Thanks. A great quote from the link:
I mean, I’m not terrible at math. I managed to scrape together an A in Calculus II, the last math class I was required to take and not coincidentally the last math class I ever took. I did it by memorizing the algorithms involved and plugging things into them, all the while desperately praying that there weren’t any deviations, however minor, on the test. This isn’t normal for me. In every other field, concepts slide naturally into my mind and I can manipulate them however they want, like fitting a bunch of Lego blocks together to make limitless possibilities.
I would guess myself that someone able to write the game theory sequences he wrote is someone able to fit all of the relevant concepts together like LEGOs.
Interesting! I have a BA in Mathematics, I was always 'good at math', and I'm currently a programmer.
I've never before considered that an "aesthetic sense" could related to mathematical ability, but it makes a lot of sense. I'm an extremely visual thinker – when I'm confused I feel blind – but I realize now that I spend a lot of time 'reasoning' by translating and transforming claims and statements and beliefs into different forms. The maximally insightful forms are almost always also the most pleasing to my eye – and I think you're right that that's not a coincidence.
Wow. And I even commented on that. And then forgot about it. Sorry :-p
So, what kind of math does Scott feel that he's bad at?
I also would like to know what the evidence is exactly that Scott is bad at math.
Your Bayesian prior should be that I know more about Scott's mathematical potential than Scott does. :-)
I don't think so. Your priors aren't worth much until you have been on both sides of the fence. There are people who are bad at musics. There are people who are bad at language. There are people who are bad at sports. Some people are bad at programming. And Scott is indeed bad at math.
He can certainly internalize some math he finds relevant, but if you take him and someone of his age but with aptitude for math and try to teach them, to the best of your abilities, some math they have never been exposed to and have no intuitive frame of reference for, you will see the difference in the uptake rate immediately. Maybe elements of abstract algebra, or something.
This is an experimental fact that you must have come across many times in your tutoring, and I don't understand why you seem to be denying that. Some people learn faster, retain better and can learn more about certain subjects than other people. Some people can use their aptitude elsewhere as crutches. The aesthetical discernment you mentioned is one of those crutches. Scott is certainly multi-talented enough to be able to do that when he has to learn math. But he will never be as good as you at it. Sure, some sub-par math teacher probably impaired his mathematical skills, but, just like you will never be Beethoven, he will never be Jonah Sinick.
I'll substantiate my claim that aesthetic sense drives a large fraction of mathematical accomplishment in future posts.
This claim seems clearly true to me, but no "aesthetic sense" is enough to do meaningful research if you don't "get" math. Scott is bad at math, and he can shore up this deficiency, to a degree, with hard work, aesthetics sense and by generally being brilliant at many other things.
How do you know Scott is bad at math?
Perhaps this is already discussed elsewhere and I'm failing at search. I'd be amazed if the below wasn't already pointed out.
On rereading this material it strikes me that this text is effectively inaccessible to large portions of the population. When I binged on these posts several years ago, I was just focused on the content for myself. This time, I had the thought to purchase for some others who would benefit from this material. I realized relatively quickly that the purchase of this book would likely fail to accomplish anything for these people, and may make a future attempt more difficult.
I think many of my specific concerns apply to a large percentage of the population.
- The preface and introductions appear aimed at return readers. The preface is largely a description of 'oops', which means little to a new reader and is likely to trigger a negative halo effect in people who don't yet know what that means. - "I don't know what he's talking about, and he seems to make lots of writing mistakes."
- There isn't a 'hook'. Talking about balls in urns in the intro seems too abstract for people. The rest of the sequences have more accessible examples, which most people would never reach.
- Much of the original rhetoric is still in place. Admittedly that's part of what I liked about the original posts, but I think it limits the audience. As a specific example, a family member is starting high school, likes science, and I think would benefit from this material. However her immediate family is very religious, to the point of 'disowning' a sister when they found out about an abortion ~25 years ago. The existing material uses religion as an example of 'this is bad' frequently enough that my family member would likely be physically isolated from the material and socially isolated from myself. 87% of America (86% global) have some level of belief in religion. The current examples are likely to trigger defensive mechanisms, before they're education about them. (Side-note: 'Waking Up: A Guide to Spirituality Without Religion – by Sam Harris' is a good book, but has this same exact issue.)
- Terminology is not sufficiently explained for people seeing this material with fresh eyes. As an example, ~15% of the way through 'New Improved Lottery' talks about probability distributions. There was no previous mention of this. Words with specific meanings, that are now often used, are unexplained. 'Quantitative' is used and means something to us, but not to most people. The Kindle provided dictionary and Wikipedia definitions are not very useful. This applies to the chapter titles as well, such as 'Bayesian Judo'.
- The level of hyperlinks, while useful for us, is not optimal for someone reading a subject for the first time. A new reader would have to switch topics in many cases to understand the reference.
- References to LessWrong and Overcoming Bias and only make sense to us.
Eliezer and Robb have done a lot to get the material into book state... but it's preaching to the choir.
Specifically what I think would make this more accessible:
- A more immediate hook along the lines of 'Practicing rationality will help you make more winning decisions and be less wrong.' (IE: keep reading because this=good and doable) Eliezer was prolific enough that I think good paragraphs likely already exist; but need connectors.
- Where negative examples are likely to dissuade large numbers of people, find better examples. In general avoid mentions of specific politics or religion in general. It's better to boil the frog.
- Move or remove all early references to Bayes. 'Beliefs that are rational are call Bayesian' means nothing to most people. Later references might as well be technobabble.
- Make sure other terminology is actually explained/understandable before it's used in the middle of an otherwise straightforward chapter. I'd try 1n & 2n-gramming the contents against Google Ngrams to identify terminology we need to make sure is actually explained/understood before casual use.
- Get this closer to a 7th grade reading level. This sets a low bar at potential readers who can understand 'blockbuster' books in English. (This might be accomplished purely with the terminology concern/change above)
- Change all hyperlinks to footnotes.
- Discuss LessWrong, Overcoming Bias, Eliezer, Hanson in the preface as 'these cool places/people where much of this comes from' but limit the references within the content.
Is there any ongoing attempt or desire to do a group edit of this into an 'Accessible Rationality'?
What's the payoff of changing hyperlinks to footnotes? Given all of the other, substantive, issues you raised, that seems unlikely to make any significant difference.
One detail that I've noticed repeated in several of the links, and links of links, is the following claims:
- The first of Kegan’s adult stages ... the Socialized Mind. ... Fifty eight percent of adults operate at or below this level of mental complexity.
- The second adult stage Kegan terms the Self-Authoring Mind. ... Approximately 35% of the adult population is at this plateau of development.
- The last adult stage Kegan calls the Self-Transforming Mind. ... Less than 1% of adults attain this level of consciousness.
So where are the other 6+% of adults?
Also, you could have easily explained constructive development theory here. It doesn't seem particularly complicated. In fact, I put off reading this post for a while, waiting until I'd read the links, but then read it anyway, before I'd read more than a fragment of the first link. My understanding didn't change after reading any of the links, or the links of the links.
But I can see how this could be a very useful idea, even if I think statements like this one are basically bullshit:
Kegan’s and similar theories have been validated by researchers all over the world ...
Just based on what little I've read so far, I'd peg this as roughly as 'true' as the Internal Family Systems Model - Wikiwand, which I find immensely useful.
There are some good ideas here that I can pick up on. Among the things that I already successfully implement, it may sound stupid, but I think of my different brain modules as different people, and have different names for them. That way I can compliment or admonish them without thinking, "Oh..kay, I'm talking to myself?" That makes it easier to remember that I'm not the only one reacting and making the sole decisions, but avoids turning everything into similar-sounding entities (me, myself, I, my brain, my mind, etc.) Example: This morning, I kept getting the feeling that something was not quite right, I felt lighter for some reason. I recognized that feeling as Jeffery trying to tell me something, so I had to stop and evaluate what I had done that morning so far. I realized that I was still wearing my slippers, and probably would not have realized it until I retracted my kickstand to leave for work. I gave credit where credit is due, and thought (without speaking) "Good catch, Jeffery!" (Jeffery [spelled that way because I "mistyped" it both times just now, before deciding that that's how he wants to spell it] is the one who handles the autopilot functions of my daily life, and while he does his best in unfamiliar situations, usually does not consult and does foolish things unless I have programmed him with routines. He is named after the anthropomorphic half chicken/half goat/half man protector of the "Deadly Maze" in Chowder. I interpreted the Deadly Maze as an allegory for the subconscious mind.)
This is basicaly Internal Family Systems Model tho its focus is therapy, i.e. improving dysfunctional behavior.
But your point of regularly communicating with your various 'parts' seems like a really good idea. How well have you maintained this as a habit since your comment?
In 2010 NASA hold a press conference that they made a discovery that supposedly expands the definition of life. Today the consensus among scientists seems to be that the finding is bullshit.
While incompetence is likely the better explanation than malice, it's still a fake.
Myself, I accept that I'm really trusting a network of people and that I can't practically verify almost anything I'm told.
The point is that the network you are trusting was likely wrong about a big discovery that NASA claimed to have made in this decade. Maybe even the biggest claimed discovery of NASA in this decade.
Good point. But my trusting a network of people, or really many (overlapping) networks of people, doesn't mean that I trust every specific claim or theory or piece of information. It just means that I've learned that they're overall trustworthy, or trustworthy to a specific (perhaps even quantifiable) extent, or maybe only trustworthy for certain kinds of claims or theories or information.
If you had to verify, personally, that the ESA actually controlled a spacecraft that orbited a comet, etc., how would you do it?
Good question. Intercepting the data stream sent back from the spacecraft would probably be possible (direct imaging at that range isn't in the cards), but it would take some rather sensitive equipment. It might be possible to find amateur astronomers who tracked it during its launch or during its flybys of Earth in 2005, 2007, and 2009, though, and derive a trajectory from that; it's not "personal", but if you don't trust that kind of data, you'd be getting far into conspiracy-theory territory.
That'd only get you so far, though. Rosetta's flight plan was pretty complicated and included both several gravity-assist flybys and maneuvers under its own power, so if you doubt ESA's ability to do anything other than get mass near the comet, that'd be tricky to verify.
ETA: Googled "amateur spacecraft tracking" and found a response to almost precisely this question. Turns out there are a few amateur groups with the resources to find the carrier signals from deep-space probes. They even have a Yahoo group.
Great response. You're not fully resolving the potential skepticism I identified, but that's impossible anyways. What should be ultimately convincing is that good theories generate good predictions, and you should expect good theories to be connected to other good theories.
Unfortunately, I think a lot of people are firmly in "conspiracy-theory territory" already and aren't consistently testing their beliefs. I can sympathize because I know I spend a lot of time generating and trusting weak theories about, e.g. other people's motivations, my likely performance on a particular project.
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I like it, but suggest that you link back to the previous entry in the sequence and/or the sequence index.
The sequence index
The previous post – Introduction to Prisonner's Dilemma
The following post – Interlude for Behavioral Economics