The Relativity of Wrong (1989) | Hacker News Reader

The Relativity of Wrong (1989)

hermiene.net

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On a related note, sometimes someone may be wrong because he knows more about the subject (but not enough).

A canonical example could be about the "leap year" rules.

For context, the Earth makes a full rotation around the Sun in about 365.2425 days, so we use leap years to compensate:

- add 1 day every 4 years (365 + 1/4 = 365.25)

- but not every 100 years (365.25 - 1/100 = 365.24)

- but add a day anyway every 400 years (365.24 + 1/400 = 365.2425)

Suppose most people only know the first part (1 additional day every 4 years). If we ask "is 2000 a leap year?", they would answer "Of course, 2000 is a multiple of 4". And they would get the correct result.

Now, suppose someone started to study the "subject" (here, there is nothing to study, this is a trivial example for illustration), and is aware of the second rule (but not the third one). He would say "Ahah, no, 2000 is not a leap year, because it is a multiple of 100". But he would get the wrong answer.

My impression is that this kind of mistakes happens often while learning a subject: by studying, we encounter exceptions or surprising facts, that we may apply too broadly (to the point we make absurd claims, but that appear absurd for the wrong reasons).

Far more broadly, think of logic as just a low-dimensional approximation of something complex.

Humans deal with logic and are taught “i before e except after c” etc. But even with describing human languages that may be inadequate.

What AI does is it essentially makes a model by which you can search a latent space quickly — both to clasify input and to generate output.

You can throw the recorded motions of the planets and stars at it and it might find physical laws that have 80 variables while humans want to deal only with simplified versions like Kepler’s laws of motion.

In the vacuum of space those laws may be enough but when it comes to the complexity of chemistry, biology, genetics, politica, etc. the AI might have way better model that we can never understand. Like for dietary recommendations. Would people follow them?

And what if they are wrong in some other ways? Like how humans beat AlphaGo through its blind spot or how you can fool face recognition by wearing a hoodie etc.

The bimodal variation of this is the famous (?) quote about the U.S. civil war, which goes something like: in elementary school, you learn the Civil War was about slavery. In high school, you learn it was about economics. In college, you learn it was actually about slavery.

"A little knowledge is a dangerous thing."

From "A Little Learning," by Alexander Pope

A little learning is a dangerous thing; Drink deep, or taste not the Pierian spring: There shallow draughts intoxicate the brain, And drinking largely sobers us again.

In IT we call those people "power users", the absolute bane of tech support.

In power-user-land we call IT glorified gatekeepers.

Neither would be entirely accurate and not every of either is always one of either and either can be both at the same or different times..

Oh there is plenty of bad IT. But I'd wager at least 2/3 is just overworked and understaffed so the "less important" stuff get sidelined and IT dept just becomes a hole no request comes back from unless your boss yells enough...

This can come up in other interesting ways.

There are human behaviors that appear to be entirely selected for (and then kept around via culture) [0].

In this case a population may do something like have pregnant women avoid eating sharks which are otherwise a normal part of their diet. They don't know why they don't eat the sharks, they just don't. It turns out the sharks contain something that causes birth defects. Commonly people think someone must have realized this and then that original knowledge was forgotten, but it's quite likely it was never known and the behavior was entirely selected (pregnant women that didn't eat the sharks more successfully reproduced).

When you press the women to answer why they don't know, if forced to answer they make something up (it'll give my baby shark skin).

You could imagine someone thinking that's stupid and then eating the sharks and getting a baby with birth defects.

I think this explains a lot about why superstitious belief is so common in humans and animals.

Reason is obviously selectively advantageous, but a little reason incorrectly or over confidently applied can also be harmful, most people are bad at individual reasoning (endless conspiracy theories) and are often better off with consensus.

For every contrarian that unlocks massive value by being contrarian and correct there are ten cranks that just hold false beliefs that potentially harm themselves and others.

[0]: https://slatestarcodex.com/2019/06/04/book-review-the-secret...

Also applies to creativity.

- Knowledge = little ==> little creativity to add something new

- Knowledge = mid ==> great creativity

- Knowledge = high ==> little creativity to add something new

I feel like that's mostly anecdotal. Nobody remembers the "mid knowledge people that did nothing interesting"

Could you please expand on this?

State of the art is that X is impossible. An expert knows that, and therefore does not pursue it.

A non-expert doesn't know X is impossible, pursues it and solves it.

I don't have any specific example, though.

There's a famous story that's a good example here, I think: George Dantzig solved two open problems in statistical theory, which he had mistaken for homework after arriving late to a lecture at university.

https://en.wikipedia.org/wiki/George_Dantzig

> In 1939, a misunderstanding brought about surprising results. Near the beginning of a class, Professor Neyman wrote two problems on the blackboard. Dantzig arrived late and assumed that they were a homework assignment. According to Dantzig, they "seemed to be a little harder than usual", but a few days later he handed in completed solutions for both problems, still believing that they were an assignment that was overdue. Six weeks later, an excited Neyman eagerly told him that the "homework" problems he had solved were two of the most famous unsolved problems in statistics. He had prepared one of Dantzig's solutions for publication in a mathematical journal. This story began to spread and was used as a motivational lesson demonstrating the power of positive thinking. Over time, some facts were altered, but the basic story persisted in the form of an urban legend and as an introductory scene in the movie Good Will Hunting.

Love that story.

I think I get it. Applying lateral or novel thinking to a problem unfamiliar...

The true expert realizes what question is being asked, and grabs a calendar.

Two people, equally knowledgeable and given the same problem, will not necessarily come up with the same solution. Leap years are not a mathematical fact; they are an engineering solution to a mathematical challenge. An expert looking at orbits is unlikely to decide that we must specifically add an extra day to February; you only know that we use this solution by deriving it from calendars.

A simpler example may be that a person with one clock knows the time, but a person with two clocks is never quite sure.

It's a popular phrase, but it doesn't make sense if you think about it. The person with two clocks can average the time of both of them and get a result they can be more confident in than the person with only one.

That only works if both clocks are wrong in opposite directions and so confidence wouldn't be appropriate. Taking the average might work if you've got a whole bunch of clocks and they show a distribution such as a bell curve - that's what's required to become more confident than the single clock owner.

I'm assuming the error of every clock has the same probability distribution. I think this is a reasonable assumption, because the phrase only mentions the number of clocks. In this case, the more clocks you average the lower your expected error.

But with just two clocks, the distribution isn't evident. They could both be running fast and thus the average would be worse than the clock showing the earlier time. You'd have no way of knowing without consulting more clocks.

Also, with clocks you should be measuring the rate at which they measure time. Typically clocks can run fast or slow which means that the time shown is a function of how long they've been running since they were last correct.

It's possible for the person with the single clock to get lucky and have a more accurate time than the average, but the original quote says "knows the time". Using the traditional definition of knowledge as "justified true belief", somebody with a lucky clock does not truly know the time. Their belief is true, but not justified. It's really the person with multiple clocks who has more accurate knowledge of the time. The more clocks they average the more justification they have for their belief.

The single clock owner doesn't have to be especially lucky. Imagine if they had a clock that was two minutes fast and the dual clock owner had one that was merely a minute fast and the other was ten minutes slow. The average would be less accurate, despite owning the most accurate clock. Two clocks just don't work for statistical analysis (three clocks are unlikely to help either).

Also, the single clock owner is justified in believing that they have the correct time as there's nothing to suggest that they could be wrong. Two clocks introduces doubt where there was none before.

Rather than using "justified" true belief, humans tend to go for the easier option and would be more likely to go to the person with just one clock, until they find someone with enough clocks and clout to point out the likely correct time.

I have many clocks and typically I am sure about the time. I keep them in sync or know which one is off.

Sorry for the offtopicness but could you please email hn@ycombinator.com?

I don't mean to pester you but there's an important issue with your account that we need you to know about.

How do you keep them in sync? I bet you're using an established time source.

Walk around with a wristwatch. Even if the watch isn't synced to something authoritative, you can still use it to get all the clocks the same as each other (and the watch).

What if the watch runs fast - how do you synchronise the other clocks to an untrustworthy watch? For extra points, assume that the clocks are all in different rooms so you can only see one at a time and it takes an unknown number of seconds to go from one room to another.

The easy answer is that the watch doesn't run that fast. If it runs, say, 10 seconds fast a day (which is a lot), then if walking from one room to the other takes a minute, the watch is off by... 0.007 seconds. I'm not going to be setting the clock that accurately.

But if the clock just runs consistently fast (and if I know how fast it runs), then I can use the watch to measure how long it took to walk from one clock to the other, and from that I can compute the correct time to set the second clock to.

How could you know how fast it runs without comparing to an accurate time source? Maybe it's running slow and you don't even realise it.

Well, I can compare it to all the clocks.

But, you know, if I have no accurate source of time, why do I bother having a watch and N clocks?

You're a clock collector?

This follows a pattern I've noticed where an expert's approach may seem similar to a pure novice's. With only the intermediate practitioner seeming to follow any rules.

This is so common there's a meme template :)

https://pbs.twimg.com/media/FffvEX5UAAAysZC?format=jpg&name=...

First you learn the conventional wisdom.

Then, you learn that the conventional wisdom is wrong.

Finally, you learn that you didn't actually learn the conventional wisdom the first time around, typically by rediscovering it yourself.

I think this is pretty much what the term "midwit" refers to

  Socrates then, by a series of ignorant-sounding questions, forced the others into such a mélange of self-contradictions that they would finally break down and admit they didn't know what they were talking about.

  It is the mark of the marvelous toleration of the Athenians that they let this continue for decades and that it wasn't till Socrates turned seventy that they broke down and forced him to drink poison.

It's seldom pleasant to be (accurately) instructed in your own ignorance, particularly by someone pretending not to know anything. Asimov's theory that Socrates' death was a result of his habit of patronizing everyone rather than the actual charges is plausible.

Also, in internet arguments, there's nothing more infuriating than the other person appointing themselves as some kind of modern-day Socrates and "teaching" you.

Forgive me, if I may be so kind as to ask, but what makes you think such people are trying to "teach" you?

Hm, that's an interesting question. What makes you want to ask this?

There can be a balance here. Often I’ll have a viewpoint and when I hear a different one, I won’t immediately say I disagree. Instead I’ll ask questions to discover where the gap in our understanding lies. Then, it may be helpful to share that I have additional knowledge (I’d I do), or to learn something I was missing, or to recognize we value different things and move on. Immediate disagreement is often far less productive.

Methods for coming to understanding between parties acting in good faith really fascinates me. One thing I've noticed is the fundamental crux often lies with some assumption each party finds so fundamental that they wouldn't bother to state it, and don't even necessary realize they hold the view *.

As a gross example, my wife told me the other day of a buyer of some CraigsList item that called to say she couldn't find our address. They went back and forth each getting more and more flummoxed by the other's statement of what streets were where. Finally it was discovered that the caller was in Cambridge, Ontario, having misnavigated CraigsList, while we were in Cambridge, MA.

It is mistakes so fundamental as these that are hard to discover. One help I've often found is to bring in a fresh third party.

* Saying to "state your assumptions" seems futile to me. There are too many. The sun will rise, time will continue to tick by at the same rate, your friend didn't change his name yesterday, Coke still sells soft drinks.

As a counterpoint, people acting in bad faith can continue asking questions. It's usually known as "sealioning"

https://wondermark.com/c/1k62/

Like many people, I took a college course that talked all about Socrates and we read the Apologia and stuff.

I had assumed that it was basically all fiction. That there was some guy who kept being annoying by asking questions, so much so that he was put to death, it's just a little too cute to be historical fact.

And that all of us discussing this stuff as if it actually happened is actually just an exercise in reiterating the truthiness of the underlying idea; that if we said it was fiction at the start, we'd be doing lit analysis, rather than philosophy.

Right?

No, there's pretty good evidence that Socrates did exist, though there is debate about what he actually believed and taught, since in Plato's later dialogues the character of Socrates typically was advancing Plato's position. See here: https://en.m.wikipedia.org/wiki/Socratic_problem

I don't necessarily mean that Socrates is a totally fictional character. Just that basically everything we know about his "character" is made up.

Like, he did exist, but the Socrates that we know doesn't talk like that, didn't have those ideas, wasn't that clever, didn't do any of the stuff described, wasn't put to death in such a fashion, etc. Those were all just made up as a way for Plato to forward his ideas; because in those days you couldn't just dryly talk about ideas, you needed to have characters and a story and so on.

If you're going to assume that, then why not assume that Plato was equally made up and just a story?

The impressive thing about Asimov — incidental to the quality of the writing — is he probably sat down and blasted that out in an hour top-to-bottom with no edits. Volumetrically one of the most impressive authors in history.

There's a funny story in one of his essays where he's talking to Heinlein about this strange habit other writers have of endlessly redrafting.

"I just write down the first draft, read it through from start to finish and write up the second draft, and that's it," Asimov says.

"What's the second draft for?" Heinlein says.

This seems in contrast to Borges, who was never done with corrections and redrafting, going as far as to buy back an edition of a book already in print so that he could make additional corrections (or so the story goes...).

Anyway, I'm a fan of Asimov.

One supposes Borges was able to arrive at the final copy by alternately holding up the first and second drafts in any predefined pattern he wanted...

see also: George Lucas "fixing" the star wars movies and making the originals impossible to find.

Have you ever seen the first draft of Star Wars? It's pretty bad.

I'm a fan of Borges.

It made the point in the first few paragraphs and the rest was a long winded beating of a dead horse. It could have done with more editing.

Not me. I’d like a lot more. Particularly I’d like this part fleshed out:

> This particular thesis was addressed to me a quarter of a century ago by John Campbell, who specialized in irritating me.

I only know of Campbell from “A Hero With a Thousand Faces”. I’d love to read more about how Campbell specialized in irritating Asimov.

> I’d love to read more about how Campbell specialized in irritating Asimov

Campbell (John, not Joseph; you got the wrong Campbell) specialized in irritating lots of people.

First, he was one of Scientology's early advocates (Dianetics, actually), and all kinds of pseudoscientific ideas. Even other scifi authors thought this weird.

His pseudoscientific ideas obviously clashed with Asimov's atheist and rational mindset about the world.

Campbell also bought into bizarre scifi/racist/supremacist theories which were not well received by his fellow authors. He was very pushy and meddlesome as an editor -- that alone wasn't unusual in scifi & pulp magazines of the time -- but he was also obsessed about specific and weird directions that he insisted most stories he published must follow.

For example, Philip K. Dick didn't really like Campbell's insistence that most scifi stories must feature telepaths, and also that telepaths must be benevolent and superior and take over humanity. PKD thought this reminded him too much of Nazi "master race" theories, and didn't like Campbell as a result.

The one good thing in Campbell's record: he wrote "Who Goes There", the original story then turned into the "Thing" movies. The story is quite good, too!

Thank you for clarifying my mistake!

You might be thinking of Joseph Campbell, not John Campbell (https://en.wikipedia.org/wiki/John_W._Campbell)

Thank you for clarifying my mistake!

The author of “A Hero With a Thousand Faces” is Joseph Campbell. I think he might be talking about John W. Campbell who was a fellow sci-fi author.

Thank you for clarifying my mistake!

Going from discussing the curvature of the Earth to the finite speed of light wasn't to dunk on the student, it was to demonstrate the increasing relative correctness of our universal theories.

I suppose I would've been more engaged if I didn't already know all of these historical anecdotes. As it is I quickly began skimming.

This is a very common thing in writers from the 1920s to the 60s---they made their living selling articles to magazines that paid a fraction of a cent per word. If they wanted to eat, they had to hammer something out as fast as physically possible.

Interestingly, this highlights that despite popular belief, the scientific process is not about being right or wrong but rather what's powerful.

A theory is promoted because it is powerful in explaining observations and providing tools for humanity until it is improved by the next one. You can build a gun with gravitation but you need relativity for a rocket.

Quoting from the article "Newton's theory of gravitation, while incomplete over vast distances and enormous speeds, is perfectly suitable for the Solar System. Halley's Comet appears punctually as Newton's theory of gravitation and laws of motion predict. All of rocketry is based on Newton, and Voyager II reached Uranus within a second of the predicted time. None of these things were outlawed by relativity."

We need relativity to correct the atomic clocks on GPS satellites so as to maintain positional accuracy to a few feet, but getting the satellites up there needed only Newtonian mechanics.

All models are wrong; some models are useful.

> the scientific process is not about being right or wrong but rather what's powerful.

Ugh, this is something that bothers me all to hell and back about the non-scientific minded.

"Your science was wrong about (this minute detail), therefore whatever completely made up bullshit I thought up without any supporting evidence is totally valid"

Asimov is such a poignant writer, I can't help but smile when I read him.

I’m glad he decided to invent an English Literature correspondent to pick on, and also the 1990s was a better society than one that votes to poison a disliked person.

It is also funny that he gave this character the name of one of his editors, who he actually disassociated from when said editor started going a bit off the rails.

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As much as I enjoy Asimov, I have to say that he is wrong. The gap between what we know and what is true might have decreased immensely, but it is still infinite. Any quantifiable increase is 0 in relation to infinity. Asimov's counter-argument that we are quantifiably less wrong than we were in the past simply does not overcome this core issue. If there is an infinite amount of knowledge separating what we know from what is true, then we can learn an infinite amount of things and still have an infinite amount of things left to learn.

To feel justified in thinking the universe is "essentially" understood is to be OK with one's concept of the "essential nature" of the universe to be inherently divergent from a future concept, which according to Asimov's own argument is going to be more correct than our own.

To me, it reads as a bitterness towards mortality, a sort of sour grapes: the insights we will have about the universe at some future time must not be very interesting compared to what we know now, because I won't be around to know them.

edit: I guess I shouldn't be surprised that Asimov's perspective is shared here. It's very easy to understand the essential nature of the universe when you define the universe as the parts you understand.

I don't think human beings in 1000 years will look at our current understanding as special in any way. As transformative as our era is, it will be dwarfed by the scale of transformation in future eras. It's just the most transformative era so far. That's temporal bias, nothing more.

One way to see Asimov's "infinity of wrongness" is perhaps as a fractal. You could view the bulbs in the mandelbrot as being a kind of knowledge, and the "main bulb" occupying the majority of the area belonging to the set as the set of truths known about our universe. The mandelbrot set is infinite in complexity, however its area is finite and bounded!

Or as ironing out the wrinkles on a great big t-shirt, where each wrinkle is sub-wrinkled with smaller wrinkles and so on. We've "ironed out" the biggest wrinkles, there are infinitely more but they are much smaller. We're perhaps over half-way ironed, in a quantitative sense.

I disagree fundamentally. You may as well ask me to imagine Earth as a disc, with multiple rotating spotlights shining down on it and a giant ice wall around the edges. I understand what the image is trying to convey, I simply do not agree that this is the shape of the thing I experience.

I think you missed the entire point of the essay. You should actually read it.

Science is incremental, revolutions in science mostly just adjust the edges of our knowledge, at more and more extreme corner cases (extreme high energies, extreme high/low temperatures, etc). No, we absolutely don't know it all, but as always, new knowledge and theories will only affect those edges, and refine the predictions for the nth+1 decimal place.

By and by, the science that directly affects our daily lives has remained stable and most progress has been in the engineering to put all this knowledge to practical and efficient use.

I like how in English one can make it appear if one is skilfully and logically dismissing an argument without actually even trying to. I don't presume that this was your intent, but the phenomenon is quite interesting and I quite confidently believe dangerous (in that it contributes to some degree to inaccurate models in the minds of those who ingest such text, and those models are what drive action, much of which is harmful...which is easy to see in {choose your outgroup}, but far less easy to see in one's ingroup).

I think your use of infinity isn't particularly helpful here as it leads to the contradiction that knowing more doesn't lessen the knowledge gap, whereas it does appear to do so.

Maybe, a better interpretation would be that as we learn and understand more, we approach the limits of knowledge. Now it may take an infinite amount of knowledge to actually reach the limits of knowledge (c.f. an infinite series can approach a finite value, but takes forever to get there), but it can still be shown that we are getting nearer.

The other aspect is that as we understand more, we appreciate that there's even more to understand, but that can be thought of as our precision increasing and looking at the available knowledge in greater detail.

There is no contradiction because there is no limit of knowledge.

The limit of y = e^x is infinity. You can keep increasing x and y will increase exponentially. So you plot the function, let's say with the x axis going up to 10 and the y axis going up to e^10. The graph shows very clearly that, while there was progress before, we have even more progress now. Exponentially more, even! What came before is dwarfed by what we have now; if you look at the range of y for x values 9-10 you can see how little of a difference all those others values (1-8) had between one another, compared to the changes we have now. The rate of change is so high that we're basically in an era of semi-complete knowledge. We must be at some kind of inflection point, this is truly a unique era of understanding.

Then you repeat. Set the x axis to 100, and the y axis up to e^100. Oh wait, it's the same graph. That's because it's always the same graph. It's scale-invariant. The slope at every point is always whatever y is.

We're always at right at the limit of explaining the "essential nature" of the universe because the "essential nature" of the universe can only be (to us) what we can understand it to be. We chose e^10 as the limit of the y-axis in our first exercise because that's all the knowledge we knew about. We chose e^100 as the limit of the y-axis in our second exercise because that, too, was all the knowledge we knew about. Choosing these random values as the limits of our function (i.e. the limit of the "essential nature of the universe") leaks information into the visualization that will always paint a picture showing that we're at the most transformative time there ever was.

When we do it that way, we will always come to the same _wrong_ conclusion. We will always dwarf what came before and be dwarfed by what comes after. To think that we're actually living in an inflection point is hubris, it's wishful thinking, it's the sour grapes of mortality.

> There is no contradiction because there is no limit of knowledge.

I don't think we know enough to be able to state that definitively. It's feasible that the universe behaves mathematically (it seems to so far) and thus possible to gain a thorough understanding of the underlying principles, if not the specific facts (c.f. with understanding how to produce integers yet not "knowing" all the integers).

Even if the universe doesn't have underlying rules to be discovered, there's still a limit to number of configurations available to particles etc. within our visible universe. Although that number might appear to be infinite to us, it's actually drastically closer to zero than to infinity.

So, if there is indeed some finite limit, then using y = e^x would be the wrong function as that doesn't approach a finite value.

This leads to a more fundamental question: What is the universe?

Is the optimal move in an a given chess board considered knowledge? If so, can't we create entirely new sets of knowledge from the emergent properties of an arbitrary set of rules called a "game"? If we can create an infinite set of arbitrary combinations of rules and states (games), then knowledge should be infinite. Maybe not all knowledge is scientifically applicable, but we have learned a great deal about science and engineering from studying chess. In fact, we are starting to learn more about learning as a process and not as some magical thing that human beings can do, just from studying the best way to make decisions in this totally-contrived and scientifically-useless game.

Taking this a step further, let's look at the animal kingdom. If learning about the intricacies of the mating habits of birds can help an arbitrary bird increase its impact on the future gene pool, is that knowledge not worth something to the bird? To bird society? Are the things we learn about ourselves knowledge? They certainly have utility. Is there any limit to what we can learn about ourselves, about the stochastic process of life? Is life not part of the universe?

Is computer science even knowledge? It seems if we're more directly concerned with the physical nature of the universe, we ought not to care about what the system of a computer actually does; we only need to care about what it is, about its physical structure. Except, that's not actually how we pursue knowledge or science at all.

In my view, Asimov's sentiment can be reduced to a complete tautology: we're at the point where we know almost everything there is to know about the things we think we can know.

There aren't an infinite number of chess positions, moves or even games, so that's not a good example. It's possible to come up with a number game that could have infinite possibilities, but that doesn't mean that the universe could even contain some of the options within our visibility. Our current state of knowledge about the universe strongly suggests that there's a finite limit to the available knowledge (I.e. between the Planck scale and the visible horizon due to the speed of light).

A googolplex looks to be the first number we've found that is too big to be contained in our universe.

You're right--chess is a decidedly finite game. Even so, we have not "solved" this simple, finite game--not even close! If we're not close to solving such a trivial game, how can we be close to the limit of the knowledge of the universe?

A googolplex is "too big to be contained" in our universe yet here we are talking about it. We can perform operations on this number, compare it to other numbers, and even come up with mathematical proofs showing that it's too big to exist. There are an infinite amount of numbers larger than a googolplex and we could have an infinite amount of conversations about them. The material limit of the universe does not limit our ability to create information, to learn things.

There isn't enough space in the universe for an infinite series, either, yet we can (and do) still use them, we reason about them, we learn from them. We can even reduce some infinite series to a finite number. The material bounds of the universe are not a limit of knowledge.

I think you're mistaking the map for the territory. A googolplex is a representation of a number, but not the number itself, although it's simple enough that we can get away with using the representation as it's obvious what the form of the number would be. However a number such as tree(3) is unimaginably bigger, but more crucially, we don't know anything about the form of the number beyond its size and we can't sensibly use it in calculations.

Now both of those numbers are finite and we could try to figure out how many numbers we could "describe" such as tree(3), but that would be limited by the number of symbols (i.e numbers, operators, letters and words) that could be used (i.e we would have less than a googolplex different numbers that could be represented using maths, language and thought). That's still going to be a finite number.

If the Universe is the territory than Knowledge is the map. I'm not at all mistaking the map for the territory: I'm pointing out that the set of maps that can describe a given territory are virtually infinite. Asimov is saying the map is almost complete and I'm saying there are an infinite number of maps left to go.

Cartographers in the 18th centuries were "basically done" mapping out the Earth. In the 20th century we were able to use satellite imagery to get the "full picture". Does that mean we have perfect knowledge of the Earth? Absolutely not. There is never a final frontier of knowledge.

> The gap between what we know and what is true might have decreased immensely, but it is still infinite.

The other two commenters have taken different approaches to infinity, but it seems that your argument doesn't hold even for a plain-as-in-real-numbers infinity.

Being satisfied with finite knowledge gains, I have no hope to achieve 1% of infinity (or any other fraction of infinity).

The universe is infinite in size, another assumption. If I'd fly on vacation to Tenerife, a quantifiable shift of my position by mere thousands of miles would be "zero in relation to infinity". Yet, it's not unimportant for my rest. Talking about infinity doesn't automatically cancel all the finite measurements and bring them to zero.

One might plausibly assert that while the particulars of the universe may be infinite, the fundamental rules which govern the universe are finite and thus at least in principle entirely knowable. While I don't think the 20th century makes an air tight case for the latter, I think it isn't an unreasonable conclusion to draw from 20th Century Physics either.

It's surprising that we find ourselves in a universe which does appear to obey certain laws. There's a whole bunch of assumptions made to help us understand how things work and it turns out they're mostly correct. i.e. It's more astounding that we CAN understand the universe and how well maths can act as a model/language to understand it.

Not that surprising. A universe without predictable laws would be unlikely to host life. I mean physics really only knows how to do statics and oscillations and those things work because many systems are at equilibrium or just slightly perturbed from it, probably because of the mysterious low entropy condition which defines the past.

Well, we can start by asserting that we do not know everything. We can assert this from the contra positive: If we did know everything, then we would have an acceptable solution to all of our problems. Since we do not, it stands to reason that we don't know everything.

Once we accept that the assertion is valid, then it raises the likelihood that our understanding of the world is incomplete in some way. And furthermore is incomplete to different degrees along multiple dimensions of knowledge. Whether incomplete or wrong is a word choice, it doesn't change what's missing. So with each new discovery, our understanding improves, our wrongness decreases.

> If we did know everything, then we would have an acceptable solution to all of our problems. Since we do not, it stands to reason that we don't know everything.

This can be proven false by contradiction: it may be possible to _know_ that one of our problems has no solution.

> This can be proven false by contradiction: it may be possible to _know_ that one of our problems has no solution.

This claim requires a bit more explanation, not sure if possible. Can you elaborate, or use an example?

It's amazing the amount of people who dismiss current findings by claiming we were wrong in the past, so nothing can be trusted.

I think people just yearn for certainties and unchangeable anchors in reality, which is why the beliefs that something is designed made by one constant being or force of nature are so prevalent.

"You told me this is reality and now it changed, why I should believe in it again?"

Schools don't get into people's heads how science works enough, and how it is less "discovering the truth" and more "narrowing the uncertainty on how stuff works"

Absolutely!

> "You told me this is reality and now it changed, why I should believe in it again?"

Because that's not what "belief" ought to mean. When you were told that scientific thing in the past, you should have been told that it was believed to be that way using this flawed collection of evidence, analyzed and synthesized by imperfect intelligences, which should have lead to that postulate about reality holding an asterisk with whatever degree of confidence it deserved.

If that uncertainty is something you can't accept, maybe science (and reality) is not for you. Try mathematics instead.

Well. For me, Immanuel Kants' (1724-1804) "Ding an sich" (The thing in itself) lays the groundwork for modern science. My translation would be: "Since our senses are so easily fooled, we will never grasp the thing in itself." IMAO a reasonable scientist says: "We can only say what is least likely wrong." Can you win elections with sentences like these?

I'm dumb and ignorant, therefore we all are.

Well, yes, but some more than others.

It is an over reaction, but it is true. in both fields.

Scientific: scientific knowledge on a subject is never solved. it merely approaches the solution. it was wrong in the past, it is less wrong today, but still wrong.

Cultural: The cultural truths of today were wrong in the past and will be wrong in the future.

I think the correct take away is not so much "nothing can be trusted" as it is "trust, but verify"

There is no parallel between scientific knowledge and whatever you're calling "cultural truths". To the extent that there is lasting progress in culture, it is through art, music, and literature, not through "truth". Truth is the realm of science alone. Yadda-yadda genital mutilation: that is not culture, it's ignorant cruelty, and science can indeed show that, by showing that it causes health problems, causes pain even in babies, brings none of the claimed benefits, etc. Most of the old-hat cultural-relativism arguments come down to plain-old scientific ignorance, just as if there were cultures out there that still believed the Earth is flat. Those are not "cultural truths", they are scientific ignorance.

> "trust, but verify"

We're talking about the collective knowledge and understanding of all of humanity. How are you going to verify for yourself the value of the Planck constant and the exact curvature of the Earth and the exact age of the Universe? Are you going to build your own $50-billion particle accelerator to verify the existence and strength of the Higgs field? Through decades of study you may get to the point where you can indeed verify one of the millions of foundational truths that we build further knowledge upon.

"Trust, but verify" doesn't belong here. You should not "trust", nor can you possibly "verify". It's more like "understand". These truths must fit together cohesively, or if they don't, it should be glaring unsolved problem (e.g. gravity vs. quantum mechanics). Test new ideas against the rest of the theory to relentlessly look for contradictions or poor fits. Develop your mental model. You never need to really "trust"; everything has a wrongness error-bar around it. The wrongness error-bar of the shape of the Earth is very small; it includes subtle corrections due to slight variations in the gravitational field and the pull of other bodies, but it does not include a flat Earth.

> that is not culture, it's ignorant cruelty

Being ignorant and cruel does not make something separate from culture. Many things in culture are ignorant and cruel. Being demonstrably unhealthy and without benefit is also tangential to being part of culture. Even science is not separate from culture: science has a culture, with its own biases, as has been shown many times.

> Truth is the realm of science alone.

That's interesting. Mathematicians might say truth is the realm of mathematics alone. Philosophers might say they claim it, or nobody does. I think you just have to define what you mean by truth (is it eternal and unchanging?), and once you do that, you open the doors to a lot of other reasonable claimants. This is not an argument for relativism, this is me saying there are different kinds of truth, not that there is no such thing as truth, or that there is no such thing as falsity.

>Truth is the realm of science alone.

This statement isn't a scientifically based statement nor could it be one since science can't measure the truth-value of epistemological claims - your claim can't be true by your own standard.

HN comments are small and my comments are limited by the amount of procrastination my day is able to endure. "Truth is the realm of science alone" is a lot of things significantly abbreviated into a pithy and over-simplified HN comment. You could levy the same criticism at almost everything anyone ever says on an internet forum, including "scientifically based statement" (whatever that means) and "science can't measure the truth-value of epistemological claims".

I'm asserting that the only useful definition of the word "truth", and the core of the definition that almost everyone is actually grasping at when they talk about "truth", is the particular kind of truth that science seeks, and any other definition of "truth" inevitably leads to statements that would be "true" under that definition but clearly nonsensical. Basically if you want "truth" to act "truthy" in all the ways we expect "truth" to behave, then your definition of "truth" is exactly the one that is sought by science and nothing else (here I am including mathematics as a branch of science, even though it's probably better to think of it the other way around).

Here's my definition of truth: the body of statements which are self-consistent with some set of pre-selected axioms. A false statement is one which is inconsistent with those axioms. Plenty of statements are neither (e.g. "this statement is false").

You claim this is not a "scientifically based statement", but really it's just a definition, plus an assertion that other definitions are not useful. The latter is actually falsifiable: show me a useful definition of "truth" that doesn't reduce to this definition. Of course I haven't given you the exact criteria for doing this nor evidence that my assertion is correct, but this is an HN comment; what do you really expect?

> science can't measure the truth-value of epistemological claims

I don't see why that should be true. I can claim to have certain knowledge and science can test me on those claims. If your definition of "epistemological claims" only includes those philosophy-ejaculate sentences that cannot be tested by science, then your definition is useless and boring.

>If your definition of "epistemological claims" only includes those philosophy-ejaculate sentences that cannot be tested by science, then your definition is useless and boring.

The entirety of your post above is comprised of sentences that cannot be tested by science. There's lots that can't be tested by science like mathematics (no mathematical truth has ever been proven by science), logic (no syllogism can be proved by science), epistemology (no claims about truth per se or what knowledge is per se or how one can gain knowledge can be proved by science), philosophy of science (most of your post was not science but the kind of blundered epistemology and philosophy of science folks who haven't studied the topics repeat), etc. The problems here have been hashed out by philosophers of science, worth re-examining your biases against primary forms of human reasoning here.

Since science is rooted in mathematics and logic, hopefully you at least admit of the possibilities of truths there. And if you spend some time learning about these things and actually think them through, you'll eventually realize the inevitability that those truths can only. be meaningfully true if you have space for the possibility of other philosophic truths in spaces like epistemology. Worth considering if there's a possibility of ethical truth as well, might not be a great idea to throw that out.

> The entirety of your post above is comprised of sentences that cannot be tested by science.

I've literally given you a falsifiability test. Most of my sentences are not "claims", only claims can be tested, and all of my claims can.

> Since science is rooted in mathematics and logic, hopefully you at least admit of the possibilities of truths there

Honestly this makes it clear you're not even reading my full comments, because I address this directly. Whatevs, nobody is obligated to read what I write, but if you haven't read it, why reply?

> if you spend some time learning about these things and actually think them through

> the kind of blundered epistemology and philosophy of science folks who haven't studied the topics repeat

Gatekeeping and personal attacks. It takes a lot of hubris to believe that anyone who has reached a different conclusion than you must have not studied the subjects. "Well if you actually thought about this, you'd realize..." has never convinced anyone of anything except that you're clearly not worth talking to.

(0) is a great book that explains very neatly why even long disproved models of physics were right, only less right then newer models.

(0) https://en.wikipedia.org/wiki/Reality_Is_Not_What_It_Seems

"Virtually all that we know today, however, would remain untouched and when I say I am glad that I live in a century when the Universe is essentially understood, I think I am justified."

I think most people at most times would have agreed with that.

But the difference would be in the meaning of "the Universe"; the "basic rules of gravity" would hardly be the important part to most peoples at most times.

Oh, and...

"I received a letter from a reader the other day. It was handwritten in crabbed penmanship so that it was very difficult to read....however low on the social scale..."

Nice.

"*I received a letter from a reader the other day. It was handwritten in crabbed penmanship so that it was very difficult to read.

I get the sense that Dr. Asimov was too little of a "people person" to usefully discuss the all-too-common human urge to tell others that you are right, and they are wrong. Or positive ways to handle that urge.

OTOH, he may have been quite aware that "read more Asimov, and be more smug about being right more often" was a major motive for people buying his non-fiction writing.

Asimov was a people person though. He wasn't a nerd in the typical sense; he went to parties, conventions, meetings, mingled with people, belonged to multiple clubs, etc.

From Wikipedia:

> "Asimov was an able public speaker and was regularly hired to give talks about science. He was a frequent participant at science fiction conventions, where he was friendly and approachable. He patiently answered tens of thousands of questions and other mail with postcards and was pleased to give autographs."

I think that, in driving home a valid point, this essay gives the wrong impression of Asimov as someone who would scold his readers.

This:

http://www.asimovonline.com/oldsite/future_of_humanity.html

is a transcript of a 1974 talk/lecture that shows how fun and modest he was, while still delivering a lot of interesting points to ponder.

> Those people who think they know everything are a great annoyance to those of us who do. -- Isaac Asimov

Useful discussion is an interesting scope for someone with the broad, in-depth knowledge of a vast array of subjects he demonstrates in the linked essay.

Funny, if you like this particular variety of snark. But there's a huge bait and switch in the argument. The English major doubts that we have "finally got the basis of the Universe straight" (in Asimov's words). But Asmimov's primary example of the "relativity of wrong" is the shape of the Earth, which is a particular fact about a particular object. Being charitable, almost no-one (not even the kind of English Lit majors that HN loves to hate!) doubts that we can learn facts about the shape and size of particular objects. It doesn't necessarily follow from this that we should be optimistic about the fundamental correctness of our best theories in the physical sciences. As the English Lit major was no doubt aware, there were plenty of people at the turn of the 20th century who thought that physics was basically finished and that there was nothing left to do except add more decimal places to the results.

I don't think that's quite right. Another example given by Asimov is Newton's equations, which are obviously not facts about a particular object. We still today accept them as right (in the right contexts), teach them in universities, and use them when they're useful.

I think Asimov's point is that if someone in Newton's time said "I'm glad to live in a time when we finally understand everything there is to know about the motion of cannon balls", they'd be justified: even though technically there were relativistic corrections to be made, they're pretty much irrelevant for the stated purposes (understanding how cannonballs move). And so in the same way he thinks he's justified in saying that in the 20th century we finally understood the basics of the Universe, even though we still don't know (in his words):

> the nature of the big bang and the creation of the Universe, the properties at the center of black holes, some subtle points about the evolution of galaxies and supernovas, and so on

I don't think the cannon ball example quite works because 18th century fluid dynamics wasn't up to the job. (People weren't firing cannon balls in a vacuum.)

Apart from that, I take your point, but I don't find Asimov's attempt to argue that Einstein's theory is just a minor correction to Newton's very convincing. If this were really the case it would make it a bit of a mystery why Einstein was a big deal. The two theories make very similar predictions in a wide range of circumstances, but they're very different conceptually. Asimov is similarly breezy about quantum mechanics, but physicists at the time didn't seem to see quantum mechanics as just a very minor adjustment to classical physics.

Except you don't need fluid dynamics for cannon ball trajectory over sufficiently short distances, or with the constraints on barrel quality and reproducibility of the time.

The same is true of quantum mechanics: physicists were excited about it, but it went going to make existing experimental results and predictions incorrect in context.

The Bohr model of the atom is completely "wrong" but it's still useful enough to foundational in understanding nuclear magnetic resonance analysis.

Yes, scientific progress tends to be empirically conservative. But people outside science (like the Eng Lit major) are often less interested in specific predictions than in the overall picture of reality painted by our current best scientific theories. This picture does change quite radically from time to time. The history of different models of the atom (going back to the radically incorrect 'plum pudding' model) is a good example. To point this out is not to attack science. Indeed, science would be far less interesting and exciting if its entire history was nothing but a sequence of small and incremental refinements.

Very much agree...and furthermore:

> It doesn't necessarily follow from this that we should be optimistic about the fundamental correctness of our best theories in the physical sciences.

The disagreement was over the universe, so my first question is: does "the universe" include humans, or not (and: who decides the fact of the matter)? Because all one has to do is watch the news to realize we certainly don't have everything fully figured out....I often wonder if our (from my vantage point anyways) belief that we "pretty much"[1] do may exacerbate this.

[1] Colloquial language, figures of speech, etc are a fantastic and endless source of delusion, that typically cannot be realized.

The real response to the guy is, "so what". Who cares if we used to be wrong, that's how empiricism works, we posit falsifiable claims until they're proven wrong.

New life goal: "There is very little that is new to me; I wish my corresponders would realize this."

Second life goal: To have corresponders

Asimov had a humorous style of writing. Of course when he wrote "there is very little that is new to me" he was aware of how arrogant that sounded; he's playing this for laughs. He could also be quite self-deprecating.

Every VC and founder needs to read this post - there are no absolute rights or wrongs. So, whatever worked for Google will not work for Instacart.. whatever thesis of investing worked in the last decade will not work in the next decade.. Start from first principles!

I guess all models are wrong but some of them are useful. And more useful than others—

> In the first sentence, he told me he was majoring in English Literature, but felt he needed to teach me science. (I sighed a bit, for I knew very few English Lit majors who are equipped to teach me science, but I am very aware of the vast state of my ignorance and I am prepared to learn as much as I can from anyone, however low on the social scale, so I read on.)

I couldn't imagine writing the parenthetical.

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