Street-Fighting Mathematics | Hacker News Reader

Street-Fighting Mathematics

mitpress.mit.edu

327 pointsmemexy72 comments

For the people who did not notice, in the "Open Access" tab you can download the PDF of the whole book legally and for free.

There is also a second book by the same author which is a bit harder and more comprehensive, and also open access:

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

Also available as part of the MIT OCW[0]

[0] https://ocw.mit.edu/courses/mathematics/18-098-street-fighti...

I took this course during a January term. It was great fun and Sanjoy was a great teacher, with tons of energy and enthusiasm.

Another great book along the same lines is Polya's "How to Solve It" [1] with the brief summary [2].

[1] https://en.wikipedia.org/wiki/How_to_Solve_It

[2] https://math.berkeley.edu/~gmelvin/polya.pdf

I appreciate the tutor-like approach to asking questions in the text, but I really need the answers as well. I had to look them up, and I only ran across the book from John Weatherwax. I don't feel inclined to purchase a $20 book of solutions when I'm using the original text via open-access. I guess I'll just have to order the physical copy of both books to keep my conscience clear.

I really appreciate the Open Access. Thank you MIT.

"Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT"

That short course looks like its still available on edx - though it's archived - I seem to be able to access the material.

https://www.edx.org/course/street-fighting-math

The content looks quite interesting for a mathematician too—so I'm sorry that the advertising needs to be antagonising.

But even Keep the Aspidistra Flying was basically mutilated by circumstance [1] and it's still a great book. So, I'll take the insults towards mathematicians with humour and actually read some of it—I often switch between grumpy rigour to applicative speed. We all need to earn an income.

[1] https://en.wikipedia.org/wiki/Keep_the_Aspidistra_Flying#Lit...

Edit: Just to be clear, my comment on mathematicians is not on your quote, but this quote from OP's post:

> an antidote to mathematical rigor mortis

How on earth is any of the advertising antagonizing? I had to read through the course page twice to look for anything remotely resembling a criticism and came up blank.

If it is the quote you added to the bottom of your comment, my question still stands. That isn't an insult to anyone (certainly not mathematicians) but rather a comment that many people freeze up when it comes to mathematics (at least that was my interpretation).

> How on earth is any of the advertising antagonizing?

The word "antidote" is used in the book's summary, which is defined as (via Google) "a medicine taken or given to counteract a particular poison." One could take the "poison" to be mathematical rigor, or something similar.

Perhaps this does not change your opinion, but I do not think the original comment was completely off base.

There is a somewhat common attitude towards abstract mathematics that its preciseness is something of a bother to people and that it requires some kind of "cure".

Immanuel Kant wrote about it [1] and many engineers have a varying degree of animosity towards pure mathematics. So, in the book's description they say this:

This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.

I don't like the advertising, or the description if you will, as it basically tries to discount rigour. One can simply say it's an addition to the usual rigour of mathematics for the sake of daily street fighting style problem solving. The way they state it, however, it sounds like they are saying that rigorous math is not necessary.

My reference to George Orwell is simply that when he wrote Keep the Aspidistra Flying his publishers made him write a lot of things he didn't want to write, and they even specified the amount of words the books needed to have (which is is somewhat understandable, but limiting still).

[1] https://en.wikipedia.org/wiki/Critique_of_Pure_Reason. However, note that this is about metaphysics and one can argue that pure mathematics is not what he was critisising and that his work doesn't directly try to disprove the use of axioms, without which mathematics cannot exist.

> even Keep the Aspidistra Flying was basically mutilated by circumstance

You think the British intelligentsia would react kindly to an honest portrayal of the class system?

Anything more recent than https://twitter.com/johncleese/status/1254130854462455813 ?

Orwell's book's structure was dictated by the publishers, but I still love the content. My allusion was because I am wondering why the description needs to insult pure mathematics in order to promote Street Fighting Mathematics.

And similarly to Orwell's book, it seems like Street Fighting Mathematics does actually have interesting content, despite whatever the reason may be that they need an "antidote" for general mathematics.

I see what you're saying.

I think the author meant the same thing as Feynman when he described the "Greek" and "Babylonian" approaches to mathematics.

For all but a select few (pure mathematicians), the "Babylonian" approach is a lot more fun. Both approaches are clearly necessary and useful in different settings.

With the advent of systems like the Lean theorem prover, the two approaches may start to see a lot more overlap.

I discovered Prof Mahajan through his "Teaching College-Level Science and Engineering" course on MIT OCW. I must have watched it six times during graduate school. He also has an OCW course based on this book.

http://web.mit.edu/sanjoy/www/

Stanford has an excellent physics course, "Back-of-the-Envelope Physics," based on Mahajan's work. On the first day we worked out how much to feed a baby every day assuming they are spherical heat emitters of radius 1 meter... (also, you got points off the problem sets if your answers were _too_ precise).

That's a big baby.

A baby elephant has close to a 1m diameter. Maybe an elephant?

Calculations are so much easier when it's a unit circle/sphere.

Here's my favorite trick: the radians of an angle in a unit circle is equal to the length of the arc of that unit circle.

That's not exactly a trick. It's the point of the definition.

I think you're being needlessly pedantic. Just because it's easy to derive doesn't mean it's immediately obvious. I only realized it when I watched a 3Brown1Blue video where he pointed it out as interesting property of the unit circle. That alone tells me its not that obvious to many.

You did not get parents comment. Its not a derivation its a definition.

Personally, that again sounds like a very pedantic and obvious point to me. However, I could be wrong so feel free to break down your point further.

My interpretation is that I think you guys are missing the fact that the intent of my original comment is in the context approximations, from which you can see the use of the 'trick' is correct.

To break it down a little further: the trick I am referring to is in practice it's often convenient to scale approximations so that you can use the unit circle for calculations, since you can use the radians as a measurement of arc length. If it's not a unit circle, the angle != arc length, so that convenience is lost.

> Just because it's easy to derive doesn't mean it's immediately obvious

is what I was responding to. My point is this -- there is no derivation happening there. If it was pedantic, obvious and simple to you as you claim, I wonder why you claimed that it was a derivation.

To you the distinction between a definition and a derivation might be a pedantic one, I have doubts on whether that is an universal or even an useful position to have.

Of course https://en.m.wikipedia.org/wiki/Spherical_cow

Made me think of that one: topologically a dog is a sphere https://i.redd.it/pqq10ddcgdc41.jpg

Ever since I was in high school and first read about topology in George Gamow's "One, two, three ... infinity", I always perceived dogs as tori. Now I'm too old to change that perception.

That sounds really fun. Do you remember what the approach was?

I know that these lumped models are standard in heat transfer calcs, but the application to humans is always interesting. It reminds me a lot of thermal comfort models built to represent human comfort relative to environmental conditions. They all tend to use simplified heat balances to model the heat exchange (with net loss/gain resulting in feeling cold, hot respectively), and there's a couple (Pierce Two-Node Model) which uses two thermal lumps, one for the internal core, and the other for the skin.

I have a copy of this book and haven't read it. I keep fearing my background won't be strong enough. I struggle with some high school math (I did get a math degree many years ago but haven't kept up with even basic algebra, and it shows). This book's preface says it complements How to Solve It, another book I've been scared to crack open.

Nonetheless the thinness of the book and the foreword about applications and real world math are very promising. Maybe I should try it out. Any thoughts from someone who has read it?

It is great and the math is easy. There are a couple clever tricks ( like how to calculate pi), but nothing beyond high school math.

thanks :)

I remember first reading this book around the same time I read "How to Solve It". They were both popular within highschool-level math competition circles. If you have a college math degree, you should be fine!

Sanjoy's graduate thesis covers some of the same material, and is also good reading:

https://thesis.library.caltech.edu/5338/

I feel that to some extent this should be similar to estimation questions that consultants face in their interviews. Questions like:

- How many gas stations are there in Paris?

- How much savings does the leading bank of the USA have?

- Estimate the population of Indonesia (to someone who is not that familiar with Asia).

It's probably a great deal more complicated than these type of questions. But if there is a course like this and a student still feels as overwhelmed by these type of questions, then I feel the title should be updated accordingly.

The reason I'm also mentioning this is because I'm curious if anyone did both and can attest to whether one does get better at estimation questions like the one I outlined. If so, I just might want to take this course, as I'd like a deeper exploration on the topic than just consultant interview estimation questions.

fwiw the types of questions you mention are often refered to as Fermi problems, after the famous physicist.

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

Thanks for that.

Awesome! I'll take a look at that.

FWIW: it was worth quite a bit :)

An article by Douglas Hofstadter, On Number Numbness, eloquently described these types of estimation problem and the inability of human to comprehend the scale of large number.

It was discussed on HN some time ago.

https://news.ycombinator.com/item?id=20672411

>The reason I'm also mentioning this is because I'm curious if anyone did both and can attest to whether one does get better at estimation questions like the one I outlined.

You can get better at them over time.

Questions like these spawn a handful of new questions, and those questions might recurse into more questions.

You can find multiple paths forward given what kinds of information you can collect and what kinds of metrics can be used. You can estimate what the accuracy will be from each hypothetical path and you can estimate how much work it will be to collect such information.

It isn't always necessary to solve these kinds of questions this second. Sometimes an interviewer might want a really rough estimate solved then instead of being presented with different paths of research, but imho it's always best to talk about paths forward first, and it is best to hash out and clarify exactly what they want and mean. Only then once it is clear they do not want high accuracy and a simple estimate, then you can do just that.

In the real world you almost never want a low accuracy instant estimate, so I imagine you would look good by showing you can build a path to figuring it out at a higher degree of accuracy than just some basic estimate.

I agree with a lot of this but I find instant estimated of low accuracy are very useful to me regularly. It's when you actually only need to know if something will fall within a certain range.

For example, I need to reprocess some documents and don't know how many will be affected. The scope of the change means that it can't affect more than a few hundred thousand, and I know I can easily reprocess a few million before it becomes an issue. I can leave the estimate there, even though it's "between one and 500k" because all I really need to answer is "is it under 3M?". Similarly there are cases the other way where I know quickly that the scale means certain approaches aren't possible despite not really knowing what the actual value is.

Learning how to identify what questions are important and easy to answer quickly has been something very useful.

I agree with this, which is why I found it a good moment to ask a bit more about the discipline itself with regards to this thread. I'm suspecting that more people disagree than they are commenting here as I'm seeing some downvotes. Unfortunately, they're not participating in the discussion as it would be quite interesting to tease out more why this is or isn't a useful skill. Apparently, opinions on the topic are a bit polarized.

Personally, another thing I find it useful for is for salary negotiations when you're talking face to face. Simply being able to guestimate a company's revenue, amount of clients, cost and their mindset gives you an idea if a low ball or high ball offer is due to mindset or due to finances.

I find in general that estimations of these types are amazingly good for when you really only have a few seconds, or to warrant further inspection. Like you said, if something is orders of magnitude away, then you already know the answer.

How can you see downvotes? I haven't gotten any and that's all I can see.

Taking a stab in the dark here but it might be because YC is mostly software engineers and these kinds of problems rarely fit into the domain. It's a useful skill set, absolutely, but isn't something taught in computer science.

On the data science side this has to be used all the time for most problems, but there are not many data scientists or other kinds of analysts on YC, so the kinds who use these tools are more than likely not going to be represented.

You see -1 points, and so on.

At the moment it's slightly more upvoted, I wish I could actually see all upvotes and downvotes as it'd tell me how controversial my comment is.

I took Sanjoy's Bayesian inference course at Olin College of Engineering. One of the few courses during my undergrad experience that just gave me pure joy and excitement. He's one of those people who can explain seemingly complex concepts to a 6 years old.

This is an awesome book - its techniques have served me well in the years since reading it. Its small size and high information density make it a good carry-on for flights and long bus or train journeys.

On a side note, does anyone know why certain books are restricted for sale only in certain subcontinents? For example this book is "Not for sale on the Indian subcontinent."

As far as I can tell, textbook publishers practice price discrimination so that they can sell less expensive versions of the same book in markets where profit is maximized at a different price. Retailers are only permitted to sell the appropriate version in the appropriate market.

Personally I have seen many textbooks available in the US/Canada version and Indian Subcontinent version (generally the same text, often for sale at <25% the price). My guess is that it's common to see India in particular because there is a large market for English-language textbooks there.

It falls along the same line of argument that big Journal Publishing groups like Elsevier and Springer do the same when giving subscriptions to countries across Europe vs Africa. I heard this in a talk from a former director of Radboud University in Netherlands who is now spearheading the Open Science movement in Europe.

Ha, I misread the title as "Street-Fighting Mathematicians" and expected something about characters such as Galois (https://en.wikipedia.org/wiki/%C3%89variste_Galois)

I suspect that would be a short book.

I was expecting a hard data approach to a style of unarmed combat. Wouldn't even be the first time something like that's been written: https://www.amazon.ca/dp/1904658849?tag=duc12-20&linkCode=og...

I'm reminded of the Steven Wright joke: Imagine Pulitzer prizefighting.

A beautiful book. I have all my students read it and I use its ideas every day in research.

>> Not for sale on the Indian subcontinent.

huh?

I don't know if it is the case for this book, but many text books have vastly cheaper versions that are printed in India. Usually they are on much thinner paper. (I saw these during postgrad when some of the international students would bring texts from their home country.)

Could they have been pirating the books? In my home country (Turkey), there were alternative sellers (basically photocopiers) who made pirate copies of books (usually on much thinner paper and washed out colors) and sold them. They were exactly like bookstores and they'd have the books you needed in stock. They usually sold textbooks for 1/10th of the price.

This also happened. But there was a completely legal tier of regional editions, my guess is also that this note is there because the regional rights were transferred to someone else.

In South Africa, we also have different versions from the US and they are not pirated. They are usually called international versions. It does have to do with pricing here vs. the US, but they are still expensive for a student.

Pretty sure it wasn't piracy. For instance see this[0] book (not affiliated), at the bottom left it says "Restricted! For sale only in India, Bangladesh, Nepal, Pakistan, Sri Lanka & Bhutan"

[0] https://www.amazon.in/Abstract-Algebra-3ed-David-Dummit/dp/8...

If I remember correctly. A lot of books actually print in India. Then are sent to other countries.

"Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy."

Reasoning by analogy sounds dodgy to me.

Dodgy how?

I've always found that it's difficult to get a student to even venture a guess about the answer to a problem. If they do make a guess then they probably have a mental model about how the situation should work... and then teaching becomes easy: either their model is good or it needs tweaking.

You gotta have the confidence to be wrong.

Using analogy to teach people something new makes sense and it's done all the time with positive effect.

But using an analogy to infer something that hasn't been observed? Unless the analogy is very close to the subject, it doesn't make much sense to me.

I read the book and it's pretty solid, you can read more about how he introduces reasoning by analogy in the book itself.

Often people find it easier to reason about real life situations than equivalent formal abstractions. This passage from a novel I read recently demonstrated this principle well. No idea if the statistics are correct, but for me at least the first formulation required some reasoning and the second was immediately obvious.

https://books.google.com/books?id=_zQsDwAAQBAJ&lpg=PT54&ots=...

Reasoning by analogy is akin to modeling. A model is presumed to capture a sufficient number of principal components that by permuting those, you can usefully predict the behavior of the target system.

That said, I agree with you. IMO, systems that can't be factored into quantifiable components can't be modeled accurately -- i.e. analogies.

Like the field of economics, where too often, analogies that are based qualitatively on only one or two factors are often proposed as sufficient to explain the behavior of diverse international economies, IMO analogies have proven to be insufficient bases for larger theories.

Same goes for philosophy and science. Analogistic thinking too often leads down garden paths. Too untestable.

I was actually expecting a book that explains real street fighting with mathematics (like kinetics of certain moves, optimizing impact on the opponent, etc.). I am a bit disappointed after reading the abstract...

I was expecting a book about mathematical modelling of games from the Street Fighter fighting game series.

I've learned from acquaintances who grew up in "tough" places, where street fights are more common, that violence is more about social posturing than it is about the actual fighting. In these places one's reputation can be protection. If everyone knows Bob will escalate situations to a physical fight, then few people will confront Bob. I've heard it's analogous to mutually assured destruction, where the "crazier", more inclined toward violence an individual is, the less likely it is they will end up in street fights.

I imagine if you wanted to study fighting in a mathematical way, you would want to study experts. MMA fighters, boxers, Muay Thai fighters all optimize their bodies and technique toward effective fighting. I bet there would be interesting science/math there, but I doubt street fighting would actually yield much insight.

Rory Miller calls the most common social posturing "the Monkey Dance."

http://chirontraining.blogspot.com/2013/03/cofv8-monkey-danc...

related discussion: https://news.ycombinator.com/item?id=23429390

(to reply directly: leverage is useful, mixed game strategies are useful, beyond that I can't think of other applicable theories. Miller points out that non-posturing violence is usually as unfair as possible, so maybe big-O notation?)

I had a similar reaction, expecting the text to show the mathematics of how to win street fights. I expected to read about arm length in conjunction with weapon use in equation form to solve for the maximum number of opponents who could be beaten. Then, the click-bait headline led me to a reall cool looking mathematics book! I still want the original book, though....

Reply on news.ycombinator.com