
Street-Fighting Mathematics - alixaxel
https://mitpress.mit.edu/books/street-fighting-mathematics
======
sn9
Follow that up with his slightly more advanced _The Art of Insight in Science
and Engineering_ [0].

I feel like these two books plus Art Benjamin's _Secrets of Mental Math_ [1]
would put your Fermi calculation abilities on another level.

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

~~~
JadeNB
Without meaning to slight those who have the latter ability, I think that
building your problem-solving muscles, as I believe that this book tries to
encourage, is _far_ more important than building your mental-math muscles. (I
say this as someone who takes pride in my own very limited capacity for mental
math.) While these muscles are not totally unrelated, it is possible to be
good at either skill and poor at the other; and, to the extent that it is
necessary to choose, I had much rather live in a society of people who can
solve problems well but ponderously slowly than one of people who can find
lightning-fast answers, but only when others have already asked the right
questions.

~~~
lomnakkus
> I think that building your problem-solving muscles, as I believe that this
> book tries to encourage, is far more important than building your mental-
> math muscles. (I say this as someone who takes pride in my own very limited
> capacity for mental math.) While these muscles are not totally unrelated, it
> is possible to be good at either skill and poor at the other

I can only agree, but I may be biased because I'm a lot better at the problem-
solving than the mental-math :). I'm always impressed by the mental agility of
people like Art Benjamin, but I'm not convinced it's quite as _valuable_ when
it comes to it... given that computers can outperform him by orders of
magnitude.

Btw, both of Mahajan's books are great, but if were to say which was more
valuable to the general public I'd say it was Streeth-fighting. In my
educational efforts, I've always been astounded at how bad people are at
_minimally_ sanity-checking their results when doing math problems. Even
order-of-magnitude sanity checks seemed to beyond most of my students. In
physics[1] you at least have units to sanity check against, but you'd be
surprised how few students actually understand even unit-math enough to be
able to check that they weren't comparing an acceleration value (m/s^2) to
speed (m/s).

(Assuming SI units. You can do this completely generally by having abstract
units "dimension" and "time", "mass", etc.)

[1] If there's one complaint I have against _Math_ education it's that all my
educators actively _encouraged_ eliding the units even for problems based on
physics. I'm not sure if this was just to try to trip students up on tests,
but it was absolutely _horrible_ from an educational perspective. _ALWAYS_
keep the goddamn units so you can at least minimally sanity check your result!

~~~
ollyfg
If there is one thing I've learned from university, it's this. Keeping units
makes your writing messier and longer, but when it comes to checking they are
absolutely invaluable. Your equation to give you volumetric flow gave you
(kg/s)? Well density is (kg/m^3) so just divide your answer by density! (this
is a problem my friend was having just yesterday)

~~~
bigger_cheese
I think the problem is they don't teach the same units everywhere in the
world.

I grew up in Australia with SI units I do a lot of work with
Fluid/Thermodynamic calcs. I have a bunch of reference values in my head. I
know 1 Atmosphere is ~101.3 kPa, I know speed of sound in dry air is ~330 m/s
I know how much energy it takes to raise the temperature of various
substances. I know the densities of common materials in my head. All of that
helps me sanity check calculations - at a glance I can see things 'this fan is
producing too much suction, not possible' or 'There is not enough input energy
to see a temperature rise that high' things like that.

I have no idea about any of the non SI units. I couldn't tell you how long a
"yard" is or how heavy a "pound" is usually it is fine but occasionally I come
across numbers in technical papers or datasheets or similar with stuff in
wacky units - PSI, BTU and Fahrenheit are the worst offenders when I have to
deal with them it just blue screens my mental models. I see those units so
infrequently I have no concept of what a 'reasonable' value expressed in those
units looks like. I imagine people who don't work in SI units everyday hit the
same difficulties in reverse.

~~~
lomnakkus
This is interesting because there's actually a unit-agnostic way of doing
units more generally... it's "dimensional" rather than unit-based. So
regardless of the base units you'll do "length" (which works for all three
axes: length, depth, breadth) and "mass" (which works for kg, pounds,
whatever) and "acceleration", "force", etc.

Obviously this is slightly more lax and perhaps error-prone than your standard
m/s or m/(s^2), etc., but it's one of the lamentably few things computers can
do well!

EDIT: ... and I should elaborate: In some sub-fields of Physics they usually
go even further and just re-normalize everything to units of 1, so that e.g.
the speed of light is c is 1. At that point it's really just about convenience
since sqrt(1) = 1, and 1^x = 1, etc. (Lorentz Transformation.)

~~~
JadeNB
I believe that bigger_cheese is lamenting his or her inability to do
_numerical_ sanity checking in other units. (This loss of numerical
information is, perhaps, what you meant by saying that the unit-agnostic
approach is 'more lax'.)

For example, if I am looking for a force and I get an answer of 1000 lbs, then
dimensional analysis tells me that at least I got a force; but, if my
intuition tells me _only_ that the actual force is on the order of magnitude
of 1000 N, then I don't know whether my actual answer is way too big, way too
small, or about right, unless I know how to convert between Newtons and
pounds.

Incidentally, while "units of 1" make correct calculations easy, I think that
they are a bad idea precisely because they subvert unit checking; it's hard to
know just by looking that 1 + 1 is 1 speed of light + 1 light-year, and hence
dimensionally inconsistent.

(Even keeping all SI units can miss some important distinctions; for example,
nothing about their SI units (inverse time) allows us to distinguish angular
frequency
([https://en.wikipedia.org/wiki/Angular_frequency](https://en.wikipedia.org/wiki/Angular_frequency))
from temporal frequency
([https://en.wikipedia.org/wiki/Frequency](https://en.wikipedia.org/wiki/Frequency)),
and yet much woe accrues to he or she who does not distinguish radians/time
from cycles/time!)

~~~
lomnakkus
Oh, yes, re-read it and right you are.

------
lolptdr
free download of the book (for the lazy):
[https://mitpress.mit.edu/sites/default/files/titles/free_dow...](https://mitpress.mit.edu/sites/default/files/titles/free_download/9780262514293_Street_Fighting_Mathematics.pdf)

Mahajan also offers paperback and ebook options.

~~~
anarcat
i often wonder why "free downloads" often mean "PDF" while ePUB needs to be
paid for... in my case, it is certainly less convenient to have a PDF because
i use an e-reader, but everyone has tablets these days that read PDFs fine...

~~~
gberger
> i often wonder why "free downloads" often mean "PDF" while ePUB needs to be
> paid for

> it is certainly less convenient to have a PDF

There's your answer.

------
sremani
Link to Archived Course on EdX.

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

------
borski
This was easily my favorite course at MIT, and there were a lot I liked.

In fact, I liked this course so much that the CTF team I started back in
college was named "The Art of Approximation in Science and Engineering," the
name of the course taught by this professor / that used this book.

Highly recommend.

------
stblack
This is a very good book to refine tactical approaches to several classes of
math problems. I read it last year and, at the time, I wished I had come upon
it sooner.

------
akc1
There is also a class at MIT under the same name:
[http://ocw.mit.edu/courses/mathematics/18-098-street-
fightin...](http://ocw.mit.edu/courses/mathematics/18-098-street-fighting-
mathematics-january-iap-2008/)

------
jadc
The course was also presented on edX: [https://www.edx.org/course/street-
fighting-math-mitx-6-sfmx](https://www.edx.org/course/street-fighting-math-
mitx-6-sfmx)

you can enroll and view the archives.

------
pareci
The problem is not math. The problem is not fighting. The problem is not the
street. The problem is ego. Until you lose yours, you will not grasp logic.

~~~
irascible
Read this in Master Pos' voice.

