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Read the masters (federicopereiro.com)
189 points by fpereiro on July 14, 2012 | hide | past | web | favorite | 53 comments

Or, if the masters are too hard at first, see if their pupils have written annotations. I tried Turing, couldn't even understand why what he was talking about was important (or why his "computers" seem so much... lamer than the ones I was used to), and then found Charles Petzold's "Annotated Turing".


He takes Turing's "On Computable Numbers..." and mixes in chapters giving the necessary background on the history of mathematics, number theory, logic, etc. in-line (albeit, it takes about 100 pages to get to the first sentence of Turing's paper). I whole-heartedly recommend it.

Another vote for The Annotated Turing. Really does a great job of shedding light on a rather esoteric paper.

> Another thing that resonated deeply with me was how Newton studied a book by a French mathematician (I don’t remember which one): he started reading the book – when he found it too hard, he started over. That’s what he did until he understood the whole thing. So, he didn’t go and read something more basic, or tried to found someone who could explain it. He just stayed with the source until he groked it.

Approach this advice with caution. Yes, it might work great if you're working with a great book that has good coverage of all the fundamentals of the topic and presents it in a logical order. Many books don't do this. Starting over when you get stuck can just throw you into an endless loop if the required information just isn't in the book you picked to learn from. Know when to branch out to other sources of information instead of looping back. Don't be afraid to make a quick interlude to Wikipedia if you need to.

(Personally, I prefer to just backtrack to the information I missed instead of starting over from scratch. Starting over seems to waste a lot of time, but if you missed one concept, there's a chance you missed more.)

Indeed. Many brilliant, groundbreaking work is produced by geniuses who are lousy writers, so sometimes secondary sources are necessary to get past roadblocks.

Still, it's a good reminder to try reading primary sources, when so many people seem to be learning from screencasts and blog posts three degrees removed from them.

"Many brilliant, groundbreaking work is produced...lousy writers." I, um, yeah. Oops.

I agree with this. I'm currently reading John McCarthy's paper "Recursive functions of symbolic expressions and their computation by machine" linked to in the article, which I've been meaning to read. I don't have any real formal maths/computer science education so looping over would have been futile in many cases and Wikipedia, namely http://en.wikipedia.org/wiki/List_of_mathematical_symbols, has been an invaluable resource for me in understanding the paper (and other things in the past).

Another example is partial recursive functions, which I didn't know the definition of. A quick Google/Wikipedia search helped here.

I've found myself looping over once or twice to make sure I haven't missed anything and, if not, proceeded to search for definitions or further explanations.

I'm not entirely sure if this approach would work for other papers such as the Turing ones, since I'm familiar with Lisp already, but it's working very well for the paper I mentioned earlier.

There's a lot to recommend for backtracking. Newton backtracked multiple times to understand the math from an astrology book he picked up.

Also, if you're inexperienced, how are you to tell who the Master's are? I fear that whatever book is renowned for its difficulty will become the Master's book. The advice is like, find the steepest slope you can, then climb it. You may not get very far, but you'll feel good that you got anywhere at all.

Or the "original communicators." When you start to read the masters of every field, you realize they are in some sort of a conversation that spans centuries and you get to participate. One problem with this approach is these are dead teachers so no question & answer session for you, and usually the material is hard to comprehend at first. That is exactly what you need it, a material that elevates you, something that pushes you from understanding less to understanding more. Lastly, during this exercise you will find amazingly that there are really only a few original teachers and that most of what we read today are simply digest of what was originally written and discovered by a handful of experts. So it is probably in your best interest to take it straight from the horse's mouth.

Yes, I am repeating Adler's How To Read.

One of my favorite stories in this vein:

You may know that we often read Plato but never read Socrates, and you might have wondered why the hell we don't go back to the 'originals'. Reading Plato's dialogue "Phaedrus" gives an answer near the end: Socrates apparently believed "that writing is unfortunately like painting; for the creations of the painter have the attitude of life, and yet if you ask them a question they preserve a solemn silence." Socrates of course was famous for using questions to try and ferret out truth; the idea that you couldn't have a conversation with a book seemed to make Socrates very cautious. He expresses other concerns as well: that memory must be exercised to be strong, and that writing would thus lead to a weakening of memory; also that writing makes it easier to pretend to know something which you don't really understand; and that people will write texts which cannot be used to learn the subject but only can be used as an aid to remember it.

Thus ironically, Socrates seemed to believe that books would end the existence of knowledge. This presumably was the reason that he never wrote down his own philosophy, and his students had to do it for him.

Feynman had some similar advice to not read too much. He'd get just the basic idea, stop reading, and try to solve the problem himself. There's a similar anecdote about Turing. You don't have to be a genius to profit from this approach, though of course it affects how far you can take it.

I am currently reading Plato's works (chronologically). As you mention I keep asking myself "why did he not write anything? he knew he was a teacher of virtues." Now I am looking forward to the answer in Phaedrus.

Socrates, by means of Plato, Plato, by means of Aristotle, and Aristotle himself are all examples of masters, original communicators. Much of the way we think today, not just the philosophy, but even the mechanism, has to do with their writings. For example it appears the concept that something is either right or wrong comes from Aristotle, and that affects even our laws and sciences where as other cultures may have 4 possibilites: right, wrong, both right and wrong, and neither one nor the other. (I have not verified this, I just heard it last week)

One additional point: the masters almost always had great ideas they took too far.

The "conversation" that spans centuries consists of brilliant minds each getting a little glimpse into something sublime, then spending most of their lives taking these concepts to the extreme -- past where they are useful.

This means that the pattern that many young learners have, where they latch on to a person and then hero-worship, (this is the guy who figured it all out!) makes for a really bad way to follow the conversation. You're always trying to find the best person, and you're always trying to make his/her ideas fit into all of the material. Much better to passively and fluidly accept new information. Think of it more like meeting a bunch of really smart people in a bar, listening to their philosophy of life, then meeting the next bunch. The question becomes absorbing and understanding and being able to apply the way they think, not the ultimate truth. Most things you consume are not physics. Hell, at some level physics isn't even physics. Humans are model-builders, and the models are always incomplete. The kind of certainty we yearn for just doesn't exist in the real world.

Perhaps another way of putting this would be "Deep learning lightly held"

The "conversation" that spans centuries consists of brilliant minds each getting a little glimpse into something sublime, then spending most of their lives taking these concepts to the extreme -- past where they are useful.

I agree. Theory vs. Practicality, Pure Science vs. Engineering.

Seems like in the article and the comments there are three categories of "master" here: Theoreticians, Mechanics, and Explainers. People who destroy and replace models, people who take models into places we never envisioned, and people who can explain models to others. (These categories work across both fiction, non-fiction, and science)

I wonder as we learn if we don't naturally move from one of these categories to another. I'd wager it's from explainer to theoretician to mechanic. It'd be interesting to see some research in this area.

I actually believe the mindset this author has (along with many university professors) makes learning far more difficult for students and discourages them from staying in STEM (math and science) degrees.

I have consistently found that for me to tackle difficult concepts I need multiple points of view, specifically views that simplify the topic tremendously. My professors never encouraged me to seek multiple sources and usually pushed overly complex, decades-old textbooks on my peers and I. The "masters" typically write to a niche, university-based audience and do not tailor their original works for the masses.

I certainly agree that if one wants a complete understanding of a field or subject they should eventually study original works, however to encourage them as a starting or leverage point for understanding difficult subjects is poor advice in my opinion.

I completely agree. As a high-school student, I was completely turned off by the quality of books that I was reading ('textbooks that conform to the curriculum set by the education board'). It was only when I started reading the masters (in this case Resnick Halliday for physics, Thomas & Finney for calculus) that I really started to like math and physics and chose to major in engineering

More silly, macho, "real programmer" nonsense. It's like saying that the best way to learn calculus is to pick up a calculus book in first grade and read it over and over until it all becomes clear. Yeah, that's the express lane to mastery.

If you want to master something, sequentially master its prerequisites and methodically work your way up. If you do that, then a lot of the ideas of the masters will have begun occurring to you before you even read their works, and you will be the sort of person they were writing for.

Trouble with this is that prerequisites differ. I taught myself multivariable calculus out of a differential geometry textbook that I lacked roughly an entire degree's worth of "prerequisites" to, in order to pass a bog-standard calculus course, because I found the ostensibly "easier" approach advocated by the undergraduate calc book utterly incomprehensible.

This is why you look at the related works section first. If you don't know any of them, go find those articles and do your favorite recursive look up of those articles until you find documents that you can grok.

At that point you work forward, annotating, high lighting, and answering a few questions like:

* What is the take away message?

* What is the people problem?

* What questions does this leave you with?

* What previous questions were answered?

When he writes that Newton too just read and re-read through the Master's, he's wrong.

"How Newton was introduced to the most advanced mathematical texts of his day is slightly less clear. According to de Moivre, Newton's interest in mathematics began in the autumn of 1663 when he bought an astrology book at a fair in Cambridge and found that he could not understand the mathematics in it. Attempting to read a trigonometry book, he found that he lacked knowledge of geometry and so decided to read Barrow's edition of Euclid's Elements."


When Newton failed to grasp something, he backtracked. When he failed to understand that, he backtracked again. I think many people when confronted with a failure of understanding may be disinclined, throw their hands up, and say, this isn't for me. Newton, instead, continued to work his way back up the chain until he found material that helped him understand.

I think this article does a disservice to the lessons we might learn from Newton by suggesting that he just smashed his head against the same book until he understood it.

I think the argument here isn't to reread a trigonometry book until you get it, regardless of your knowledge of the prereqs. The message I took is to find the book written by a/the master in the field of trigonometry, living or dead, in order to learn trig. If you don't yet understand geometry which is needed to understand trig, then find a book by the most renowned scholar in geometry.

It's sort of like that telephone game we play in elementary school, where the message gets passed around the room and ends up nothing like it started. Learn from the source of these insights, not from someone else who learned it and is giving you their interpretation.

A few days ago,i stumbled on Newton's Principia in my college library, and i could not help noticing how accessible he was relative to his pupils.On the very first page,he gives only one rule for finding derivatives that applies in ALL cases plus worked out examples on how it works.I felt like i had wasted too much of my time in college reading too many useless tomes.

This seems to be false according to the scan here: http://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PA1#v=o...

It is in fact rewarding, and something of a corrective to the viewpoint of the OP, to page through the first pages of the Principia you linked to.

Doing this helps to understand why going back to some original sources is not very rewarding at all. The 1600s were a long time ago.

Can you explain what rule this is? I'm highly curious as to what rule can solve all derivatives, and it might be useful for me.

Sure: the line tangent to any point on a smooth curve approximates a sufficiently small bit of the curve surrounding the point arbitrarily well.

Newton's contribution wasn't this, however, but the extension of Descartes' algebraic tangent-finding methods to curves represented by "infinite polynomials", which he neither uses nor explains in the Principia. If you're looking to learn Newton's flavor of calculus "from the master", here it is:


f'(x) = lim h->0 (f(x+h)-f(x))/h

If that's the really the rule ekm2 is referencing, the rest of his comment falls apart. This rule is found in the first section about derivatives in any college or high school calculus textbook. They lead you on for a good many pages that calculus problems are actually practically solved by reference to this equation, then grudgingly admit (after forcing you to use it many times) that the power rule, among others, exists.

I assume he's referring to this [1], although Newton invented his calculus because he couldn't use this approach to solve practical problems.

[1] http://en.wikisource.org/wiki/The_Mathematical_Principles_of...

Sometimes this leads to a considerably different flavor as well, which is interesting. Often papers are remembered for their "results", but sometimes the results are only a small part of the paper, and positioned much differently by the original author.

This is the case with Turing, for example. If you go by Turing in the secondary literature, he comes across as very mathematical, formal, rigorous. Which he was, but he was also very aesthetically oriented, playful, and philosophical. Many of his original papers are really quite "weird" in a way, at times even allusive/metaphorical. So you get a bit different view of him if you read the originals. (Due credit: I was reminded of that in Turing's case by this article, which aims to convince humanities scholars that they should read Turing: http://www.furtherfield.org/features/articles/why-arent-we-r...)

I’m not a programmer but I loved this line from the post:

But if you don’t mind too much feeling like a baby, and if you can create some space in your life where you aren’t forced to be an adult, then give the masters a try.

I think this is very good advice for many things.

I can't agree enough with this, except the part about staying with it. I think sometimes we have to come at the same material from several different directions before it actually makes sense to us. Perhaps it's our preferred mode of learning, or maybe just how old we are and our personality types. Don't know.

So for a long time I avoided a lot of the literary masters. As a programmer, I thought they were way too artsy and "fluffy" for my tastes. I wanted something with hard science and boolean logic in it, dammit.

But around 40 I listened to the Learning Company's "Great Authors of the Western Literary Tradition." It was like a guided tour of a huge amount of masterpieces. From this overview i could pick and choose what to consume. As I read each work, i had already been "prepped" by listening to a lecturer describe what made the work so outstanding.

So I picked up "Anna Karenina" Wow! Tolstoy could sketch a character like nobody else. I read some Dickinson. What a great, simple, yet complex way she had of describing inner emotional states!

Still couldn't get all of it. Joyce is on my list, but I procrastinate. I had another go at Melville and loved it, but I couldn't generate enough momentum to make it through Moby Dick. Both writing and reading styles have changed. I'd love to learn Greek and have a go at the true classical works, but I will never have the time, sadly.

I'm hoping to get another overview or introduction and then make a go at some of the rest of the material. I've loved reading the literary masters.

What I find is that you need a preparation or background to really absorb and appreciate the masters. This is the same as having to have a background in baseball to understand a baseball game. Otherwise, without context, it's very difficult to understand what parts work, what parts don't, and where the beauty is. (This is called a liberal education, by the way). The more broad and deep background you have, the more you can appreciate the masters in many fields.

Also I'd separate cargo cult liberal arts with actual understanding. To me there's tons of venues that exist to convince you that you're smarter than some other slob. They pitch quite a bit of snob appeal. I'd avoid that. You end up thinking you have class when all you're really doing is running around in a mob consuming whatever was on NPR last week. To me developing a sense of what the crowd thinks is beautiful versus truly coming to a personal grip with the masters is completely missing the point. I'm sure there's a social aspect to art consumption but to me a true master spans the test of time. While it's possible that something can be popular today and 100 years from now, for me using social proof as some form of merit for masterworks is almost diametrically opposed to the entire concept of what makes art truly great in the first place.

Fair warning, however: once you start consuming works from the masters it makes mediocre works hard to stomach. Oddly enough, bad material is fine. I still love me some pulp fiction and trashy pop music. It's the stuff that tries to be highbrow but you know is going to be gone with the wind in ten years that's impossible to take.

While I empathize with your aesthetic preferences, I don't think that you're talking about the same thing as the article. Everyone reads the literary masters in school. No one reads Newton.

Unfortunately, learning Greek is going to be a difficult task and as you say yourself it needs time that most people don't have. It will also NOT help you in reading the classics, Ancient Greek, although familiar with modern Greek is one of the most structured but difficult languages to master. Most of the Greek translations from Ancient to Modern are very bad pieces works that don't give justice to the original text -good translations exist but I am afraid they are not the best sellers when it comes to the classics.

What I would recommend is the series "LOEB", they have the original text and one of the best English translations available. It's also one of the best ways to learn Greek -after you learn the basics.

I fully agree with your point of "not bashing your head" against something. At least for me, I only understand it when I'm truly ready. If not, I just go read something else (preferrably another source/master, or random crap) and then come back.

I feel it's like exposure to a new language. You just need to get soaked in it, rather than trying to actively direct the process.

Nice idea, however if you lack fundamental knowledge in an area, prepare for this.


(P.s sorry about the title. I guess thats how they get more eye balls on it).

I'm not sure what the purpose of that was. Clearly, you CAN light a small bulb with a battery and wire, as done in the video and introductory physics classes everywhere. So... is it the fact that the students were unable to figure out that the battery produced insufficient power to light the big bulb? That shows a lack of "fundamental understanding about electricity"? More like a lack of knowledge about power requirements of household light bulbs.

One core message of the video is that when lacking fundamental knowledge, that no matter how 'advanced' your knowledge is, certain processes are beyond your true understanding.

So jumping into an advanced topic is good, but you really need to apply rigor to ensure you understand the important fundamentals. Obviously trying to understand everything possible can be inefficient or even unnecessary.

All the same its worth considering.

Most of them weren't making a circuit -- just running the wire from one end of the battery to the base of the bulb. That shows a very fundamental lack of understanding of what's going on, without even getting into things like the power requirements of the bulb.

I'm not sure they lack such understanding. Isn't this what psychologists call cognitive bias, or something like that? I believe there was a thread here on HK about it, a study showing that people often do irrational things because they assume they know everything. You know? People just think "geez, that is easy..." and rush to answear the first thing that comes to mind, just to discover that they missed the details and feel really stupid :P

Ah, ok, that makes more sense. I guess I assumed that they only showed the students holding the items after trying, not their actual effort. Now I'm a bit depressed.

I think the 'problem' was that you need two wires to close the circuit.

It's easier to hold one of the contacts of the battery directly on the bulb and one end of a single wire on the bottom of the battery, all with one hand, then use another hand to touch the wire to the other contact on the light bulb. The problem is they didn't intuitively understand bigger light bulbs when operated on lower voltage (and thus lower current).

The funny physics answer would be to assemble correctly and then point out that it's lit, just exceedingly dimly (producing mainly IR).

This is so true: I remember in high school studying calculus from a random book which made me think that calculus was about was a bunch of tricks for doing integration and differentiation. A few years later when I first start working through Spivak's excellent book on Calculus, It was one of the hardest things I had ever done but the sheer magnificent beauty of the structure on which most of modern calculus is built on and how it gradually evolved comes to light. It is really both a journey in history and time and building mental models that reoccur through so many branches of mathematics.

There is an interesting question. Does the advice "read the masters" also applies to teaching?

My teacher at university pointed me to Moore's method named by great american mathematician Robert Lee Moore. Moore selected students without previous knowledge of the subject and let them "invent" the subject - definition, theorems, proofs.


So great teachers do not "teach masters" but rather teach to "think like masters". If you know how to think, "reading the master" feels more like a dialogue.

The list of the article reminds me of this post http://cstheory.stackexchange.com/questions/1168/what-papers...

Be cautious when reading the "classics" of fields such as physics or philosophy (unless you are interested in the history of the field). Socrates was wrong about a few things and so was Einstein.

This is just a nitpick, but why is SRP (Wu) in your list? Looks a bit out of place there.

That's a very good question!

Although SRP may not be timeless, or even seminal (though I doubt this last statement), I found this paper to be beautifully written. Its concepts are very very clear. Above all, the paper seems to be so alive and enjoyable.

For these reasons, besides the practicality of SRP, I suspect that this paper may well turn out to be a classic.

Thank you so much for noticing this! I've just corrected the links.

thanks! for this post...really a nice insight.

No problemo. Am glad that my minor bout of OCD came in useful.

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