Why no one is exponentially smarter than others(medium.com)
medium.com
Why no one is exponentially smarter than others
https://medium.com/tractatus-logico-universalis/on-why-no-one-is-likely-to-be-exponentially-smarter-than-others-66615846ed97
59 comments
Not to mention that smart people usually do amazing things by just changing the rules and making the problem easier to solve (you can only make a horse go so fast or pull so much, but you can invent an automobile or train)
This whole analogy I realized after thinking about it is just computer science baby babble.
Fundamentally it comes down to not formally specifying the problem (not saying I can, I can’t and neither can anyone else that I’m aware of)
People always want to cling to quantitative interpretations of qualitative problems, and then declare QED, despite the whole thing being predicated off a false premise to begin with (like the thing we’re discussing is an appropriate candidate for an algorithmic interpretation to begin with).
And without a formal specification of the problem, we have no formal way of checking our solution.
This whole analogy I realized after thinking about it is just computer science baby babble.
Fundamentally it comes down to not formally specifying the problem (not saying I can, I can’t and neither can anyone else that I’m aware of)
People always want to cling to quantitative interpretations of qualitative problems, and then declare QED, despite the whole thing being predicated off a false premise to begin with (like the thing we’re discussing is an appropriate candidate for an algorithmic interpretation to begin with).
And without a formal specification of the problem, we have no formal way of checking our solution.
Firstly, have you read ImaCake[1]?
Secondly, if you're so smart, why didn't you write this essay, and refute it yourself?
[1] https://news.ycombinator.com/item?id=21622871
Secondly, if you're so smart, why didn't you write this essay, and refute it yourself?
[1] https://news.ycombinator.com/item?id=21622871
[deleted]
I take slight issue with your examples. Do "Elon, Jobs, Gates" really come to mind first when talking "exponential" genius and accomplishment over say Einstein, Gauss, Neumann etc?
That’s fair, and I didn’t mean the list to be comprehensive. I guess when I chose those people I was just thinking about examples of one person achieving huge scale, but yeah on second thought you’re totally right. I’d be honored to admit I was wrong for not mentioning them :)
Competence is, for the most part, distributed normally, but productivity looks something more like pareto.
I think a better model is not that some are exponentially smarter than others, but that some folks are operating close to the problem manifold and the rest aren't.
AKA, some people are solving classes of problems in approximately the most efficient way (or relatively more efficient way) and most people are computing solutions in exponentially inferior ways.
AKA, some people are solving classes of problems in approximately the most efficient way (or relatively more efficient way) and most people are computing solutions in exponentially inferior ways.
To put it real lightly, it's a real stretch to make any kind of analogy between the human brain does work and the way that semiconductor based processors do work. The author's reference to Stephan Wolfram's idea of universality (developed in a prior essay) seems unfortunate:
>“The key unifying idea that has allowed me to formulate the Principle of Computational Equivalence is a simple but immensely powerful one: that all processes, whether they are produced by human effort or occur spontaneously in nature, can be viewed as computations.”
To borrow a metaphor from a recent HN thread about an eponymous paper called "How to recognize AI snake oil" [1], there's an "incomplete and crude but useful breakdown" on you can apply towards AI problems: genuine and useful progress in perception, imperfect but improving work in automating judgment, and fundamentally dubious attempts to predict social outcomes.
Let's think about where the idea of a theory of mind based on computational complexity to determine "smartness" lands -- it's certainly not stimulus detection, it's certainly not automating judgment, but it is about predicting or modeling social outcomes. I would say that this application Wolfram's idea is fundamentally dubious. Because of this, it's hard for me to say that the premise, argument or conclusion of this essay is anything but fundamentally dubious.
To at least leave a useful suggestion: this essay is missing an adequate definition and exploration of what "smart" is, why it's a facet of human nature and history, and what issues the concept causes. To the author, I'd recommend starting off by building a better foundation there before jumping to conclusions that are hard to take seriously.
[1] https://news.ycombinator.com/item?id=21577156
To borrow a metaphor from a recent HN thread about an eponymous paper called "How to recognize AI snake oil" [1], there's an "incomplete and crude but useful breakdown" on you can apply towards AI problems: genuine and useful progress in perception, imperfect but improving work in automating judgment, and fundamentally dubious attempts to predict social outcomes.
Let's think about where the idea of a theory of mind based on computational complexity to determine "smartness" lands -- it's certainly not stimulus detection, it's certainly not automating judgment, but it is about predicting or modeling social outcomes. I would say that this application Wolfram's idea is fundamentally dubious. Because of this, it's hard for me to say that the premise, argument or conclusion of this essay is anything but fundamentally dubious.
To at least leave a useful suggestion: this essay is missing an adequate definition and exploration of what "smart" is, why it's a facet of human nature and history, and what issues the concept causes. To the author, I'd recommend starting off by building a better foundation there before jumping to conclusions that are hard to take seriously.
[1] https://news.ycombinator.com/item?id=21577156
1. ?? You do realize there are self-appointed geniuses who actually make this kind of arguments, right?
2. That snake-oil AI paper guy, right though he may be here, you know he's jealous of Bitcoin, right? Wrote a whole academic paper trying to justify how Bitcoin wouldn't exist w/o academia. If he was so smart, why didn't he write Bitcoin himself?
3. If this was so obvious and you're so smart, why didn't you write it yourself?
2. That snake-oil AI paper guy, right though he may be here, you know he's jealous of Bitcoin, right? Wrote a whole academic paper trying to justify how Bitcoin wouldn't exist w/o academia. If he was so smart, why didn't he write Bitcoin himself?
3. If this was so obvious and you're so smart, why didn't you write it yourself?
Are you seriously asking me why I didn't write something which I just told you is a worthless thing to spend time writing about? Probably because I think it's a worthless thing to spend time writing about. I'm not sure what you're trying to prove here.
Look, just because I don't buy your argument doesn't mean I buy the premise that "genius" exists the way it's constructed in society. I find that pretty fallacious too, but for different reasons. I don't think you're going to get to the core of why genius is a flawed concept with a strained analogy to computational complexity (which doesn't work) rather than by digging into historical context. I think if you focus on that, you'll probably make more progress on coming up with something interesting to say.
Look, just because I don't buy your argument doesn't mean I buy the premise that "genius" exists the way it's constructed in society. I find that pretty fallacious too, but for different reasons. I don't think you're going to get to the core of why genius is a flawed concept with a strained analogy to computational complexity (which doesn't work) rather than by digging into historical context. I think if you focus on that, you'll probably make more progress on coming up with something interesting to say.
The PhD example late in this essay is one that I have lived. I am a failed PhD student who worked for 4 years on my research with no first author publications to show for it. The professors from my old school always express surprise and confusion that I didn't succeed since I apparently have the right combination of smarts. But, to me, my failure is more down to bad luck and unfortunate circumstance than any inate ability.
I would love to hear other's experiences with PhDs in the context of the essay's example.
I would love to hear other's experiences with PhDs in the context of the essay's example.
Related things I've posted to Hacker News:
https://news.ycombinator.com/item?id=17843735
https://news.ycombinator.com/item?id=17519881
https://news.ycombinator.com/item?id=16725676
https://news.ycombinator.com/item?id=16541610
https://news.ycombinator.com/item?id=15911873
https://news.ycombinator.com/item?id=14675362
A key connecting idea in all of them is this reference to "Disciplined Minds": http://disciplinedminds.tripod.com/ "In this riveting book about the world of professional work, Jeff Schmidt demonstrates that the workplace is a battleground for the very identity of the individual, as is graduate school, where professionals are trained. He shows that professional work is inherently political, and that professionals are hired to subordinate their own vision and maintain strict "ideological discipline." The hidden root of much career dissatisfaction, argues Schmidt, is the professional's lack of control over the political component of his or her creative work. Many professionals set out to make a contribution to society and add meaning to their lives. Yet our system of professional education and employment abusively inculcates an acceptance of politically subordinate roles in which professionals typically do not make a significant difference, undermining the creative potential of individuals, organizations and even democracy. Schmidt details the battle one must fight to be an independent thinker and to pursue one's own social vision in today's corporate society."
However, even given that experience of enforced ideological conformity to a social power structure (which some people may find an unexpected horror while others go "meh, so what else is new?"), academia is an increasingly bad deal for reasons explained by David Goodstein (the vice-provost of CalTech testifying to Congress in the 1990s on why the economics of academia have changed since the 1970s and peer review is starting to fail as a consequence) and Philip Greenspun (explaining why most women he has met are too socially savvy and socio-economically astute to play the PhD game with plans for an academic career):
http://www.its.caltech.edu/~dg/crunch_art.html "We must find a radically different social structure to organize research and education in science after The Big Crunch. That is not meant to be an exhortation. It is meant simply to be a statement of a fact known to be true with mathematical certainty, if science is to survive at all. The new structure will come about by evolution rather than design, because, for one thing, neither I nor anyone else has the faintest idea of what it will turn out to be, and for another, even if we did know where we are going to end up, we scientists have never been very good at guiding our own destiny. Only this much is sure: the era of exponential expansion will be replaced by an era of constraint. Because it will be unplanned, the transition is likely to be messy and painful for the participants. In fact, as we have seen, it already is. Ignoring the pain for the moment, however, I would like to look ahead and speculate on some conditions that must be met if science is to have a future as well as a past."
http://philip.greenspun.com/careers/women-in-science "This is how things are likely to go for the smartest kid you sat next to in college. He got into Stanford for graduate school. He got a postdoc at MIT. His experiment worked out and he was therefore fortunate to land a job at University of California, Irvine. But at the end of the day, his research wasn't quite interesting or topical enough that the university wanted to commit to paying him a salary for the rest of his life. He is now 44 years old, with a family to feed, and looking for job with a "second rate has-been" label on his forehead. Why then, does anyone think that science is a sufficiently good career that people should debate who is privileged enough to work at it? Sample bias. ... What about personal experience? The women that I know who have the IQ, education, and drive to make it as professors at top schools are, by and large, working as professionals and making 2.5-5X what a university professor makes and they do not subject themselves to the risk of being fired. With their extra income, they invest in child care resources and help around the house so that they are able to have kids while continuing to ascend in their careers. The women I know who are university professors, by and large, are unmarried and childless. By the time they get tenure, they are on the verge of infertility. ..."
From a completely different angle, see also Carol Dweck's research and recommendations about a "Growth Mindset": https://en.wikipedia.org/wiki/Carol_Dweck#Mindset_work "Her key contribution to social psychology relates to implicit theories of intelligence, per her 2006 book Mindset: The New Psychology of Success. According to Dweck, individuals can be placed on a continuum according to their implicit views of where ability comes from. Some believe their success is based on innate ability; these are said to have a "fixed" theory of intelligence (fixed mindset). Others, who believe their success is based on hard work, learning, training and doggedness are said to have a "growth" or an "incremental" theory of intelligence (growth mindset). Individuals may not necessarily be aware of their own mindset, but their mindset can still be discerned based on their behavior. It is especially evident in their reaction to failure. Fixed-mindset individuals dread failure because it is a negative statement on their basic abilities, while growth mindset individuals don't mind or fear failure as much because they realize their performance can be improved and learning comes from failure. These two mindsets play an important role in all aspects of a person's life. Dweck argues that the growth mindset will allow a person to live a less stressful and more successful life. ... Dweck advises, "If parents want to give their children a gift, the best thing they can do is to teach their children to love challenges, be intrigued by mistakes, enjoy effort, and keep on learning. That way, their children don't have to be slaves of praise. They will have a lifelong way to build and repair their own confidence." Dweck warns of the dangers of praising intelligence as it puts children in a fixed mindset, and they will not want to be challenged because they will not want to look stupid or make a mistake. She notes, "Praising children's intelligence harms motivation and it harms performance.""
https://news.ycombinator.com/item?id=17843735
https://news.ycombinator.com/item?id=17519881
https://news.ycombinator.com/item?id=16725676
https://news.ycombinator.com/item?id=16541610
https://news.ycombinator.com/item?id=15911873
https://news.ycombinator.com/item?id=14675362
A key connecting idea in all of them is this reference to "Disciplined Minds": http://disciplinedminds.tripod.com/ "In this riveting book about the world of professional work, Jeff Schmidt demonstrates that the workplace is a battleground for the very identity of the individual, as is graduate school, where professionals are trained. He shows that professional work is inherently political, and that professionals are hired to subordinate their own vision and maintain strict "ideological discipline." The hidden root of much career dissatisfaction, argues Schmidt, is the professional's lack of control over the political component of his or her creative work. Many professionals set out to make a contribution to society and add meaning to their lives. Yet our system of professional education and employment abusively inculcates an acceptance of politically subordinate roles in which professionals typically do not make a significant difference, undermining the creative potential of individuals, organizations and even democracy. Schmidt details the battle one must fight to be an independent thinker and to pursue one's own social vision in today's corporate society."
However, even given that experience of enforced ideological conformity to a social power structure (which some people may find an unexpected horror while others go "meh, so what else is new?"), academia is an increasingly bad deal for reasons explained by David Goodstein (the vice-provost of CalTech testifying to Congress in the 1990s on why the economics of academia have changed since the 1970s and peer review is starting to fail as a consequence) and Philip Greenspun (explaining why most women he has met are too socially savvy and socio-economically astute to play the PhD game with plans for an academic career):
http://www.its.caltech.edu/~dg/crunch_art.html "We must find a radically different social structure to organize research and education in science after The Big Crunch. That is not meant to be an exhortation. It is meant simply to be a statement of a fact known to be true with mathematical certainty, if science is to survive at all. The new structure will come about by evolution rather than design, because, for one thing, neither I nor anyone else has the faintest idea of what it will turn out to be, and for another, even if we did know where we are going to end up, we scientists have never been very good at guiding our own destiny. Only this much is sure: the era of exponential expansion will be replaced by an era of constraint. Because it will be unplanned, the transition is likely to be messy and painful for the participants. In fact, as we have seen, it already is. Ignoring the pain for the moment, however, I would like to look ahead and speculate on some conditions that must be met if science is to have a future as well as a past."
http://philip.greenspun.com/careers/women-in-science "This is how things are likely to go for the smartest kid you sat next to in college. He got into Stanford for graduate school. He got a postdoc at MIT. His experiment worked out and he was therefore fortunate to land a job at University of California, Irvine. But at the end of the day, his research wasn't quite interesting or topical enough that the university wanted to commit to paying him a salary for the rest of his life. He is now 44 years old, with a family to feed, and looking for job with a "second rate has-been" label on his forehead. Why then, does anyone think that science is a sufficiently good career that people should debate who is privileged enough to work at it? Sample bias. ... What about personal experience? The women that I know who have the IQ, education, and drive to make it as professors at top schools are, by and large, working as professionals and making 2.5-5X what a university professor makes and they do not subject themselves to the risk of being fired. With their extra income, they invest in child care resources and help around the house so that they are able to have kids while continuing to ascend in their careers. The women I know who are university professors, by and large, are unmarried and childless. By the time they get tenure, they are on the verge of infertility. ..."
From a completely different angle, see also Carol Dweck's research and recommendations about a "Growth Mindset": https://en.wikipedia.org/wiki/Carol_Dweck#Mindset_work "Her key contribution to social psychology relates to implicit theories of intelligence, per her 2006 book Mindset: The New Psychology of Success. According to Dweck, individuals can be placed on a continuum according to their implicit views of where ability comes from. Some believe their success is based on innate ability; these are said to have a "fixed" theory of intelligence (fixed mindset). Others, who believe their success is based on hard work, learning, training and doggedness are said to have a "growth" or an "incremental" theory of intelligence (growth mindset). Individuals may not necessarily be aware of their own mindset, but their mindset can still be discerned based on their behavior. It is especially evident in their reaction to failure. Fixed-mindset individuals dread failure because it is a negative statement on their basic abilities, while growth mindset individuals don't mind or fear failure as much because they realize their performance can be improved and learning comes from failure. These two mindsets play an important role in all aspects of a person's life. Dweck argues that the growth mindset will allow a person to live a less stressful and more successful life. ... Dweck advises, "If parents want to give their children a gift, the best thing they can do is to teach their children to love challenges, be intrigued by mistakes, enjoy effort, and keep on learning. That way, their children don't have to be slaves of praise. They will have a lifelong way to build and repair their own confidence." Dweck warns of the dangers of praising intelligence as it puts children in a fixed mindset, and they will not want to be challenged because they will not want to look stupid or make a mistake. She notes, "Praising children's intelligence harms motivation and it harms performance.""
Luck matters more than we are often led to believe. One can generate luck, to an extent, through persistence.
Leonard Mlodinow has written two books that you might find both resonant and uplifting:
Feynman's Rainbow: A Search for Beauty in Physics and in Life , and The Drunkard's Walk: How Randomness Rules Our Lives.
Furthermore -- if you went to grad school and learned something, either about the subject or yourself, then the effort was not a failure. In the long game, it isn't about the degree nor the piece of paper.
Leonard Mlodinow has written two books that you might find both resonant and uplifting:
Feynman's Rainbow: A Search for Beauty in Physics and in Life , and The Drunkard's Walk: How Randomness Rules Our Lives.
Furthermore -- if you went to grad school and learned something, either about the subject or yourself, then the effort was not a failure. In the long game, it isn't about the degree nor the piece of paper.
Thanks :) I'll check them out. I think leaving was a great choice, academia is filled with madness, and I am happier not climbing up the impossible pyramid to professorship. But I am happy to support and work with those with such ambiition since they can do great things!
You get it (I was a PhD, too)
Can you share what happened?
Sure, the concise version is that I had an essential biology assay not work for three years running. It meant I couldn't do much to generate results. The pressure got to me and I burnt out hard. For whatever reason, the support network I had (including excellent supervisors) wasn't sufficient to overcome or work around the problem.
Looking back, diversifying my work and finding short term projects likely would have innoculated me against the effects of the (biggest) problem I faced.
After leaving, I have had few regrets (aside from lessons learned). I have had fun jobs, travelled, and had far less stress holding me down. Less money, sure, but more of the really important things.
Looking back, diversifying my work and finding short term projects likely would have innoculated me against the effects of the (biggest) problem I faced.
After leaving, I have had few regrets (aside from lessons learned). I have had fun jobs, travelled, and had far less stress holding me down. Less money, sure, but more of the really important things.
Thanks, sometimes life puts you in weird situations.
Related to the G's essay[1] on genius. AMA!
[1] http://paulgraham.com/genius.html
[1] http://paulgraham.com/genius.html
I think you're skirting a truly fascinating question: can "higher consciousness" violate complexity bounds?
Consider a very fast classical computer is simulating a universe with newtonian physics. There's no concept of quantum mechanics in this universe. You create a black box where people in this simulation can ask you questions. You also have a quantum computer. Now you can answer questions that require quantum computing which they cannot answer in their universe
Next step: we're a simulation in a universe which has ways to violate complexity bounds we hit with quantum computers
Next step: we're a simulation in a universe which has ways to violate complexity bounds we hit with quantum computers
You tell me: why would it? And if it could, why can't we build similar machines?
I guess for the same reason we don’t have giants walking around either, these are depending upon many random distributions of interactions that ultimately lead to a Gaussian distribution of said characteristic (height or intelligence etc) via the central limit Theorem.
Ha! Title so foolish it disproves its own premise.
Sorry! I couldn't resist.
Snark omitted, here's an alternate idea of "genius":
The word refers to a kind of spirit or daemon (same root as Genii). Consider the 'daimonion (literally, a "divine something")' of Socrates:
https://en.wikipedia.org/wiki/Daemon_(classical_mythology)#S...
> In ancient Rome, the genius (plural in Latin genii) was the guiding spirit or tutelary deity of a person, family (gens), or place (genius loci).
https://en.wikipedia.org/wiki/Genius
> Jinn, also Romanized as djinn or Anglicized as genies (with the more broad meaning of spirits or demons, depending on source), are supernatural creatures in early pre-Islamic Arabian and later Islamic mythology and theology.
https://en.wikipedia.org/wiki/Jinn
To be a genius is to be favored or assisted by one of more of these invisible people.
I don't know if they can solve any problem in NP in polynomial time but they can apparently predict winning lottery numbers which suggests to me that there must be something interesting going on from a computational complexity POV.
Snark omitted, here's an alternate idea of "genius":
The word refers to a kind of spirit or daemon (same root as Genii). Consider the 'daimonion (literally, a "divine something")' of Socrates:
https://en.wikipedia.org/wiki/Daemon_(classical_mythology)#S...
> In ancient Rome, the genius (plural in Latin genii) was the guiding spirit or tutelary deity of a person, family (gens), or place (genius loci).
https://en.wikipedia.org/wiki/Genius
> Jinn, also Romanized as djinn or Anglicized as genies (with the more broad meaning of spirits or demons, depending on source), are supernatural creatures in early pre-Islamic Arabian and later Islamic mythology and theology.
https://en.wikipedia.org/wiki/Jinn
To be a genius is to be favored or assisted by one of more of these invisible people.
I don't know if they can solve any problem in NP in polynomial time but they can apparently predict winning lottery numbers which suggests to me that there must be something interesting going on from a computational complexity POV.
If you're so smart, and this idea so obvious, why didn't you write about it?
I apologize, I didn't mean to offend you, I was just making a joke. You're actually making a great point I think.
Ahh but you see, only someone who's NOT exponentially smart would fail to see it's true. [0]
[0] https://en.wikipedia.org/wiki/The_Emperor%27s_New_Clothes
[0] https://en.wikipedia.org/wiki/The_Emperor%27s_New_Clothes
1. Author writes and posts article on HN.
2. Commenters criticize article.
3. Author responds to criticism with " why didn't you write this yourself" over and over.
Wow..
2. Commenters criticize article.
3. Author responds to criticism with " why didn't you write this yourself" over and over.
Wow..
Ironically, the author's defensive responses to criticism seem to be the only thing being exponentiated here.
[deleted]
If knowledge and skill is uniformly hierarchically decomposablbe, then everyone can do exponentially more work, over time. Technology's "increasing returns".
But there may be thresholds, such as working memory needed, because the skill or knowledge cannot be decomposed further due to interconnections.
It seems likely there exist some potential skills or knowledge that require more working memory than any human has, had or could ever have.
But there may be thresholds, such as working memory needed, because the skill or knowledge cannot be decomposed further due to interconnections.
It seems likely there exist some potential skills or knowledge that require more working memory than any human has, had or could ever have.
Intelligence is hard to define. I believe that some people are "exponentially" better for very specialized tasks, for instance, solving logical puzzles, or internalizing rhythm in music, but it isn't necessarily noticeable, and doesn't translate to great accomplishments.
Define it rigorously. We have, in terms of the amount of computation in m time steps.
No part of this is remotely rigorous. It all hinges on a few house of cards-like permises.
Nothing about that is rigorous. You still haven't convincingly demonstrated that computation works as a remotely serviceable analogy for intelligence.
Even if the conclusion may be true, I find the argument unconvincing. There exist large differences in intelligence between some species, so it's plausible to think the same could be true within a species.
One doesn’t have to be exponentially smarter than others in given moment – by compounding smart ideas and decisions one can get exponentially better outcomes in time.
Will you say that when an alien being with an IQ of 3,234,876 appears?
Gosh I wish people would stop using exponentially as a synonym for "a lot".
I had the same reaction to the headline, but in this particular article it actually means exponential.
(It does make a leap from computation to intelligence though.)
(It does make a leap from computation to intelligence though.)
They do make a point of saying that they are answering only the very specific argument of "geniuses can solve NP problems with greater efficiency than muggles". Apparently they intend to argue against muggles thinking at n^2 and geniuses thinking at n^3 in future essays.
[deleted]
or HN's favorite, "orders of magnitude"
I have not read the article but in general:
The problem I have with exponential is that you can’t have an exponential difference between two data points. Exponential is a measure of growth which can’t be seen with just two data points. However orders of magnitude can accurately describe the difference between two data points. Even though it is somewhat ambiguous as well (powers of 2,10,16?) orders of magnitude makes more sense than exponential.
The problem I have with exponential is that you can’t have an exponential difference between two data points. Exponential is a measure of growth which can’t be seen with just two data points. However orders of magnitude can accurately describe the difference between two data points. Even though it is somewhat ambiguous as well (powers of 2,10,16?) orders of magnitude makes more sense than exponential.
Are non-base 10 orders of magnitude actually used anywhere? I haven't encountered neither in either physics, CS or any other field (and I'm reading whatever I can get my hands on).
> Are non-base 10 orders of magnitude actually used anywhere? I haven't encountered neither in either physics, CS or any other field (and I'm reading whatever I can get my hands on).
In computer science, using a base of 2 (or a power thereof) for magnitudes is not uncommon.
In computer science, using a base of 2 (or a power thereof) for magnitudes is not uncommon.
I agree that it might make sense in theory, but in reality people use it extremely inflationary to make their comments sound more „science-y“.
Instead of saying „X is orders of magnitude bigger than Y“, why not simply say „X is much bigger than Y“?
Instead of saying „X is orders of magnitude bigger than Y“, why not simply say „X is much bigger than Y“?
If you're discussing a type of object that has such a wide range of magnitudes, describing it as orders of magnitude difference is a good descriptor. For example, the size of stars. One star may be ten times the size of another. Another may be 100 times the size. The next may be 1000 or 10,000 times the size. You wouldn't simply say that stars have a wide range of sizes, you would say that they have orders of magnitude difference. Likewise, you could say that one star may be several orders of magnitude larger than another.
9 is much bigger than 1.
900 is much bigger than 1 and (two) orders of magnitude greater.
900 is much bigger than 1 and (two) orders of magnitude greater.
Or "two football fields"
(without specifying which kind of football)
(without specifying which kind of football)
I don't really think 5% error margin is really worth getting upset about for a rough visualization guide.
An AFL field is about three times the size of those used in most other codes.
The only people likely to think of an AFL field are us Aussies, and only the subset of us that don’t follow rugby union.
And we’re statistically insignificant.
And we’re statistically insignificant.
The other assumption was based on the determinism of the machine. As far as I understand, the brain is not a deterministic computer. We don’t really understand how our brains work at all, but they definitely don’t work in any way shape or form to how we understand a computer to work, this leaving even more possibility for interpretation to an opposite conclusion.
Lastly, what about all the evidence of people who actually did accomplish exponentially more work than others? We have the benefit of the hindsight to check that real quick and, yup, I’d say 100% there are people who have done it. Elon, Jobs, Gates, etc...
However, I’d agree with the author if they argued that we can’t predict who will be exponentially smarter. To do that, we would have to simulate the future or have an algorithm that can tell us, which obviously presents some contradictions.
I think we all just sort have to wait and see.