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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]

#11

Post by AceJohnny2 »

abhgh wrote: post #9

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

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.

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

#12

Post by TrainedMonkey »

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.)

This makes sense. If the number is 5.5 by throwing away the .5 you lose less than 10% of precision. On the other hand if the number is 1.5 and you throw away the .5 you lose 50% precision.

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

#14

Post by dpflan »

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.

Like "Fermi Problems" and back-of-the-envelope math?

> https://en.m.wikipedia.org/wiki/Fermi_problem

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

#15

Post by 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.

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

#16

Post by 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).

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

#17

Post by abhgh »

AceJohnny2 wrote: post #11
abhgh wrote: post #9

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

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.

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.

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

#18

Post by jknz »

time-of-flight wrote: post #13

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.

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

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

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

#19

Post by Terr_ »

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.)

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.

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

#20

Post by time-of-flight »

jknz wrote: post #18
time-of-flight wrote: post #13

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.

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 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 105-212 = 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.

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