
Street-Fighting Math: Educated Guessing and Opportunistic Problem Solving (2010) [pdf] - 7402
https://mitpress.mit.edu/sites/default/files/titles/content/9780262514293_Creative_Commons_Edition.pdf
======
dpflan
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](https://news.ycombinator.com/item?id=14338411)

~~~
arglebarnacle
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.

~~~
dpflan
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...](http://online.stanford.edu/courses/mathematical-thinking-
> winter-2014)

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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...](https://mitpress.mit.edu/books/art-insight-science-and-engineering)

~~~
mavroprovato
You can download it from here: [https://ocw.mit.edu/resources/res-6-011-the-
art-of-insight-i...](https://ocw.mit.edu/resources/res-6-011-the-art-of-
insight-in-science-and-engineering-mastering-complexity-fall-2014/online-
textbook/)

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stcredzero
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.

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

~~~
Terr_
Sounds Benford-y, yeah. The biggest relative "error" in [0,99] is going to be
at 19, where the estimate (1 * 10^0) at only ~52% of the actual value (1.9 *
10^0). That local minima for accuracy recurs at 199, 1999, etc. From some
quick spreadsheet-fu, the mean underestimation for [0,9999] is 88%.

Meanwhile, with the "teens" trick, the local minimum is 29 (68.9%) and then at
299, 2999, etc, and the mean underestimation is boosted to... huh, only 91%?

Then again, I'm assuming a completely even distribution, which probably won't
be true in some contexts.

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burkaman
This is also available as an online course:
[https://ocw.mit.edu/courses/mathematics/18-098-street-
fighti...](https://ocw.mit.edu/courses/mathematics/18-098-street-fighting-
mathematics-january-iap-2008/)

~~~
itsbenweeks
And a self-paced course through edX:

[https://www.edx.org/course/street-fighting-math-
mitx-6-sfmx](https://www.edx.org/course/street-fighting-math-mitx-6-sfmx)

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jfaucett
From the forward, "With rare exceptions, the mathematics that I have found
most useful was learned in science and engineering classes [or] on my own".

This has been the case for me too. I never learned this in a class in school,
but one of the most important things I've always done when learning some
mathematic topic is try to #1 associate it with something in the real world
and #2 find a way to "guestimate" without a calculator what the answers will
be. For instance, take square roots. The sqrt of 137 will be between 11 and 12
more precisely about 11.7 and I can visualize it in my head as one side of a
2D square shape. Also squares and square roots allow me to easily think about
the area covered (size/shape) by N-dimensions in relation to the size of just
one dimension. A real world application which is interesting to note is that
the time it takes a falling object to hit the ground is equal to the square
root of the distance traveled (really 2 times the square root divided by
gravity but the general relationship is the same).

------
dpflan
More math books and discussion:

[https://news.ycombinator.com/item?id=10248651](https://news.ycombinator.com/item?id=10248651)

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sriram_malhar
I have tried this book a few times, and I'm awed by it, yet I am not
significantly better. I fear the problem is that when Sanjay refers to
educated guessing, the level of education and practice is very high indeed.
While I can marvel at the examples in the book, I would need a steady stream
of work-a-day examples to work through, ala Project Euler.

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Benjammer
This complaint about the way math is currently taught, and the ensuing new
approach, both remind me of "A Mathematician's Lament" [0] by Paul Lockhart.

[0]:
[https://www.maa.org/external_archive/devlin/LockhartsLament....](https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)

------
time-of-flight
Back in 2010 I ran across Sanjoy's method for using the musical scale to
perform more complicated arithmetic (mentally calculate pi^6 +/\- 5% within 30
seconds).

Can't wait to read the entire work.

~~~
jknz
pi^2=10 so pi^6=1000?

This is within 5% of the real answer, but does not not involve music!

~~~
time-of-flight
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 a
whole step is a frequency increase of 9/8, and the more you know the more
powerful this method is.

To solve 25000^(1/8) = x, you're looking for an interval x on the keyboard
such that if you were to go up 8 of those intervals, the frequency would jump
by 25000. Well, 25000 is just 10^5 / 2^2, or in terms of keyboard intervals,
"Go up 40 notes (repeat four more times), then down two octaves". This means
to represent a frequency increase by a factor of 25000, I need to go up 10
_5-2_ 12 = 176 half steps on a keyboard.

Divide by 8 to find x = 22 steps, which is two octaves minus a whole step on
the keyboard. The frequency change over this 22-step interval is thus (2*2)
[up two octaves] / (9/8) [down a whole step] ~ 3.5. So that's the final
answer: 3.5

The actual value of 25000^(1/8) is 3.546, so this approximation is good to
within a couple of percent.

~~~
credit_guy
A good trick for calculating powers of e is that e^3 ~ 20. So e^7 is roughly
400e, so about 1080, completely without pen and paper. This is only 1.5% off.

Your trick is cool too, by the way.

For your other challenge, I would use the enormously useful 2^10 = 1024 ~ 1000
(which the musical trick implicitly uses too, in the 40 notes is 10 times the
frequency mnemonic). So 25000 is close to 5^2 * 2^10, and it's square root is
5 * 2^5 = 160 (we can always keep in mind that 2^10 ~ 1000 is an overestimate
by 2.4%, so our 160 ~ sqrt(25000) is an overestimate by 1.2%, so an improved
approximation of sqrt(25000) is 158). 158 is very close to the midpoint of 144
and 169, so its square root is not far from the midpoint of 12 and 13. So my
approximation of 25000^(1/4) is 12.5. Finally I need to take a sqrt of that. I
know the square of 3.2 is 10.24 (our old friend 2^10 = 1024), and that's about
20% too low. Ok, we need to bump our 3.2 up by 10%, that makes is 3.52, and
that's our answer. It's only 0.7% off, but it's only by luck. For a more
general problem, keeping a tab of your first estimate as an absolute number
and your current correction as a percentage gives an error of less than 2%.

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

~~~
SimbaOnSteroids
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.

------
abhgh
I've heard good reviews. Have had this downloaded on my mobile for a few
_years_ now ... should get around to reading it "soon" -_-

~~~
AceJohnny2
I understand your problem :) I've partially solved it by dedicating my lunch
hour to (along with eating) reading some good non-fiction book. Bit by bit,
you make progress.

Obviously, you could do it some other time, but the important part is to make
it a habit, so that it feels almost automatic to do, or that you feel like
something's missing/feel guilty if you skip it.

~~~
abhgh
Actually I used to read in lunch hour. I used to specifically eat lunch later
than my peers so that I don't end up going in a group (I know, I know, I was
picking reading over society ...). But of late my workload has increased a
lot, so I'm having lunch at my desk.

You're right about making a habit. I am trying to read an hr before bedtime or
an hr right after office (when I reach home) nowadays.

------
Joboman555
I took a class with the Sanjoy (the author) this past fall. Awesome guy and a
great teacher.

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wnevets
I thought this was going to about Street Fighter[1] machine learning

[1]
[https://en.wikipedia.org/wiki/Street_Fighter](https://en.wikipedia.org/wiki/Street_Fighter)

