To use a concrete example: Kekulé conceived of the structure of benzene after having a dream where he saw an ouroboros.
The intuition is, then, crystalized in a representation of the structure of Benzene, which chemists already know intuitively. If they had only abstract, non-intuitive knowledge of the form of Benzene, they would have difficulty mapping such knowledge to e.g. spacial diagrams.
Intuitions can be more or less refined/crystalized in such a way that they can be more precisely specified, be more analytically tractable, be loadable to more different minds, etc.
Good teaching transfers intuitions, not just abstract knowledge.
Should we ask chemists to take melatonin for more vivid dreams?
If continued progress in chemistry requires insights like Kekulé′s, then, yes, why not?
The reason this is bad is because it is indicative of bottom-line thinking.
Couldn’t it be the case that is it bad for both reasons? I don’t think you’ve offered an argument that Person A’s reasons don’t apply.
Couldn’t it also be the case that the claim is already known through intuition, and proving it is the main problem? Of course checking against more things will produce higher confidence, but confidence can still exceed 99 percent before doing other checks. (Discarding disconfirming evidence is, of course, epistemically bad because it’s failing to update on observations, but it’s also possible not to find such evidence in the course of searching)
The intuition is, then, crystalized in the form of Benzene, which chemists already know intuitively. If they had only abstract, non-intuitive knowledge of the form of Benzene, they would have difficulty mapping such knowledge to e.g. spacial diagrams.
It seems to me that your are using the word “intuitively” in a very unusual way, here. I would certainly not describe chemists’ knowledge of benzene’s form as “intuitive”… can you say more about what you mean by this term?
If you ask them to picture it in their mind, they can.
If you ask them to draw it, they can.
They can very quickly recognize that a diagram of Benzene is, in fact, a diagram of Benzene.
They can quickly answer questions like “does Benzene contain a cycle?”
The generator for these is something like “they have a mental representation of the structure as a picture, prototype, graph, etc, which is hooked up to other parts of the mind and is available for quick use in mental procedures”.
When I was older, and I began to read the Feynman Lectures on Physics, I ran across a gem called “the wave equation.” I could follow the equation’s derivation, but, looking back, I couldn’t see its truth at a glance. So I thought about the wave equation for three days, on and off, until I saw that it was embarrassingly obvious. And when I finally understood, I realized that the whole time I had accepted the honest assurance of physicists that light was waves, sound was waves, matter was waves, I had not had the vaguest idea of what the word “wave” meant to a physicist.
The “[seeing] that it was embarrassingly obvious” is only the case after having the intuition.
Alright, fair enough, this is certainly… something (that is, you have answered my question of “what do you mean by ‘intuition’”, though I am not sure what I’d call this thing you’re describing or even that it’s a single, monolithic phenomenon)… but it’s not at all what people usually mean when they talk about ‘intuition’.
This revelation makes your post very confusing and hard to parse! (What’s more, it seems like you actually use ‘intuition’ in your post in several different ways, making it even more confusing.) I will have to reread the post carefully, but I can say that I no longer have any clear idea what you are saying in it (whereas before I did—though, clearly, that impression was mistaken).
but it’s not at all what people usually mean when they talk about ‘intuition’.
For my own case I immediately and exactly match Jessica’s use of “intuition” and expect that is what most people usually mean when they talk about intuition, so I think this claim requires greater justification if that seems important to you given a sample size of 3 here.
the ability to understand something instinctively, without the need for conscious reasoning.
they have a mental representation of the structure as a picture, prototype, graph, etc, which is hooked up to other parts of the mind and is available for quick use in mental procedures”.
i.e. They have the knowledge stored and accessible. The conscious reasoning has already occurred for understanding. Recalling it without (much) effort isn’t intuition, even if it happens as a response to prior training/on a most subconscious level/instinctively.
To me, “intuition” is something that comes from somewhere—a gut feeling, an inspiration, that kind of thing. Intuitively sensing/feeling/knowing what to do in a situation. Quite an experience when “auto-pilot” takes over...
Something that ‘just comes to you’ - what I would call an ‘intuition’. Which seems to fit with the original post’s usage and the example of the “the structure of benzene came in a dream”.
Something done ‘automatically/without thinking’ but has been learned i.e. the example of a chemist being able to recognise and represent benzene is not an intuition. It is knowledge that originated from an intuition.
The issue comes with the usage of “intuitively” in the comments with the examples given. The difference between something learned and something spontaneous/organic that occurs.
e.g. The person that can pick up an instrument and play it without prior training is using intuition, an instinctive feel for how to make it work versus the person that’s practised for years, conscious of their actions until they are so well trained they can play automatically.
Couldn’t it also be the case that the claim is already known through intuition, and proving it is the main problem? Of course, checking against more things will produce higher confidence, but confidence can still exceed 99 percent without doing other checks
How can something have any confidence behind it, much less greater than 99%, without evidence? 99% confidence on the basis of intuition alone is religion, not rationality.
I was fairly confident of my answer, but I still used a calculator to double-check my math. Moreover, I have computed 15*5 in the past, and I was able to check against the memory of those computations to ensure that I had the correct answer. Finally, math is not a science. Confidence applies to scientific results, which rely on experimental and observational evidence about the world to support or oppose specific hypotheses. The answer to 15*5 is not a hypothesis. It is a fact, which can be proven to be correct in the context of a particular mathematical system.
A scientific hypothesis, like the structure of benzene, is not reliant upon logical proof in the same way that a mathematical result is. If I have a proof of the answer to 15 * 5, then I know it is correct, absent any errors in my proof. However, if I have a particular hypothesis regarding the structure of benzene, or the nature of gravity, the logical soundness of the argument in favor of my hypothesis offers no evidence as to the argument’s correctness. Only evidence can entangle my logical argument with the state of the world, and allow me to use my logical argument to make predictions.
I agree 99% is probably too high in the case of Benzene (and most other scientific hypotheses not derived from established ones). Although, Einstein’s arrogance is a counterpoint.
There are empirical claims it’s possible to be very confident in without having checked, e.g. whether Australia or Asia has a larger land area, whether the average fly is larger or smaller than the average mouse, whether you’re going to be hit by a car the next time you cross the street, etc.
Einstein’s Arrogance isn’t as much of a counterpoint as you think it is. Yes, Einstein was arrogant, but we only remember his arrogance because he was right. Would we be holding Einstein’s arrogance as such a good thing if Eddington’s expedition had disconfirmed General Relativity? What if the orbital anomalies of Mercury had been explained by the presence of another planet even closer to the Sun? Without the numerous experiments confirming General Relativity, Einstein would be just another kook, with a set of papers that had interesting mathematics, perhaps, but whose hypotheses were refuted by observation.
As far as Blind Empiricism goes, I do find it telling that Japan did try the solutions that Eliezer proposed. However, due to factors that Eliezer did not consider, the Japanese government was not able to go as far with those solutions as Eliezer predicted, and as a result, the performance of the Japanese economy has remained laggardly. So perhaps Eliezer’s confidence in his ability to figure out macroeconomics from first principles isn’t as as great as he thought it was, and more empiricism is required.
Finally, with regards to The Sin of Underconfidence, while I agree that underconfidence leads one to pass up opportunities that one might have otherwise taken, I would argue that overconfidence is much worse. As Eliezer also stated:
One of chief pieces of advice I give to aspiring rationalists is “Don’t try to be clever.” And, “Listen to those quiet, nagging doubts.” If you don’t know, you don’t know what you don’t know, you don’t know how much you don’t know, and you don’t know how much you needed to know.
There is no second-order rationality. There is only a blind leap into what may or may not be a flaming lava pit. Once you know, it will be too late for blindness.
While it’s certainly possible to be very confident in empirical claims without having checked, I don’t think it’s correct to do so. I am very confident that Australia has a smaller land mass than Asia, but the reason I am so confident is because I have repeatedly seen maps and atlases that show me that fact. If I did not, I would be as confident of my answer as I would be of my answer to the question, “Which has the greater landmass, the British Isles or the Japanese Home Islands?” Similarly, I have observed numerous flies and a few mice, and thus I can claim that the average fly is smaller than the average mouse. If I had not, I would be much less confident of my answer, much like I have little confidence in my answer to, “Which is larger? The average spider or the average fly?” Finally, I have absolutely no confidence in my intuitive answer to, “Am I going to get hit by a car when I cross the street?” This is why I look both ways before stepping out into the road, even when it’s a “quiet” street. As someone who goes long-distance running, I have had enough unpleasant surprises there that I double and sometimes triple check before stepping out. Do you mean to suggest that you step out into roads without looking both ways?
(I’m not going to comment on Eliezer’s counterpoints except to say I agree with you that he was wrong about macroecon; seems easier to just discuss the theory directly)
Do you mean to suggest that you step out into roads without looking both ways?
No. But if I predicted I’d get hit with >1% probability, I’d avoid roads much more than I currently do. Due to the usual VNM considerations.
In a sense you haven’t checked whether Australia has a lower land area than Asia. You have read atlases and have (a) visually inspected the areas and gained the sense that one area is larger than the other, (b) had a background sense that maps are pretty accurate (corresponding to actual land shapes), (c) done some kind of reasoning to infer from observations so far that Australia in fact has a lower land area than Asia.
Yes, this is a semantic issue of what counts as “checking”, but that is exactly the issue at hand. Of course it’s possible to check claims against memory, intuition, mental calculation, the Internet, etc, but every such check has only limited reliability.
Finally, I will note that in this discussion, you have been making a bunch of claims, such as “99% confidence on the basis of intuition alone is religion, not rationality”, and “Only evidence can entangle my logical argument with the state of the world”, that seem incredibly difficult to check (or even precisely define), such that I cannot possibly believe that you have checked them to the standard you are demanding.
Yes, this is a semantic issue of what counts as “checking”, but that is exactly the issue at hand. Of course it’s possible to check claims against memory, intuition, mental calculation, the Internet, etc, but every such check has only limited reliability.
That is correct, but as Isaac Asimov pointed out in The Relativity of Wrong, there is a big difference between saying, “Every such check has limited reliability,” and “Checking is the the same as not checking.” If someone came to me tomorrow and said, “You’re completely wrong, quanticle, in fact Australia has a larger land mass than Asia,” I would be skeptical, and I would point out the massive preponderance of evidence in my favor. But if they managed to produce the extraordinary evidence required for me to update my beliefs, I would. However, they would have to actually produce that evidence. Simply saying, “I intuitively believe it to be true with high probability,” is not evidence.
To go back to the original claim you took issue with:
Couldn’t it also be the case that the claim is already known through intuition
In this case I did mean “intuition” to include some checks, e.g. compatibility with memory, analogy with similar cases, etc. Brains already do checks when processing thoughts (because, some thoughts register as surprising and some don’t). But these checks are insufficient to convince a skeptical audience, is the point. Which is why “I intuitively believe this” is not an argument, even if it’s Bayesian evidence to the intuition-haver. (And, trivially, intuitions could be Bayesian evidence, in cases where they are correlated with reality, e.g. due to mental architecture, and such correlations can be evaluated historically)
There seem to be some semantic disagreements here about what constitutes “evidence”, “intuition”, “checking”, etc, which I’m not that enthusiastic about resolving in this discussion, but are worth noting anyway.
But these checks are insufficient to convince a skeptical audience, is the point.
Yes, I see that as a feature, whereas you see to see it as somewhat of a bug. Given our propensity for self-deception and the limits of our brains, we should gather evidence, even when our intuition is very strong, and we should be suspicious of others who have strong intuitions, but don’t seem to have any sort of analytical evidence to back their claims up.
I don’t see any risk to hiding the origins of one’s ideas, if one has experimental evidence confirming them. Similarly, I don’t see the benefit of disclosing the sources of unconfirmed ideas. Where the idea comes from (a dream, an intuitive leap, an LSD trip, a reasoned inference from a literature review) is far less important than actually doing the work to confirm or disprove the idea.
The intuition is, then, crystalized in a representation of the structure of Benzene, which chemists already know intuitively. If they had only abstract, non-intuitive knowledge of the form of Benzene, they would have difficulty mapping such knowledge to e.g. spacial diagrams.
Intuitions can be more or less refined/crystalized in such a way that they can be more precisely specified, be more analytically tractable, be loadable to more different minds, etc.
Good teaching transfers intuitions, not just abstract knowledge.
If continued progress in chemistry requires insights like Kekulé′s, then, yes, why not?
Couldn’t it be the case that is it bad for both reasons? I don’t think you’ve offered an argument that Person A’s reasons don’t apply.
Couldn’t it also be the case that the claim is already known through intuition, and proving it is the main problem? Of course checking against more things will produce higher confidence, but confidence can still exceed 99 percent before doing other checks. (Discarding disconfirming evidence is, of course, epistemically bad because it’s failing to update on observations, but it’s also possible not to find such evidence in the course of searching)
It seems to me that your are using the word “intuitively” in a very unusual way, here. I would certainly not describe chemists’ knowledge of benzene’s form as “intuitive”… can you say more about what you mean by this term?
If you ask them to picture it in their mind, they can.
If you ask them to draw it, they can.
They can very quickly recognize that a diagram of Benzene is, in fact, a diagram of Benzene.
They can quickly answer questions like “does Benzene contain a cycle?”
The generator for these is something like “they have a mental representation of the structure as a picture, prototype, graph, etc, which is hooked up to other parts of the mind and is available for quick use in mental procedures”.
To elaborate, I will quote Guessing the Teacher’s Password:
The “[seeing] that it was embarrassingly obvious” is only the case after having the intuition.
Alright, fair enough, this is certainly… something (that is, you have answered my question of “what do you mean by ‘intuition’”, though I am not sure what I’d call this thing you’re describing or even that it’s a single, monolithic phenomenon)… but it’s not at all what people usually mean when they talk about ‘intuition’.
This revelation makes your post very confusing and hard to parse! (What’s more, it seems like you actually use ‘intuition’ in your post in several different ways, making it even more confusing.) I will have to reread the post carefully, but I can say that I no longer have any clear idea what you are saying in it (whereas before I did—though, clearly, that impression was mistaken).
For my own case I immediately and exactly match Jessica’s use of “intuition” and expect that is what most people usually mean when they talk about intuition, so I think this claim requires greater justification if that seems important to you given a sample size of 3 here.
intuition
the ability to understand something instinctively, without the need for conscious reasoning.
i.e. They have the knowledge stored and accessible. The conscious reasoning has already occurred for understanding. Recalling it without (much) effort isn’t intuition, even if it happens as a response to prior training/on a most subconscious level/instinctively.
To me, “intuition” is something that comes from somewhere—a gut feeling, an inspiration, that kind of thing. Intuitively sensing/feeling/knowing what to do in a situation. Quite an experience when “auto-pilot” takes over...
That all sounds like part of the same cluster of mental movements to me, i.e. all the stuff that isn’t deliberative.
Talking about “intuition” I distinguish between:
Something that ‘just comes to you’ - what I would call an ‘intuition’. Which seems to fit with the original post’s usage and the example of the “the structure of benzene came in a dream”.
Something done ‘automatically/without thinking’ but has been learned i.e. the example of a chemist being able to recognise and represent benzene is not an intuition. It is knowledge that originated from an intuition.
The issue comes with the usage of “intuitively” in the comments with the examples given. The difference between something learned and something spontaneous/organic that occurs.
e.g. The person that can pick up an instrument and play it without prior training is using intuition, an instinctive feel for how to make it work versus the person that’s practised for years, conscious of their actions until they are so well trained they can play automatically.
How can something have any confidence behind it, much less greater than 99%, without evidence? 99% confidence on the basis of intuition alone is religion, not rationality.
What’s 15*5? (I’m sure you can answer this in <20 seconds)
How confident are you?
How rigorously did you check?
I was fairly confident of my answer, but I still used a calculator to double-check my math. Moreover, I have computed 15*5 in the past, and I was able to check against the memory of those computations to ensure that I had the correct answer. Finally, math is not a science. Confidence applies to scientific results, which rely on experimental and observational evidence about the world to support or oppose specific hypotheses. The answer to 15*5 is not a hypothesis. It is a fact, which can be proven to be correct in the context of a particular mathematical system.
A scientific hypothesis, like the structure of benzene, is not reliant upon logical proof in the same way that a mathematical result is. If I have a proof of the answer to 15 * 5, then I know it is correct, absent any errors in my proof. However, if I have a particular hypothesis regarding the structure of benzene, or the nature of gravity, the logical soundness of the argument in favor of my hypothesis offers no evidence as to the argument’s correctness. Only evidence can entangle my logical argument with the state of the world, and allow me to use my logical argument to make predictions.
I agree 99% is probably too high in the case of Benzene (and most other scientific hypotheses not derived from established ones). Although, Einstein’s arrogance is a counterpoint.
There are empirical claims it’s possible to be very confident in without having checked, e.g. whether Australia or Asia has a larger land area, whether the average fly is larger or smaller than the average mouse, whether you’re going to be hit by a car the next time you cross the street, etc.
(See also Blind Empiricism and The Sin of Underconfidence for other general counterpoints)
Einstein’s Arrogance isn’t as much of a counterpoint as you think it is. Yes, Einstein was arrogant, but we only remember his arrogance because he was right. Would we be holding Einstein’s arrogance as such a good thing if Eddington’s expedition had disconfirmed General Relativity? What if the orbital anomalies of Mercury had been explained by the presence of another planet even closer to the Sun? Without the numerous experiments confirming General Relativity, Einstein would be just another kook, with a set of papers that had interesting mathematics, perhaps, but whose hypotheses were refuted by observation.
As far as Blind Empiricism goes, I do find it telling that Japan did try the solutions that Eliezer proposed. However, due to factors that Eliezer did not consider, the Japanese government was not able to go as far with those solutions as Eliezer predicted, and as a result, the performance of the Japanese economy has remained laggardly. So perhaps Eliezer’s confidence in his ability to figure out macroeconomics from first principles isn’t as as great as he thought it was, and more empiricism is required.
Finally, with regards to The Sin of Underconfidence, while I agree that underconfidence leads one to pass up opportunities that one might have otherwise taken, I would argue that overconfidence is much worse. As Eliezer also stated:
While it’s certainly possible to be very confident in empirical claims without having checked, I don’t think it’s correct to do so. I am very confident that Australia has a smaller land mass than Asia, but the reason I am so confident is because I have repeatedly seen maps and atlases that show me that fact. If I did not, I would be as confident of my answer as I would be of my answer to the question, “Which has the greater landmass, the British Isles or the Japanese Home Islands?” Similarly, I have observed numerous flies and a few mice, and thus I can claim that the average fly is smaller than the average mouse. If I had not, I would be much less confident of my answer, much like I have little confidence in my answer to, “Which is larger? The average spider or the average fly?” Finally, I have absolutely no confidence in my intuitive answer to, “Am I going to get hit by a car when I cross the street?” This is why I look both ways before stepping out into the road, even when it’s a “quiet” street. As someone who goes long-distance running, I have had enough unpleasant surprises there that I double and sometimes triple check before stepping out. Do you mean to suggest that you step out into roads without looking both ways?
(I’m not going to comment on Eliezer’s counterpoints except to say I agree with you that he was wrong about macroecon; seems easier to just discuss the theory directly)
No. But if I predicted I’d get hit with >1% probability, I’d avoid roads much more than I currently do. Due to the usual VNM considerations.
In a sense you haven’t checked whether Australia has a lower land area than Asia. You have read atlases and have (a) visually inspected the areas and gained the sense that one area is larger than the other, (b) had a background sense that maps are pretty accurate (corresponding to actual land shapes), (c) done some kind of reasoning to infer from observations so far that Australia in fact has a lower land area than Asia.
Yes, this is a semantic issue of what counts as “checking”, but that is exactly the issue at hand. Of course it’s possible to check claims against memory, intuition, mental calculation, the Internet, etc, but every such check has only limited reliability.
Finally, I will note that in this discussion, you have been making a bunch of claims, such as “99% confidence on the basis of intuition alone is religion, not rationality”, and “Only evidence can entangle my logical argument with the state of the world”, that seem incredibly difficult to check (or even precisely define), such that I cannot possibly believe that you have checked them to the standard you are demanding.
That is correct, but as Isaac Asimov pointed out in The Relativity of Wrong, there is a big difference between saying, “Every such check has limited reliability,” and “Checking is the the same as not checking.” If someone came to me tomorrow and said, “You’re completely wrong, quanticle, in fact Australia has a larger land mass than Asia,” I would be skeptical, and I would point out the massive preponderance of evidence in my favor. But if they managed to produce the extraordinary evidence required for me to update my beliefs, I would. However, they would have to actually produce that evidence. Simply saying, “I intuitively believe it to be true with high probability,” is not evidence.
To go back to the original claim you took issue with:
In this case I did mean “intuition” to include some checks, e.g. compatibility with memory, analogy with similar cases, etc. Brains already do checks when processing thoughts (because, some thoughts register as surprising and some don’t). But these checks are insufficient to convince a skeptical audience, is the point. Which is why “I intuitively believe this” is not an argument, even if it’s Bayesian evidence to the intuition-haver. (And, trivially, intuitions could be Bayesian evidence, in cases where they are correlated with reality, e.g. due to mental architecture, and such correlations can be evaluated historically)
There seem to be some semantic disagreements here about what constitutes “evidence”, “intuition”, “checking”, etc, which I’m not that enthusiastic about resolving in this discussion, but are worth noting anyway.
Yes, I see that as a feature, whereas you see to see it as somewhat of a bug. Given our propensity for self-deception and the limits of our brains, we should gather evidence, even when our intuition is very strong, and we should be suspicious of others who have strong intuitions, but don’t seem to have any sort of analytical evidence to back their claims up.
I don’t see any risk to hiding the origins of one’s ideas, if one has experimental evidence confirming them. Similarly, I don’t see the benefit of disclosing the sources of unconfirmed ideas. Where the idea comes from (a dream, an intuitive leap, an LSD trip, a reasoned inference from a literature review) is far less important than actually doing the work to confirm or disprove the idea.
Jessica’s very unusual use of the word ‘intuition’ is responsible for the confusion here, I think.
99% confidence on the basis of intuition[common_usage] alone is indeed religion (or whatever).
99% confidence on the basis of intuition[Jessica’s_usage] seems unproblematic.