For example, I'm 99% sure TS would agree (though he is free to correct me if I am wrong) that he didn't develop the intuitive recognitions he has (e.g. that someone has a weapon) from reading a book. Instead those intuitions came from years of interactions with, and observations of, people. Attentiveness to body language and other nonverbal signals undoubtedly played an important role. — wonderer1

Quite right. No reading or study involved. I'm fairly sure the intuition I know is acquired by paying attention to experience and being able to recognize key indicators, which are not necessarily consciously available to me.

Nope, that's pretty much it. Intuition is improved by acquiring knowledge. That's all. — Darkneos

Your intuitions about intuition could use some development.

If knowledge is justified true belief, then that is different than intuition. (Or at least the 'justification is of a different sort than what we typically think of as justification for a belief to be considered knowledge.)

Your intuitions about intuition could use some development. — wonderer1

It’s not my intuitions about it it’s just the simple fact. Even what you cited before about observing people lots of times it’s knowledge, knowledge of body language.

You’re making it more than it actually is which is something a lot of people like to do.

Intuition is rooted in knowledge. The more you know the better it is. It honestly doesn’t matter what you think about it, doesn’t change what it is.

Yes. Analog vs digital collection and processing of information becomes interesting in this respect. Analog collection of information captures an actual "imprint" of the real world. In which sense, there may actually be information captured which is unexpected or unknown. — Pantagruel

:up:

This is a good point to bring up.

Analog can preserve a more accurate representation, and per Nyquist's theorem, there are limits to how accurate a digital representation can be, as a function of sample rate. Finite bit depth of samples is another dimension of error in the case of digital.

Neural networks are able to exploit such "hidden" information and extrapolate hidden connections. In fact, that is more or less exactly how they work. By contrast, digitization only encodes what it is specifically designed to encode. — Pantagruel

That is somewhat true, but my inner pedant insists that I point out some inaccuracies.

It may be the case that there is a degree of fidelity maintained, due to the somewhat more analog properties of neurons. However, spikes in action potential are a significant feature of our neurons. So there is an element of sampling, playing a significant role in the way our neural nets work.

Rather than an analog vs digital issue, it's more a matter of how is the hardware arranged, and what sort of information processing is the hardware well suited for. Neural networks, natural or artificial, are very good at pattern recognition. Much of the 'hidden information' results in recognized patterns which happen preconsciously.

Also, it's not exactly the case that "digitization only encodes what it is specifically designed to encode". There is a trivial sense in which that is true, in that digital hardware is designed to encode bit states and can only encode bit states. However, it is very much the case that digitally instantiated artificial neural networks, after training on whatever inputs were provided to the ANN, will have a great many bit states which were not determined by the designer. This article touches on aspects of this sort of information processing, that people who care about humanity's future might want to be aware of.

https://www.technologyreview.com/2017/04/11/5113/the-dark-secret-at-the-heart-of-ai/

Discursive or conceptual cognition operates by casting concrete particulars in symbolic terms, which relies on general concepts or universals. But there is always a gap between the ideal rational cognition made possible by symbolic thought and the concrete totality. I remember being very struck by this when I moved from the high-school physics of vectors and formulas to university physics, where the plethora of approximations involved in real-world calculations were suddenly being considered. — Pantagruel

Doesn't this reflect the distinction between mathematical idealisation and reality? The former allows for complete precision as a matter of definition, of which the reality is always an approximation. — Wayfarer

I think mathematics could be construed as the extreme limit of ideal-theoretical symbolization? The golden ratio appears in organic forms, but these instantiations are close approximations to the mathematical ideal. — Pantagruel

I hope no one minds me going back to this part of the thread. There's something here I don't understand.

Both of you describe reality as approximating the mathematical ideal.

Isn't it the other way around? Isn't the mathematics a simplification of reality? When you fit a curve to your data, you don't say the data approximate the curve. --- I mean, you can, if you like, proclaim the simple formula a physical law, and explain the variance however you like, confounding this and that, and claim that in the right conditions the data would better "instantiate" the law. But you don't have to take that seriously. All you're saying is that the formula's predictions are pretty good, and in some circumstances even better. How is nature supposed to "instantiate" mathematics? Are we sure we know what that means?

You can say the same thing about, for instance, musical notation, that it's a simplification of actual music making. There was music before notation, before music theory. That musicians now play from a score, so that they in some sense "instantiate" that score in performance, changes nothing. They still do more in performance than is recorded in the score. It's a sort of ahead-of-time simplification of what a performance of it will turn out to be.

And the real question is whether logic is a similar simplification of reality -- or perhaps merely a simplification of the relations between our concepts. For instance, there's just no chance that color perception actually works the way it's suggested here -- there's the freaking dress, for example -- and we've all been in situations where we were perfectly willing to attribute two different color terms to an object. (Most recently, for me, a debate about a coworker's pants that I was dragged into.) The necessary exclusion of other colors by any color looks like a simplification of how we use our color concepts.

All these simplifications do good work and save real time and energy. They are useful approximations of reality, not the other way around.

All these simplifications do good work and save real time and energy. They are useful approximations of reality, not the other way around. — Srap Tasmaner

:up:

Both of you describe reality as approximating the mathematical ideal.

Isn't it the other way around? Isn't the mathematics a simplification of reality? — Srap Tasmaner

I think the first captures an aspiration to (for instance) draw a perfect circle without a compass.
But I very much agree when it comes to fitting functions to data.

For me, in the work I do (moderately reliable) intuition means being able to grasp almost immediately if someone has a hidden weapon on them or not and if they might be violent or not. Or if they are experiencing delusional thinking or psychoses. Or knowing if someone can do a very challenging job or not within seconds of meeting them in a job interview. I can generally tell when someone is suicidal whether they will act on it or not, based on intuition. I've gotten to the point when I meet a new worker I can often tell within a minute or two how long they will last in the field and what path brought them here - a relative, lived experience, etc. I think there are probably key indicators we can read but you need to be 'open' to them in some way and have relevant experience. — Tom Storm

Very cool to hear about this. This kind of knowledge seems to play a huge role in life and maybe doesn't get celebrated enough by bookish types. I'm guessing that driving is the average person's taste of a high stakes version of this.

I remember the specific moment I decided to trust my intuition. I was in college, at the library studying, and some guy came in and dropped his books on the next table over from where I was and dropped into a chair. I glanced over and thought to myself, dumbass. And then I upbraided myself -- Why do you do that? Don't be so quick to judge. Don't jump to conclusions, you don't know that guy. After a while he left and I left shortly after. I was heading for the stairs that were right next to the elevator and he was standing there, repeatedly pushing the down button. We were on the second floor. I decided right then that whatever I had picked up on when I first saw him, I was right. Dumbass. Probably hungover dumbass. I have trusted my intuition ever since.

The former allows for complete precision as a matter of definition, of which the reality is always an approximation. — Wayfarer

Both of you describe reality as approximating the mathematical ideal.

Isn't it the other way around? Isn't the mathematics a simplification of reality? — Srap Tasmaner

I see your point. I suppose what I meant to say is that mathematics allows for utter precision, whereas, in reality, things are generally not mathematically precise. To paraphrase Bertrand Russell, we model the world mathematically not because we know so much about it, but because we know so little. It's only those aspects which can be quantified that provide mathematical certainty. Although obviously since Galileo, this approach has provided an absolutely astonishing amount of progress. (the subject of Eugene Wigner's often-quoted essay on the Unreasonable Effectiveness of Mathematics in the Natural Sciences.)

This also resonated with me:

Discursive or conceptual cognition operates by casting concrete particulars in symbolic terms, which relies on general concepts or universals. But there is always a gap between the ideal rational cognition made possible by symbolic thought and the concrete totality. — Pantagruel

This is reminiscent of platonic or Aristotelian realism, where the concept or idea or universal - these are not synonyms but that's not important at this point - is what can be grasped with rational certainty but the actual object is an imperfect realisation of the idea or form. That is the basis of Aristotle's hylomorphic dualism which is having something of a comeback.

Also, it's not exactly the case that "digitization only encodes what it is specifically designed to encode". There is a trivial sense in which that is true, in that digital hardware is designed to encode bit states and can only encode bit states. However, it is very much the case that digitally instantiated artificial neural networks, after training on whatever inputs were provided to the ANN, will have a great many bit states which were not determined by the designer — wonderer1

I am not talking about bit states, I am talking about the objective data (information) which is digitally encoded. Since data is being specifically symbolically encoded, digital neural networks have only that known data to work with. Versus an analog system which works with a "signal" whose total data properties are not necessarily so restricted. You can talk about bit states being "information", it is a level of abstraction below that at which artificial neural nets actually operate, part of the underlying mechanism and addressed via back-propagation, which is a function of error-correction, which is determined at the top informational level.

I am not talking about bit states, I am talking about the objective data (information) which is digitally encoded. Since data is being specifically symbolically encoded, digital neural networks have only that known data to work with. Versus an analog system which works with a "signal" whose total data properties are not necessarily so restricted. — Pantagruel

I think we are talking past each other to some extent. We can hypothesize about some sort of neuromorphic hardware which maintains analog fidelity to a greater degree than current artificial or natural neural networks do. However, I'm skeptical that such a system can be practically implemented.

There is neuromorphic hardware under development, but from what I've seen, much of what is under development uses spiking/sampling. Spiking necessitates a loss of fidelity to a representation of an analog signal due to the the fact that maximum spike frequency cannot be infinite. Now, as is the case with the digitized audio that we listen to all the time these days, the loss of fidelity with a spiking architecture might be for practical purposes undetectable. However, I think it important to recognize that any sort of information processing is going to result in some loss of fidelity in the processing of an analog input.

Still, if you can cite something discussing a practically implementable information processing system which maintains analog fidelity, I'd be interested in taking a look.

You can talk about bit states being "information", it is a level of abstraction below that at which artificial neural nets actually operate, part of the underlying mechanism and addressed via back-propagation, which is a function of error-correction, which is determined at the top informational level. — Pantagruel

I referred to bit states to make clear that we are talking about digital information. Yes we can combine bits to represent numbers, but any digital representation of a number is going to have a finite bit depth, and I think it important to keep in mind, the loss of fidelity that comes with such encoding.

In the context of considering our sensory and information processing apparatus, there is strong evidence that we do not have some ideal 'purely analog' system. Simply considering the fact that our visual system relies on discrete rod and cone cells, producing outputs in the form of spike trains, points towards ideal analog representations not being what our brains have to work with.

Still, if you can cite something discussing a practically implementable information processing system which maintains analog fidelity, I'd be interested in taking a look. — wonderer1

Yes, I'm aware of the eventual loss of accuracy that results from extensive analog processing. I'm talking at a purely theoretical level where what is being processed by the neural network is already pre-sliced data. My hypothesis would be that the brain in fact operates simultaneously in a way that is analogous to digital processing (when "conceptually-constrained" information is processed) and also in a way that is more analog in nature (since, qua organic entity, we are, in fact, in contact with the universe at an "analog" level). And that intuition can be productively construed as an exploitation of information that may be embedded in our "overall sensory input" but not as yet conceptually construed. I gave the example of a cat's brain, which exhibits no indicative activity in response to a certain "hearable" tone until such time as that tone is paired with a recognized event. Thereafter, the tone is "heard" (manifests in brain activity).

Simply considering the fact that our visual system relies on discrete rod and cone cells, producing outputs in the form of spike trains, points towards ideal analog representations not being what our brains have to work with. — wonderer1

That fact that the visual system is already highly evolved and differentiated doesn't mean there aren't other aspects of exploitable analogicity. The complexity of actual connections between things in the world is anybody's guess. I'm certainly not limiting the possibilities to whatever might be the current state of the human visual system. It works well enough, for a bipedal ape.

I suppose what I meant to say is that mathematics allows for utter precision, whereas, in reality, things are generally not mathematically precise. — Wayfarer

Certainly.

To paraphrase Bertrand Russell, we model the world mathematically not because we know so much about it, but because we know so little. — Wayfarer

That's very nice, but there's a lot more to say. We only can know a little because of the creatures we are. Bandwidth is small and reality is big.

It's only those aspects which can be quantified that provide mathematical certainty. — Wayfarer

Or, again, the other way around. Nothing can "really" be measured, but only approximated. We can call what we end up with certainty or precision, but it's really usability, since processing power is also limited. That math is more precise is the whole point. I'd like to say that simplifying the world or experience into a usable form just is the mathematical impulse. It's not that some aspects of the world can be measured and some can't. Everything can be turned into math.

And the mathematical impulse to simplify and make computable -- that's also obviously what's going on with logic.

It's funny how when you read Plato, he talks as if these are all the same thing -- you know, the way he'll say "those of you interested in philosophy and mathematics, in music and astronomy". That is, those of you who have noticed how we simplify the world in order to think about it and recognize that we could do the same thing self-consciously and perhaps improve our reasoning.

:up:

we could do the same thing self-consciously and perhaps improve our reasoning. — Srap Tasmaner

@Wayfarer @wonderer1

I want to add that this is not the only option.

I'm interested in @Pantagruel's suggestion that there may be more of the analog input in the system than the digitized projection of that reality. That's really interesting.

But in a general way you could choose to self-consciously do something *different* from what your hardware does on its own, and I think this is kind of the goal in practices like meditation and phenomenology. The question that arises is how far back into the simplification process you can get, and we keep finding that the answer seems to be, not as far as you might have hoped. There are things your brain's going to do whether you like it or not.

But that still leaves some options. Can you catch it in the act? To some degree maybe you can, and again that's where I see meditation and phenomenology, but again the issue is how early in the process you catch something before it gets simplified for you.

But you may also be able to learn how your brain simplified and that in itself can be valuable.

And you can make some effort to un-simplify, to re-complexify.

Lots more to this.

I'm interested in Pantagruel's suggestion that there may be more of the analog input in the system than the digitized projection of that reality. That's really interesting. — Srap Tasmaner

Yes, it is an interesting aspect of things to consider. My knowledge of human hearing is not very up to date, but what I recall is that for low frequency sounds the system generates nerve impulses in sync with the incoming low frequency components of what is heard. So hearing may be a good sense to consider, in looking for analogicity in human neural processing. There might be some sense to be made of why we find music so affecting by looking into that. (Not something I've really thought about before, so there may be all sorts of relevant research out there that I'm not aware of.)

But in a general way you could choose to self-consciously do something *different* from what your hardware does on its own, and I think this is kind of the goal in practices like meditation and phenomenology. — Srap Tasmaner

I've never been enough of a meditator to have much to say about what understandings might be reached through meditation. However, in the vein of doing "something *different* from what your hardware does on its own", I find conversations with diverse people to be a good way of getting my brain out of the ruts it is inclined to ride in on its own.

To paraphrase Bertrand Russell, we model the world mathematically not because we know so much about it, but because we know so little.
— Wayfarer

That's very nice, but there's a lot more to say. We only can know a little because of the creatures we are. Bandwidth is small and reality is big. — Srap Tasmaner

I think you're downplaying the faculty of reason here. 'Bandwidth', obviously a technological analogy, refers to the rate at which information can be transferred. But that may not have much to do with the question of why 'the unreasonable effectiveness of mathematics'.

One passage from Plato's dialogues that I have recently re-discovered is the 'argument from equals' in the Phaedo. To paraphrase: At 74b, Socrates asks, "do not equal stones and sticks sometimes, while remaining the same, appear to one person to be equal and to another to be unequal"? The point being that sticks of equal length appear both equal and unequal, i.e., they appear to be and to not be equal.

Sticks that appear to be equal and unequal are imperfectly equal. However, the recognition of the sticks as imperfectly equal requires knowledge of perfect equality - otherwise, in virtue of what are they being recognized as imperfect? "Whenever someone, on seeing something, realizes that that which he now sees wants to be like some other reality but falls short and cannot be like that other since it is inferior, do we agree that the one who thinks this must have prior knowledge of that to which he says it is like, but deficiently so?" (74d)

This knowledge must be acquired before the recognition of the sticks as imperfectly equal, i.e., before sense perception; therefore, acquired before birth.

It is traditionally said from this and numerous other passages that Socrates (and Plato) hold that this faculty is acquired before birth, in line with belief in the pre-existence of the soul. In today's terms, however, I don't think it would be too outlandish to say that the faculty is innate. But even that is controversial: the empiricist dogma of 'tabula rasa' still has a very strong hold on naturalism. (This is why, I think, there is such controversy about platonism in mathematics.) The empiricist account will generally be 'well, we see many things that are equal or near equal, so we acquire the idea of equality from experience'. But the rationalist rejoiner might be that, were we not able to perceive the abstract 'equals' by reason, then no amount of experience will convey that insight. Furthermore that this is simply one example of the innummerable kinds of cases where we are able to derive conclusions based on foundational notions of 'equals', 'not equals' 'same as', 'different to', foundational to logic and mathematics.

Nope, that's pretty much it. Intuition is improved by acquiring knowledge. That's all.
— Darkneos

Your intuitions about intuition could use some development.

If knowledge is justified true belief, then that is different than intuition. (Or at least the 'justification is of a different sort than what we typically think of as justification for a belief to be considered knowledge.) — wonderer1

@Darkneos seems to be trading on the ambiguity of the term 'knowledge', What he said makes no sense if you consider knowledge as being JTB, but if you think of it as being know-how, then it does make sense.

Sticks that appear to be equal and unequal are imperfectly equal. However, the recognition of the sticks as imperfectly equal requires knowledge of perfect equality - otherwise, in virtue of what are they being recognized as imperfect? — Wayfarer

I think you have it exactly backwards. On cursory examination two stones or sticks may appear to be of equal length, shape or size, but on closer examination and measurement it will be seen that they are not exactly the same.

Reflection on this and on the obvious fact that no two things are ever exactly the same leads to the counterfactual notion of perfect equality as an imaginable and not logically contradictory possibility, but which does not seem to be possibility of this world.

We don't need to have a prior idea of perfect equality in order to notice that there are always differences, however minor they might be, between actual things.

Darkneos seems to be trading on the ambiguity of the term 'knowledge', What he said makes no sense if you consider knowledge as being JTB, but if you think of it as being know-how, then it does make sense. — Janus

All I can say is what the research behind it shows which seems to bear out better than mere philosophical speculation.

I think you have it exactly backwards. — Janus

You mean, Socrates, or 'the argument from reason', has it backwards. (I am quoting him.)

We don't need to have a prior idea of perfect equality in order to notice that there are always differences, however minor they might be, between actual things. — Janus

But you do need to have the ability to grasp what 'exactly equals' means.

You mean, Socrates, or 'the argument from reason', has it backwards. (I am quoting him.) — Wayfarer

Well, yes, it doesn't matter who the proponent is; the point is that the argument has it backwards (in my view).

But you do need to have the ability to grasp what 'exactly equals' means. — Wayfarer

I would say that all you need is the ability to see difference and similarity, and to examine enough things which look superficially the same, like fallen autumn leaves for example, to realize that exact similitude does not occur in nature.

It's just the other side of the coin; once we can recognize similarity and difference, and understand that there are degrees of similarity, then the idea of perfect sameness follows dialectically as an (apparently) unrealizable possibility.

It's the same with roundness, squareness, sphericity and cubicity and so on. It's also the same with colours: there is no perfect red, yellow, orange, blue, green, purple, black, white, or any other colour or tone; there are millions of possible variations.

All of which require rational ability, don’t they? I have no doubt you could train animals to recognise difference and similarity in objects through rewards, but I doubt you could train them to understand the concept. That requires the ability to abstract, which I’m reasonably confident is part of the rational-linguistic capacity of h. Sapiens.

The reason I mentioned the argument from equals, was in relation to the earlier question of the nature of mathematical intuition and the ability to grasp abstractions. The argument from equals is one of the canonical arguments for universals. I just think it is a fairly simple and direct way of pointing that out.

What is rational ability, though? The ability to compare and measure (ratio) is undeniably something we, and some animals can do. But rationality considered as valid reasoning either cannot be done in the absence of symbolic language, or if it can, how would we ever be able to tell?

I tend to agree with you that abstraction (or generalizing from particulars) relies on language. We know at least that the ability to report doing it certainly relies on language. Dogs see objects as kinds, though, even if not consciously or explicitly. They see stairs as to be walked up or down, doorways as to be walked through, balls or sticks as to be chased, bowls to be eaten or drunk from, streams to be swum in or drunk from, food of the right kinds as to be eaten, and so on.

The reason I mentioned the argument from equals, was in relation to the earlier question of the nature of mathematical intuition and the ability to grasp abstractions. The argument from equals is one of the canonical arguments for universals. I just think it is a fairly simple and direct way of pointing that out. — Wayfarer

There are other ways of explaining those abilities; from the basic capacities for counting and recognition of entities and kinds of entities that we can also observe in animals. I find those explanations more plausible that the notion of reason as something that comes from a transcendent realm to bless only the humans. To me, that is human exceptionalism; one of our biggest problems, or more accurately the source of most of our major extraordinary problems.

Darkneos seems to be trading on the ambiguity of the term 'knowledge', What he said makes no sense if you consider knowledge as being JTB, but if you think of it as being know-how, then it does make sense. — Janus

Darkneos is trolling for now. I'm not seeing any reason to reward his trolling with further responses.

I like "being know-how".

Very cool to hear about this. This kind of knowledge seems to play a huge role in life and maybe doesn't get celebrated enough by bookish types. — plaque flag

I agree. This got me thinking back to the night I met one of my girlfriends.

I was in a bar shooting pool when my friend Barb, and her friend Meri came in. I wrapped up the game of pool I was playing and went and joined them, and spent the rest of the evening talking to them. We walked out together and a big, rough looking, obviously very drunk guy walked out at the same time, taking out his car keys. I can't recall the details of what was said, but Meri very matter of factly told the guy that he was too drunk to drive, and that he needed to call a cab to drive him home. The guy went back into the bar to call a cab.

It's very much a "You have to have been there." situation, but Meri handled this guy twice her size perfectly. To me then, it was like watching magic. I would have expected to get belligerence in response if I had tried something similar, but somehow Meri intuitively recognized a means of getting compliance.

At that time Meri was working on finishing up her Ph.D. in marriage and family therapy, and undoubtedly her education played a role in her insightful handling of the situation, but things happened so quickly and smoothly that I think Meri had to have been going nearly purely on her intuitions about people, and not consciously recalling what various texts had to say.

I have huge respect for the sort of intuitions that Tom is talking about.

It’s not my intuitions about it it’s just the simple fact. Even what you cited before about observing people lots of times it’s knowledge, knowledge of body language.

You’re making it more than it actually is which is something a lot of people like to do.

Intuition is rooted in knowledge — Darkneos

Interesting. You may be making less of it than it actually is. I fully agree that intuition is related to knowledge in that one is always intuiting something in some context, and that the more detailed knowledge you have, the more intuitive knowledge becomes possible. But it is the entire nature of intuition that it extends if not transcends the current limits of what can be discursively extracted from the context. The expert diagnosis of a very experienced MD versus an intern for example.

:up:

May I ask your background? Based on our earlier discussion I can see that you are scientifically insightful.

May I ask your background? Based on our earlier discussion I can see that you are scientifically insightful. — wonderer1

Sure. Academically I have university courses in maths, physics, and astronomy, a degree in literature with a minor in philosophy (one course shy of a major). I also have a college diploma in programming and have been a computer systems administrator and analyst since 1996. Currently I'm an electronic medical records specialist and privacy officer.

Fundamentally, I am a melioristic-optimist. I believe that human actions have a real effect on the universe; and, all things being equal, assuming capability (and responsibility) is inherently more reasonable that pessimistically denying it.