Back when I was a 16 year old mediocre chess player, the captain of our high school team took me aside, set up a position and asked "Do you like white or black?" I looked at the board and said "I don't know." And channeling a Yoda then decades in the future, he said "That is why you lose."
His name was Matthew Looks, and his point was that it doesn't matter whether you're right or wrong. It only matters that you have a visceral opinion.
If you believe something or care about something strongly, it gets you to engage. If it turns out that you're objectively wrong, the clash will focus your attention and you'll learn. Just having an opinion, just caring, will bring out a better game.
This is how I interpret PG's post on taste. Having good taste is wonderful. But having taste, even bad taste, is better than not caring at all.
I agree. There are already too many people in this world with strong opinions on topics they don't fully understand. We certainly do not need even more of them.
Uh, you're both really missing the important part:
> If it turns out that you're objectively wrong, the clash will focus your attention and you'll learn.
Yeah, if you have a bunch of ill-informed wrong opinions and, out of some stubborn ignorance, you refuse to update them when the conflicting evidence comes crashing in all around you, then you will be a stupid person. However, if you have a bunch of wrong opinions which you then turn into right opinions after reality keeps kicking you in the ass, then you are on the road to being a smart person.
But if you're apathetic, you won't even notice reality kicking you in the ass. Reality won't even bother with you. You're right that having wrong opinions as a steady state is worse than having no opinion, but the whole point of GP was not to be in a steady state in the first place.
> Yeah, if you have a bunch of ill-informed wrong opinions and, out of some stubborn ignorance, you refuse to update them when the conflicting evidence comes crashing in all around you [...]
There's a ton of research demonstrating that once you've formed an opinion, you'll actively defend this opinion in the face of contrary evidence. Everyone does this to some extend, and the best prevention is to not form a premature opinion.
> But if you're apathetic [...]
That's a false dichotomy. It is very well possible to not form an opinion and still be interested in a topic.
> There's a ton of research demonstrating that once you've formed an opinion, you'll actively defend this opinion in the face of contrary evidence. Everyone does this to some extend, and the best prevention is to not form a premature opinion.
Yes, everyone does this at least a little bit because that's how human brains work. But you can be aware of it and compensate for it, if you make the truth (and, by extension, actually being right) your highest goal. Just throwing your hands in the air and giving up, seems to me equivalent to saying "everyone has biases, the best way to avoid them is to not think".
That said, obviously I am not suggesting that you just form opinions before you know anything. The example given was a chess position. The OP knew enough about chess that he could have picked a side had he taken time to examine the position well. If he had initially chosen black, but white was the stronger, he could have perhaps reached this conclusion after evaluating black's position a little more carefully. Then he could update his opinion to prefer white. But he did none of that, because he didn't care enough to form any opinion at all, even though he had enough information to do so.
> That's a false dichotomy.
Ugh, yes okay if taken absolutely literally, yes it is a false dichotomy. I mean, I guess I took it as a given that readers would understand that there are degrees of apathy, and that you might be in a mental state where sometimes you notice reality kicking you in the ass, and then sometimes you don't, and so I didn't have to explain that part, and that they would give me just enough benefit of the doubt to suppose that I also understand this, but yes it's true that apathy is not a binary thing, nor is self-awareness. Conceded. Congratulations and I award you one Internet argument point.
So just to be clear, my position is that the more apathetic you are about a thing, the less likely you are to notice your wrong opinions about that thing. Is that better?
> It is very well possible to not form an opinion and still be interested in a topic.
About as possible as it is to change your opinion on new evidence? Of course it's possible, although if I had to guess between two people which of them is interested in a topic, I'd go with the person who has the opinion, and I'd be right more often than I'd be wrong.
Perhaps it should be nuanced that this opinion should be combined with an openness to be corrected or proved wrong. Basically "Strong opinions held weakly"
> If you believe something or care about something strongly, it gets you to engage. If it turns out that you're objectively wrong, the clash will focus your attention and you'll learn.
Centuries of religion argue against this; instead, people tend to make up a ton of story to 'smooth over the cracks'. I agree that people are better at things they are interested in, but it's just not true that having a strong opinion makes you better at it. Check out the 'autism vaccers' as another counter-example.
I wish I'd known 20 years ago how important design was going to be. Getting my 10,000 hours of design isn't going to be easy. I started this course a few days ago on Udacity:
It's amazing how close pg's ideas in this essay are to those of David Deutsch's in his Beginning of Infinity, e.g. on the topic of why flowers are beautiful to humans as well as insects (https://www.youtube.com/watch?v=IMiP2SM8Tpk).
"In math and engineering, recursion, especially, is a big win. Inductive proofs are wonderfully short. In software, a problem that can be solved by recursion is nearly always best solved that way."
I don't make use of recursion very often but this statement doesn't sound right to me. Actually the opposite seems right. If you read the chapter on recursion from Concrete Mathematics (I'm thinking about the The Tower of Hanoi, Lines in the Plane and The Josephus Problem here, it seems obvious that a closed form is much faster, simpler and according to the blog post more beautiful. Does anybody with more extensive knowledge on the topic care to comment on this?
I find inductive proofs tend to leave me hanging - I become convinced that the conclusion is true, but I still have no intuition as to why. For example, Wikipedia's proof [0] that sum of 0..n == n(n+1)/2 is convincing, but unenlightening. There are proofs which seem much more "elegant" to me, for example, pairing (1+n) == (2+n-1) == (3+n-2) ... (n/2 + (n/2 + 1)) [1], or constructing triangles [also 1].
The book I mentioned above, Concrete Mathematics, talks about how to develop an intuition when it comes to induction. One of the advice mentioned is to always start with smallest cases possible because that makes the problem easier to understand. I suppose the more you practice the better your intuition becomes.
You say "closed form" which sounds alot like the javascript representation of "clousure". And I also remember the javascript "memoizer" way to solve the Fibonacci sequence. How do you exactly define "closed form" and are there any solutions that cannot be optimized by defining in such a form?????
By closed form I mean basically, "You can write down a formula."
A trivial example of a problem that cannot be solved in closed form is to construct a sequence x(n) with x(0) = 1, x(1) = x(2) = x(3) = x(4) = 0, and x(n+5) = x(n+1) - x(n). There does happen to be a formula, but it is in terms of the roots of a 5th degree polynomial whose roots cannot be written with radicals.
A more interesting class of problems is solving for f(x) = y with complicated functions f. Assuming that f is continuous, we can use binary search recursively until our answer is good enough. But generally there is no analytical answer.
Then there are problems that we can tackle with recursion on top of recursion. For example suppose that we want a numerical solutions to a non-linear first order differential equation with specified values for f(0) and f(1). It is straightforward to recursively calculate the trajectory with specified f(0) and f'(0). (For example http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods work well.) Then we can set up binary search to find the right value of f'(0) to get the desired f(1). This is not even a particularly complicated program to write, especially if you've got closures in your language. But trust me when I say that we have no hope of solving this analytically.
(A more complicated version of this technique is used to calculate what the masses of planets must be based on their gravitational influence on other planets over a very long time.)
His name was Matthew Looks, and his point was that it doesn't matter whether you're right or wrong. It only matters that you have a visceral opinion.
If you believe something or care about something strongly, it gets you to engage. If it turns out that you're objectively wrong, the clash will focus your attention and you'll learn. Just having an opinion, just caring, will bring out a better game.
This is how I interpret PG's post on taste. Having good taste is wonderful. But having taste, even bad taste, is better than not caring at all.