Incidentally, I find Leonard Susskind is brilliant at all of these things. So, for a good example, his lectures on physics are well worth watching. Heck, they’re worth watching even if you don’t care about explaining things to people.
Skatche
Karma: 594
I’m not sure about this “selection space” of universes, but if we’re talking about all possible mathematical constructs (weighted, perhaps, according to Solomonoff’s universal prior), it bears noting that even some one-dimensional, two-colour cellular automata—extremely simple systems as far as that goes—have been proven to be Turing complete. Doesn’t mean they’ll necessarily produce life, as a lot depends on initial conditions, but we know at least that they can, in principle, produce life. Given what else I’ve seen of mathematics, it seems the space of mathematically possible universes is positively teeming with critters.
AndrewHickey’s comment notwithstanding, it wouldn’t surprise me if he did say that, and if he meant it very literally, like in the batshit crazy sense. Famous mathematicians have a long and celebrated history of going off the deep end. Cf. Georg Cantor, Kurt Gödel, Alexander Grothendieck.
Well, of course. But assuming B is a rational agent, and assuming the expected damages awarded in court per trespass are additive, she’s going to wait until A has finished building his house, then take him to court for all counts of trespassing, rather than fight each one individually, since that’ll save her a great deal on time and legal fees.
It seems to me that the easement will cost, at most, the amount of money that B could get from A in court for illegally crossing B’s land. Given the additional expenditure of time and legal fees, not to mention the uncertainty of the legal outcome, it will probably be somewhat less than that.
This may vary from person to person, but I found I didn’t need a rigourous schedule to make enough progress to determine that meditation was beneficial for my mental well-being. Doing about half an hour once every few days (when I remembered to) was enough, within a few months, to grant me relaxation and greater clarity of mind. Those aren’t really the point, but it’s reason enough to push forward and see what else there is to see.
Sorry, I have a bit of a skewed perspective about what’s obvious. :P Once I perceived the connection to binary trees it seemed plain as day.
A proof in ROT13:
Gb rnpu cbffvoyr rapbqvat bs n pbhagnoyr frg ol svavgr ovg fgevatf gurer pbeerfcbaqf n ovanel gerr: ng gur ebbg abqr lbh tb yrsg (fnl) vs gur svefg ovg vf n mreb naq evtug vs vg’f n bar, gura ng gur arkg abqr lbh tb yrsg be evtug vs gur frpbaq ovg vf n mreb be bar, naq fb sbegu. Gur npghny vagrtref pbeerfcbaq gb grezvany abqrf, ernpurq ol n svavgr ahzore bs oenapuvatf. Znysbezrq ovg fgevatf, gbb, pbeerfcbaq gb grezvany abqrf, ng gur rneyvrfg cbvag gung jr pna gryy gurl’er znysbezrq. Ubjrire, fvapr gurer ner vasvavgryl znal vagrtref, naq bayl svavgryl znal cbffvoyr ovg fgevatf bs nal tvira yratgu, gurer zhfg or ng yrnfg bar vasvavgryl ybat cngu va gur gerr, naq vs jr srrq guvf frdhrapr bs mrebf naq barf vagb bhe pbzchgre, gur pbzchgre jvyy unat.
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).
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.
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.
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.
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.
These are great. Do you mind if I incorporate them into the relevant post when the time comes?
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.
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.
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.
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.
The nonexistence thing was an error of judgment. In retrospect, it originated in an unconscious assumption I was making that there must be some ground to reality, a kind of “bottom level” of which everything else is epiphenomenal. A materialist might look to quantum fields to fill that role, but when I rejected all my former beliefs, that included my belief in an external reality independent of perception. So all I was left with was thought and sensory experience, and as they were interdependently defined, rather than any one aspect taking ontological primacy, I concluded that they—and hence I—must not exist. There are any number of holes in this argument, but that’s how I was thinking at the time.
Unfortunately I’m not yet at the point where I have papers published. For the most part the ideas that come to me in peak states are not specific, easily formalizable facts. In some cases they are directives to do certain things (like the bike trip mentioned in my original post); in other cases, they give a broad direction to my studies. The Tegmark vision is one example: higher category theory seems like it could furnish me with the tools to formally analyze the mathematical universe (or parts thereof) as a topological space; but since my knowledge of category theory is rather patchy, for now I’m simply working on learning some more of the prerequisites (I just finished a course in algebraic topology).
Two cases spring to mind, however, of fairly specific and well-polished ideas that have come from peak experiences. 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). You can check that it satisfies the properties of a metric [EDIT: This doesn’t actually work, as Sniffnoy pointed out below]; couldn’t say for sure whether it’s useful for anything, since I got swine flu shortly after that, at which point it got shelved with the rest of the stuff I’d been working on. A more promising example happened quite recently: it was a game theoretic analysis of the relationship between government and citizen which, as I mentioned, might end up as another post here—probably in the discussion area. If you’d be interested to see it, that’d be all the more reason to write it.
Not quite. One of my problems with objectification is that it implies certain attitudes which—among other things—create a favourable environment for rapists. That being said, I wrote the above comment at a time when rape was particularly salient to me, and may have overstated its relevance to this issue; I would now argue, more generally, that objectification openly expressed within a social group signals to women (almost by definition!) that they are regarded as objects and will not receive the status of full personhood within that group. Because these attitudes can be difficult if not impossible for women to correct by speaking out, many make the decision to withdraw from the group, further tilting the power balance toward the men.