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How do you rank the difficulty of Koans? My intuition does a very good job by now, but caching it out has always resulted in obviously wrong corner cases.
"A Koan has the Buddha-nature if and only if all the pieces are ungrounded, except for blue pieces." is unclear to me. I am not sure whether blue pieces must be grounded or may be grounded.
Nice job!
I occasionally see people move their fingers on a flat surface while thinking, as if they were writing equations with their fingers. Does anyone do this, and can anyone explain why people do this? I asked one person who does it, and he said it helps him think about problems (presumably math problems) without actually writing anything down. Can this be learned? Is it a useful technique? Or is it just an innate idiosyncrasy?
I have the belief that I solve math, design, and logic problems more rapidly when standing/pacing in front of a whiteboard with a marker in my hand, far out of proportion to any marks I actually make (often no marks), possibly because the physical motions put me in the state of mind I developed during university.
(I don't know if it actually helps; I have not tested it)
The most plausible pattern for that one is exclusive or; an element is only in the third item if it is in exactly one of the preceding two items.
I thought about the pattern completely differently: every element is present in a 2x2 subarray.
I have a problem. I refuse to sleep.
I don't mean I can't sleep. I've done experiments where I go to bed with some audio playing that I know, from say a movie, and the next morning I do not remember anything past 5-10 minutes into it. I mean that I just don't sleep. If I have nothing going on in the morning I will stay up until the wee hours of the morning shortly before sunrise regardless of how much sleep I have gotten lately or when I woke up. The only thing that drives me to go to bed is the knowledge that I simply cannot function and feel horrible on less than three hours of sleep. I can also tell after the fact that I am quite foggy on less than 7 hours, but at the time it doesn't feel terribly odd.
I've been tracking my sleep with a tablet under my pillow for over a year now and I average between just under and just over 5 hours a night, depending on the particular month, but the standard deviation is at least two hours and it varies from 2 to 9 hours a night chaotically with no apparent pattern. Worse, in the last six months I think my age (25) is catching up to me - my productivity on low-sleep days has dropped precipitously, and nights that I used to go with 3 or 4 hours of sleep I have a tendency to oversleep through six alarms and wind up with just under 8. I think my body simply can't get by on as little sleep as I used to give it. This leads to me getting into work late (as a grad student done with class-style instruction and just doing my research and talking with faculty my schedule is quite flexible as long as I put in my time) and staying quite late, phase shifting my schedule and screwing up social aspects of my life and encouraging me to go to bed far too late and repeat the cycle.
Again the problem is not with sleeping itself, the problem is with letting myself stop doing things and actually go to bed. There is always something else I want to be doing, be it more research in the lab or reading or internetisms or talking to people 3 time zones west in California. I used to get by but now it is affecting my work and social life.
Any ideas on how to help fix this? I tried going to my university's counseling services but all they did was make sure I wasn't psychotic and suggest ritalin at which point I cancelled the followup appointment.
Ways to develop habits: start small, give yourself positive reinforcement, give yourself negative reinforcement, get someone else to force you... Try committing to no matter what go to bed without devices at midnight on Sundays? Try taking short naps at predetermined times and rewarding yourself with chocolate chips when you successfully lie down with an alarm prepped to get you back up? Try putting aside $100 in singles each month and burning one whenever you stay up after thinking "I should go to sleep"? Do you have a roommate? Can you get someone to call you at 11:30 PM each night and stay on the phone until you're tucked in? :) Have you tried reframing sleep to yourself as a productivity booster rather than a time-waster? "Okay present self, you know future you will think you could have gotten more done if you just went to sleep now rather than staying up trying to do things, so hop to bed now"
Suppose I am in the presence of a bunch of data going this way and that into and out of a bunch of black boxes. What kind of math or statistics might tell me or suggest to me that boxes 2, 7, and 32 are probably simple control systems with properties x, y, and z? Seems I should be looking for a function of the inputs that is "surprisingly" approximately constant, and if there's a simple map from that function's output to states of some subset of the outputs then we've got a very strong clue, or if we find that some output strongly negatively correlates with a seemingly unrelated time series somewhere else that might be a clue... Anyone have a link to a good paper on this?
We're looking for beta testers for the 16th "annual" Microsoft puzzle hunt. Interested folks should PM me, especially if you're in the Seattle area.
DCA lowers risk, while keeping the same EV. And the most common alternative, trying to time the market, has a long history of miserable failure by virtually all investors.
It's canonical investment advice for a reason.
Ander's claim, which I see repeated a lot, seems to be that it is positive EV rather than neutral. That's the bit that raises my hackles.
Yes, it is similar to rebalancing.
The benefit is that you get more shares during the times when it is down, the mathematics helps reduce your average cost.
For example, lets say I take $3000 and buy a stock all at once at $50. I get 60 shares. Now instead, what if I buy $1000 each at 3 different times, once at $40, once at $50, and once at $60. I end up with 25+20+16.66 shares = 61.66 shares, even though the average price I bought at was identical.
This is generally a good idea, whether one is buying stocks or Bitcoin or anything else.
It works similar to reallocating. For example, lets say you wanted to keep 10% of your net worth in Bitcoin (or anything else). If Bitcoin doubles in price, you now are misallocated, and have close to 20% of your net worth in it (if other things stayed the same), so you would sell some. If it dropped by 50%, you would have a little over 5% of your new net worth in it, so you would need to buy some. This helps you to, on average, buy low and sell high, even without really knowing what you are doing. You don't want to reallocate constantly, due to trading fees, but you need to do it sometimes, to gain the benefit.
Fleshing out my intuition.
For that argument for DCA to go through, we must justify that it's the correct argument to choose from these three:
For example, lets say I take $3000 and buy a stock all at once at $50 for 1 share. I get 60 shares. Now instead, what if I buy $1000 each at 3 different times, once at $40 for 1 share, once at $50 for 1 share, and once at $60 for 1 share. I end up with 25+20+16.66 shares = 61.66 shares, even though the average price per share I bought at was identical. (original argument)
For example, lets say I take $3000 and buy a stock all at once at 0.02 shares for $1. I get 60 shares. Now instead, what if I buy $1000 each at 3 different times, once at 0.025 shares for $1, once at 0.02 shares for $1, and once at 0.0167 shares for $1. I end up with 25+20+16.66 shares = 61.66 shares, because the average shares per dollar I bought at was 0.02057 which is better than 0.02. (original argument with prices preserved, "average metric was the same" changed, and conclusion changed)
For example, lets say I take $3000 and buy a stock all at once at 0.02 shares for $1. I get 60 shares. Now instead, what if I buy $1000 each at 3 different times, once at 0.025 shares for $1, once at 0.02 shares for $1, and once at 0.015 shares for $1. I end up with 25+20+15 shares = 60 shares, because the average shares per dollar I bought at was 0.02 which is identical to 0.02. (original argument with prices changed, "average metric was the same" preserved, and conclusion changed)
Yes, it is similar to rebalancing.
The benefit is that you get more shares during the times when it is down, the mathematics helps reduce your average cost.
For example, lets say I take $3000 and buy a stock all at once at $50. I get 60 shares. Now instead, what if I buy $1000 each at 3 different times, once at $40, once at $50, and once at $60. I end up with 25+20+16.66 shares = 61.66 shares, even though the average price I bought at was identical.
This is generally a good idea, whether one is buying stocks or Bitcoin or anything else.
It works similar to reallocating. For example, lets say you wanted to keep 10% of your net worth in Bitcoin (or anything else). If Bitcoin doubles in price, you now are misallocated, and have close to 20% of your net worth in it (if other things stayed the same), so you would sell some. If it dropped by 50%, you would have a little over 5% of your new net worth in it, so you would need to buy some. This helps you to, on average, buy low and sell high, even without really knowing what you are doing. You don't want to reallocate constantly, due to trading fees, but you need to do it sometimes, to gain the benefit.
When I see the concept of dollar cost averaging my math intuition module throws up a big red "This Is Clearly Wrong" sign. I never seem to have that thought when I have the time and inclination to tease out what's wrong and write a clear explanation of why it's BS (or find out that it's not).
Today is no exception. But here are some pointers my math intuition module is producing which say "investigate this, it will show you what's wrong":
If you flip a coin and invest the lump sum $3000 at either $40, $50, or $60 with equal probability, your expected value is 61.66 shares, not 60.
The "average price" should be the harmonic mean, not the arithmetic mean, and buying at the harmonic mean gets you 61.66 shares.
If you have the option of buying $3000 worth at $50, that doesn't mean you could switch to instead buying at a non-zero-variance-distribution with arithmetic mean $50 over time.
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Does anyone have software or procedures they have found useful for evaluating large, hard, inference problems? I don't know what the right class of problem is. Mine is that I have several years and lots and lots of notes of symptoms a family member has exhibited, including subjective recollections all the way to MRIs, and I'd like to organize my thoughts and inferences around what common cause(s) might be, priors, weight of evidence, etc.
I plan to improvise, but I'd like to steal first.