SatvikBeri
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#6:
Assume WLOG Then by monotonicity, we have If this chain were all strictly greater, than we would have istinct elements. Thus there must be some uch that By induction, or all
#7:
Assume nd construct a chain similarly to (6), indexed by elements of If all inequalities were strict, we would have an injection from o L.
#8:
Let F be the set of fixed points. Any subset S of F must have a least upper bound n L. If x is a fixed point, done. Otherwise, consider which must be a fixed point by (7). For any q in S, we have Thus s an upper bound of S in F. To see that it is the least upper bound, assume we have some other upper bound b of S in F. Then
To get the lower bound, note that we can flip the inequalities in L and still have a complete lattice.
#9:
P(A) clearly forms a lattice where the upper bound of any set of subsets is their union, and the lower bound is the intersection.
To see that injections are monotonic, assume nd s an injection. For any function, If nd that implies or some which is impossible since s injective. Thus s (strictly) monotonic.
Now s an injection Let e the set of all points not in the image of and let ote that since no element of s in the image of Then On one hand, every element of A not contained in s in y construction, so On the other, clearly so QED.
#10:
We form two bijections using the sets from (9), one between A’ and B’, the other between A—A’ and B—B’.
Any injection is a bijection between its domain and image. Since nd s an injection, s a bijection where we can assign each element o the uch that Similarly, s a bijection between nd Combining them, we get a bijection on the full sets.
Thanks! Edited.
Thanks! Edited. Yeah, I specifically focused on variance because of how Bayesian updates combine Normal distributions.
Kalman Filter for Bayesians
Systemizing and Hacking
Yes.
Inference & Empiricism
I’m specifically giving up games that encourage many short check-ins, e.g. most phone games and idle games. Binges aren’t a big issue for me, they tend to give me joy and renewal. But frequent check-in games make me less happy and less productive.
“Prefer a few large, systematic decisions to many small ones.”
Pick what percentage of your portfolio you want in various assets, and rebalance quarterly, rather than making regular buying/selling decisions
Prioritize once a week, and by default do whatever’s next on the list when you complete a task.
Set up recurring hangouts with friends at whatever frequency you enjoy (e.g. weekly). Cancel or reschedule on an ad-hoc basis, rather than scheduling ad-hoc
Rigorously decide how you will judge the results of experiments, then run a lot of them cheaply. Machine Learning example: pick one evaluation metric (might be a composite of several sub-metrics and rules), then automatically run lots of different models and do a deeper dive into the 5 that perform particularly well
Make a packing checklist for trips, and use it repeatedly
Figure out what criteria would make you leave your current job, and only take interviews that plausibly meet those criteria
Pick a routine for your commute, e.g. listening to podcasts. Test new ideas at the routine level (e.g. podcasts vs books)
Find a specific method for deciding what to eat—for me, this is querying system 1 to ask how I would feel after eating certain foods, and picking the one that returns the best answer
Accepting every time a coworker asks for a game of ping-pong, as a way to get exercise, unless I am about to enter a meeting
Always suggesting the same small set of places for coffee or lunch meetings
A good general rule here is to think in terms of what percentage of your portfolio (or net worth) you want in a specific asset class, rather than making buying/selling a binary decision. Then rebalance every 3 months.
For example, you might decide you want 2.5%-5% in crypto. If the price quadrupled, you would well about 75% of your stake at the end of the quarter. If it halved, you would buy more.
The major benefit is that this moves you from making many small decisions to one big decision, which is usually easier to get right.
It’s widely believed that humans basically lived in <200 person tribes that didn’t interact with each other too much before agriculture, so one might wonder how anything got any amount of adoption.
And only about 100 years ago, humanity essentially forgot the cure for scurvy: http://idlewords.com/2010/03/scott_and_scurvy.htm
Examples of Mitigating Assumption Risk
One thing I’d add to that list is that the post focuses on refining existing concepts, which is quite valuable and generally doesn’t get enough attention.
Providing Slack at the project level instead of the task level is a really good idea, and has worked well in many fields outside of programming. It is analogous to the concept of insurance: the RoI on Slack is higher when you aggregate many events with at least partially uncorrelated errors.
One major problem with trying to fix estimates at the task level is that there are strong incentives not to finish a task too early. For example, if you estimated 6 weeks, and are almost done after 3, and something moderately urgent comes up, you’re more likely to switch and fix that urgent thing since you have time. On the other hand, if you estimated 4 weeks, you’re more likely to delay the other task (or ask someone else to do it).
As a result, I’ve found that teams are literally likely to finish projects faster with higher quality if you estimate the project as, say, 8 3-week tasks with 24 weeks of overall slack (so 48 weeks total) than if you estimate the project as a 8 6-week tasks.
This is somewhat counterintuitive but really easy to apply in practice if you have a bit of social capital.
Nitpick: as I understand, Feyerabend would agree. His main argument seems to be “any simple methodology for deciding whether a scientific theory is true or false (such as falsificationism) would have missed important advances such as heliocentrism, Newton’s theory of gravity, and relativity, therefore philosophers of science should stop trying to formulate simple accept/reject methodologies.”
I could have been clearer—hiring is definitely a case where you get some points for following consensus, unlike, say, active investing where you’re typically measured on alpha. And following consensus on some parts of your process is fine if you have an edge elsewhere (e.g. Google and Facebook pay more than most, so having consensus-level assessment is fine.) But I would argue that for most startups you’ll see something like order-of-magnitude improvements through Process C.
Competitive Truth-Seeking
I think the main cause is that people who view themselves are solving a problem are often using the procedure “look at the current pattern and try to find issues with it.” A process that complements this well is “look at what’s worked historically, and do more of it.”
Some examples I wrote about a while back: lesswrong.com/lw/iro/systematic_lucky_breaks/
In my head, it feels mostly like a tree, e.g:
“I must have spelled oshun right”
–Otherwise I can’t write well
– –If I can’t write well, I can’t be a writer
–Only stupid people misspell common words
– –If I’m stupid, people won’t like me
etc. For me, to unravel an irrational alief, I generally have to solve every node below it–e.g., by making sure that I get the benefit from some other alief.
I think the prior that bubbles usually pop is incorrect. We tend to call something a bubble in retrospect, after it’s popped.
But if you try to define bubbles with purely forward-looking measures, like a period of unusually high growth, they’re more frequently followed by periods of unusually slow growth, not rapid decline. For example, Amazon’s stock would pass just about any test of a bubble over most points in its history.
I expect something similar with education, spending will likely remain high, but grow more slowly than it did in the last 20 years. That’s especially true because of the structure of student loans, people can’t really just default.
But to answer the more direct question: assuming that there is a rapid drop in education spending, how could we profit from it? Vocational schools seem like the most obvious bet, e.g. to become a programmer, dental assistant, massage therapist, electrician, and so on.
Certification services that manage to develop a reputation will become strong as well, e.g. SalesForce certificates are pretty valuable.
You could directly short lenders such as Sallie Mae.
Recruitment agencies that specialize in placing recent college graduates will likely suffer.
Management consulting firms rely heavily on college graduates, and so do hedge funds to a lesser extent.