Comment author: Zetetic 04 May 2011 05:57:50PM *  2 points [-]

"I think that it is a relatively good approximation to truth - which is much too complicated to allow anything but approximations-that mathematical ideas originate in empirics, although the genealogy is sometimes long and obscure. But, once they are so conceived, the subject begins to live a peculiar life of its own and is better compared to a creative one, governed by almost entirely aesthetical motivations, than to anything else and, in particular, to an empirical science. There is, however, a further point which, I believe, needs stressing. As a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only indirectly inspired by ideas coming from "reality" it is beset with very grave dangers. It becomes more and more purely aestheticizing, more and more purely I'art pour I'art. This need not be bad, if the field is surrounded by correlated subjects, which still have closer empirical connections, or if the discipline is under the influence of men with an exceptionally well-developed taste. But there is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. At the inception the style is usually classical; when it shows signs of becoming baroque, then the danger signal is up."

John Von Neumann, written in his article The Mathematician

Comment author: Skatche 04 May 2011 06:45:35PM 3 points [-]

I'm inclined to disagree. Deep abstraction gives us powerful tools for solving less abstract problems, including those that come out of the empirical sciences. Even fields developed with a deliberate eye to avoiding practical applications have sometimes turned out to make significant contributions to the sciences (I understand knot theory, for example, began this way, but has since turned out to have important applications in biochemistry).

Comment author: abramdemski 25 April 2011 02:58:17AM 11 points [-]

Happens to the best of us. However, it is worth emphasising that you have provided little evidence with your writing that the actual ideas coming from peak experiences are worth much. You have provided a great deal of indication that the motivational aspect of these ideas is useful, though.

Comment author: Skatche 26 April 2011 11:19:56PM 3 points [-]

However, it is worth emphasising that you have provided little evidence with your writing that the actual ideas coming from peak experiences are worth much. You have provided a great deal of indication that the motivational aspect of these ideas is useful, though.

You may be right. I will have to think about this. A lot of the imperative ideas ("Go do this!") that I've had while manic have had decidedly positive results - notably my bike trip to Georgia and the decision to devote a lot more of my time and mental energy to mathematics, founding the communal house I currently live in, but I'm going to have to try and remember some concrete examples of declarative ideas that have come to me in that state before I continue to make that claim.

Comment author: thomblake 26 April 2011 02:46:00PM 10 points [-]

This relates to something I've been arguing hereabouts since before the founding of Less Wrong. Basically, if you reduce all of your decision-making to a mathematical algorithm, then you're limiting the power of your decision-making to those parts of your brain that can do math. But our brains can do amazing things if we let them, and are mostly not very good at math.

a good cognitive hazmat suit

I want one!

the traffic light shimmered silvery-blue, like an arc of liquid electricity creeping across the surface, and then returned to normal.

I would wonder if something like that actually happened - it might have been an unfamiliar trick of the light or electrical malfunction...

Once I was walking down the back of West Rock at twilight and suddenly noticed everything was done up in strange, bright colors - the rocks were teal and purple, the leaves were emerald green, etc. After several minutes, the experience didn't go away, and so I picked up a representative purple rock and brought it back to civilization, thinking that would dispel the clearly hallucinatory magic. I immediately asked a passerby, "What color is this rock?", to which the response was indeed "purple". I resolved thenceforth to pay a little more attention to my surroundings.

Comment author: Skatche 26 April 2011 11:14:55PM *  0 points [-]

I would wonder if something like that actually happened - it might have been an unfamiliar trick of the light or electrical malfunction...

It's entirely possible. I recall I stayed at that intersection for a few minutes, watching the light and trying to figure out how such a thing might have happened, before concluding I had hallucinated it - but I can't make any guarantees that I was very thorough, given my mental state at the time. I don't think an electrical malfunction would have produced what I saw, but a trick of the light is plausible.

Comment author: Risto_Saarelma 08 November 2010 02:28:05PM 2 points [-]

This would be better if the human character was voiced by an actual human and the robot were kept as it is. The bad synthesized speech on the human character kicks this into the unintentional uncanny valley, while the robot both has a better voice and can actually be expected to sound like that.

Comment author: Skatche 26 April 2011 09:59:46PM *  1 point [-]

For reference: this video was evidently made on Xtranormal. Xtranormal is a site which takes a simple text file containing dialogue, etc. and outputs a movie; the voices are synthesized because that's how the site works. Voice actors would be nice, of course, but that's a rather more involved process.

Comment author: baiter 25 April 2011 03:04:36PM 2 points [-]

For those interested in these topics I suggest reading Robert Anton Wilson's nonfiction, specifically the Cosmic Trigger series and Prometheus Rising.

Comment author: Skatche 25 April 2011 04:56:14PM *  4 points [-]

Seconded and thirded. These books had a very deep and lasting impact on my development and worldview. Fair warning to those unfamiliar with his writings: they're chock-full of memetic hazards, but that's kind of the point. Wilson argues that we stand to benefit a great deal from being able to occupy unusual or even "false" belief systems (I use scare quotes because I think he would be reluctant to use that word), provided we can learn to consciously choose these systems and not get attached to them.

Comment author: GilPanama 25 April 2011 05:54:33AM *  24 points [-]

How to step outside the rational box without going off the deep end. Essentially, techniques for maintaining a lifeline back to normality so you can explore the further reaches of the psyche in some degree of safety.

I developed some of these!

I had a manic episode as well, but it was induced by medication and led to hypersocial behavior. I quickly noticed that I was having bizarre and sudden convictions, and started adopting heuristics to deal with them. I thought I was normal, or even better than normal. Then I realized that such a thought was very abnormal for me, and compensated.

Mania, for me, was like thinking in ALL CAPS ABOUT THINGS I USUALLY IGNORED. It was suddenly giving credence to religion not because I ceased to be an atheist, but because WE ARE ALL CONNECTED REALLY! It was fuzzy thinking, but damned if it didn't make people like me more for a bit. It was looking people IN THE EYE, BECAUSE THAT IS WHAT TRUST AND SOCIAL COMMUNICATION IS ALL ABOUT, all the time, when I am normally shy of eye contact.

(If you find the CAPSLOCK intrusions in the above paragraph annoying, imagine THINKING THIS WAY and you begin to see why mania is a very tiring thing and NOT RECOMMENDED unless you REALLY KNOW WHAT YOU'RE DEALING WITH.)

Compensation strategies:

  • Another person in the mental ward, who had lived with mania for a longer time, taught me that breathing exercises can help. Stretch arms upward; inhale. Slowly lower them, exhaling. Repeat as needed.

  • I realized that because I was now trusting people (read: believing everything I heard), I was susceptible to getting extremely paranoid. This is not as contradictory as it sounds. After all, if you trust people who don't trust their doctors, you will trust in their paranoia. I therefore told myself, repeatedly, to trust my doctors. Over and over. This self-brainwashing was a good move in hindsight. Chaining myself to the mast of somebody else's sane clinical judgment protected me and insured that I left the mental ward quickly.

  • I tended to think that I should try to "help people." Mania amplified that hero complex. I therefore repeated a mantra to myself, over and over, with manic fervor: People help themselves. People help themselves. You don't help people. People help themselves.

  • I was encouraged by a visiting parent to take notes of ideas, so I could pursue them later. Result: Lots of notes that I later sorted out into "reasonable" and "not worth pursuing." This was helpful. Nothing permanently insightful, but some decent ideas.

  • Another mantra: Even brilliant ideas are wrong 99% of the time. No matter how good your idea is, it is probably wrong. You are probably wrong. You are probably wrong. Under normal circumstances, this isn't a great mantra. During mania, it is essential.

If anybody ever questions my credentials as a rationalist, I think I can safely say that I tried very hard to be a traditional rationalist with an eye for biases even when I was technically not in my right mind.

Comment author: Skatche 25 April 2011 06:43:01AM 4 points [-]

These are great. Do you mind if I incorporate them into the relevant post when the time comes?

Comment author: JohnH 24 April 2011 12:27:04AM 1 point [-]

mathematical truths contain zero information, since they are automatically true in every possible world

This is a false assertion, they are only true if the axioms used to conclude them correspond to reality. There are proofs that rely on the Axiom of Choice which is not accepted (as far as I can tell) by everyone on this site (as well as the axiom of infinity?). There are proofs that rely on the GCH or Large Cardinal Axioms or V=L which are not among the accepted axioms and proven to be independent of the other axioms.

Comment author: Skatche 24 April 2011 08:58:40PM 0 points [-]

This is a fair point, but I'm referring to information in the information theoretic sense; in this technical sense, mathematical truths are indeed not information.

There are proofs that rely on the GCH or Large Cardinal Axioms or V=L which are not among the accepted axioms and proven to be independent of the other axioms.

I'm aware that the Axiom of Choice is required for some important results of practical import (Tychonoff's theorem, for example, is equivalent to it), but do you know of any important and useful results following from the GCH, etc.? I've only looked into this a little; foundational math is not really my field.

Comment author: [deleted] 24 April 2011 07:40:26PM *  3 points [-]

Interesting article, I will need to think quite thoroughly about this for some time. In the meantime I hope I can bothered you with a quick question:

What is your gender?

This might seem irrelevant, silly (as perhaps it is easy to deduce from your handle for someone of a different background that me or because you mentioned it in some other post I haven't read) or even offensive (it is certainly not meant that way), but I assure you that this is simply because I want to understand you better (in order to get part 1 to 3 right). It may seem not much can be derived from such information when dealing with unorthodox cognitive spaces or exploring the perspective of those who are neurodiverse in relation to me (and this post is arguably as much about the latter as the former), but every little bit helps me shift my estimation of the odds to where they should be. Actually on second thought I think simply the differential demographics of different kinds of neurodiversity and their interaction with society means gender is hugely important.

Comment author: Skatche 24 April 2011 08:49:51PM 4 points [-]

I'm male. I gather certain psychotic-spectrum disorders are more common in men than in women, so this doesn't strike me as entirely irrelevant.

Comment author: teageegeepea 24 April 2011 06:59:52AM 3 points [-]

I forget if I've linked it here before, but here's a critique of a commonly claimed connection between mystical experiences and genuine enlightenment or creativity.

Comment author: Skatche 24 April 2011 04:00:41PM *  7 points [-]

That's a critique of LSD, not mystical experiences in general, as a creativity enhancer, and even then, I think the author is leaving out a fair bit of evidence to the contrary. Though he never officially confirmed this, Francis Crick is believed to have been on LSD when he discovered the helical structure of DNA. Less controversially, many of the programmers in the early days of Silicon Valley are known to have done a fair bit of coding on acid; Steve Jobs himself is known to have taken a fair bit of it in his day. Here's another article claiming that Kary Mullis, a Nobel prize-winning chemist, was assisted by LSD in his discovery of a certain polymerase chain reaction used to amplify DNA sequences. And, to end on a more whimsical note, Dock Ellis once pitched a no-hitter on LSD.

If more people haven't come forward with important discoveries on acid, we shouldn't be too surprised: most people haven't tried it, and even if you have, it's a significant career risk to admit it. I do agree that acid on its own is not enough - there's still a fair bit of work to be done while sober - but to say that it's done nothing for us is simply not true.

Comment author: Sniffnoy 24 April 2011 05:47:39AM 7 points [-]

One was a metric on the space of events over a given probability space; it popped into my head as I was waking from a dream during the peak of my mania. If you're interested: for events A and B, we can define d(A,B)=1-P(A|B)P(B|A).

This doesn't appear to actually be true. :-/ Say we take our probability space to be [0,1], and we take A=[0,2/3], C=[1/3,1], and B=[0,1]. Then d(A,B)=d(B,C)=1/3, so d(A,B)+d(B,C)=2/3, but d(A,C)=3/4>2/3. Any ideas on how to fix?

(Also strictly speaking it would be a pseudometric on the set of positive probability events, with two events being equivalent if they differ by a set of probability 0, but that's nitpicking.)

Comment author: Skatche 24 April 2011 03:28:33PM 2 points [-]

Eeeesh. You're right. In my defense, I think I checked the properties while I was still half-asleep, and I must have fudged the triangle inequality. I fiddled with it a bit, but couldn't find any obvious way to make it work. Thanks for your correction.

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