Epistemic status: describing a general phenomenon; may not be correct on every specific point. may have used scientific terms in an annoying metaphorical fashion. elements of pointing out the bleeding obvious, hopefully framed in a novel way.
tl;dr:positive feedback loops are a thing, thinking in systems/exponentially is hard, intersectionality is underrated.
“For to everyone who has, more will be given, and he will have an abundance. But from the one who has not, even what he has will be taken away.”
In 2013, unknown author Robert Galbraith published his debut novel… to crickets.
The first print run of The Cuckoo’s Calling was 1500 copies. It’s not clear how many actually sold. The book occupied 4709th place on Amazon’s bestseller charts.
And there, perhaps it would have stayed, if the cuckoo in the nest had remained undiscovered. The secret unravelled after a few months: ex-military security contractor Galbraith was a pseudonym for J.K. Rowling. As soon as the news broke, The Cuckoo’s Calling soared to the number one spot on Amazon. Sales increased by 150,000 per cent overnight. Copies from that first neglected print run are now worth thousands of dollars.
What’s the difference between Robert Galbraith and J.K. Rowling? Clearly, being a talented writer is necessary, but not sufficient. Rowling has momentum on her side. At this point, she could publish the contents of a bowl of alphabet soup, and it would still sell better than 99 per cent of novels by hopeful first-time authors.
This is a ‘no duh’ example, designed to get you nodding your head along. But momentum is everywhere, and it’s rarely in plain sight. Without being consciously aware of doing so, I’ve written about it in four domains:
Popular things often get their start through what amounts to good luck. The rapid ascent is driven by something even more powerful than rocket fuel: social contagion. Our opinions and preferences cluster together, but it’s not because we’ve carefully evaluated them on their merits. We just want to feel close to our fellow social apes, and have something to gossip about around the water cooler.
In other words, popularity is a lot like herpes. After catching a lucky initial break, it manages to spread to a few hosts, then rides the exponential growth curve until it has planted its gentle, blistery kiss on 60 per cent of the population.
With enough time on his side, [Fry’s] 93 cents transforms into $4.3 billion. If your gut instincts are screaming that this is staggeringly, ridiculously, wrong—well, you’re not alone.
As Mark Zuckerberg put it: “Humans don’t understand exponential growth. If you fold a paper 50 times, it goes to the moon and back.”
This is a delicious example, not only because the imagery is so jarring—whoa, a tiny sheet of paper can do that?—but because the Zuck himself got it wrong. If you fold a piece of paper 50 times over, it doesn’t make a paltry return trip to the moon—it goes all the way to the freakin’sun. Humans don’t understand exponential growth, indeed.
Something idea-based can be sold over and over again with almost no extra time or effort. It’s infinitely scalable. Your debut album might sell 10 copies (three of which your mum bought) or 10 million, but the amount of work that went into recording it was the same.
Scalable careers don’t follow a normal distribution, with a clear relationship between effort and reward. Instead, they produce grotesque inequalities. It doesn’t necessarily matter how good you are, or how hard you work: a select few people capture almost all the rewards, while everyone else gets next to nothing.
What’s life like for a moderately fit and muscular person? Well, everything works in your favor. The wind is at your back. You’ve got momentum.
The fitter you are, the better your hormonal and metabolic health, the lower your bodyfat, the more relaxed you can be with your diet, the more fun life is, the more motivation you have to train, the cooler feats you can perform, the deeper the habit is ingrained, and so on, in an endless positive feedback loop.
In fact, it’s even better than that. Almost all these factors are mutually reinforcing. If you do screw up, and drunkenly devour an entire box of cereal, or take a week off from the gym to clock a new video game, it’s no biggie. Any one link can seize up for a while, and the cycle will keep on turning without it.
…and a few more examples I’ve collected, but haven’t written about:
Sociologist Robert Merton coined the term ‘The Matthew Effect’, after the parable of the talents line quoted up top.
Merton noticed that famous scientists often get credited for discoveries made by lesser-known researchers or grad students toiling in obscurity. Similarly, the success of any given paper often depends on the prominence of the author, and how many early citations it happens to receive:
So great is this problem that we are tempted to turn again to the Scriptures to designate the status-enhancement and status-suppression components of the Matthew effect. We can describe it as the Ecclesiasticus component, from the familiar injunction ‘Let us now praise famous men’.
Psychologists have discovered the same effect in education. The longer it takes kids to learn how to read, the slower the development of their other cognitive skills and performance:
The longer this developmental sequence is allowed to continue, the more generalized the deficits will become, seeping into more and more areas of cognition and behavior. Or to put it more simply – and sadly – in the words of a tearful nine-year-old, already falling frustratingly behind his peers in reading progress, “Reading affects everything you do."
For most intents and purposes, the efficient markets hypothesis is correct. But even the Nobel prize-winning EMH creator, Eugene Fama, has admitted there is one major anomaly: momentum, which he describes as the “biggest embarrassment to the theory”.
Here’s Fama’s old advisor, Benoit Mandelbrot, on the long memory of market pricing:
What a company does today—a merger, a spin-off, a critical product launch—shapes what the company will look like a decade hence; in the same way, its stock-price movements today will influence movements tomorrow.
…a bottom line emerges. Stock prices are not independent. Today’s action can, at least slightly, affect tomorrow’s action. The standard model is, again, wrong.
The principle of cumulative advantage spans physics, biology, psychology, economics, and culture. It almost seems like some underlying feature of the universe. Here’s Mandelbrot again:
“Can you seriously compare the wind to a financial market, a gale to a rally, a hurricane to a crash? In terms of the underlying causes, certainly not. But mathematically, yes. It is an extraordinary feature of science that the most diverse, seemingly unrelated, phenomena can be described with the same mathematical tools.”
On the macro scale of the universe—the birth of stars, complex life bootstrapped from mud—momentum is kind of miraculous. For a brief candle-flicker, we get to resist the relentless march of entropy; create defiant bastions of order and beauty amongst the chaos.
On the micro scale of individual human affairs—wealth, waistlines, popularity, power—momentum is kind of terrifying. It makes us, and it breaks us. The 1 per cent control almost half of the world’s wealth, a small number of startups succeed astronomically, most books are sold by the J.K Rowlings of the world.
Momentum leaves behind a distinctive calling card, which looks something like this:
If this graph was drawn to scale, the tail would extend several kilometres off your computer screen. For self-published ebooks, it’s worse: the median number of sales is zero.
You will know these various patterns as the ‘80/20 rule’, power laws, long-tails, and Pareto distributions. The economist Vilfredo Pareto devoted years to the pattern which now bears his name. Surely he has some kind words to say about his curvy wife?
At the bottom of the [curve], men and women starve and children die young. In the broad middle of the curve all is turmoil and motion: people rising and falling, climbing by talent or luck and falling by alcoholism, tuberculosis and other kinds of unfitness. At the very top sit the elite of the elite, who control wealth and power for a time — until they are unseated through revolution or upheaval by a new aristocratic class.
If each instance of the Matthew effect stayed in its own lane, that would be unfair enough. But as Pareto points out, they’re all hopelessly entangled. Each of these domains – money, opportunity, health, education, talent, prestige – not only compounds on itself; but spills over into the other buckets too. Some interactions are obvious: a successful author will almost by definition make more money. Others are less so: a fit and healthy person might get promoted over an equally-qualified overweight person, for no good reason at all.
And that’s the positive side of the ledger…
The Downward Spiral
My dear, here we must run as fast as we can, just to stay in place. And if you wish to go anywhere you must run twice as fast as that.
Momentum also works in reverse.
Imagine your partner breaks up with you. You start drinking more. The drinking affects your work. You become isolated from friends and family. You stop exercising and looking after yourself. Eventually, you lose your job. Now you have money problems, on top of your declining physical and mental health, and total lack of support network. Things don’t tend to deteriorate in a linear fashion: you spiral downwards faster and faster, until you fall off a cliff.
The further down you slip, the harder it is to regain lost ground.
I had a little taste of this recently. A series of bad things came along in quick succession. Each of them would have been OK in isolation; together, they put me into a tailspin. I pride myself on being put-together, but I unravelled disturbingly quickly. Order begets order; chaos begets chaos. It was an uncomfortable reminder that everyone is always only a few strokes of misfortune away from the abyss: there but for the grace of God go I.
Further Down the Spiral
Just to make it explicit: the title of this post is an homage to Scott Alexander's essay Meditations on Moloch. As Scott points out in his epic close-reading of an Allen Ginsberg poem, there are obvious things we could do to make the world a better place, but some invisible force stymies our efforts:
If everyone hates the current system, who perpetuates it? And Ginsberg answers: “Moloch”. It’s powerful not because it’s correct – nobody literally thinks an ancient Carthaginian demon causes everything – but because thinking of the system as an agent throws into relief the degree to which the system isn’t an agent.
The same alien ‘otherness’ applies to momentum. A handful of A-list actors are inundated with roles, when tens of thousands of talented hopefuls would jump at the chance to eat the scraps from their table. One per cent of everyone owns half the wealth, while billions of others are desperately poor.
In every area of life, the people who are least in need of further advantage are most likely to receive it.
Almost everyone is unhappy with this distribution of outcomes, but blaming ‘capitalism’ or ‘the government’ or whichever tribe you happen to hate might be missing the point. If there is some blind force of nature operating behind the scenes, then the exact same pattern will continue to persist (which might explain why socialist utopias don’t tend to go exactly as planned).
Back to Pareto, for more cheerful words of encouragement:
“There is no progress in human history. Democracy is a fraud. Human nature is primitive, emotional, unyielding. The smarter, abler, stronger, and shrewder take the lion’s share. The weak starve, lest society become degenerate: One can compare the social body to the human body, which will promptly perish if prevented from eliminating toxins.”
Assume we are dealing with some kind of all-pervasive force of nature. Moloch works tirelessly to destroy everything humans hold dear. The Matthew Effect/momentum is more like the blind, alien god of evolution [LW · GW]—responsible for creating everything humans hold dear, but in the same mindless fashion, smites entire species into oblivion.
The universe is neither hostile nor benevolent; it’s utterly indifferent. What to do?
The Lord Giveth, and The Lord Taketh Away
The parable of the talents says: you better use it or lose it. Get some momentum behind you. Start saving money as early as possible. Reduce debt aggressively. Build behaviours that compound, and nip bad habits in the bud as soon as possible. Stay the hell away from the abyss.
Saving that first $100,000, as Charlie Munger put it, is a bitch. You have to be the little rocket trying to escape the Earth’s gravitational pull, with all your engines on full thrust. Then you can take your foot off the gas a little, but don’t get complacent. If you lose your momentum, you’ll drift back to earth, slowly at first, then faster and faster, until you slam into the ground at 200 kph.
You have to fight tooth and claw to get some momentum, and then stay up there just as long as you possibly can.
This moral sounds suspiciously demonic. But unlike Moloch’s favourite games, which are zero or negative-sum, climbing the pyramid doesn’t always involve stamping on the fingers of those below you.
Improving your own health and fitness doesn’t make anyone else sickly. Making a consistent habit of reading, or learning new skills, doesn’t make other people dumber. Contrary to popular belief, getting richer doesn’t necessarily make other people poorer. And of course, one of the best ways of getting rich in the first place is refusing to pay a premium for popular things that arepopular only because they are popular.
Extending a Helping Hand
If you help yourself without hurting anyone, that’s great, but it still leaves loads of people stuck at the bottom of the curve.
Three encouraging observations: First, even if the overall pattern never changes, at least the individual data-points can move around.
We know this happens, because even mighty empires topple. Generational wealth doesn’t last forever. Celebrities burn out or fade away. Trees get struck by lightning. Stars implode. In dynamic societies, everyone gets their turn at the top.
The second encouraging observation is that momentum reaches a point of diminishing returns.
Sometimes there are hard physical limits: a redwood can only grow so tall before it takes more energy to pump water up from its roots than its new needles can harvest through photosynthesis. After a certain point, a fit person has to train harder and harder to eke out smaller and smaller gains, and so on.
Even where there are no physical limits, there’s a rapid drop-off in marginal utility. A famous person receives more offers and opportunities than they know what to do with. The same goes for wealth. After the first couple million bucks, Bill Gates tells us, it’s the same hamburger.
If you take these two observations together, it makes a lot of sense to extend a helping hand up, rather than keep pushing for smaller and smaller gains. The pattern persists, but you create a lot more mobility up and down the curve.
Above and Beyond
Maybe Pareto was wrong.
The third encouraging observation is that mobility might be increasing, without a bloody revolution. [EDIT: had another look, I don't think the data actually supports me here. damn!]
Human nature is primitive and emotional, but not unyielding. Even though we struggle to wrap our monkey-minds around compound interest—much less social contagion and non-linear causality—we’re getting less bad at it.
It’s pretty cool that J.K. Rowling deliberately tried to play life on hard-mode again. It’s much more exciting that more than 100 billionaires have pledged to give away most (or all) of their fortunes. And that thousands of ordinary people have made a lifetime commitment to give at least 10 per cent of their income to the most effective charities.
The parable of the talents is pretty cut-throat. My guess is that it’s meant to be descriptive, not normative. And lots of people—even those at the top—aren’t OK with it.
Sure, it’s the natural order of things. But nature also gave us strychnine, parasitic wasps, and cuddly meerkats that systematically murder their infants. Nature is not to be trusted.
What’s the moral of the story? As far as I can see:
work your butt off to get some momentum behind you,
keep a watchful eye out for any signs of entropy creeping in,
once you hit the point of diminishing returns, focus your efforts on helping other people up.
John Wesley, the founder of Methodism, delivered a famous sermon on this topic in the 18th century. I think he summed it up more pithily:
"Having, First, gained all you can, and, Secondly saved all you can, Then give all you can."
Number 4 is even worse than that. Physical health is deeply entangled with mental health. Many never get the generator spinning because the first 6-18 months can have fairly illegible feedback loops depending on where you start. And it can be stupid stuff. I only managed to start running once I got really frustrated and tried 12 pairs of shoes to find some that didn't bother my feet. It was a hassle, but it permanently solved the problem since I now know what parameters to look for. Compounding small permanent wins doesn't look all that impressive until you hit the knee of the curve and then it goes from famine to feast. Getting those success spirals ramping up is why Peterson is telling people to clean their room and why Marie Kondo's book bills it as Life Changing Magic. If you internalize the meta pattern instead of thinking it's just about cleaning your room you're off to the races. (IFS is KonMarie for the inside of your head)
I've also referred to this as instantiating the spoon reinvestment act. Determining to reinvest a portion of any gained spoons in spoon generating activities. See also, slack: https://thezvi.wordpress.com/2017/09/30/slack/
Absolutely. Another way of thinking about it is a punctuated equilibrium: in some domains it feels like nothing is happening for the longest time, then you suddenly experience 'overnight' success. I have noticed that I find projects with delayed or noisy feedback loops super stressful, even if I know there's a solid expected payoff waiting in the wings.
I am a fan of Marie Kondo and Peterson for the exact reason you describe, and enough people have mentioned IFS now that I'll have to check it out. What's the 'spoon' thing in reference to? This seems to be one of those LW-isms that I've missed somehow.
Promoted to curated: I think this was a bit overlooked by other readers, and so I think is particularly valuable to promote. It also serves as maybe the best system-1 introduction to attachment-effects/momentum/heavy-tail distributions that I've seen so far, and as such I am quite confident I will refer to it multiple times in the future.
Overall the post is well written, and I particularly appreciate the heavy use of quotations and concrete examples, which make the post a lot livelier than I think it would have been otherwise.
I do think some of the optimism is unwarranted, and I think you tried to be a bit too "call-to-actiony" at the end, in a way that I think wasn't fully epistemically justified by the rest of your post. I think a more muted ending, or maybe more justification for your recommendations would help the post. But overall I still really enjoyed it and found it quite valuable.
Thanks for the feedback - much appreciated! I agree that the end isn't well supported (at least, in the post). I write for a general audience who want clear, actionable takeaways. If I cross-post something in the future, I'll think about editing it more heavily to fit the LW norms (i.e. explain rather than persuade).
It seems like it’s pretty consistently talking about attachment style effects, do you have an example of where it conflates that causal mechanism with something else? (I.e. it pretty consistently talks about the phenomenon “having more of X gives you even more of X” which can happen for a variety of reasons, but seems like a common enough phenomena to have a common abstraction for)
I don't know what you mean by attachment style, but some examples of the conflation...
Momentum is this: even if JK Rowling's next book is total crap, it will still sell a lot of copies. Because people have beliefs, and because they enjoyed her previous books, they have a prior that they will enjoy also the next one. It would take them several crap book to update.
Power laws are ubiquitous. This should be unsurprising - power laws are the simplest functional form in the logarithmic picture. If we use some sort of simplicity prior, we are guaranteed to find them. If we use first terms of Taylor expansion, we will find them. Log picture is as natural as the linear one. Someone should write a Meditation on Benford's law - you have an asymptotically straight line in log-log picture of the probability than a number starts with some digits (in almost any real-life set of numerical values measured in units; you can see this must be the case because of invariance to unit scaling)
This is maybe worth emphasizing: nobody should be surprised to find power laws. Nobody should propose universal causal mechanism for power laws, it is as stupid as proposing one causal mechanism for straight lines in linear picture.
They are often the result of other power-law distributed quantities. To take one example from the op... initial distribution of masses for an initail population of new stars is a truncated power law. I don't know why, but the proposed mechanisms for this is for example turbulent fragmentation of the initial cloud, where the power law can come from the power spectrum of super–sonic turbulence.
Sure, but where does the post talk about power laws? It only talks about momentum-like effects, and there is a large literature on how preferential attachment can give rise to power-laws, so it has some relation, but I don’t see the article talking about power-laws in isolation. I brought up power-laws in the curation notice, because they frequently show up in situations with increasing marginal returns and multiplicative feedback loops, but I don’t see how the article encourages any kind of conflation in this area given that it practically makes no reference to it.
I also think you vastly overstate the case for power-laws. Most power-laws are much better fit by a log-normal distribution. See this paper for more details. I think the prior for log-normal should be higher than the prior for power-law, because of the multiplicative equivalent of the central limit theorem.
I'm still confused what you mean by momentum-like effects. Momentum is a very beautiful and crisp concept - the dual (canonical conjugate) of position, with all kinds of deep connections to everything. You can view the whole universe in the dual momentum space.
If the intention is to have a concept ca in the shape of "all kinds of dynamics which can be rounded to dx=a.x" I agree it may be valuable to have a word for that, but why overload momentum?
You asked for an example of where it conflates that causal mechanism with something else. I picked one example from this paragraph
So, as I understand it, I gave you an example (the distribution of star masses) which quite likely does not have any useful connection to preferential attachment or exponential grow. I'm really confused after your last reply what is the state of our disagreement on this.
I'm actually scared to change the topic of the discussion what simplicity means, but the argument is roughly this: if you have arbitrary well behaved function, in the linear picture, you can approximate it locally by a straight line (the first term in the Taylor series, etc.). And yes, you get better approximation by including more terms from the Taylor series expansion, or by non-linear regression, etc. Now, if you translate this to the log-log picture, you will find out that power law is in some sense the simplest local approximation of anything. This is also the reason why people often mistakenly use power laws instead of lognormal and other distributions - if you truncate the lognormal and look just on part of the tail you can fit it with power law. Btw you nicely demonstrate this effect yourself - preferential attachment often actually leads to Yule-Simon distribution, and not a power law ... but as usually you can approximate it.
Oh, I assumed the author was referring to this explanation for the distribution of star masses:
Here we propose a new approach exploiting the techniques from the field of network science. We represent a system of dense cores accreting gas from the surrounding diffuse interstellar medium (ISM) as a spatial network growing by preferential attachment and assume that the ISM density has a self-similar fractal distribution following the Kolmogorov turbulence theory. We effectively combine gravoturbulent and competitive accretion approaches and predict the accretion rate to be proportional to the dense core mass: dM/dt∝M. Then we describe the dense core growth and demonstrate that the power-law core mass function emerges independently of the initial distribution of density fluctuations by mass. Our model yields a power law solely defined by the fractal dimensionalities of the ISM and accreting gas. With a proper choice of the low-mass cut-off, it reproduces observations over three decades in mass. We also rule out a low-mass star dominated "bottom-heavy" IMF in a single star-forming region.
I agree that if this is indeed the case, the author should provide a direct link to this theory, and ideally mention it explicitly as a theory among many.
I actually think the theory linked above is likely to be wrong, but don’t have any similar senses for all the other links provided in the same paragraph, which seem to me to pretty robustly be systems in which preferential attachment plays a large role.
I think the case of the star-distribution is more likely to be an honest error where the author heard about the preferential attachment theory for the distribution of star-sizes somewhere else, and used it as an example here even though it probably isn’t the most elegant explanation of the phenomena, which I do think should be pointed out.
I agree that if the author wanted to imply that “all power-law distributions are the result of momentum as defined in this article” then that would be bad, but I think the author overwhelmingly used examples that point towards a much narrower set of phenomena that also happen to produce things that look like power-laws (which I agree with you should appear for a lot of different reasons and should not be thought to be much evidence for any specific underlying causal model).
1. Going through two of the adjacent links in the same paragraph:
With the trees, I only skimmed it, but if I get it correctly, the linked article proposes this new hypothesis: Together these pieces of evidence point to a new hypothesis: Small-scale, gap-generating disturbances maintain power-function size structure whereas later-successional forest patches are responsible for deviations in the high tail.
and, also from the paper
Current theories explaining the consistency of tropical forest size structure are controversial. Explanations based on scaling up individual metabolic rates are criticized for ignoring the importance of asymmetric competition for light in causing variation in dynamic rates. Other theories, which embrace competition and scale individual tree vital rates through an assumption of demographic equilibrium, are criticized for lacking parsimony, because predictions rely on site-level, size-specific parameterization
(I also recommend looking on the plots with the "power law", which are of the usual type of approximating something more complex with a straight line in some interval.)
So, what we actually have in this: apparently different researchers proposing different hypothesis to explain the observed power-law-like data. It is far from conclusive what the actual reason is. As something like positive feedback loops is quite obvious part of the hypothesis space if you see power-law-like data, you are almost guaranteed to find a paper which proposes something in that direction. However, note that article actually criticizes previous explanations based more on "Matthews effect", and proposes disturbances as a critical part of the explanation.
(Btw I do not claim any dishonesty from the author anything like that.)
Halo and Horn effects are likely evolutionary adaptive effects, tracking something real (traits like "having an ugly face" and "having higher probability of ending up in trouble" are likely correlated - the common cause can be mutation load / parasite load; you have things like the positive manifold).
And so on.
Sorry but I will not dissect every paragraph of the article in this way. (Also it seems a bit futile, as if I dig into specific examples, it will be interpreted as nit-picking)
2. Last attempt to gesture toward whats wrong with this whole. The best approximation of the cluster of phenomena the article is pointing toward is not "preferential attachment" (as you propose), but something broader - "systems with feedback loops which can be in some approximation described by the differential equation dx = b.x".
You can start to see systems like that everywhere, and get a sense of something deep, explaining life, universe and everything.
One problem with this: if you have a system described by a differential equation of the form "dx = f(x,..)", and the function f() is reasonable, you can approximate it by its Taylor series "f(x)=a+b.x+c.x.x+..". Obviously, the first order term is b.x. Unfortunately (?) you can say this even before looking on the system.
So, vaguely speaking, when you start thinking in this way, my intuition is it puts you in a big danger of conflating something about how you do approximations with causal explanations. (I guess it may be a good deal for many people who don't have s-1 intuitions for Taylor series or even log() function)
I actually had some similar alarm bells go off for conflation of concepts in the op, especially because the post specifically gestures at one concept and doesn't give explanations of the different examples where this might come up.
However, on second thought I think I do like the concept this builds. To phrase it in your formal terms, I think it's very useful to notice all the systems in which the Taylor series for f has b>0, ESPECIALLY when it's comparably easy to control f via b∗x rather than just a.
In this light, you can view momentum, exponential growth, heavy-tails, etc., as all cases where a main component of controlling or predicting future x is by paying attention to the b∗x term, and I claim this is an important revelation to have at a variety of levels.
Perhaps more relevant to your actual crux, I also get shudders when people overload physics terms with other meanings, but before they were physics terms they were concepts for intuitive things. Given that we view the world through physical metaphors, I think it's quite important for us to use the best-fitting words for concepts. Then we can remind people of the different variants when people run into conflationary trouble. If we start off by naming things with poor associations we hold ourselves back more. If you have alternative name to "momentum" for this that you also think have good connotations though, I'd love to hear them.
The second thing first: "...but before they were physics terms they were concepts for intuitive things" is actually not true in this case: momentum did not mean anything, before being coined in physics. Than, it become used in a metaphorical way, but mostly congruently with the original physics concepts, as something like "mass"x"velocity". It seems to me easy to imagine vivid pictures based of this metaphor, like advancing army conquering mile after mile of enemy territory having a momentum, or a scholar going through page after page of a difficult text. However, this concept is not tied to the b∗x term (which is one of my cruxes).
To me, the original metaphorical meaning of momentum makes a lot of sense: you have a lot of systems where you have something like mass (closely connected to inertia: you need great force to get something massive to move) and something like velocity - direction and speed where the system is heading. I would expect most people have this on some level.
Now, to the first thing second: I agree that it may be useful to notice all the systems in which the Taylor series for f has b>0, ESPECIALLY when it's comparably easy to control f via b∗x rather than just a. However, some of the examples in the original post do not match this pattern: some could be just systems where, for example, you insert heavy-tailed distribution on the input, and you get heavy-tailed distribution on the output, or systems where the a term is what you should control, or systems where you should actually understand more about f(x) than the fact that is is has positive first derivative at some point.
What should be a good name for b∗x>0 I don't know, some random prosaic ideas are snowballing, compound, faenus (from latin interest on money, gains, profit, advantage), compound interest. But likely there are is some more poetic name, similarly to Moloch.
1. Be born to the right parents, in the right circumstances (not helpful, but important to acknowledge).
2. Apply yourself strategically in areas that compound (e.g. knowledge and skills, saving and investing, resistance training, networking).
3. Apply your effort wherever the yield is highest. All of these domains follow an S-shaped curve, with early exponential growth running into an upper ceiling of diminishing returns. At any given point in time, it might make sense to focus primarily on accumulating money, at another, skills and knowledge, at another, health and fitness, etc.
4. Choose goals that are complementary, so that each 'bucket' also helps to fill the others, and there's no single point of failure (or at the very least, avoid goals which conflict with one another).
5. Keep doing 2-4 forever. Even if you never hit that knee-shaped curve, a consistent and cumulative effort over time is pretty powerful in and of itself.
After analysing the cases when I was in up and down momentum, I concluded that there are other additional points:
1.A new activity has initially up momentum, as it creates new connections, people are interested in your new project and you are inspired. An old activity creates down momentum, even if the quality of the product has improved, as people become bored with it. (There are counterexamples, e.g. Sequences).
2. You may learn to "feel" which action has up momentum or down momentum and navigate accordingly.
I doubt there are tricks. Find and reinforce the feedback loops that seem to lead where you want. Look for surprising correlations (diet and work performance, for instance). Be lucky in your starting position and smartlucky in the behaviors you choose to focus on.
Also, recognize that half of people _ARE_ below median on any measure. In large populations, there are very close to 0 who are the literal best at anything. Make sure your satisfaction level is achievable, even as you seek topics on which you might excel.
minor error - in the sentence "For self-published ebooks, it’s worse: the median number of sales is zero.", it should say modal (most common number) instead of median (number in the middle of the distribution).
Well, can't disagree with such an abstract approach. Must be true somewhere.
But I do. The world must look like that if you run a fast strategy. From here where I am with a slow strategy in the upper middle of the range where it looks mostly flat and the ends far away and the strategy is mostly to keep it that way.