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Street-Fighting Mathematics
- nchelluri 6y agoI 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?
- blp 6y agoIt is great and the math is easy. There are a couple clever tricks ( like how to calculate pi), but nothing beyond high school math.
- nchelluri 6y agothanks :)
- ghj 6y agoI 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!
- melvinroest 6y agoI 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.
- estomagordo 6y agofwiw the types of questions you mention are often refered to as Fermi problems, after the famous physicist. https://en.wikipedia.org/wiki/Fermi_problem https://en.wikipedia.org/wiki/Fermi_problem
- gchokov 6y agoThanks for that.
- melvinroest 6y agoAwesome! I'll take a look at that. FWIW: it was worth quite a bit :)
- magnio 6y agoAn 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 https://news.ycombinator.com/item?id=20672411
- proverbialbunny 6y ago>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.
- seven4 6y ago"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 https://www.edx.org/course/street-fighting-math
- mikorym 6y agoThe 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#Literary_significance_and_criticism 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
- rmrfstar 6y ago> 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?
- 082349872349872 6y agoAnything more recent than https://twitter.com/johncleese/status/1254130854462455813 https://twitter.com/johncleese/status/1254130854462455813 ?
- mikorym 6y agoOrwell'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.
- deleted 6y ago[deleted]
- stiff 6y agoFor 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-engineering https://mitpress.mit.edu/books/art-insight-science-and-engin...
- sfsylvester 6y agoAlso available as part of the MIT OCW[0] [0] https://ocw.mit.edu/courses/mathematics/18-098-street-fighting-mathematics-january-iap-2008/readings/ https://ocw.mit.edu/courses/mathematics/18-098-street-fighti...
- evanb 6y agoI took this course during a January term. It was great fun and Sanjoy was a great teacher, with tons of energy and enthusiasm.
- rmrfstar 6y agoAnother 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 https://en.wikipedia.org/wiki/How_to_Solve_It [2] https://math.berkeley.edu/~gmelvin/polya.pdf https://math.berkeley.edu/~gmelvin/polya.pdf
- codemonkey-zeta 6y agoI 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.
- annoyingnoob 6y agoI really appreciate the Open Access. Thank you MIT.
- smlckz 6y ago>> Not for sale on the Indian subcontinent. huh?
- noelwelsh 6y agoI 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.)
- terminalcommand 6y agoCould 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.
- iguy 6y agoThis 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.
- mikorym 6y agoIn 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.
- iambrj 6y agoPretty 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/8126532289/ref=sr_1_7?dchild=1&keywords=abstract+algebra&qid=1593094249&sr=8-7 https://www.amazon.in/Abstract-Algebra-3ed-David-Dummit/dp/8...
- dls2016 6y agoI 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/ http://web.mit.edu/sanjoy/www/
- jansan 6y agoI 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...
- fnrslvr 6y agoI was expecting a book about mathematical modelling of games from the Street Fighter fighting game series.
- codemonkey-zeta 6y agoI'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.
- 082349872349872 6y agoRory Miller calls the most common social posturing "the Monkey Dance." http://chirontraining.blogspot.com/2013/03/cofv8-monkey-dance.html http://chirontraining.blogspot.com/2013/03/cofv8-monkey-danc... related discussion: https://news.ycombinator.com/item?id=23429390 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?)
- IncRnd 6y agoI 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....
- 99_00 6y ago"Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy." Reasoning by analogy sounds dodgy to me.
- dls2016 6y agoDodgy 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.
- 99_00 6y agoUsing 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.
- conistonwater 6y agoI read the book and it's pretty solid, you can read more about how he introduces reasoning by analogy in the book itself.
- henron 6y agoOften 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=-BxTWmpzSI&pg=PT53#v=onepage&f=false https://books.google.com/books?id=_zQsDwAAQBAJ&lpg=PT54&ots=...
- randcraw 6y agoReasoning 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.
- tadhgpearson 6y agoThis 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.
- archi42 6y agoHa, I misread the title as "Street-Fighting Mathematicians" and expected something about characters such as Galois (https://en.wikipedia.org/wiki/%C3%89variste_Galois https://en.wikipedia.org/wiki/%C3%89variste_Galois)
- troymc 6y agoI suspect that would be a short book.
- SuoDuanDao 6y agoI 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=ogi&th=1&psc=1 https://www.amazon.ca/dp/1904658849?tag=duc12-20&linkCode=og...
- MaxBarraclough 6y agoI'm reminded of the Steven Wright joke: Imagine Pulitzer prizefighting.
- rpmuller 6y agoSanjoy's graduate thesis covers some of the same material, and is also good reading: https://thesis.library.caltech.edu/5338/ https://thesis.library.caltech.edu/5338/
- hardmath123 6y agoStanford 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).
- baggy_trough 6y agoThat's a big baby.
- dzdt 6y agoA baby elephant has close to a 1m diameter. Maybe an elephant?
- saeranv 6y agoCalculations 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.
- baggy_trough 6y agoThat's not exactly a trick. It's the point of the definition.
- saeranv 6y agoI 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.
- srean 6y agoYou did not get parents comment. Its not a derivation its a definition.
- seesawtron 6y agoOn 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."
- jamesmaniscalco 6y agoAs 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.
- seesawtron 6y agoIt 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.
- slyu 6y agoI 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.
- knzhou 6y agoA beautiful book. I have all my students read it and I use its ideas every day in research.