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.
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.)
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.
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.
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.
Yes, I am repeating Adler's How To Read.
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.
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)
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"
I agree. Theory vs. Practicality, Pure Science vs. Engineering.
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 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.
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.
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?
"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.
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.
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.
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:
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...)
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.
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.
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 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.
(P.s sorry about the title. I guess thats how they get more eye balls on it).
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.
The funny physics answer would be to assemble correctly and then point out that it's lit, just exceedingly dimly (producing mainly IR).
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.
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.