461 karma · joined July 15, 2009
The terminology (gibberish) I used is nothing more than a convenient but very precise shorthand for communicating abstractions. The reason these particular abstractions are given special names by mathematicians is that they occur over and over again. There is a lot of conceptual leverage to be gained if you are able to see the same patterns in seemingly unrelated problems.
As Poincaré put it, "Mathematics is the art of giving the same name to different things". I'd argue it's worth knowing some of those names.
Mathematically, an n-dimensional space is R^n, that is, the cross product of the real numbers (R) with itself n times. Each copy of R lets you specify a number independently of all the others.
Mathematics is just careful abstraction. If you are abstracting away certain aspects of your problem and carefully making deductions about what is left, you are doing mathematics. As you point out, this can be taken too far but any tool can be used poorly in the hands of a novice.
I used that service in the past to send myself a message from me pre-PhD-completion self to my post-PhD-completion self to ask how it was. Although it was basically procrastination at the time it was surprising and strangely cathartic to receive an email from a very different sounding me.
When you fingers crave Vi but your eyes crave OS X.
First of all, it's great to see people having a look at it and offering encouragement and constructive feedback. Thanks.
Annotatr was more a proof of concept and fun hack than anything else. While Bosco and I did want to offer an alternative to existing commenting systems for scientific papers (Nature, PLoS, CiteULike, etc.) we also realised that a big difficulty is getting continued engagement.
Some time after we put it up, I adapted annotatr and turned it into mldiscuss, a site for commenting on papers from ICML 2010:
Before, during, and after the conference this site had quite a bit of activity but has since died off. I guess the lesson here is that a narrow focus (a single conference) works better than a broad one (scientific papers) -- at least in the short term. I'll likely extend mldiscuss for this year's ICML to see if it can pick up a bit more momentum.
For example, there is an ACM Portal page ( http://portal.acm.org/citation.cfm?id=1553489 ) for a paper I wrote that is freely available from the conference site ( http://machinelearning.org/archive/icml2009/abstracts.html ).
There is no indication on the ACM page (the DOI on that page just returns the ACM page) that this content is available elsewhere without the $15 fee.
It's bordering on unscrupulous in my opinion.
It seems the main point of difference is that you found the meandering digressions annoying whereas I really enjoyed them. For me, understanding the topics (computation, recursion, use/mention, self-reference) wasn't the main reason for reading the book. The blurring of form and function in the writing and general playfulness were just as important and anything but boring.
PG, Feynman, and _why are useful points of reference. I like all three but recognise how different the latter one is to the former two. A similar distinction would be between Coetzee (precision) vs. Wallace (verbosity). I strenuously suggest you avoid Wallace even though I think both authors are amazing. :) Having enjoyed Wallace's non-fiction book on infinity, "Everything and More", I recommended it to a work mate (also a programmer) and he hated it. Upon reflection, I think he has similar tastes to you and would probably not like GEB either.
Out of interest, what style of fiction (if any) do you enjoy?
Hofstadter doesn't make any claims to being an expert in any of the areas he discusses (at least not in 1979). I think of GEB as an extremely idiosyncratic but well written piece of popular science. He provides plenty of further reading for those who want to delve into the various topics he touches upon.
I'm a programmer with a maths background[1] and I've read the book twice–once when I was 19 and again when I was 26. Both times I really enjoyed the digressions, language games, dialogues, and playfulness of the book. I got the sense Hofstadter was deeply curious and enthusiastic about the topics he explores and did a wonderful job at sharing that enthusiasm.
In my opinion it is a great example of writing for the sheer joy of exploring ideas. I can see how approaching such a book with a "just the facts please" attitude might end badly.
[1]: I've been told I'm a strange math/programmer though. I enjoy a wide range of literature too: Cervantes, Nabokov, Wallace, and Coetzee being some of my favourite authors.
The fact it doesn't do anything fancy is part of its appeal. The storage format is plain text so you can always view/edit it in any editor (there are plugins for vim, textmate, etc). Having it sync with an iPhone app is also very nice.
That's an admirable goal but don't sacrifice too much of your time with the family now chasing after the dream of time with your family later.
Let me guess, you're an engineer?
Regarding your programming analogy, I think of it slightly differently -- scales : playing :: touch-typing : programming. Sure, you don't need it but it will make you a more efficient coder if you don't always have to look at the keys.
Another view is that learning scales is a way of compiling a whole lot of low-level muscle knowledge so you can think and play at a higher level of abstraction. You don't always think about programming in terms of Turing machines because languages hide that level of detail.
I agree with your last point though: you do need immersion and an "ear" to play well. However, practising technique and learning theory are not mutually exclusive. For example, learning a language is easier if you study some grammar as it gives you useful concepts for processing the spoken language you hear while immersed.
I currently use justified alignment, but given the mounting evidence against it I might switch to ragged right next time I'm playing with the CSS.
Fallacy? Counterfactual? Hypothetical?
It's playing around at the limits of human reason. I don't see it as any different to most sports, music, and art. All are appreciated by different groups of people but, ultimately, "useless" if you do not value the enjoyment gained from exploration for its own sake.
If you've ever tried to write your own code to handle dates you'll notice that much of the essential complexity comes from the crazy rules we use to define calendar years, etc.
I suspect a SO falls into the latter category. :)