(To be clear: I agree with the rest of the OP, and with your last remark.)
has anybody ever managed to convince a bunch of literature Nobel laureates to take IQ tests? I can't find anything by Googling, and I'm skeptical.
I just read this piece by Erik Hoel which has this passage relevant to that one particular sentence you quoted from the OP:
Consider a book from the 1950s, The Making of a Scientist by psychologist and Harvard professor Anne Roe, in which she supposedly measured the IQ of Nobel Prize winners. The book is occasionally dug up and used as evidence that Nobel Prize winners have an extremely high IQ, like 160 plus. But it’s really an example of how many studies of genius are methodologically deeply flawed. ...
Roe never used an official IQ tests on her subjects, the Nobel Prize winners. Rather, she made up her test, simply a timed test that used SAT questions of the day. Why? Because most IQ tests have ceilings (you can only score like a 130 or 140 on them) and Roe thought—without any evidence or testing—that would be too low for the Nobel Prize winners. And while she got some help with this from the organization that created the SATs, she admits:
The test I used is not one that has been used before, at least in this form.
And furthermore:
I was not particularly concerned at the outset over the fact that I had no norms for this test. That is, I had no idea what any other population would do on the same test.
In other words, she had an untested set of SAT questions that she gave to Nobel prize winners not knowing how anyone else would do on them. This is pretty problematic. Normally IQ tests try to achieve some form of group-level neutrality; e.g., many of the major modern IQ tests are constructed from the outset so as not show any average difference between male and female takers, to be as culturally-invariant as possible, etc. And while Roe didn’t publish without any comparison group to her chosen geniuses whatsoever, the comparison that she did use was only a graduating class of PhD students (sample size unknown, as far as I can tell) who also took some other more standard IQ tests of the day, and she basically just converted from their scores on the other tests to scores on her make-shift test of SAT questions. Yet, here are the raw numbers of how the Nobel-prize winners do on the test she created:
Notice anything? The Nobel Prize winners all scored rather average. In fact, pretty low, in some cases. But Roe then goes on to claim that their IQ is extremely high, based on her statistical transformations:
I must caution that these equivalents have been arrived at by a series of statistical transformations based on assumptions which are generally valid for this type of material but which have not been specifically checked for these data. Nevertheless I believe that they are meaningful and a fair guide to what the situation is. The median score of this group on this verbal test is approximately equivalent to an IQ of 166.
Wait a minute. How did this conversion to a median IQ of 166 take place? After all, the scientists are scoring in the middle of the range on the test. They are getting a lot of questions wrong. E.g., Biologists who won the Nobel Prize got a 56.6 on the Verbal but we know that was far from the maximum score, Experimental Physicists got an even lower 46.6, etc. How then did she arrive at the group altogether having an astoundingly-high median verbal IQ of 166? Assuming that those at the upper range of scoring got close to most of the questions right (she mentions this is true, some only missed 4-10 questions at the maximum range), then how can getting only roughly two-thirds of the questions right translate to an IQ in the 160s?
Perhaps these SAT questions were just impossibly hard? Judge for yourself. Here’s one of the two examples she gives of the type of questions the Nobel Prize winners answered:
In each item in the first section, four words were given, and the subject had to pick the two which were most nearly opposite in meaning and underline them.
Here is one of the items: 1. Predictable 2. Precarious 3. Stable 4. Laborious.
This. . . isn’t very hard (spoiler: 2 & 3). So the conclusion of a median verbal IQ of 166 is deeply questionable, and totally reliant on this mysterious conversion she performed.
This sort of experimental setup would never fly today (my guess is the statistical conversion had all sorts of problems, e.g., Roe mentions extraordinarily high IQ numbers for PhD students at the time that don’t make sense, like an avg. IQ of 140). A far more natural reading of her results is to remove the mysterious conversion and look at the raw data, which is that the Nobel-prize-winning scientists scored well but not amazingly on SAT questions, indicating that Nobel Prize winners would get test scores above average but would not ace the SATs, since the average was far below the top of the possible range.
(I don't think Erik's arguments here have any relevance whatsoever to the OP's project though.)
I’ve written something like six or seven personal wikis over the past decade. It’s actually an incredibly advanced form of procrastination1. At this point I’ve tried every possible design choice.
Lifecycle: I’ve built a few compiler-style wikis: plain-text files in a git repo statically compiled to HTML. I’ve built a couple using live servers with server-side rendering. The latest one is an API server with a React frontend.
Storage: I started with plain text files in a git repo, then moved to an SQLite database with a simple schema. The latest version is an avant-garde object-oriented hypermedia database with bidirectional links implemented on top of SQLite.
Markup: I used Markdown here and there. Then I built my own TeX-inspired markup language. Then I tried XML, with mixed results. The latest version uses a WYSIWYG editor made with ProseMirror.
And yet I don’t use them. Why? Building them was fun, sure, but there must be utility to a personal database.
At first I thought the problem was friction: the higher the activation energy to using a tool, the less likely you are to use it. Even a small amount of friction can cause me to go, oh, who cares, can’t be bothered. So each version gets progressively more frictionless2. The latest version uses a WYSIWYG editor built on top of ProseMirror (it took a great deal for me to actually give in to WYSIWYG). It also has a link to the daily note page, to make journalling easier. The only friction is in clicking the bookmark to localhost:5000. It is literally two clicks to get to the daily note.
And yet I still don’t use it. Why? I’m a great deal more organized now than I was a few years ago. My filesystem is beautifully structured and everything is where it should be. I could fill out the contents of a personal wiki.
I’ve come to the conclusion that there’s no point: because everything I can do with a personal wiki I can do better with a specialized app, and the few remaining use cases are useless. Let’s break it down.
I've tried three different times to create a personal wiki, using the last one for a solid year and a half before finally giving up and just defaulting to a janky combination of Notion and Google Docs/Sheets, seduced by sites like Cosma Shalizi's and Gwern's long content philosophy (emphasis mine):
... I have read blogs for many years and most blog posts are the triumph of the hare over the tortoise. They are meant to be read by a few people on a weekday in 2004 and never again, and are quicklyabandoned—and perhaps as Assange says, not a moment too soon. (But isn’t that sad? Isn’t it a terrible ROI for one’s time?) On the other hand, the best blogs always seem to be building something: they are rough drafts—works in progress15. So I did not wish to write a blog. Then what? More than just “evergreen content”, what would constitute Long Content as opposed to the existing culture of Short Content? How does one live in a Long Now sort of way?16
My answer is that one uses such a framework to work on projects that are too big to work on normally or too tedious. (Conscientiousness is often lacking online or in volunteer communities18 and many useful things go undone.) Knowing your site will survive for decades to come gives you the mental wherewithal to tackle long-term tasks like gathering information for years, and such persistence can be useful19—if one holds onto every glimmer of genius for years, then even the dullest person may look a bit like a genius himself20. (Even experienced professionals can only write at their peak for a few hours a day—usually first thing in the morning, it seems.) Half the challenge of fighting procrastination is the pain of starting—I find when I actually get into the swing of working on even dull tasks, it’s not so bad. So this suggests a solution: never start. Merely have perpetual drafts, which one tweaks from time to time. And the rest takes care of itself.
Fernando unbundles the use cases of a tool for thought in his essay; I'll just quote the part that resonated with me:
The following use cases are very naturally separable: ...
Learning: if you’re studying something, you can keep your notes in a TfT. This is one of the biggest use cases. But the problem is never note-taking, but reviewing notes. Over the years I’ve found that long-form lecture notes are all but useless, not just because you have to remember to review them on a schedule, but because spaced repetition can subsume every single lecture note. It takes practice and discipline to write good spaced repetition flashcards, but once you do, the long-form prose notes are themselves redundant.
(Tangentially, an interesting example of how comprehensively subsuming spaced repetition is is Michael Nielsen's Using spaced repetition systems to see through a piece of mathematics, in which he describes how he used "deep Ankification" to better understand the theorem that a complex normal matrix is always diagonalizable by a unitary matrix, as an illustration of a heuristic one could use to deepen one's understanding of a piece of mathematics in an open-ended way, inspired by Andrey Kolmogorov's essay on, of all things, the equals sign. I wish I read that while I was still studying physics in school.)
Fernando, emphasis mine:
So I often wonder: what do other people use their personal knowledge bases for? And I look up blog and forum posts where Obsidian and Roam power users explain their setup. And most of what I see is junk. It’s never the Zettelkasten of the next Vannevar Bush, it’s always a setup with tens of plugins, a daily note three pages long that is subdivided into fifty subpages recording all the inane minutiae of life. This is a recipe for burnout.
People have this aspirational idea of building a vast, oppressively colossal, deeply interlinked knowledge graph to the point that it almost mirrors every discrete concept and memory in their brain. And I get the appeal of maximalism. But they’re counting on the wrong side of the ledger. Every node in your knowledge graph is a debt. Every link doubly so. The more you have, the more in the red you are. Every node that has utility—an interesting excerpt from a book, a pithy quote, a poem, a fiction fragment, a few sentences that are the seed of a future essay, a list of links that are the launching-off point of a project—is drowned in an ocean of banality. Most of our thoughts appear and pass away instantly, for good reason.
I enjoyed Brian Potter's Energy infrastructure cheat sheet tables over at Construction Physics, it's a great fact post. Here are some of Brian's tables — if they whet your appetite, do check out his full essay.
Energy quantities:
Units and quantities
Kilowatt-hours
Megawatt-hours
Gigawatt-hours
1 British Thermal Unit (BTU)
0.000293
iPhone 14 battery
0.012700
1 pound of a Tesla battery pack
0.1
1 cubic foot of natural gas
0.3
2000 calories of food
2.3
1 pound of coal
2.95
1 gallon of milk (calorie value)
3.0
1 gallon of gas
33.7
Tesla Model 3 standard battery pack
57.5
Typical ICE car gas tank (15 gallons)
506
1 ton of TNT
1,162
1 barrel of oil
1,700
1 ton of oil
11,629
12
Tanker truck full of gasoline (9300 gallons)
313,410
313
LNG carrier (180,000 cubic meters)
1,125,214,740
1,125,215
1,125
1 million tons of TNT (1 megaton)
1,162,223,152
1,162,223
1,162
Oil supertanker (2 million barrels)
3,400,000,000
3,400,000
3,400
It's amazing that a Tesla Model 3's standard battery pack has an OOM less energy capacity than a typical 15-gallon ICE car gas tank, and is probably heavier too, yet a Model 3 isn't too far behind in range and is far more performant. It's also amazing that an oil supertanker carries ~3 megatons(!) of TNT worth of energy.
Energy of various activities:
Activity
Kilowatt-hours
Fired 9mm bullet
0.0001389
Making 1 pound of steel in an electric arc furnace
0.238
Driving a mile in a Tesla Model 3
0.240
Making 1 pound of cement
0.478
Driving a mile in a 2025 ICE Toyota Corolla
0.950
Boiling a gallon of room temperature water
2.7
Synthesizing 1 kilogram of ammonia (NH3) via Haber-Bosch
11.4
Making 1 pound of aluminum via Hall-Heroult process
7.0
Average US household monthly electricity use
899.0
Moving a shipping container from Shanghai to Los Angeles
2,000.0
Average US household monthly gasoline use
2,010.8
Heating and cooling a 2500 ft2 home in California for a year
4,615.9
Heating and cooling a 2500 ft2 home in New York for a year
23,445.8
Average annual US energy consumption per capita
81,900.0
Power output:
Activity or infrastructure
Kilowatts
Megawatts
Gigawatts
Sustainable daily output of a laborer
0.08
Output from 1 square meter of typical solar panels (21% efficiency)
0.21
Tesla wall connector
11.50
Tesla supercharger
250
Large on-shore wind turbine
6,100
6
Typical electrical distribution line (15 kV)
8,000
8
Large off-shore wind turbine
14,700
15
Typical US gas pump
20,220
20
Typical daily production of an oil well (500 barrels)
35,417
35
Typical transmission line (150 kV)
150,000
150
Large gas station (20 pumps)
404,400
404
Large gas turbine
500,000
500
Output from 1 square mile of typical solar panels
543,900
544
Electrical output of a large nuclear power reactor
1,000,000
1,000
1
Single LNG carrier crossing the Atlantic (18 day trip time)
2,604,664
2,605
3
Nord Stream Gas pipeline
33,582,500
33,583
34
Trans Alaska pipeline
151,300,000
151,300
151
US electrical generation capacity
1,189,000,000
1,189,000
1,189
This observation by Brian is remarkable:
A typical US gas pump operates at 10 gallons per minute (600 gallons an hour). At 33.7 kilowatt-hours per gallon of gas, that’s a power output of over 20 megawatts, greater than the power output of an 800-foot tall offshore wind turbine. The Trans-Alaska pipeline, a 4-foot diameter pipe, can move as much energy as 1,000 medium-sized transmission lines, and 8 such pipelines would move more energy than provided by every US electrical power plant combined.
US energy flows Sankey diagram by LLNL (a "quad" is short for “a quadrillion British Thermal Units,” or 293 terawatt-hours):
I had a vague inkling that a lot of energy is lost on the way to useful consumption, but I was surprised by the two-thirds fraction; the 61.5 quads of rejected energy is more than every other country in the world consumes except China. I also wrongly thought that the largest source of inefficiency was in transmission losses. Brian explains:
The biggest source of losses is probably heat engine inefficiencies. In our hydrocarbon-based energy economy, we often need to transform energy by burning fuel and converting the heat into useful work. There are limits to how efficiently we can transform heat into mechanical work (for more about how heat engines work, see my essay about gas turbines).
The thermal efficiency of an engine is the fraction of heat energy it can transform into useful work. Coal power plant typically operates at around 30 to 40% thermal efficiency. A combined cycle gas turbine will hit closer to 60% thermal efficiency. A gas-powered car, on the other hand, operates at around 25% thermal efficiency. The large fraction of energy lost by heat engines is why some thermal electricity generation plants list their capacity in MWe, the power output in megawatts of electricity.
Most other losses aren’t so egregious, but they show up at every step of the energy transportation chain. Moving electricity along transmission and distribution lines results in losses as some electrical energy gets converted into heat. Electrical transformers, which minimize these losses by transforming electrical energy into high-voltage, low-current before transmission, operate at around 98% efficiency or more.
I also didn't realise that biomass is so much larger than solar in the US (I expect this of developing countries), although likely not for long given the ~25% annual growth rate.
Energy conversion efficiency:
Energy equipment or infrastructure
Conversion efficiency
Tesla Model 3 electric motor
97%
Electrical transformer
97-99%
Transmission lines
96-98%
Hydroelectric dam
90%
Lithium-ion battery
86-99+%
Natural gas furnace
80-95%
Max multi-layer solar cell efficiency on earth
68.70%
Max theoretical wind turbine efficiency (Betz limit)
59%
Combined cycle natural gas plant
55-60%
Typical wind turbine
50%
Gas water heater
50-60%
Typical US coal power plant
33%
Max theoretical single-layer solar cell efficiency
33.16%
Heat pump
300-400%
Typical solar panel
21%
Typical ICE car
16-25%
Finally, (US) storage:
Type
Quads of capacity
Grid electrical storage
0.002
Gas station underground tanks
0.26
Petroleum refineries
3.58
Other crude oil
3.79
Strategic petroleum reserve
4.14
Natural gas fields
5.18
Bulk petroleum terminals
5.64
Total
22.59
I vaguely knew grid energy storage was much less than hydrocarbon, but I didn't realise it was 10,000 times less!
Are we already at the point where AI, or some app, can summarize podcasts accurately and extract key takeaways with relatively technical interviewees like Dylan, so we don't need 5 hours (or even 2.5h at 2x)?
I often draw a distinction between the political elites of Washington DC and the industrial elites of Silicon Valley with a joke: in San Francisco reading books, and talking about what you have read, is a matter of high prestige. Not so in Washington DC. In Washington people never read books—they just write them.
To write a book, of course, one must read a good few. But the distinction I drive at is quite real. In Washington, the man of ideas is a wonk. The wonk is not a generalist. The ideal wonk knows more about his or her chosen topic than you ever will. She can comment on every line of a select arms limitation treaty, recite all Chinese human rights violations that occurred in the year 2023, or explain to you the exact implications of the new residential clean energy tax credit—but never all at once. ...
Washington intellectuals are masters of small mountains. Some of their peaks are more difficult to summit than others. Many smaller slopes are nonetheless jagged and foreboding; climbing these is a mark of true intellectual achievement. But whether the way is smoothly paved or roughly made, the destinations are the same: small heights, little occupied. Those who reach these heights can rest secure. Out of humanity’s many billions there are only a handful of individuals who know their chosen domain as well as they do. They have mastered their mountain: they know its every crag, they have walked its every gully. But it is a small mountain. At its summit their field of view is limited to the narrow range of their own expertise.
In Washington that is no insult: both legislators and regulators call on the man of deep but narrow learning. Yet I trust you now see why a city full of such men has so little love for books. One must read many books, laws, and reports to fully master one’s small mountain, but these are books, laws, and reports that the men of other mountains do not care about. One is strongly encouraged to write books (or reports, which are simply books made less sexy by having an “executive summary” tacked up front) but again, the books one writes will be read only by the elect few climbing your mountain.
The social function of such a book is entirely unrelated to its erudition, elegance, or analytical clarity. It is only partially related to the actual ideas or policy recommendations inside it. In this world of small mountains, books and reports are a sort of proof, a sign of achievement that can be seen by climbers of other peaks. An author has mastered her mountain. The wonk thirsts for authority: once she has written a book, other wonks will give it to her.
While I don't work in Washington, this description rings true to my experience, and I find it aesthetically undesirable. Greer contrasts this with the Silicon Valley aesthetic, which is far more like the communities I'm familiar with:
The technologists of Silicon Valley do not believe in authority. They merrily ignore credentials, discount expertise, and rebel against everything settled and staid. There is a charming arrogance to their attitude. This arrogance is not entirely unfounded. The heroes of this industry are men who understood in their youth that some pillar of the global economy might be completely overturned by an emerging technology. These industries were helmed by men with decades of experience; they spent millions—in some cases, billions—of dollars on strategic planning and market analysis. They employed thousands of economists and business strategists, all with impeccable credentials. Arrayed against these forces were a gaggle of nerds not yet thirty. They were armed with nothing but some seed funding, insight, and an indomitable urge to conquer.
And so they conquered.
This is the story the old men of the Valley tell; it is the dream that the young men of the Valley strive for. For our purposes it shapes the mindset of Silicon Valley in two powerful ways. The first is a distrust of established expertise. The technologist knows he is smart—and in terms of raw intelligence, he is in fact often smarter than any random small-mountain subject expert he might encounter. But intelligence is only one of the two altars worshiped in Silicon Valley. The other is action. The founders of the Valley invariably think of themselves as men of action: they code, they build, disrupt, they invent, they conquer. This is a culture where insight, intelligence, and knowledge are treasured—but treasured as tools of action, not goods in and of themselves.
This silicon union of intellect and action creates a culture fond of big ideas. The expectation that anyone sufficiently intelligent can grasp, and perhaps master, any conceivable subject incentivizes technologists to become conversant in as many subjects as possible. The technologist is thus attracted to general, sweeping ideas with application across many fields. To a remarkable extent conversations at San Fransisco dinner parties morph into passionate discussions of philosophy, literature, psychology, and natural science. If the Washington intellectual aims for authority and expertise, the Silicon Valley intellectual seeks novel or counter-intuitive insights. He claims to judge ideas on their utility; in practice I find he cares mostly for how interesting an idea seems at first glance. He likes concepts that force him to puzzle and ponder.
This is fertile soil for the dabbler, the heretic, and the philosopher from first principles. It is also a good breeding ground for books. Not for writing books—being men of action, most Silicon Valley sorts do not have time to write books. But they make time to read books—or barring that, time to read the number of book reviews or podcast interviews needed to fool other people into thinking they have read a book (As an aside: I suspect this accounts somewhat for the popularity of this blog among the technologists. I am an able dealer in second-hand ideas).
Out of curiosity, I asked Claude Sonnet 3.5 to create a checklist-style version of The Way to "serve as a daily reminder and also guide to practical daily action and thinking", with the understanding that (quoting Zvi) "The Way that can be specified is not The Way". Seems decent. (All bullet lists are meant to be checkboxes, except the last list of bullets.)
The Way: A Living Checklist
Note: The Way that can be specified is not The Way. This is an incomplete approximation, meant to guide rather than constrain.
Core Principles
Truth-Seeking
Have I written down my actual beliefs clearly and publicly?
Am I ready to be proven wrong and update accordingly?
Have I avoided fooling myself, especially about things I want to be true?
Am I reasoning things out explicitly, step by step?
Have I shown my work so others can check my reasoning?
Action & Impact
Am I actually Doing The Thing, rather than just talking about it?
Have I found ways to create concrete improvements today, rather than waiting for perfect solutions?
Am I focusing on real outcomes rather than appearances or process?
Do I have meaningful skin in the game?
Am I using my comparative advantage effectively?
Decision Making
Have I considered the actual price/tradeoffs involved?
Am I making decisions under uncertainty rather than waiting for perfect information?
Have I avoided false dichotomies and found the nuanced path?
Am I being appropriately careful with irreversible decisions?
Have I maintained enough slack in my systems and decisions?
Learning & Growth
Am I willing to look stupid to become less wrong?
Have I learned from my mistakes and updated my models?
Am I experimenting and iterating to find better approaches?
Have I sought out worthy opponents who can challenge my thinking?
Am I building deep understanding rather than surface knowledge?
Character & Conduct
Have I been honest, even when it's costly?
Am I following through on my commitments?
Have I avoided needless cruelty or control?
Am I using power and influence responsibly?
Have I maintained my integrity while pursuing my goals?
Balance & Wisdom
Have I found room for joy and fun without compromising effectiveness?
Am I building lasting value rather than chasing short-term gains?
Have I avoided both reckless abandon and paralyzing caution?
Am I considering both practical utility and deeper principles?
Have I remained adaptable as circumstances change?
Remember
The Way is hard
The Way is not for everyone
The Way changes as reality changes
Violence is not The Way
The perfect need not be the enemy of the good
Having skin in the game focuses the mind
Mundane utility matters
The Way includes both effectiveness and joy
This checklist is intentionally incomplete. The Way that matters is the one you find through doing the work.
While Dyson's birds and frogs archetypes of mathematicians is oft-mentioned, David Mumford's tribes of mathematicians is underappreciated, and I find myself pointing to it often in discussions that devolve into "my preferred kind of math research is better than yours"-type aesthetic arguments:
... the subjective nature and attendant excitement during mathematical activity, including a sense of its beauty, varies greatly from mathematician to mathematician... I think one can make a case for dividing mathematicians into several tribes depending on what most strongly drives them into their esoteric world. I like to call these tribes explorers, alchemists, wrestlers and detectives. Of course, many mathematicians move between tribes and some results are not cleanly part the property of one tribe.
Explorers are people who ask -- are there objects with such and such properties and if so, how many? They feel they are discovering what lies in some distant mathematical continent and, by dint of pure thought, shining a light and reporting back what lies out there. The most beautiful things for them are the wholly new objects that they discover (the phrase 'bright shiny objects' has been in vogue recently) and these are especially sought by a sub-tribe that I call Gem Collectors. Explorers have another sub-tribe that I call Mappers who want to describe these new continents by making some sort of map as opposed to a simple list of 'sehenswürdigkeiten'.
Alchemists, on the other hand, are those whose greatest excitement comes from finding connections between two areas of math that no one had previously seen as having anything to do with each other. This is like pouring the contents of one flask into another and -- something amazing occurs, like an explosion!
Wrestlers are those who are focussed on relative sizes and strengths of this or that object. They thrive not on equalities between numbers but on inequalities, what quantity can be estimated or bounded by what other quantity, and on asymptotic estimates of size or rate of growth. This tribe consists chiefly of analysts and integrals that measure the size of functions but people in every field get drawn in.
Finally Detectives are those who doggedly pursue the most difficult, deep questions, seeking clues here and there, sure there is a trail somewhere, often searching for years or decades. These too have a sub-tribe that I call Strip Miners: these mathematicians are convinced that underneath the visible superficial layer, there is a whole hidden layer and that the superficial layer must be stripped off to solve the problem. The hidden layer is typically more abstract, not unlike the 'deep structure' pursued by syntactical linguists. Another sub-tribe are the Baptizers, people who name something new, making explicit a key object that has often been implicit earlier but whose significance is clearly seen only when it is formally defined and given a name.
Mumford's examples of each, both results and mathematicians:
Explorers:
Theaetetus (ncient Greek list of the five Platonic solids)
Ludwig Schläfli (extended the Greek list to regular polytopes in n dimensions)
Bill Thurston ("I never met anyone with anything close to his skill in visualization")
the list of finite simple groups
Michael Artin (discovered non-commutative rings "lying in the middle ground between the almost commutative area and the truly huge free rings")
Set theorists ("exploring that most peculiar, almost theological world of 'higher infinities'")
Mappers:
Mumford himself
arguably, the earliest mathematicians (the story told by cuneiform surveying tablets)
the Mandelbrot set
Ramanujan's "integer expressible two ways as a sum of two cubes"
Oscar Zariski, Mumford's PhD advisor ("his deepest work was showing how the tools of commutative algebra, that had been developed by straight algebraists, had major geometric meaning and could be used to solve some of the most vexing issues of the Italian school of algebraic geometry")
the Riemann-Roch theorem ("it was from the beginning a link between complex analysis and the geometry of algebraic curves. It was extended by pure algebra to characteristic p, then generalized to higher dimensions by Fritz Hirzebruch using the latest tools of algebraic topology. Then Michael Atiyah and Isadore Singer linked it to general systems of elliptic partial differential equations, thus connecting analysis, topology and geometry at one fell swoop")
Wrestlers:
Archimedes ("he loved estimating π and concocting gigantic numbers")
Calculus ("stems from the work of Newton and Leibniz and in Leibniz's approach depends on distinguishing the size of infinitesimals from the size of their squares which are infinitely smaller")
Euler's strange infinite series formulas
Stirling's formula for the approximate size of n!
Augustin-Louis Cauchy ("his eponymous inequality remains the single most important inequality in math")
Sergei Sobolev
Shing-Tung Yau
Detectives:
Andrew Wiles is probably the archetypal example
Roger Penrose (""My own way of thinking is to ponder long and, I hope, deeply on problems and for a long time ... and I never really let them go.")
Strip Miners:
Alexander Grothendieck ("he greatest contemporary practitioner of this philosophy in the 20th century... Of all the mathematicians that I have met, he was the one whom I would unreservedly call a "genius". ... He considered that the real work in solving a mathematical problem was to find le niveau juste in which one finds the right statement of the problem at its proper level of generality. And indeed, his radical abstractions of schemes, functors, K-groups, etc. proved their worth by solving a raft of old problems and transforming the whole face of algebraic geometry)
Leonard Euler from Switzerland and Carl Fredrich Gauss ("both showed how two dimensional geometry lay behind the algebra of complex numbers")
Eudoxus and his spiritual successor Archimedes ("he level they reached was essentially that of a rigorous theory of real numbers with which they are able to calculate many specific integrals. Book V in Euclid's Elements and Archimedes The Method of Mechanical Theorems testify to how deeply they dug")
Aryabhata
Some miscellaneous humorous quotes:
When I was teaching algebraic geometry at Harvard, we used to think of the NYU Courant Institute analysts as the macho guys on the scene, all wrestlers. I have heard that conversely they used the phrase 'French pastry' to describe the abstract approach that had leapt the Atlantic from Paris to Harvard.
Besides the Courant crowd, Shing-Tung Yau is the most amazing wrestler I have talked to. At one time, he showed me a quick derivation of inequalities I had sweated blood over and has told me that mastering this skill was one of the big steps in his graduate education. Its crucial to realize that outside pure math, inequalities are central in economics, computer science, statistics, game theory, and operations research. Perhaps the obsession with equalities is an aberration unique to pure math while most of the real world runs on inequalities.
In many ways [the Detective approach to mathematical research exemplified by e.g. Andrew Wiles] is the public's standard idea of what a mathematician does: seek clues, pursue a trail, often hitting dead ends, all in pursuit of a proof of the big theorem. But I think it's more correct to say this is one way of doing math, one style. Many are leery of getting trapped in a quest that they may never fulfill.
I kind of envy that you figured this out yourself — I learned the parallelipiped hypervolume interpretation of the determinant from browsing forums (probably this MSE question's responses). Also, please do write that blog article.
And if I keep doing that, hypothetically speaking, some of those discoveries might even be original.
Yeah, I hope you will! I'm reminded of what Scott Aaronson said recently:
When I was a kid, I too started by rediscovering things (like the integral for the length of a curve) that were centuries old, then rediscovering things (like an efficient algorithm for isotonic regression) that were decades old, then rediscovering things (like BQP⊆PP) that were about a year old … until I finally started discovering things (like the collision lower bound) that were zero years old. This is the way.
What were you outputting over a million words in a week for?
And given that there are 7 x 16 x 60 = 6,720 minutes in a week of 16-hour days, you'd need to output 150 wpm at minimum over the entire duration to hit a million words, which doesn't seem humanly possible. How did you do it?
Graham’s hierarchy is useful for its intended purpose, but it isn’t really a hierarchy of disagreements. It’s a hierarchy of types of response, within a disagreement. Sometimes things are refutations of other people’s points, but the points should never have been made at all, and refuting them doesn’t help. Sometimes it’s unclear how the argument even connects to the sorts of things that in principle could be proven or refuted.
If we were to classify disagreements themselves – talk about what people are doing when they’re even having an argument – I think it would look something like this:
Most people are either meta-debating – debating whether some parties in the debate are violating norms – or they’re just shaming, trying to push one side of the debate outside the bounds of respectability.
If you can get past that level, you end up discussing facts (blue column on the left) and/or philosophizing about how the argument has to fit together before one side is “right” or “wrong” (red column on the right). Either of these can be anywhere from throwing out a one-line claim and adding “Checkmate, atheists” at the end of it, to cooperating with the other person to try to figure out exactly what considerations are relevant and which sources best resolve them.
If you can get past that level, you run into really high-level disagreements about overall moral systems, or which goods are more valuable than others, or what “freedom” means, or stuff like that. These are basically unresolvable with anything less than a lifetime of philosophical work, but they usually allow mutual understanding and respect.
Scott's take on the relative futility of resolving high-level generators of disagreement (which seems to be beyond Level 7? Not sure) within reasonable timeframes is kind of depressing.
A bit more on the high-level generators:
High-level generators of disagreement are what remains when everyone understands exactly what’s being argued, and agrees on what all the evidence says, but have vague and hard-to-define reasons for disagreeing anyway. In retrospect, these are probably why the disagreement arose in the first place, with a lot of the more specific points being downstream of them and kind of made-up justifications. These are almost impossible to resolve even in principle.
“I feel like a populace that owns guns is free and has some level of control over its own destiny, but that if they take away our guns we’re pretty much just subjects and have to hope the government treats us well.”
“Yes, there are some arguments for why this war might be just, and how it might liberate people who are suffering terribly. But I feel like we always hear this kind of thing and it never pans out. And every time we declare war, that reinforces a culture where things can be solved by force. I think we need to take an unconditional stance against aggressive war, always and forever.”
“Even though I can’t tell you how this regulation would go wrong, in past experience a lot of well-intentioned regulations have ended up backfiring horribly. I just think we should have a bias against solving all problems by regulating them.”
“Capital punishment might decrease crime, but I draw the line at intentionally killing people. I don’t want to live in a society that does that, no matter what its reasons.”
Some of these involve what social signal an action might send; for example, even a just war might have the subtle effect of legitimizing war in people’s minds. Others involve cases where we expect our information to be biased or our analysis to be inaccurate; for example, if past regulations that seemed good have gone wrong, we might expect the next one to go wrong even if we can’t think of arguments against it. Others involve differences in very vague and long-term predictions, like whether it’s reasonable to worry about the government descending into tyranny or anarchy. Others involve fundamentally different moral systems, like if it’s okay to kill someone for a greater good. And the most frustrating involve chaotic and uncomputable situations that have to be solved by metis or phronesis or similar-sounding Greek words, where different people’s Greek words give them different opinions.
You can always try debating these points further. But these sorts of high-level generators are usually formed from hundreds of different cases and can’t easily be simplified or disproven. Maybe the best you can do is share the situations that led to you having the generators you do. Sometimes good art can help.
The high-level generators of disagreement can sound a lot like really bad and stupid arguments from previous levels. “We just have fundamentally different values” can sound a lot like “You’re just an evil person”. “I’ve got a heuristic here based on a lot of other cases I’ve seen” can sound a lot like “I prefer anecdotal evidence to facts”. And “I don’t think we can trust explicit reasoning in an area as fraught as this” can sound a lot like “I hate logic and am going to do whatever my biases say”. If there’s a difference, I think it comes from having gone through all the previous steps – having confirmed that the other person knows as much as you might be intellectual equals who are both equally concerned about doing the moral thing – and realizing that both of you alike are controlled by high-level generators. High-level generators aren’t biases in the sense of mistakes. They’re the strategies everyone uses to guide themselves in uncertain situations.
This doesn’t mean everyone is equally right and okay. You’ve reached this level when you agree that the situation is complicated enough that a reasonable person with reasonable high-level generators could disagree with you. If 100% of the evidence supports your side, and there’s no reasonable way that any set of sane heuristics or caveats could make someone disagree, then (unless you’re missing something) your opponent might just be an idiot.
Depends on the app. Tinder for instance has a section called "What are you looking for?" that everyone else can see, whose selectable options include "New friends", "Still figuring it out", "Short-term fun", "Long-term partner", and a mix of the last two. People in my area use a pretty even mix of these, and their signaling is usually honest.
For most dating app users, I'm genuinely uncertain how representative both assumptions are, and I'd be curious to see more data regarding both (Aella's surveys maybe?)
For me, neither assumption holds; I suspect this makes me un-representative of most users:
I decouple dating from sex, and do use these apps to find platonic acquaintances
I swipe right mostly if I predict the person is interesting to meet up with, and swipe left on the majority of "lust at first sight" profiles
There's also Scott's Why Does Ozempic Cure All Diseases? from awhile back. The Nature article takes a more straightforward scientific journalism approach and largely focuses on immediate biological mechanisms, while Scott is Scott.
I enjoyed these passages from Henrik Karlsson's essay Cultivating a state of mind where new ideas are born on the introspections of Alexander Grothendieck, arguably the deepest mathematical thinker of the 20th century.
In June 1983, Alexander Grothendieck sits down to write the preface to a mathematical manuscript called Pursuing Stacks. He is concerned by what he sees as a tacit disdain for the more “feminine side” of mathematics (which is related to what I’m calling the solitary creative state) in favor of the “hammer and chisel” of the finished theorem. By elevating the finished theorems, he feels that mathematics has been flattened: people only learn how to do the mechanical work of hammering out proofs, they do not know how to enter the dreamlike states where truly original mathematics arises. To counteract this, Grothendieck in the 1980s has decided to write in a new way, detailing how the “work is carried day after day [. . .] including all the mistakes and mess-ups, the frequent look-backs as well as the sudden leaps forward”, as well as “the early steps [. . .] while still on the lookout for [. . .] initial ideas and intuitions—the latter of which often prove to be elusive and escaping the meshes of language.”
This was how he had written Pursuing Stacks, the manuscript at hand, and it was the method he meant to employ in the preface as well. Except here he would be probing not a theorem but his psychology and the very nature of the creative act. He would sit with his mind, observing it as he wrote, until he had been able to put in words what he meant to say. It took him 29 months.
When the preface, known as Récoltes et Semailles, was finished, in October 1986, it numbered, in some accounts, more than 2000 pages. It is in an unnerving piece of writing, seething with pain, curling with insanity at the edges—Grothendieck is convinced that the mathematical community is morally degraded and intent on burying his work, and aligns himself with a series of saints (and the mathematician Riemann) whom he calls les mutants. One of his colleagues, who received a copy over mail, noticed that Grothendieck had written with such force that the letters at times punched holes through the pages. Despite this unhinged quality, or rather because of it, Récoltes et Semailles is a profound portrait of the creative act and the conditions that enable our ability to reach out toward the unknown. (Extracts from it can be read in unauthorized English translations, here and here.)
On the capacity to be alone as necessary prerequisite to doing groundbreaking work:
An important part of the notes has Grothendieck meditating on how he first established contact with the cognitive space needed to do groundbreaking work. This happened in his late teens. It was, he writes, this profound contact with himself which he established between 17 and 20 that later set him apart—he was not as strong a mathematician as his peers when he came to Paris at 20, in 1947. That wasn’t the key to his ability to do great work.
I admired the facility with which [my fellow students] picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle—while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things that I had to learn (so I was assured), things I felt incapable of understanding[.] ...
In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of 30 or 35 years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birth-right, as it was mine: the capacity to be alone.
The capacity to be alone. This was what Grothendieck had developed. In the camp during the war, a fellow prisoner named Maria had taught him that a circle can be defined as all points that are equally far from a point. This clear abstraction attracted him immensely. After the war, having only a limited understanding of high school mathematics, Grothendieck ended up at the University of Montpellier, which was not an important center for mathematics. The teachers disappointed him, as did the textbooks: they couldn’t even provide a decent definition of what they meant when they said length! Instead of attending lectures, he spent the years from 17 to 20 catching up on high school mathematics and working out proper definitions of concepts like arc length and volume. Had he been in a good mathematical institution, he would have known that the problems he was working on had already been solved 30 years earlier. Being isolated from mentors he instead painstakingly reinvent parts of what is known as measurement theory and the Lebesgue integral.
A few years after I finally established contact with the world of mathematics at Paris, I learned, among other things, that the work I’d done in my little niche [. . . had] been long known to the whole world [. . .]. In the eyes of my mentors, to whom I’d described this work, and even showed them the manuscript, I’d simply “wasted my time”, merely doing over again something that was “already known”. But I don't recall feeling any sense of disappointment. [. . .]
(I think that last sentence resonates with me in a way that I don't think it does for most science & math folks I know, for whom discovery (as opposed to rediscovery) takes precedent emotionally.)
This experience is common in the childhoods of people who go on to do great work, as I have written elsewhere. Nearly everyone who does great work has some episode of early solitary work. As the philosopher Bertrand Russell remarked, the development of gifted and creative individuals, such as Newton or Whitehead, seems to require a period in which there is little or no pressure for conformity, a time in which they can develop and pursue their interests no matter how unusual or bizarre. In so doing, there is often an element of reinventing the already known. Einstein reinvented parts of statistical physics. Pascal, self-teaching mathematics because his father did not approve, rederived several Euclidean proofs. There is also a lot of confusion and pursuit of dead ends. Newton looking for numerical patterns in the Bible, for instance. This might look wasteful if you think what they are doing is research. But it is not if you realize that they are building up theirability to perceive the evolution of their own thought, their capacity for attention.
On the willingness to linger in confusion, and the primacy of good question generation over answering them:
One thing that sets these intensely creative individuals apart, as far as I can tell, is that when sitting with their thoughts they are uncommonly willing to linger in confusion.To be curious about that which confuses. Not too rapidly seeking the safety of knowing or the safety of a legible question, but waiting for a more powerful and subtle question to arise from loose and open attention. This patience with confusion makes them good at surfacing new questions. It is this capacity to surface questions that set Grothendieck apart, more so than his capacity to answer them. When he writes that his peers were more brilliant than him, he is referring to their ability to answer questions1. It was just that their questions were unoriginal. As Paul Graham observes:
People show much more originality in solving problems than in deciding which problems to solve. Even the smartest can be surprisingly conservative when deciding what to work on. People who’d never dream of being fashionable in any other way get sucked into working on fashionable problems.
Grothendieck had a talent to notice (and admit!) that he was subtly bewildered and intrigued by things that for others seemed self-evident (what is length?) or already settled (the Lebesgue integral) or downright bizarre (as were many of his meditations on God and dreams). From this arose some truly astonishing questions, surfacing powerful ideas, such as topoi, schemes, and K-theory.
On working with others without losing yourself:
After his three years of solitary work, Grothendieck did integrate into the world of mathematics. He learned the tools of the trade, he got up to date on the latest mathematical findings, he found mentors and collaborators—but he was doing that from within his framework. His peers, who had been raised within the system, had not developed this feel for themselves and so were more susceptible to the influence of others. Grothendieck knew what he found interesting and productively confusing because he had spent three years observing his thought and tracing where it wanted to go. He was not at the mercy of the social world he entered; rather, he “used” it to “further his aims.” (I put things in quotation marks here because what he’s doing isn’t exactly this deliberate.) He picked mentors that were aligned with his goals, and peers that unblock his particular genius.
I do not remember a single occasion when I was treated with condescension by one of these men, nor an occasion when my thirst for knowledge, and later, anew, my joy of discovery, was rejected by complacency or by disdain. Had it not been so, I would not have “become a mathematician” as they say—I would have chosen another profession, where I could give my whole strength without having to face scorn. [My emphasis.]
He could interface with the mathematical community with integrity because he had a deep familiarity with his inner space. If he had not known the shape of his interests and aims, he would have been more vulnerable to the standards and norms of the community—at least he seems to think so.
I've read most of your stories over at Narrative Ark and wanted to remark that The Gentle Romance did feel more concrete than usual, which was nice. Given how much effort it took for you however, I suppose I shouldn't expect future stories at Narrative Ark to be similarly concrete?
I'm surprised to see this take so disagree-voted, given how sensible the policy of adopting a vibes-invariant strategy is. Anyone who disagree-voted care to explain?
The part of Ajeya's comment that stood out to me was this:
On a meta level I now defer heavily to Ryan and people in his reference class (METR and Redwood engineers) on AI timelines, because they have a similarly deep understanding of the conceptual arguments I consider most important while having much more hands-on experience with the frontier of useful AI capabilities (I still don't use AI systems regularly in my work).
I don't think you need that footnoted caveat, simply because there isn't $150M/year worth of room for more funding in all of AMF, Malaria Consortium's SMC program, HKI's vitamin A supplementation program, and New Incentives' cash incentives for routine vaccination program all combined; these comprise the full list of GiveWell's top charities.
Another point is that the benefits of eradication keep adding up long after you've stopped paying for the costs, because the counterfactual that people keep suffering and dying of the disease is no longer happening. That's how smallpox eradication's cost-effectiveness can plausibly be less than a dollar per DALY averted so far and dropping (Guesstimate model, analysis). Quoting that analysis:
3.10.) For how many years should you consider benefits?
It is not clear for how long we should continue to consider benefits, since the benefits of vaccines would potentially continue indefinitely for hundreds of years. Perhaps these benefits would eventually be offset by some other future technology, and we could try to model that. Or perhaps we should consider a discount rate into the future, though we don’t find that idea appealing.
Instead, we decided to cap at an arbitrary fixed amount of years set to 20 by default, though adjustable as a variable in our spreadsheet model (or by copying and modifying our Guesstimate models). We picked 20 because it felt like a significant enough amount of time for technology and other dynamics to shift.
It’s important to think through what cap makes the most sense, though, as it can have a large effect on the final model, as seen in this table where we explore the ramifications of smallpox eradication with different benefit thresholds:
They used to consider speedrunning games a guilty pleasure, but after goal-factoring their supposed guilty pleasure concludes that the guilt doesn't align with their actual goals and values and feeling bad about enjoying speedrunning doesn't really serve any productive purpose, so now they enjoy speedrunning unabashedly.
Maybe it's more correct to say that understanding requires specifically compositional compression, which maintains an interface-based structure hence allowing us to reason about parts without decompressing the whole, as well as maintaining roughly constant complexity as systems scale, which parallels local decodability. ZIP achieves high compression but loses compositionality.
I think what explains the relative ease of progress in physics has more so to do with its relative compositionality in contrast to other disciplines like biology or economics or the theory of differential equations, in the sense Jules Hedges meant it. To quote that essay:
For examples of non-compositional systems, we look to nature. Generally speaking, the reductionist methodology of science has difficulty with biology, where an understanding of one scale often does not translate to an understanding on a larger scale. ... For example, the behaviour of neurons is well-understood, but groups of neurons are not. Similarly in genetics, individual genes can interact in complex ways that block understanding of genomes at a larger scale.
Such behaviour is not confined to biology, though. It is also present in economics: two well-understood markets can interact in complex and unexpected ways. Consider a simple but already important example from game theory. The behaviour of an individual player is fully understood: they choose in a way that maximises their utility. Put two such players together, however, and there are already problems with equilibrium selection, where the actual physical behaviour of the system is very hard to predict.
More generally, I claim that the opposite of compositionality is emergent effects. The common definition of emergence is a system being ‘more than the sum of its parts’, and so it is easy to see that such a system cannot be understood only in terms of its parts, i.e. it is not compositional. Moreover I claim that non-compositionality is a barrier to scientific understanding, because it breaks the reductionist methodology of always dividing a system into smaller components and translating explanations into lower levels.
More specifically, I claim that compositionality is strictly necessary for working at scale. In a non-compositional setting, a technique for a solving a problem may be of no use whatsoever for solving the problem one order of magnitude larger. To demonstrate that this worst case scenario can actually happen, consider the theory of differential equations: a technique that is known to be effective for some class of equations will usually be of no use for equations removed from that class by even a small modification. In some sense, differential equations is the ultimate non-compositional theory.
Any good ideas on how to check / falsify this? I've been thinking of checking my own AI-driven job loss predictions but find it harder to specify the details than expected.
Upvoted and up-concreted your take, I really appreciate experiments like this. That said:
This isn't necessarily overwhelming evidence of anything, but it might genuinely make my timelines longer. Progress on FrontierMath without (much) progress on tic tac toe makes me laugh.
I'm confused why you think o1 losing the same way in tic tac toe repeatedly shortens your timelines, given that it's o3 that pushed the FrontierMath SOTA score from 2% to 25% (and o1 was ~1%). I'd agree if it was o3 that did the repeated same-way losing, since that would make your second sentence make sense to me.
In some ways, Robinson’s path as a science fiction writer has followed a strange trajectory. He made his name writing about humanity’s far-flung future, with visionary works about the colonization of Mars (“The Mars Trilogy”), interstellar, intergenerational voyages into deep space (“Aurora”), and humanity’s expansion into the far reaches of the solar system (“2312”). But recently, he’s been circling closer to earth, and to the current crisis of catastrophic warming.
Futuristic stories about space exploration feel irrelevant to him now, Robinson said. He’s grown skeptical that humanity’s future lies in the stars, and dismissive of tech billionaires’ ambitions to explore space, even as he acknowledged, “I’m partially responsible for that fantasy.”
In his more recent novels — works like “New York 2140,” an oddly uplifting climate change novel that takes place after New York City is partly submerged by rising tides, and “Red Moon,” set in a lunar city in 2047 — he has traveled back in time, toward the present. Two years ago, he published “The Ministry for the Future,” which opens in 2025 and unfolds over the next few decades, as the world reels from floods, heat waves, and mounting ecological disasters, and an international ministry is created to save the planet.
This was a surprisingly ignorant comment by T. K. Van Allen, given that O'Neill was a physicist and included all his calculations. I suspect Van Allen never actually read the 'Steel structure' math in O'Neill's essay The Colonization of Space. The rest of Van Allen's bullet points also seem ignorant of O'Neill's calculations further down in the essay. I don't disagree with the bottomline that the cost is prohibitive, I just wished Van Allen engaged with O'Neill's math.
In science and technology, there is a broad and integrative kind of knowledge that can be learned, but isn’t taught. It’s important, though, because it makes creative work more productive and makes costly blunders less likely.
Formal education in science and engineering centers on teaching facts and problem-solving skills in a series of narrow topics. It is true that a few topics, although narrow in content, have such broad application that they are themselves integrative: These include (at a bare minimum) substantial chunks of mathematics and the basics of classical mechanics and electromagnetism, with the basics of thermodynamics and quantum mechanics close behind.
Most subjects in science and engineering, however, are narrower than these, and advanced education means deeper and narrower education. What this kind of education omits is knowledge of extent and structure of human knowledge on a trans-disciplinary scale. This means understanding — in a particular, limited sense — everything.
To avoid blunders and absurdities, to recognize cross-disciplinary opportunities, and to make sense of new ideas, requires knowledge of at least the outlines of every field that might be relevant to the topics of interest. By knowing the outlines of a field, I mean knowing the answers, to some reasonable approximation, to questions like these:
What are the physical phenomena? What causes them? What are their magnitudes? When might they be important? How well are they understood? How well can they be modeled? What do they make possible? What do they forbid?
And even more fundamental than these are questions of knowledge about knowledge:
What is known today? What are the gaps in what I know? When would I need to know more to solve a problem? How could I find what I need?
It takes far less knowledge to recognize a problem than to solve it, yet in key respects, that bit of knowledge is more important: With recognition, a problem may be avoided, or solved, or an idea abandoned. Without recognition, a hidden problem may invalidate the labor of an hour, or a lifetime. Lack of a little knowledge can be a dangerous thing.
Looking back over the last few decades, I can see that I’ve invested considerably more than 10,000 hours in learning about the structures, relationships, contents, controversies, open problems, limitations, capabilities, developing an understanding of how the fields covered in the major journals fit together to constitute the current state of science and technology. In some areas, of course, I’ve dug deeper into the contents and tools of a field, driven by the needs of problem solving; in others, I know only the shape of the box and where it sits.
This sort of knowledge is a kind of specialty, really — a limited slice of learning, but oriented crosswise. Because of this orientation, though, it provides leverage in integrating knowledge from diverse sources. I am surprised by the range of fields in which I can converse with scientists and engineers at about the level of a colleague in an adjacent field. I often know what to ask about their research, and sometimes make suggestions that light their eyes.
Note that the title above isn’t “how to learn everything”, but “how to learn about everything”. The distinction I have in mind is between knowing the inside of a topic in deep detail — many facts and problem-solving skills — and knowing the structure and context of a topic: essential facts, what problems can be solved by the skilled, and how the topic fits with others.
This knowledge isn’t superficial in a survey-course sense: It is about both deep structure and practical applications. Knowing about, in this sense, is crucial to understanding a new problem and what must be learned in more depth in order to solve it. The cross-disciplinary reach of nanotechnology almost demands this as a condition of competence.
Studying to learn about everything
To intellectually ambitious students I recommend investing a lot of time in a mode of study that may feel wrong. An implicit lesson of classroom education is that successful study leads to good test scores, but this pattern of study is radically different. It cultivates understanding of a kind that won’t help pass tests — the classroom kind, that is.
Read and skim journals and textbooks that (at the moment) you only half understand. Include Science and Nature.
Don’t halt, dig a hole, and study a particular subject as if you had to pass a test on it.
Don’t avoid a subject because it seems beyond you — instead, read other half-understandable journals and textbooks to absorb more vocabulary, perspective, and context, then circle back.
Notice that concepts make more sense when you revisit a topic.
Notice which topics link in all directions, and provide keys to many others. Consider taking a class.
Continue until almost everything you encounter in Science and Nature makes sense as a contribution to a field you know something about.
Why is this effective?
You learned your native language by immersion, not by swallowing and regurgitating spoonfuls of grammar and vocabulary. With comprehension of words and the unstructured curriculum of life came what we call “common sense”.
The aim of what I’ve described is to learn an expanded language and to develop what amounts to common sense, but about an uncommonly broad slice of the world. Immersion and gradual comprehension work, and I don’t know of any other way.
This process led me to explore the potential of molecular nanotechnology as a basis for high-throughput atomically precise manufacturing. If broad-spectrum common sense were more widespread among scientists, there would be no air of controversy around the subject, milestones like the U.S. National Academies report on molecular manufacturing would have been reached a decade earlier, and today’s research agenda and perception of global problems would be very different.
I think I prefer either of Drexler's approach, Sarah Constantin's / Scott's fact-posting, and Holden Karnofsky's learning by writing, all of which can start with endless breadth but also require (quoting Drexler) deep structure and practical applications as focusing mechanisms, to the sort of learning that I think might be incentivised by budding panologists having to maximise their minimum score across some standardised battery of tests. I also liked Sarah's suggestion at the end:
Ideally, a group of people writing fact posts on related topics, could learn from each other, and share how they think. I have the strong intuition that this is valuable. It's a bit more active than a "journal club", and quite a bit more casual than "research". It's just the activity of learning and showing one's work in public.
What makes a good Royal Navy Officer? Motivation. Motivation matters more for performance evaluations and advancement to leadership than general intelligence or personality traits. Does this mean intelligence is not so important? Perhaps for this particular job it is so, especially in peacetime and until a high level is reached, more than that I would say it is a liability.
I prefer JFA's reinterpretation:
Let me reinterpret the findings: among a specific population of high achieving people, differences in motivation explains more than intelligence. I assume you would find the same thing among top.performing students. You have a truncated sample that's been selected on the outcome of interest (I.e. leadership). That's interesting as far as it goes, but this study seems plagued by survivorship bias if you actually want to learn about what variables predict what kind of people make it into top leadership.
One frustrating conversation was about persuasion. Somehow there continue to be some people who can at least somewhat feel the AGI, but also genuinely think humans are at or close to the persuasion possibilities frontier – that there is no room to greatly expand one’s ability to convince people of things, or at least of things against their interests.
This is sufficiently absurd to me that I don’t really know where to start, which is one way humans are bad at persuasion. Obviously, to me, if you started with imitations of the best human persuaders (since we have an existence proof for that), and on top of that could correctly observe and interpret all the detailed signals, have limitless time to think, a repository of knowledge, the chance to do Monty Carlo tree search of the conversation against simulated humans, never make a stupid or emotional tactical decision, and so on, you’d be a persuasion monster. It’s a valid question ‘where on the tech tree’ that shows up how much versus other capabilities, but it has to be there. But my attempts to argue this proved, ironically, highly unpersuasive.
Scott tried out an intuition pump in responding to nostalgebraist's skepticism:
Nostalgebraist: ... it’s not at all clear that it is possible to be any better at cult-creation than the best historical cult leaders — to create, for instance, a sort of “super-cult” that would be attractive even to people who are normally very disinclined to join cults. (Insert your preferred Less Wrong joke here.) I could imagine an AI becoming L. Ron Hubbard, but I’m skeptical that an AI could become a super-Hubbard who would convince us all to become its devotees, even if it wanted to.
Scott: A couple of disagreements. First of all, I feel like the burden of proof should be heavily upon somebody who thinks that something stops at the most extreme level observed. Socrates might have theorized that it’s impossible for it to get colder than about 40 F, since that’s probably as low as it ever gets outside in Athens. But when we found the real absolute zero, it was with careful experimentation and theoretical grounding that gave us a good reason to place it at that point. While I agree it’s possible that the best manipulator we know is also the hard upper limit for manipulation ability, I haven’t seen any evidence for that so I default to thinking it’s false.
(lots of fantasy and science fiction does a good job intuition-pumping what a super-manipulator might look like; I especially recommend R. Scott Bakker’s Prince Of Nothing)
But more important, I disagree that L. Ron Hubbard is our upper limit for how successful a cult leader can get. L. Ron Hubbard might be the upper limit for how successful a cult leader can get before we stop calling them a cult leader.
The level above L. Ron Hubbard is Hitler. It’s difficult to overestimate how sudden and surprising Hitler’s rise was. Here was a working-class guy, not especially rich or smart or attractive, rejected from art school, and he went from nothing to dictator of one of the greatest countries in the world in about ten years. If you look into the stories, they’re really creepy. When Hitler joined, the party that would later become the Nazis had a grand total of fifty-five members, and was taken about as seriously as modern Americans take Stormfront. There are records of conversations from Nazi leaders when Hitler joined the party, saying things like “Oh my God, we need to promote this new guy, everybody he talks to starts agreeing with whatever he says, it’s the creepiest thing.” There are stories of people who hated Hitler going to a speech or two just to see what all the fuss was about and ending up pledging their lives to the Nazi cause. Even while he was killing millions and trapping the country in a difficult two-front war, he had what historians estimate as a 90% approval rating among his own people and rampant speculation that he was the Messiah. Yeah, sure, there was lots of preexisting racism and discontent he took advantage of, but there’s been lots of racism and discontent everywhere forever, and there’s only been one Hitler. If he’d been a little bit smarter or more willing to listen to generals who were, he would have had a pretty good shot at conquering the world. 100% with social skills.
The level above Hitler is Mohammed. I’m not saying he was evil or manipulative, just that he was a genius’ genius at creating movements. Again, he wasn’t born rich or powerful, and he wasn’t particularly scholarly. He was a random merchant. He didn’t even get the luxury of joining a group of fifty-five people. He started by converting his own family to Islam, then his friends, got kicked out of his city, converted another city and then came back at the head of an army. By the time of his death at age 62, he had conquered Arabia and was its unquestioned, God-chosen leader. By what would have been his eightieth birthday his followers were in control of the entire Middle East and good chunks of Africa. Fifteen hundred years later, one fifth of the world population still thinks of him as the most perfect human being ever to exist and makes a decent stab at trying to conform to his desires and opinions in all things.
The level above Mohammed is the one we should be worried about.
What about just not pursuing a PhD and instead doing what OP did? With the PhD you potentially lose #1 in
I actually think that you can get great results doing research as a hobby because
it gives you loads of slack, which is freedom to do things without constraints. In this context, I think slack is valuable because it allows you to research things outside of the publishing mainstream.
and less pressure.
I think these two things are crucial for success. The slack allows you to look at risky and niche ideas are more likely to yield better research rewards if they are true, since surprising results will trigger further questions.
Also, since you are more likely to do better at topics you enjoy, getting money from a day job allows you to actually purse your interests or deviate from your supervisor’s wishes. Conversely, it also allows you to give up when you’re not enjoying something.
Wikipedia says it's a SaaS company "specializing in AI-powered document processing and automation, data capture, process mining and OCR": https://en.wikipedia.org/wiki/ABBYY
To be clear, GiveWell won’t be shocked by anything I’ve said so far. They’ve commissioned work and published reports on this. But as you might expect, these quality of life adjustments wouldnt feature in GiveWell’s calculations anyway, since the pitch to donors is about the price paid for a life, or a DALY.
Can you clarify what you mean by these quality of life adjustments not featuring in GiveWell's calculations?
To be more concrete, let's take their CEA of HKI's vitamin A supplementation (VAS) program in Burkina Faso. They estimate that a $1M grant would avert 553 under-5 deaths (~80% of total program benefit) and incrementally increase future income for the ~560,000 additional children receiving VAS (~20%) (these figures vary considerably by location by the way, from 60 deaths averted in Anambra, Nigeria to 1,475 deaths averted in Niger) then they convert this to 81,811 income-doubling equivalents (their altruistic common denominator — they don't use DALYs in any of their CEAs, so I'm always befuddled when people claim they do), make a lot of leverage- and funging-related adjustments which reduces this to 75,272 income doublings, then compare it with the 3,355 income doublings they estimate would be generated by donating that $1M to GiveDirectly to get their 22.4x cash multiplier for HKI VAS in Burkina Faso.
So: are you saying that GiveWell should add a "QoL discount" when converting lives saved and income increase, like what Happier Lives Institute suggests for non-Epicurean accounts of badness of death?
You mention in another comment that your kid reads the encyclopaedia for fun, in which case I don't think The Martian would be too complex, no?
I'm also reminded of how I started perusing the encyclopaedia for fun at age 7. At first I understood basically nothing (English isn't my native language), but I really liked certain pictures and diagrams and keep going back to them wanting to learn more, realising that I'd comprehend say 20% more each time, which taught me to chase exponential growth in comprehension. Might be worth teaching that habit.
Society seems to think pretty highly of arithmetic. It’s one of the first things we learn as children. So I think it’s weird that only a tiny percentage of people seem to know how to actually use arithmetic. Or maybe even understand what arithmetic is for.
I was a bit thrown off by the seeming mismatch between the title ("underrated") and this introduction ("rated highly, but not used or understood as well as dynomight prefers").
The explanation seems straightforward: arithmetic at the fluency you display in the post is not easy, even with training. If you only spend time with STEM-y folks you might not notice, because they're a very numerate bunch. I'd guess I'm about average w.r.t. STEM-y folks and worse than you are, but I do quite a bit of spreadsheet-modeling for work, and I have plenty of bright hardworking colleagues who can't quite do the same at my level even though they want to, which suggests not underratedness but difficulty.
(To be clear I enjoy the post, and am a fan of your blog. :) )
