Our Intuitions

At the beginning of the week, I mentioned I’m reading Our Mathematical Universe (2014), by Max Tegmark. His stance on inflation, and especially on eternal inflation, got me really thinking about it. Then all that thinking turned into a post.

It happened again last night. That strong sense of, “Yeah, but…” With this book, that’s happening a lot. I find something slightly, but fundamentally, off about Tegmark’s arguments. There seems an over-willingness to accept wild conclusions. This may all say much more about me than about Tegmark, which in this case is perfect irony.

Because what set me off this time was his chapter about human intuition.

So I must preface my thoughts about his preface to his thoughts by saying I may very well be completely full of crap. It wouldn’t be the first time, so caveat lector. (In truth, this rule always applies.)

But I just know I’m right. 😀 😉


Tegmark’s argument, one I’ve heard before, is:

Firstly, that our perceptions, our senses, are both untrustworthy and vastly incomplete. They are easily fooled into illusions, and we at best perceive reality only dimly through a dark glass.

For one example, our eyes perceive photons only in a very narrow range. We can’t even see ultraviolet or infrared photons, which are “right next door” — some animals can. And that’s a tiny slice of the spectrum from radio frequency photons to gamma frequency photons.

Another example is high-frequency sound that animals such as bats use to navigate, but which are beyond our ability to perceive. (And dogs live in a scent-based world also beyond our ken.)

Secondly, our entire model of reality comes from this tiny subset of reality that we can perceive. The implication is that our understanding of reality is thus limited by our perceptions and mental models.

It’s a bit like the idea that South Seas Islanders couldn’t even see Captain Cook’s ships because they had no cognitive framework for them. (I suspect they would have seen something. I’m dubious the ships would have been invisible to them.)

Thirdly, our “intuitions” (a word worth unpacking), because they’re based on the above faulty senses and incomplete world model, are limited to our evolutionary past and can’t be trusted in science.


Which yes, absolutely.

It is true our internal model of reality is but a wireframe of the real thing. It is true our intuitions are based on the low-speed, low-energy macro world of our senses and evolution. It is true we’re prone to illusions, external and self-induced, in our perceptions and thinking.

But that doesn’t mean we throw out the baby with the bathwater.

Imperfect does not mean worthless.[1]

Reality shines through in our perceptions, and our intuitions are based on an apparently factual, consistent, lawful and casual reality. The proof is in the pudding: Our models work.

Even on a simple level. Part of my model of reality (and I’m sure part of yours) involves the persistence of objects. Things don’t appear without cause; they don’t disappear without cause; they don’t even move without cause.

This lawful behavior is so consistent that it’s a fundamental tenant of physics: The laws of reality are identical in all frames of reference.

The bottom line is that rational thought applies in a lawful universe.

Mathematics, which seems to somehow be the language of that law, is the ultimate in rational thought. (One reason to learn math is that it teaches rational analytical thinking. I highly recommend it.)


My gripe is that I hear this as an argument most often in two places: As a preface to a very speculative theory, or as a vaguely ad hominem counter-argument when lacking a good argument against the actual topic.

In the latter case, it deflects from the points of the argument to the person making the argument. That’s just not a valid argument.

In the former case, it attempts to forestall disagreement: If you think this idea is crazy, that’s just a failure of your intuition. (I’m not crazy! You just can’t see what I can see.)

Maybe so. (Maybe not.) This argument always comes with the examples of Copernicus and others who, by gosh, turned out to be right when everyone said they had to be wrong. But historically, most speculative ideas turn out to be wrong. The path behind is littered with incorrect ideas.

Even some of the ideas that were right, were right for the wrong reasons. Consider the case of Einstein’s cosmological constant. First it was right according to the perceived (incorrect) model, then it was a greatest blunder, finally it was right for a completely unexpected reason.

And in all cases what made us change our minds, what got past the fortress of our intuition, was facts. Or, at the least, unassailable argument based on facts.

I agree my intuitions are limited. I change them — have changed them — when presented with sufficient evidence. But certainly not just because someone questions my intuition.

§ §

I think it’s worth looking into what the word intuition really means.

It can have a pejorative sense, that intuitions are based on thin air or emotions. There used to be a phrase “woman’s intuition” that seemed to wave away the deeper social perceptions most women have compared to most men.

For that is what intuition is, our deeper perceptions.

Intuition is not from thin air or emotion, it’s from the underlying cognitive processes of our mind. Some studies have shown that at least some of our intuitions are more accurate than our more considered opinions.

What’s often missed is that intuition can be informed by years of experience or knowledge. Many of the most brilliant scientific discoveries have come from intuitions. It can also be the key to success in athletics or music.

The power of a savant is an intuitive power. That’s the sort of analytical strength intuition can have.


I see the human brain as the most powerful active tool nature ever produced. Human brains, in a brief time span, have sent two spacecraft out beyond the reaches of the Solar system, not to mention robots on Mars and the Moon.

We’ve developed theories of the smallest of small (quantum mechanics) and largest of large (cosmology, general relativity). We are something the universe created that is figuring out the universe. This tool, this brain, is the mechanism of our intuition.

It’s true we perceive only a narrow slice of reality. It’s true we are prone to illusions. But that slice allows us to manipulate the world very effectively, and we can often recognize illusions for what they are.

We have the accounts of others, which provides a consensus view and which leads to convergence of the human view of reality. We also have our instruments, which have far greater observational range than we do.

The power of this view is demonstrated in those spacecraft and robots. It’s demonstrated in every aspect of our technology. It’s demonstrated in how you are reading these words right now.

§ §

In my eyes, a related issue involves the tendency to see people as no more than Pavlov’s dogs.

There is truth to the idea that we can be unconsciously conditioned, and to the extent it is true, I loath it and actively resist it. I think it doesn’t need to be as true with us as it is with animals, because humans have self-awareness.

The light bulb on this point went on when I was reading an article about how saying “thank you,” can be detrimental, if there’s a large power imbalance, on the premise it conditions subservience. I question the idea that appropriate gratitude must lead to a false self-identity.

This tendency to see humans so slavish to our inner programming seems to deny our ability to rise above that programming — which is something that living in civilized society calls upon us to do. It seems to excuse us from working to be better.

A post for another day.


In closing, I must give Tegmark kudos for being upfront from the start about what is real physics and what is his speculation. He has a chart in front of the book laying it out. (That said, I think his dividing line and mine on mainstream physics aren’t quite the same.)

He’s even upfront about his idea being extreme. (Which it totally is.)

Stay intuitional, my friends!

[1] Unless the whole point is being perfect. Which is really hard.

About Wyrd Smythe

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

24 responses to “Our Intuitions

  • Wyrd Smythe

    One nice thing for me is that much of this post sat in my Drafts folder for a very long time. Tegmark gave me the perfect excuse to finish it and remove one more item from my backlog, so yay!

  • Athena Minerva

    It’s a good book I found and I even wrote an article on it too.

  • Wyrd Smythe

    Just for fun, and to commemorate John Conway, I started playing around with implementing Life in Python. Here’s an early attempt:

    (I would have posted this back on the Robots page, but it already has a lot of videos on it.)

  • SelfAwarePatterns

    To me, intuitions are judgments made using cognitive shortcuts, shortcuts that may be innate or habitual. If the situation resonates with the reason the shortcut evolved or was learned, it may be accurate, or at least useful. But we evolved the ability to reason because it often isn’t.

    I do think intuition often fails us when considering scientific concepts. When thinking about special or general relativity, I always have an impulse to relate events back to some absolute time frame, even though I know intellectually that’s wrong. I’m constantly having to check myself. And I don’t know that common intuitions are of any use for foundational quantum physics.

    When I bring up Copernicus as a comparison, it isn’t to say we should accept the compared notion, merely that it’s wrong to summarily dismiss it. People between 1543 and 1609 didn’t really have epistemic grounds for accepting Copernicus’ model as true. But due to its mathematical rigor and compatibility with observations, they also didn’t have grounds to summarily dismiss it as a candidate for reality, even though many did due to its intensely counter-intuitive implications. For that, I think it remains an important cautionary example.

    Anyway, I intuitively feel you’ll see things differently. 😉

    • Wyrd Smythe

      Well, when you put it that way … 😀 😀

      “To me, intuitions are judgments made using cognitive shortcuts,”

      When you say “cognitive shortcuts”… would you agree sometimes our intuitions are better than our conscious analysis of a situation? That sometimes intuition is the unconscious analysis of factors beneath our conscious notice? Or, in your view, is “intuition” always a faulty judgement?

      “When thinking about special or general relativity,”

      This gets at what I was saying about informed intuition. When one studies a topic long enough, one’s thinking about it becomes intuitional.

      That’s why “woman’s intuition” really is a thing. In general, women have better social training and, therefore, social awareness than men. They can identify patterns in social flow that are invisible to others (usually men). That seems like magic to the blind (so it gets a label), but constitutes valid correct analysis to the sighted.

      When one works with mathematics a lot, one develops intuitional thinking about math. People who work with machines a lot develop intuitions about machines. I suspect even quantum physicists, in time, develop intuitions about quantum physics. (I have intuitions about programming languages to the point of, when working really hard on something, sometimes dreaming in code. (You may have intuitions about neuroscience. We both likely do about SF.))

      “When I bring up Copernicus as a comparison, it isn’t to say we should accept the compared notion, merely that it’s wrong to summarily dismiss it.”

      Understood, and I agree.

      What I’m talking about is not a case of “summarily” dismissing something. It’s a case of considered judgement and rational analysis, and the implication that is casual or purely emotional is what’s dismissive.

      In the case of Copernicus, the kind of intuition I’m talking about is on his side, not on the side of his detractors. No one ever talks about Copernicus having an intuition — he did. Informed by his experience. That’s why he was sure he was right.

      The detractors were, for the most part, adhering to tradition, to mainstream, to conservative instincts. (Which isn’t what I mean by intuition.) As you say, his ideas had a rigor that was hard to dismiss. (Even within science, one dead scientist at a time.)

      I agree without reservation about not dismissing, summarily or otherwise, something presented with rigor.

      But disagreeing is not dismissing, especially when that disagreement is thoughtful and rational. I think people sometimes use these intuition arguments, not against being dismissed, but against being disagreed with when they find themselves challenged to respond on point.

      It’s just not a valid argument either way, for or against an idea (it’s a heuristic, at best). The only truly valid arguments involve the axioms and logic of the idea itself.

      • SelfAwarePatterns

        I think intuition in certain situations for certain people can be more effective than their ability to reason on specific topics. That said, it’s a very unreliable and treacherous thing.

        For example, parole boards often deny parole to people because of their intuitions about the candidate. No doubt they tell themselves how grounded in experience their intuitions are. But statistical analysis of their decisions show that their judgments are significantly harsher just before lunch and just before quitting time.

        We all use intuition everyday. For many common circumstances it’s fine. It’s the uncommon ones where we shouldn’t trust it, where it will betray us.

        On Copernicus, people disagreeing with his model had what they took to be thoughtful and rational reasons. If the Earth moved, why couldn’t anyone feel the movement? Why wasn’t the flight of birds or the movement of clouds affected? Why didn’t the stars show parallax? If the Earth wasn’t at the center, why did things fall toward it? Why did scripture imply what it did?

        The thing is, when you unpack each of those things, they’re actually just wrappers around intuitions.

      • Wyrd Smythe

        Is it fair to say you see intuition as mainly faulty due to being tied to our prejudices and orthodoxy?

      • SelfAwarePatterns

        I wouldn’t say “mainly.” As I noted above, people’s intuitions can be affected by physiological factors like hunger and fatigue. I know my judgments tend to be different when I’m in pain, angry, or scared vs when things are going fairly well. So, prejudices and orthodoxy are part of it, but it’s broader than that, and much of it is far more primal. (Although I suppose prejudices and orthodoxy are often heavily influenced by those things too.)

      • Wyrd Smythe

        Pretty much everything you say about intuition is negative, so how is your view not “mainly” that is has little value?

        You’ve often asserted you ‘just feel’ that the brain is a computer. Is that an informed intuition that should be taken seriously? Or should it be disdained?

      • SelfAwarePatterns

        I noted above that we use intuitions all the time. They’re a necessary part of our cognitive toolkit. We don’t have time to think through every conclusion in our day to day lives. But reason evolved to deal with novel situations. The more novel, the less reliable intuitions become.

        I’ve given you the logic many times why I, along with most neuroscientists, see neural processing as computation.

      • Wyrd Smythe

        “The more novel, the less reliable intuitions become.”

        Which opposes what Einstein asserts in the quotes below. I’m wondering why you don’t seem to value that form of intuition.

        Maybe I’m doing you a disservice in thinking your view on intuition is negative. I don’t mean to, but looking back at what you said here, it’s hard to think otherwise. You don’t say much positive about it, but you refer to “cognitive shortcuts” that may be “innate or habitual.” You point out it can be affected by “hunger and fatigue.” (Is that not true of our thinking in general?)

        You also said intuition “often fails us when considering scientific concepts.” And “I don’t know that common intuitions are of any use for foundational quantum physics.” In contrast, Einstein and many others see their informed intuition as a necessary part of their scientific toolkit.

        You do say that “in certain situations for certain people can be more effective than their ability to reason on specific topics. That said, it’s a very unreliable and treacherous thing.” Since you didn’t elaborate on certain people or specific topics, it reads as another negative view to me.

        You cited parole boards and how unreliable their intuition is.

        And finally, “For many common circumstances it’s fine. It’s the uncommon ones where we shouldn’t trust it, where it will betray us.” Einstein is saying (and I agree) that it’s sometimes in uncommon situations were informed intuition can be so valuable.

        All together it gives the impression you don’t see much value in intuition. I genuinely apologize if I’m misunderstanding, but given what you’ve said about it in the past, and given what you’ve said here, I think you don’t see it as a valuable cognitive process.

        Given how intuition is an aspect of human consciousness, maybe it suffers from the same multi-aspect nature that makes consciousness so hard to pin down. There are different kinds of thinking we can label “intuitive”…

        “On Copernicus, people disagreeing with his model had what they took to be thoughtful and rational reasons.”

        From our frame of reference, the Sun going around the Earth is a reasonable intuition. As you pointed out, that’s what it seems like. As a first approximation, it’s an entirely legitimate point of view.

        As such, it became the orthodoxy of its time. Copernicus approached with a speculative idea contrary to the orthodoxy, which (my point is) reacted appropriately in the scientific context. I think science should be slow to respond to contrary views until enough other minds have a chance to consider the evidence. In some regards, the story is about science working.

        The other thing about Copernicus is that he had an intuition, too, that got him to his idea in the face of the orthodox view. So there is the informed intuition of Copernicus and the ignorant intuitions of those without background and the inertial intuition of knowledgeable but conservative people. We may have stepped into another definitional pile.

        I was watching a (really good) video series by Welch Labs about the complex numbers last night. Along the way to the complex numbers are a number of similar intuitive battles. The negative numbers bothered people, for instance. Zero bothered some people. Irrational numbers really bothered some, and “imaginary” numbers (far better to have used the term “lateral”) were just a bridge too far for some.

        Yet in all cases there are strong mathematical intuitions that these things aren’t just correct, but necessary.

        So,… do you see what I mean about the Yin-Yang nature of intuition? That’s why it’s an invalid argument point. What kind of intuition is meant? The conservative inertial type? Or the brilliant insight type? It is not, on its own, a basis for accepting or rejecting an argument. Only the merits of the argument are grounds for that.

      • Wyrd Smythe

        “I’ve given you the logic many times why I, along with most neuroscientists, see neural processing as computation.”

        Neurons seem like logic gates and there seem to be parallels regarding memory. Ideas that I and others have thoroughly debunked on logical grounds. Which leaves the intuition of similarity.

        As I recall, you’ve explicitly said you “just feel” the comparison is apt. It’s an intuitive judgement. And, yes, it is one shared by many in the field.

        My question, given the lack of a strong logical equivalence, given how people defend the idea, and given your assertions about intuition’s lack of value in science, why is the equivalence view not similar to those whose intuition was that the Sun went around the Earth?

        The alternative is that informed scientific intuition has definite cognitive value.

      • SelfAwarePatterns

        In my view, intuition can be a valid starting point, but only a starting point. But it seems clear this is another area where we have to agree to disagree.

        Neural computation entered that category long ago. 🙂

      • Wyrd Smythe

        You’re kinda disagreeing with Einstein, but it’s your call.

        I wasn’t getting at the computationalism debate itself (which I agree is pointless), but to the degree to which intuition informs both that perception and the resistance to opposition.

        Ultimately the intuition argument is a two-edged sword capable of cutting those who wield it.

  • Wyrd Smythe

    Ha! Odometer moment. 11,000 comments on the blog (peanuts, I know).

    This is comment #11,001… 😀

  • Wyrd Smythe

    Speaking of programming intuition, I’m LOL because I just spent 30 minutes trying to figure out why a certain function wasn’t working in a little app I’m creating.

    My intuition after all these years is that, no matter how perfect the code looks, no matter how many times I’ve checked that it’s perfect,… it’s not perfect. The crash is always pilot error.

    Even when I finally narrow the problem down to one line of code that looks perfect even when I’ve stared at it for several minutes,… it’s not perfect.

    It’s always some little thing. An undotted “i” or an uncrossed “t” somewhere. This was a synchronization error between a logging format string and supplied parameters. The string wasn’t expecting any!

    Log.info('GUI:Quit ' % str(args))

    Oops! Dumb error. All one can do is sit back and laugh. 😀 😀

  • Wyrd Smythe

    I had a feeling (an intuition?) that Einstein had spoken about the value of intuition. In fact, the word appears 29 times on his Wikiquote page. Here are a few:

    The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them. ~Principles of Research (1918)

    I believe in intuitions and inspirations. I sometimes feel that I am right. I do not know that I am. When two expeditions of scientists, financed by the Royal Academy, went forth to test my theory of relativity, I was convinced that their conclusions would tally with my hypothesis. I was not surprised when the eclipse of May 29, 1919, confirmed my intuitions. I would have been surprised if I had been wrong. ~Viereck interview (1929)

    A new idea comes suddenly and in a rather intuitive way. But intuition is nothing but the outcome of earlier intellectual experience. ~Letter to Dr. H. L. Gordon (1949)

    (He’s talking about what I called “informed” intuition. As he says, it’s a product of our “intellectual experience.”)

    For it is intuition that improves the world, not just following a trodden path of thought. Intuition makes us look at unrelated facts and then think about them until they can all be brought under one law. To look for related facts means holding onto what one has instead of searching for new facts. Intuition is the father of new knowledge, while empiricism is nothing but an accumulation of old knowledge. Intuition, not intellect, is the ‘open sesame’ of yourself. ~Einstein and the Poet (1983)

    I have faith in the universe, for it is rational. Law underlies each happening. And I have faith in my purpose here on earth. I have faith in my intuition, the language of my conscience, but I have no faith in speculation about Heaven and Hell. I’m concerned with this time—here and now. ~Einstein and the Poet (1983)

    Totes, Al!

  • rung2diotimasladder

    “I think it’s worth looking into what the word intuition really means.”

    I agree. It’s one of those words that has different interpretations and can turn a discussion into a mess in no time.

    In more philosophical contexts, I tend to think of ‘intuition’ in the Kantian sense: “Thoughts without content are empty, intuitions without concepts are blind.” For Kant, intuitions are immediate singular representations of objects, and concepts are what intuitions have in common. This dog, Geordie vs. dogs in general.

    But then there’s pure intuition of space and time. All-pervasive stuff.

    Anyway, I tend to think we err more in judgment than intuition.

    • Wyrd Smythe

      I think that’s a very good point. I might still throw intuition into the mix by adding that errs in judgement can come from intuitions that don’t quite match reality.

      I do agree intuitions are immediate and singular. I see them as how our below-conscious awareness and thoughts speak to our conscious mind. Working with any topic long enough trains your brain to think in those terms, both at a conscious and unconscious level. Those holistic gestalt thoughts that bubble up come from those trained areas.

      Our physical intuitions likewise come from deeper areas of our brain, some innate to physical brains, some hardwired by our genetic evolutionary history, so by programming we learn from birth. I might go so far as calling learning to walk the process of obtaining the walking intuitions.

      When we learn a musical instrument, or learn to dance, we spend most of the beginning time thinking about how to do it. Once we’ve trained the brain, much of that becomes intuitive. (Driving is another example. How many of us can drive somewhere without really being conscious of doing it at all?)

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