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I like this model.
I'm not a researcher, but I would guess the generating process is quite iterative. Someone writes down the first crappy definition that comes to mind, they slog through some attempts to formulate theorems and prove them, gain some insights that help them refine the definition a bit, then repeat the process. I would also guess this kind of iteration makes the process more tractable than coming up with the "right" definition on the first try.
See also the visual novel Eliza, which explores a similar idea: https://www.zachtronics.com/eliza/
Big fan of this idea, but I need to be careful where/how I apply it. Otherwise:
"Why did you break up with your significant other?"
"Well, you see, their snoring bothered me but I didn't want to use a deterministic strategy that destroys all the expected value, so I decided to roll a d20, and I got a 2."
The "step-by-step what I did before each physics exam" sounds interesting and useful, would you be open to sharing it here?
Alas, people often don’t let you use them, such as this account where someone who was immunocompromised wasn’t allowed to use one on a flight, and thinks that’s how they got Covid-19.
Nit: Does the linked tweet say the person was in contact with an immunocompromised person, rather than immunocompromised himself?
I agree that 4 is a concern.
I disagree about 2. After having (a) participated in the weekend experiment and (b) done some "back-channel" references on Duncan, my impression is that he hates the fact that leadership will isolate him from the group he really wants to be a part of. I expect that if the experiment is successful, Duncan will eagerly set aside leadership and integrate himself with the group.
Going to class was not voluntary for me either. The consequences of not going to class included: parents screaming at me, parents kicking my ass (tiger parent style; we didn't do "grounding" in my household), truancies going onto my "permanent record", a full day of detention on a Saturday, etc. Things that people call "voluntary" don't usually result in physical and emotional damage if you don't do them.
Nonetheless, I skipped class a few times in middle school, and I suffered the consequences as a result. Were the consequences worth the glorious days of freedom that I spent skateboarding near the beach, sitting in a local comic book store marathoning manga, etc.? Maybe; maybe not.
But whether I go to class is a choice that I alone have the freedom to make. My parents and the school can set the consequences, and they can apply a lot of pressure to make particular options more or less appealing, but they can never take away my ability to choose.
What do you all think of "General Semantics"? Is it worth e.g. trying to read "Science and Sanity"? Are there insights / benefits there that can't be found in "Rationality: AI to Zombies"?
For Linux users (or Mac OS X users that use the Terminal) who want to pick up a journaling habit:
I set up the following aliases to DRAMATICALLY reduce the "activation energy" for writing a journal entry:
alias jcd='cd <journal directory>'
alias today='jcd; vi `date +%Y-%m-%d`; cd -'
alias yesterday='jcd; vi `date -r \`expr \\\`date +%s\\\` - 86400\` +%Y-%m-%d`; cd -'
So if I want to write a journal entry, I just type 'today' and get started. Note that this also has the secondary benefit of keeping journal entries nicely organized by date.
BTW, I am no writer, but this technique has gotten me to write a decent amount over the years:
$ jcd; cat * | wc -w
92804
Here's how I calculate 15% tips in my head. After getting used to this approach, I could consistently beat friends who were fumbling with their smartphones.
BTW, math majors have a reputation for NOT being able to do mental arithmetic, so being a math major who could do this was a fun and ironic way to defy stereotypes.
Preparation. Memorize the product of each digit with 1.5
- 1 x 1.5 = 1.5
- 2 x 1.5 = 3.0
- 3 x 1.5 = 4.5
- 4 x 1.5 = 6.0
- 5 x 1.5 = 7.5
- 6 x 1.5 = 9.0
- 7 x 1.5 = 10.5
- 8 x 1.5 = 12.0
- 9 x 1.5 = 13.5
Step 1. Round your bill to two significant digits (35.76 -> 36)
Step 2. Recall the product of the first digit with 1.5 (3 x 1.5 = 4.5). The tip is going to be pretty close to the product you recalled (4.50)--you just need to adjust it upwards a bit using the second digit.
Step 3. Recall the product of the second digit with 1.5 (6 x 1.5 = 9), divide the product you recalled by 10 (9 / 10 = 0.9), and add it to the result of Step 2 (4.50 + 0.90 = 5.40) to get your final result.
Congratulations! You've just calculated your 15% tip to within an accuracy of 10 cents. If you want more speed, you can round your bill to just the first significant digit and skip Step 3--this will give you a 15% tip to within an accuracy of 1 dollar. Alternatively, if you want to impress your friends with more accuracy, you can keep more significant digits around and continue adjusting.
I wanted to stop using Facebook, so I deleted my account and then blocked the domain.
Now I don't have any friends anymore, and I have a lot of free time.
I wanted to invest my money, but I didn't want to waste any effort thinking or worrying about it, so I made an account on Wealthfront, set up a monthly recurring transfer, and then put it out of my mind.
I hope the quote didn't come across as "travel sucks, period". Admittedly, with the opening "Travelling is a fool's paradise", it's hard for the quote to come across any other way. But my interpretation is not so much that Emerson is against travel; it's that Emerson is against yearning for travel as the magic solution to all of your problems. No matter where you go, you bring yourself--so if the problems lie within yourself, no amount of travelling will let you escape them.
You sound like an awesome person who would love life even if you didn't get to travel (perhaps less, but still). When you chose to set out on your adventures, what was your motivation (I would be pretty surprised if it was to "lose your sadness")?
I sometimes wish I could drag various rationalists to my job at the ICU for a while, make them see the kind of teamwork and cooperation that happens in a place where cooperation is a default and a necessity.
Sci-fi plot brewing.
I'd be very interested in a story that goes into detail about the Cyprus experiment (fill an island with all "alphas", instead of the usual "alpha, beta, gamma, delta, epsilon" distribution, and see what happens) from Brave New World.
Better yet, fill an island with all "rationalists" and see what happens.
+1 for probably missing more criteria than any other suggestion given here.
- You do need expensive equipment
- You do need to be in a particular location (ninja school)
- You do need special credentials (what, you think anyone can become a ninja?)
- Good luck getting reliable information online
- Good luck learning without a teacher
- If you make a mistake, you don't get "rapid feedback, leading to rapid growth", you just die
- How is ninjutsu intellectually stimulating?
Admittedly, I think I'll have to grudgingly give you "unforgiving" and "badass".
Upvoted. This is the 3rd time in the last week that I've heard someone mention sales as a useful skill, but how do you train it short of actually getting a job in sales?
This is a fascinating perspective.
For me, optimizing code (both style and performance) can, at times, almost feel like gardening (aka relaxing and theraputic). On the other hand, I really like math, yet I've generally found that it requires WAY more effort than programming.
Perhaps this is why you have a math PhD and I don't ;-)
That... definitely explains my failure at "dating a single person for a long time" and my (relative) success at "chatting to someone you don't know".
What you say is absolutely true on a large scale.
When I say that programming is a very "independent" activity, what I'm trying to describe is the fact that at any time, I can think to myself, "I want do some programming", and within 30 seconds, be doing some programming. In particular, I don't have to call someone, convince them that "no, this will be fun", fail, try convincing someone else, succeed, wait for them to head over, etc. etc., by which point my impulse to do some programming has completely disappeared.
You might be surprised how much of a difference this makes, especially for an INTJ like me ;-)
Why do you think something ought to be done about it?
Perhaps to remove "social pressure relating to gender roles" as a confounding factor, so that people can do a better job of finding roles that are good fits for their own individual characteristics?
What do you think that we ought to do about it?
Perhaps we can start by encouraging "sidekick-identified" males to speak up?
Travelling is a fool's paradise. Our first journeys discover to us the indifference of places. At home I dream that at Naples, at Rome, I can be intoxicated with beauty, and lose my sadness. I pack my trunk, embrace my friends, embark on the sea, and at last wake up in Naples, and there beside me is the stern fact, the sad self, unrelenting, identical, that I fled from. I seek the Vatican, and the palaces. I affect to be intoxicated with sights and suggestions, but I am not intoxicated. My giant goes with me wherever I go.
Ralph Waldo Emerson on If You Demand Magic, Magic Won't Help
I learned a few interesting memory tricks from the movie Memento. One thing you can try is to tattoo important information on yourself, so that you don't forget it.
I can think of a few security caveats for sensitive information though:
- It's probably better if you choose a location that's not easily visible (e.g. chest, part of your arm that's covered by a shirt), though you should probably choose a location that's still somewhat accessible (i.e. not your lower back)
- If you absolutely have to use a more visible location, like your forehead, make sure you get the sensitive information tattoo'd BACKWARDS, so that only you can read it (and only when you're looking in a mirror)
On a more serious note, I find it much easier to remember random alphanumeric characters "kinesthetically" (i.e. by developing muscle memory for the act of actually typing the password), as suggested by polymathwannabe. The only downside to this approach is that it's extremely difficult for me to enter such a password on a cell phone.
A while back, I tried reading Jaynes carefully (i.e. working lots of derivations while reading). I'll share my thoughts, but since I stopped after two and a half chapters, YMMV if you read further.
(1) I felt like I was reading a physics textbook. I'm a recovering physics major, and the experience gave me a serious case of Griffiths deja vu. For example, Jaynes does things like:
- Play fast and loose with Taylor series expansions
- Give arguments based on intuition and/or symmetry
- Assume all functions are well-behaved
- Use concepts / notation from calculus that I've completely forgotten (or never learned)
If you've taken university level physics before, then you should feel somewhat at home reading the first few chapters of Jaynes. If not, I would recommend putting in a bit of extra effort to make sure that you understand EVERY step of important arguments / derivations.
(2) After several days of effort, I got to the point where... you could show that if an urn has 3 red balls and 7 black balls, then the probability of drawing a red ball is 3/10. Yay!
Ok, fine, to put it another way, by making a few VERY basic assumptions about reasoning under uncertainty, you can show that the laws of probability are uniquely determined.
If you think this is the coolest revelation ever, then you should definitely read Jaynes. On the other hand, If you'd rather learn how to win at poker, or analyze randomized algorithms, or do calculations about 3d random walks in a cylinder, or something, then Jaynes is probably not the right textbook for you at this time.
So, onto your questions:
What math topics do I already need to understand to prepare myself for this?
Calculus, how to Taylor expand, how to carefully and patiently follow a long argument. I would recommend against going down a deep rabbit hole though (e.g. I would discourage trying to learn "all of multivariable calculus" before starting Jaynes).
Is there a better book to learn probability theory?
It depends; probability theory is a huge topic, and you can attack it from many different angles depending on your goals and interests (e.g. where you want to apply it, whether you're learning it as a prerequisite for another topic). That said, if what you're after is LessWrong / CFAR street cred, then I would probably stick with Jaynes ;-)
Here are some alternatives:
- Start with a problem book, maybe this one
- Go for something that's a bit more math-ey (and less physics-ey)
- Richard Hamming is cool
I am definitely interested in getting better at both "talking with other people" and "observing"; how would you measure your progress in these two cases?
Nice recommendations, thanks.
Going from dual 2-back to dual 3-back was pretty hard! I had to (1) completely ignore audio, master 3-back with visuals only, (2) completely ignore visuals, master 3-back with audio only, then (3) try to combine them.
Great article! Thanks for sharing.
A lot of this article feels like "Everyone can be a winner! Everyone can get a trophy for participation! Yay!" As a result, I'm having a hard time restraining my cynicism. For example:
Plenty of “cool careers” sound better than they turn out to be.
How convenient; now you have a great excuse for why you don't have a "cool career".
Status is often the enemy of success.
How convenient; now you have a great excuse for why you're not high status.
Just remember is this one rule: Don't innovate. Replicate. Copy a successful simple business. Innovations are too risky
How convenient; now you have a great excuse for why you're not innovating.
At the end of the day though, everyone has a different definition of success; I think that if you've honestly determined that your own definition of success doesn't require a "cool career" (or high status, or innovation, or whatever), then this article offers exceptional advice.
Great advice! I noticed something like this happening last time I tried to binge-read a webcomic. Initially I'm really engaged and frequently laughing, but a few hours later I end up clicking through strips in zombie mode.
I'm currently taking time off from school to focus on my eduction.
Upvoted just for this. I'm very interested in learning more--what are you reading, what skills are you learning, what projects are you finishing?
As for part-time jobs, if I were in your position I might look into freelancing (e.g. web design) or working in a library (one of my former classmates had a great experience with this, and was able to get a lot of work done on the job).
In all likelihood, you will not make the next billion-dollar nonprofit. You will not make the next billion-dollar business. You will not become the next congressperson in your district. This does not mean that you have not done a good job. It should not demoralize you in any way once you fail hardly to do these things.
At what point have you done a good job? On the other hand, at what point should you be demoralized? Yes, the answer depends on your personal philosophy, but how should someone who doesn't have a solid understanding of their personal philosophy think about such questions?
Thanks for the great review! Your tip to swap 24 and 25 was helpful, as was your warning about inconsistent notation. However, one benefit of "inconsistent notation" is that it really forces you to develop a clear understanding.
Anyway, I'll add some additional thoughts.
Overall, I got a lot out of this. Naive Set Theory clarified a lot of foundational concepts I had previously taken for granted. It also made me crack up at times; for example:
- The slight feeling of discomfort that the reader may experience in connection with the definition of natural numbers is quite common and in most cases temporary.
- We want to be told that the successor of 7 is 8, but to be told that 7 is a subset of 8 or that 7 is an element of 8 is disturbing.
I personally found the trickiest part to be the proof of Zorn's lemma. So for posterity, here's a sketch of the proof that might be helpful for following the full proof given in the text:
Zorn's lemma. Let X be a partially-ordered set such that every chain in X has an upper bound (in X); then X has a maximal element.
Proof sketch.
- Let S be collection of weak initial segments of elements of X, ordered by set inclusion; show that if S has a maximal set, then X has a maximal element
- Let C be the collection of all chains in X, ordered by set inclusion; show that if C has a maximal set, then S has a maximal set (the text uses a script X in place of C)
- Use the axiom of choice to construct an "extension" function g on C that extends a non-maximal set by one element, and leaves a maximal set unchanged
- Define a special kind of subset of C called a tower
- The definition of a tower is incredibly clever, and it rigorously describes the intuitive idea of "keep adding elements until you get a maximal set"
- Let t be the "smallest possible tower" (i.e. the intersection of all towers), and let A be the union of every set in t; show that g leaves A unchanged
- Conclude that C has a maximal set (A); thus S has a maximal set; thus X has a maximal element
Finally, here's the full list of ingredients in the axiom soup (note that the Peano "axioms" are actually proved, not taken as axioms):
- Axiom of extension (page 2): Two sets are equal if and only if they have the same elements.
- Axiom of specification (page 6): To every set A and to every condition S(x) there corresponds a set B whose elements are exactly those elements x of A for which S(x) holds.
- Axiom of pairing (page 9): For any two sets there exists a set that they both belong to.
- Axiom of unions (page 12): For every collection of sets there exists a set that contains all the elements that belong to at least one set of the given collection.
- Axiom of powers (page 20): For each set there exists a collection of sets that contains among its elements all the subsets of the given set.
- Axiom of infinity (page 44): There exists a set containing 0 and containing the successor of each of its elements.
- Axiom of choice (page 59): The Cartesian product of a non-empty family of non-empty sets is non-empty.
- Axiom of substitution (page 75): If S(a, b) is a sentence such that for each element a in the set A the set {b : S(a, b)} can be formed, then there exists a function F with domain A such that F(a) = {b : S(a, b)} for each a in A.
I hope so too! Also, I donated an additional $500 of actual USD which should hopefully be more stable.
It's cool that you guys accept XRP! I sent you all of my XRP (worth about $500).