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My masters degree involved a good bit of category theory. Personally, I don't see how it has any use outside of mathematics. (Note 'maths' includes 'mathematical logic' - so it's still a broad field of applicability).
I am highly motivated to be persuaded otherwise, and hence will be watching this series of posts with keen interest.
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<disclaimer>
I am not a working mathematician, and have not published any papers. My masters thesis involved a lot of category theory - but only relatively simple category-theoretic concepts (it was an application of category theory to a subfield of mathematical logic).
Limits, free objects, adjunctions, natural transformations etc. but not higher-order categories, topoi/toposes or anything fancy like that.
</disclaimer>
<handwavy discussion of technical math>
As I understand it, the usual application of category theory is mostly to things involving natural transformations (it is said the need for a way to formalize natural transformations is what led to the invention of category theory) - and even then, it seems mostly to be applied to nice algebraic objects with (category theoretic) limits, and slight generalizations of these. So, to groups and rings and modules, and then to some categories made of stuff kinda like those things.
There's also the connection to topology and logic, via simplicial complexes, homotopies, toposes, type theory etc. which seems very interesting to me. It seems useful if you want to think about constructive mathematics (i.e., no law of excluded middle) - which is promising for maths involving some notion of 'computation' (for a given abstraction of computation) which has obvious applications to computing (especially automated theorem provers / checkers).
In these senses, I can certainly see its use as another mathematical field, and a good way of reasoning IN MATHS or ABOUT MATHS. But I don't quite understand its tremendous reputation as this amazing mathematical device, and less so its applications outside of what I've mentioned above.
</handwavy discussion of technical math>
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In particular, from my admittedly limited knowledge, category theory only seems useful:
a) If you already have a bunch of different fields and you want to find the connections.
b) If you want to start up a new field, and you need a grounding (after which the useful stuff will be specifically in the field being developed, and not a general category theory result).
c) For good notation / diagrams / concepts for a few things.
EDIT: Interested to hear the opinion of someone who actually works with category theory on a regular basis.
I find that what helps for me is re-writing maths as I'm learning it.
When I glance at an equation or formula (especially an unfamiliar one), I usually can't take it in because my mind is trying to glance it all at once. I have to force myself to scan it slowly, either by re-writing it, writing out its definition, or by (holding a ruler under it) and scanning one symbol at a time.
Then again, I'm currently studying a postgraduate degree in maths and I'm not someone who's ever considered themselves 'bad at math'.
This comment resonates with me. I am also a Christian-turned-Atheist.
When something bad happens, or I feel in danger, or I don't know what to do, usually I want to send up a prayer. Then I have to catch myself and remember that yeah, that's not going to help.
last paragraph teaches false lesson on cleverness
What exactly do you believe the false lesson to be and why do you think it's false?
I interpreted it as meaning one should take into account your prior for whether someone with a gambling machine is telling the truth about how the machine works.
So much for "the map is not the territory", I guess.
That's a useful template and in some cases the advice...
This may vary somewhat with the audience and I believe the claim...
Note, that I did notice the change. I do think that to facilitate proper understanding of a sentence, 'but' should be used slightly differently from 'and', even if both are technically correct.
So, Viliam_Bur, do I understand correctly?
You are saying the major tradeoff isn't between:
- Speak 'bluntly' in situation X
- Speak 'politely' in situation X
It is between:
- Speak 'bluntly' in every situation (default)
- Invest effort to learn to speak more 'politely'
(The costs-benefit calculation is a long-term one performed over all potential situations, not a short-term one performed over each specific situation)
I agree; this makes sense to me.
In certain cases, bluntness can be useful. However, by this I mean it can be useful if you are able to let people be blunt to you. See Crocker's Rules and the related article on Radical Honesty.
If everyone in a certain social context operate on such a system (whether explicitly or implicitly), then there is some benefit to these people in terms of saving time and cognitive effort in the short term, and in the long term if they haven't yet spent time on developing 'politeness'.
I also recall reading 'and', if not in that book then in one on a similar topic.
I believe the basic format for using 'and' is: "I believe X is good, and it could be even better if you did Y".
Contrast:
- "Your speech was good, but consider using more specific examples"
- "Your speech was good. However, it could be improved with more specific examples."
- "Your speech was good. Yet I think that using more specific examples would improve it."
- "Your speech was good, and I think you could increase the impact even further if you also included more specific examples."
(Note: The one with 'yet' sounds a bit awkward to me, I'm not sure I know how to use it in this situation).
Sure the use of the word 'and' is neither neccessary nor sufficient to make the sentence more positive, but I think that (given a bit of practice) it naturally causes you to do so. Much the same as the word 'yet', but (I think) more strongly.
I could theoretically say "Your speech was good, but I think you could increase the impact even further if you also included more specific examples.", but using the word 'but' doesn't really force me to do so the way that using 'and' would, and doesn't come across as quite as supportive. The word 'but' actually sounds slightly wrong to me in this sentence.
I'm not sure Twelve Virtues of Rationality is the best place to start. To be honest, I was a bit confused reading it the first time, and it only made sense to me after I had spent some time on lesswrong getting used to Eliezer's writing-style.
For myself (as I know it was for many others), I got here via Harry Potter and the Methods of Rationality. I'd say it's a great place to start many people off, but perhaps not the majority. Along with that, what got me convinced to start reading lesswrong was my interest in biases and importantly being convinced that I, myself, am biased.
Thus I would propose one starts off with a single post about some bias, especially one that convinces the reader that this is not an abstract experiment involving random test-subjects. I think that Hindsight Devalues Science works excellently for this purpose, although it's obviously not written as an introductory essay.
Follow this up with some posts from Map And Territory, namely: What Do We Mean by Rationality, What is Evidence, and The Lens that Sees its Flaws, in that order, to give a basic introduction to what rationality actually is. This could be followed by one or two more posts from Mysterious Answers to Mysterious Questions, so why not start with the first two: Making Beliefs Pay Rent in Anticipated Experiences and Belief in Belief.
Now, you could finally digress to Twelve Virtues Of Rationality and then maybe try your hand at the whole Map and Territory Sequence (skipping over those posts you've already seen), alternatively you could finish reading the Mysterious Answers to Mysterious Questions sequence first.
After this, I no longer provide any advice as to reading order. You could choose to follow the order provided by XiXiDu above. I provide the following as one order which would at least do better than picking articles at random:
Finish reading Mysterious Answers to Mysterious Questions if you haven't already done so.
The whole mega-sequence of How to Actually Change Your Mind contains a lot of pretty important stuff, but will take a while to read.
The rest of Lesswrong. ;)
Summary:
- Hindsight Devalues Science
- What Do We Mean by Rationality
- What is Evidence
- The Lens that Sees its Flaws
- Making Beliefs Pay Rent in Anticipated Experiences
- Belief in Belief
And then follow with either of:
Path a
- Twelve Virtues Of Rationality
- Map and Territory Sequence
- Mysterious Answers to Mysterious Questions Sequence
Path b
- Mysterious Answers to Mysterious Questions Sequence
- Twelve Virtues Of Rationality
- Map and Territory Sequence
Which concludes my recommendation.
Relevant to this topic: Keith Johnstone's 'Masks'. It would be better to read the relevant section in his book "Impro" for the whole story (I got it at my university library) but this collection of quotes followed by this video should give enough of an introduction.
The idea is that while the people wear these masks, they are able to become a character with a personality different from the actor's original. The actor doesn't feel as if they are controlling the character. That being said, it doesn't happen immediately: It can take a few sessions for the actor to get the feel for the thing. The other thing is that the Masks usually have to learn to talk (albeit at an advanced pace) eventually taking on the vocabulary of their host. It's very interesting reading, to say the least.
Ok, thanks for clarifying. It actually makes a lot more sense for you to be sarcastic and I read it that way at first. I only got confused once I started considering the non-sarcastic possibility.
Ah, good to know.
As an example of illusion of transparency: On first reading, I interpretred your phrase 'highly-trustworthy-looking site' as sarcastic. Since it's a Webster's site, I'm going to guess that you were not intending to be sarcastic?
Yes, I don't think Joseph's intention was to get Archimedes to understand a Rubix cube. I believe his intention was to get Archimedes to play with 'trivial toys' and so he thought talking about Rubix cubes might do the trick.
The problem is not that they come up with a hypothesis too early, it's that they stop too early without testing examples that are not supposed to work. In most cases people are given as many opportunities to test as they'd like, yet they are confident in their answer after only testing one or two cases (all of which came up positive).
The trick is that you should come up with one or more hypotheses as soon as you can (maybe without announcing them), but test both cases which do and don't confirm it, and be prepared to change your hypothesis if you are proven wrong.
The problem is not that they are trying examples which confirm their hypothesis it's that they are trying only those examples which test their hypothesis.
The article focuses on testing examples which don't work because people don't do this enough. Searching for positive examples is (as you argue) a neccessary part of testing a hypothesis, and people seem to have no problem applying this. What people fail to do is to search for the negative as well.
Both positive and negative examples are, I'd say, equally important, but people's focus is completely imbalanced.
I believe CronoDAS was referring to overcast days when they said the sky is sometimes white.
Oops, interference.
The context here is a human dealing with a human. Thus it can be considered a useful heuristic to think "will what I write/say cause someone to lose social status?" and depending on the reply that your brain returns, judge whether it could be considered offensive (since this might prove to be a more accurate means of judging offense than trying to do so directly).
Naturally, if you were actually trying to develop an artificial intelligence that needed to refrain from offending people, it probably wouldn't be as easy as just 'calculating the objective status change' and basing the response on that.
"I wish I could believe that no one could possibly believe in belief in belief in belief..."
You wish you could believe Eliezer? Is this a dliberate stroke of irony or a subconcious hint at the fact that you do have an empathic understanding of the thought processes behind tailoring your own beliefs?