of SFM is helpful in this kind of very abstract context where a detailed understanding of unfamiliar sorts of concepts and mechanics is crucial.

Re: Street-Fighting Math: Educated Guessing and Opportunistic Problem Solving (2010) [pdf]

#22

Post by SimbaOnSteroids »

airay wrote: post #4

Sanjoy is rad. This should be a must-read for engineering school.

At my local Boeing plant the engineers write WAG (wild a-- guess) on something when they're spitballing and don't want to do the math, I wonder how frequently a WAG can be made more precise if this were more widely read.

Re: Street-Fighting Math: Educated Guessing and Opportunistic Problem Solving (2010) [pdf]

#23

Post by stcredzero »

jonsen wrote: post #8
stcredzero wrote: post #2

There was this estimation technique one of the Sixty Symbols professors talked about, where you do all of the calculations, but you only keep one significant digit. It's something you can do quickly in your head while conversing with someone, but tells you pretty reliably if something is feasible.

When the first digit becomes 1 keep two digits. A small effort for much higher precision. (Something to do with Benford's Law? Maybe.)

I like it! It's small additional effort for more precision. However, the estimation technique above is optimized for very small effort. You can do the very lightweight version in the middle of a conversation in your head without unduly derailing the conversation. It's a different tool with different trade offs. It's the keychain multitool of estimation methods.

Re: Street-Fighting Math: Educated Guessing and Opportunistic Problem Solving (2010) [pdf]

#25

Post by dpflan »

arglebarnacle wrote: post #21
dpflan wrote: post #5

I feel this was a response to this recent submission as perhaps an example of a math text that is less traditional? (Could be interesting to look at the discussion and see how this text holds up?) Why do many math books have so much detail and so little enlightenment? (2010) > https://news.ycombinator.com/item?id=14338411

It's an interesting comparison to be sure, but I'm not sure Street-Fighting Math has a lot to offer graduate-level pure math texts (the subject of that post). I own and love the book, and did a lot of pure math in my math undergrad degree. But SFM is closer to the tradition of Martin Gardner's long-running "Mathematical Games" column in Scientific American than real higher pure math education. I think that's because…

True. The title alone lets you know it's not teaching you braid theory. But in terms of providing a different perspective to read, teaching, learning mathematics - that is where the comparison or interesting bits could lay. Also, have you (or anyone here) taken the Stanford course "Introduction to Mathematical Thinking"?

> http://online.stanford.edu/courses/mathematical-thinking-win...

Re: Street-Fighting Math: Educated Guessing and Opportunistic Problem Solving (2010) [pdf]

#26

Post by pps43 »

The other book [1] is even better. Unfortunately, there is no free lunch. Knowing when it's ok to cut corners is more important than how to cut corners, and there does not seem to be an easy way to learn that.

[1] https://mitpress.mit.edu/books/art-insight-science-and-engin...

Re: Street-Fighting Math: Educated Guessing and Opportunistic Problem Solving (2010) [pdf]

#27

Post by posterboy »

time-of-flight wrote: post #20
jknz wrote: post #18

Earlier quoted context omitted.

pi^2=10 so pi^6=1000? This is within 5% of the real answer, but does not not involve music!

I chose a coincidentally easy problem (whoops). Here's another one, less accessible to attack: Find e^7. Or 25000^(1/8). The trick to using the musical scale is that it's logarithmic in frequency but linear in key (ABCDEFG). The frequency step between adjacent notes is 2^(1/12); the frequency jump over an octave is 2; the frequency jump over 40 notes is 10. There are other handy ratios to remember, like that going up…

For one, actual scales aren't exactly purely logarithmic because of physical limitations (overtones in low freqs) and secondly music has nothing more to do with it than any other log scale, eg ... well I don't actually a more common one

Re: Street-Fighting Math: Educated Guessing and Opportunistic Problem Solving (2010) [pdf]

#28

Post by mavroprovato »

pps43 wrote: post #26

The other book [1] is even better. Unfortunately, there is no free lunch. Knowing when it's ok to cut corners is more important than how to cut corners, and there does not seem to be an easy way to learn that. [1] https://mitpress.mit.edu/books/art-insight-science-and-engin...

You can download it from here: https://ocw.mit.edu/resources/res-6-011-the-art-of-insight-i...

Re: Street-Fighting Math: Educated Guessing and Opportunistic Problem Solving (2010) [pdf]

#29

Post by jonsen »

time-of-flight wrote: post #20
jknz wrote: post #18

Earlier quoted context omitted.

pi^2=10 so pi^6=1000? This is within 5% of the real answer, but does not not involve music!

I chose a coincidentally easy problem (whoops). Here's another one, less accessible to attack: Find e^7. Or 25000^(1/8). The trick to using the musical scale is that it's logarithmic in frequency but linear in key (ABCDEFG). The frequency step between adjacent notes is 2^(1/12); the frequency jump over an octave is 2; the frequency jump over 40 notes is 10. There are other handy ratios to remember, like that going up…

If you memorize some of the "nice" log10 approximations like

  ...
  log10 2   ~= 0.3
  log10 2.5 ~= 0.4
  log10 3   ~= 0.5
  log10 4   ~= 0.6
  ...
then 25000^(1/8) could be done mentally as

  log10 of 25000 is 4.4
  4.4 / 8 is 0.55
  antilog10 of 0.55 is approximately 3.5
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