Can "Infinity" ever be more than a mathematical abstraction?

[Write4U]

Of course. But you are confusing the map with the territory. I perfectly well agree that math is "unreasonably effective" in the physical sciences. The claim that the universe IS the math is a claim of metaphysics.

Tegmark does not clain that the universe is math. He proposes that it has only mathematical properties.....difference. On the face of that sounds reasonable to me. I cannot conceive of a universe which does not have mathematical properties. Even chaos is a mathematical term.

From the standpoint of someone who's studied more math than physics, my understanding is that mathematicians don't care in general whether their work is "real". Their work has value purely as abstraction. No connection with reality is ever implied when it comes to math. Math only tells you what's logically true based on the axioms ... and we don't even know for sure that our axioms are consistent!

Well, as bookkeeper my maths were an accurate accounting and reflection of the real assets and liabilities of the company, as verified by our yearly inventory count and cash in the bank. This is not trivial.

So math is more like chess, a game with formal rules that's fun to play. We wouldn't say, "The universe is a game of chess and we're the pieces." That would be taken as stoner philosophy, agree?

I would not compare mathematics to a game, but more to the rules of how a game is played....difference.

But Tegmark says, "The universe is math," just because certain aspects of the universe can be described to a given degree of approximation subject to the limitations of the experimental or observational apparatus and technique. Confusing map with territory. And believing one's maps and models are real, as opposed to our own mind's interpretation of what's real. Math may be "out there," but it's also "in here," coded in our brains at a very low level. Wouldn't you like to know why it is that the human brain can do math at all? Tegmark's not asking the hard questions.

Tegmark says that the universe could not exist unless it followed some form of mathematical function because all physical things in the universe have values and values interact through mathematical functions.
As to our ability to represent the mathematical values and functions with a symbolic language is considered to be our greatest evolutionary asset. But humans are not the only ones who can perform mathematical calculations. A Lemur and many other species can tell the difference between more and less, and are able to do a form of rudimentary calculus based on that mental ability.

To imagine mathematics is exact in its description of reality is to commit a grave fallacy of the philosophy of science. And then to believe the math "is" rather than models the world ... that's just wrong.

It is not necessecary for our symbolic language to be reality as long as it can represent universal functions accurately.

I hope you don't mind if I don't engage with the rest of your post, although I enjoyed your diagram.

Thank you and suit yourself if you do wish to pursue this perspective.

I actually dropped in to mention that I confirmed Aaronson's negative impression (not of the book, which everyone agrees is stimulating and educational regardless of whether you believe in his ultimate thesis.

I have problems myself with some of Tegmarks presentations, but as have dealt with mathematics for a greater part of my life, I find the concept of a certain mathematical aspect to the very creation and evolution of the universe.
David Bohm called this progreesion as the "enfolded order" (potential values and functions) becoming expressed in the physical world as the "unfolded order". The word "order" being key.

But I did want to pass on this one quote from Peter Woyt, who writes the great physics blog Not Even Wrong.

Tegmark’s career is a rather unusual story, mixing reputable science with an increasingly strong taste for grandiose nonsense. In this book he indulges his inner crank, describing in detail an uttery empty vision of the “ultimate nature of reality.” What’s perhaps most remarkable about the book is the respectful reception it seems to be getting

There's plenty more where that came from. Woit's review is here, http://www.math.columbia.edu/~woit/wordpress/?p=6551.

And Aaronson's review is here: https://www.scottaaronson.com/blog/?p=1753

Well , perhaps they are right, I am not qualified to judge, but many scientist seem to accept the premise and I can only ask, "how does the universe function if not by some form of mathematics?"

I probably won't read the book. But I am actually planning to make a run at reading his original paper. I have the pdf and it's not that overly long and I can probably get a better sense of his terminology and ideas. I'm sure I'll learn a lot from studying his work.

I haven't read his book either. But I see no other option to his premise and I haven't read anything that can replace the power of mathematics in all of reality.

But on the metaphysics, it seems laughably wrong to be. Mathematical structures are very abstract. And in fact one of the criticisms is that he doesn't actually spend much time talking about the actual math. I get the feeling that "math" for Tegmark is "the equations that physicists use," and not math as actually practiced by mathematiciansI have studied a fair number of those abstract entities that go by the name of "mathematical structures." And believe me, the universe isn't one of those. Not unless you believe that the universe is an artifact of set theory. Or you're arguing some sort of structuralist position that the structures are independent of our representations of them. Tegmark understands none of this as far as I know.

All patterns are fundamentally mathematical in essence, as are equations which merely show that one thing has the same value as another thing, but seen from a different persective.
And to say mathematical structures are very abstract, I recommend this short but delightful Ted Talk by Roger Antonsen, who clearly demonstrates the connection between ratios and reality.
https://www.ted.com/talks/roger_antonsen_math_is_the_hidden_secret_to_understanding_the_world

So anyway I think it's unfortunate if the interesting discussion of whether infinity might be actually instantiated in the physical world got sidetracked into what Tegmark thinks. That's another criticism of Tegmark. That his brand of pop metaphysics wrapped up in scientism crowds out intelligent discussion of the fundamentals. I'm not going to talk about Tegmark anymore. But I am going to make a serious run at his paper, which by the way is here if anyone's interested. https://arxiv.org/pdf/0704.0646.pdf

Ok thanks for listening. No more Tegmark rants from me but I would love to talk about what it means for actual infinity to be instantiated in the world. And I'd welcome specific pointers to claims that actual infinity is instantiated in some theory. Sean Carroll's Wiki page didn't say anything about it.

Thank you for the link, I now feel compelled to read it, just to confirm if my first impression is correct.

And I agree with you that any assumption of a mathematical nature to the universe has nothing to do with infinity per se.

 

[someguy1]

I really suggest you take the time to watch at least all of part 1 lecture. The physical unattainability of infinity is labored somewhat to begin with. But how that fits into infinities as applied to cosmology where actual infinity is often assumed wrt size of our universe, and then to multiverse concepts, is very sound imo. The followup Q & A to part 1 is also good. Part 2 gets technical in places but has a nice roundup at the end - a triumph of common sense if you like. Anyway your choice.

Ok I power-watched most of the second half. I confess that I much prefer written text. I can absorb info in text a lot faster than sitting through a lecture.

I gather that in the end he rejects physical infinity as untestable hence not science. So I'm glad I watched because he's agreeing with me!

He also did a couple of things typical of the genre that I find annoying. One, he repeated that infinity is "unreachable." But in fact in the past 140 years mathematicians have a very deep and beautiful theory of actual infinity. You cannot in my opinion legitimately talk about infinity without acknowledging what's been going on in modern set theory. And since set theory underlies the formal structure of virtually all modern math; and modern math is the foundation of physics; it's not possible to give a complete account of infinity in physics without incorporating the modern foundations of math. The entire subject is ignored in all these multiverse conversations.

Second, he repeated the misunderstanding that in an infinite universe you must have infinitely many duplicates. He misunderstands or deliberately ignores infinitary probability, in which an event with probability 0 may still happen, and one with probability 1 might fail to happen. The best you can actually say with certainty is that SOME state recurs infinitely many times, but probably not the state representing you or me.

So all in all a good summary of the state of the subject, and he agrees with me. Thanks for pointing me at the vid. I'll try to watch more in small doses, there's a lot of good stuff in there.

 

[someguy1]

This is why we can name them in the first place. They can be measured and represented with mathematical symbols.

That doesn't mean they ARE the mathematical symbols, or the abstract mathematical objects the symbols describe. You're imbuing notation with ontological power.

 

[Write4U]

That doesn't mean they ARE the mathematical symbols, or the abstract mathematical objects the symbols describe. You're imbuing notation with ontological power.

They don't have to be human symbols, and yes human mathematics are the abstract symbolic representation of values and functions. But even here we need not stay with numbers per se. We can use the decimal system, the english system, the binary system, or morse code, or colors, or even sound waves, or even a geometric object or a pattern to represent a number. This is the power contained in mathematical equations.

Do see the Roger Antonsen clip. It is short and really entertaining as well as profound in content.

It makes no difference what symbols we use as long as they are consistent and represent a specific value or function. An abacus works just as well as a computer, it's just slower.

 

[NotEinstein]

That doesn't mean they ARE the mathematical symbols, or the abstract mathematical objects the symbols describe. You're imbuing notation with ontological power.

Yeah, Write4U does that all the time. Coupled with a few misconceptions of reality here and there, and a complete disregard for traditional definitions of words, this leads to a whole bunch of seeming word-salad. It's not, though; Write4U simply hold an atypical philosophical position. He just has severe trouble expressing himself in wording that others can understand, and seems to be unable to change this. Note too that Write4U often doesn't explain things himself; he refers to clips and videos, often misinterpreted by him due to his own views. But using his own definitions, it does make sense, and the clips and videos do support his position.

So don't be too harsh on the guy; the way you are interpreting what you read, is almost 100% certainly not what Write4U meant to write. He can't help it; he simply has his own language.

 

[Speakpigeon]

If the universe is a geometric object, then it is by definition a mathematical object, no?

This is what Tegmark says:

https://arxiv.org/pdf/0704.0646.pdf
I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure.

..."our physical world is an abstract mathematical structure"?!
To me, that's pure gobbledygook. So, could you explain what that could possibly mean?
Here is a clue as to the problem. The definition of the word "abstract":

Abstract
adj
1. having no reference to material objects or specific examples; not concrete
2. not applied or practical; theoretical
3. hard to understand; recondite; abstruse
4. (Art Terms) denoting art characterized by geometric, formalized, or otherwise nonrepresentational qualities
5. defined in terms of its formal properties: an abstract machine.
6. (Philosophy) philosophy (of an idea) functioning for some empiricists as the meaning of a general term: the word'man' does not name all men but the abstract idea of manhood

Which definition did Tegmark had in mind exactly?
I guess he might just as well have said that the universe doesn't exist for real. That it's just an idea.
I would say that before you get into serious stuff you better learn your English.
And that's just one word, line 4 in the abstract... Not a good start.
EB

 

[Write4U]

Yeah, Write4U does that all the time. Coupled with a few misconceptions of reality here and there, and a complete disregard for traditional definitions of words, this leads to a whole bunch of seeming word-salad. It's not, though; Write4U simply hold an atypical philosophical position. He just has severe trouble expressing himself in wording that others can understand, and seems to be unable to change this. Note too that Write4U often doesn't explain things himself; he refers to clips and videos, often misinterpreted by him due to his own views. But using his own definitions, it does make sense, and the clips and videos do support his position.

So don't be too harsh on the guy; the way you are interpreting what you read, is almost 100% certainly not what Write4U meant to write. He can't help it; he simply has his own language.

I admit that like every one else I use my own language and if, as you say, the links and clips I provide do support my posits, then what is the problem, unless you want to dismiss the links and clips as well?

If I just post the links and clips I am told to put it into my own words and when I do I am told I don't make any sense except the links support my posits? Now that's weird.

 

[Speakpigeon]

Yeah, Write4U does that all the time. Coupled with a few misconceptions of reality here and there, and a complete disregard for traditional definitions of words, this leads to a whole bunch of seeming word-salad. It's not, though; Write4U simply hold an atypical philosophical position. He just has severe trouble expressing himself in wording that others can understand, and seems to be unable to change this. Note too that Write4U often doesn't explain things himself; he refers to clips and videos, often misinterpreted by him due to his own views. But using his own definitions, it does make sense, and the clips and videos do support his position.

So don't be too harsh on the guy; the way you are interpreting what you read, is almost 100% certainly not what Write4U meant to write. He can't help it; he simply has his own language.

Yes, I've given up on trying to make sense of the "word salad" but it appears Tegmark is doing it as well. See my previous post.
EB

 

[NotEinstein]

I admit that like every one else I use my own language

Actually, most people use the same language (i.e. definition of words).

and if, as you say, the links and clips I provide do support my posits, then what is the problem,

They only support your position when using your definition of words. They often don't support your position when using the traditional definitions of words. And because you are often unable to give your definition of words, it's difficult for others to see this and understand you.

unless you want to dismiss the links and clips as well?

This is the exact opposite of what I've said, so I don't know where you got that idea from?

If I just post the links and clips I am told to put it into my own words and when I do I am told I don't make any sense except the links support my posits? Now that's weird.

It's not weird for the precise reasons I just gave. Putting things "into your own words" doesn't really help us understand your language; it is very difficult to learn Chinese when the other person only speaks Chinese. It'd be much more helpful if the other people also spoke English...

You should try putting things in other people's words; that the best way to get your ideas across.

 

[NotEinstein]

Yes, I've given up on trying to make sense of the "word salad" but it appears Tegmark is doing it as well. See my previous post.

I don't doubt it; one can always find somebody with weird and inconsistent ideas, and that's certainly not helpful in understanding, no. It's the deliberate cherry-picking of using only that person's views to support oneself (which is an argument from authority as well) that, to me, is more problematic.

 

[Write4U]

..."our physical world is an abstract mathematical structure"?!
To me, that's pure gobbledygook. So, could you explain what that could possibly mean?
Here is a clue as to the problem. The definition of the word "abstract":

I understand that sentence to mean; the essence of the spacetime fabric contains a form of mathematical logic which determines how physical objects attain actual and potential values (Tegmark identifies 32 values) and how these values interact via certain functions (Tegmark identifies a handfull of equations). I see no inherent problem with that perspective.

 

[Write4U]

It'd be much more helpful if the other people also spoke English...

That's funny...and I agree...

 

[Write4U]

I understand that sentence to mean; the essence of the spacetime fabric contains a form of mathematical logic which determines how physical objects attain actual and potential values (Tegmark identifies 32 values) and how these values interact via certain functions (Tegmark identifies a handfull of equations). I see no inherent problem with that perspective.

But I also agree that this does not have much to do with the concept of infinity.

 

[Speakpigeon]

I understand that sentence to mean; the essence of the spacetime fabric contains a form of mathematical logic which determines how physical objects attain actual and potential values (Tegmark identifies 32 values) and how these values interact via certain functions (Tegmark identifies a handfull of equations). I see no inherent problem with that perspective.

Your "essence" here is ambiguous:

essence
a. The intrinsic or indispensable quality or qualities that serve to characterize or identify something: The essence of democracy is the freedom to choose.
b. Philosophy The inherent, unchanging nature of a thing or class of things, especially as contrasted with its existence.

I assume you're no philosopher so I would guess you mean "essence" as per the first of these two definitions. So, we're talking not about the reality of the universe but about the way human beings characterise it. The essence of space-time is just the intrinsic or indispensable quality or qualities that serve to characterize or identify the universe. The essence is indeed an abstraction, not the real thing itself, but our representation of it. An essence in this sense is necessarily an abstraction, an idea, not something that would exist out there in the physical world.
Yet, Tegmark actually says the physical universe is abstract: "our physical world is an abstract mathematical structure".
So, again, even according to your own interpretation, he says the physical universe is just an idea, not a real physical universe, which of course makes the whole sentence contradictory.

So, no, the physical world isn't an abstracty structure, mathematical or not, and Tegmark should learn his English or pass for a moron.
EB

 

[Seattle]

https://blogs.scientificamerican.co...-insider-tips-for-criticizing-the-multiverse/

Here's an interesting post/article/response by Max Tegmark addressing comments that his book is "empty" or whatever the various criticisms are. There is nothing earth shaking in this link. It just shows that Tegmark is aware of the issues and shows his state of mind.

Even in this article however he still misstates (at least in my understanding) some of the choices. Such as "A fourth argument, made in my book, is that if there’s an external reality completely independent of us humans, then there’s a fourth type of multiverse realizing all mathematically possible universes."

There can be an external reality independent of humans without that implying a "multiverse realizing all mathematically possible universes".

Of course, when you read his hypothesis you know what he means but without the entire context some of his comments are very misleading.

Here is a Wiki article (mainly criticisms)...

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

I realize that the OP was about infinity and it referenced Wegmark and the thread now seems to be mainly about his book but that's fine with me as well (it's better than talking about aliens) and I've included these links to be informational (since I just ran into them myself while looking for criticisms/reviews of his book).

 

[Write4U]

Your "essence" here is ambiguous:

The way things seem to work in accordance to recurring natural imperatives?
David Bohm called it the "Wholeness and the Implicate Order"

Bohmian mechanics inherits and makes explicit the nonlocality implicit in the notion, common to just about all formulations and interpretations of quantum theory, of a wave function on the configuration space of a many-particle system. It accounts for all of the phenomena governed by nonrelativistic quantum mechanics, from spectral lines and scattering theory to superconductivity, the quantum Hall effect and quantum computing. In particular, the usual measurement postulates of quantum theory, including collapse of the wave function and probabilities given by the absolute square of probability amplitudes, emerge from an analysis of the two equations of motion: Schrödinger’s equation and the guiding equation. No invocation of a special, and somewhat obscure, status for observation is required.

https://plato.stanford.edu/entries/qm-bohm/

But I realize this is now way off from the OP question.
I read post #4 and was impressed with logic why infinity cannot exist in reality.
And as I understand the concept, if an equation yields a result of infinity, it is flawed

 

[Q-reeus]

I gather that in the end he rejects physical infinity as untestable hence not science. So I'm glad I watched because he's agreeing with me!

Yes but goes further. And imo convincingly argues that multiverse advocate claims that bubble universes are born with infinite size ignore restrictions imposed by quantum physics. In particular Heisenberg uncertainty principle. This attention to physically imposed limitations vs assumed idealizations means that our universe, as a presumed 'typical' bubble formed ~ 14by ago, cannot be infinite in size!

He also did a couple of things typical of the genre that I find annoying. One, he repeated that infinity is "unreachable." But in fact in the past 140 years mathematicians have a very deep and beautiful theory of actual infinity. You cannot in my opinion legitimately talk about infinity without acknowledging what's been going on in modern set theory. And since set theory underlies the formal structure of virtually all modern math; and modern math is the foundation of physics; it's not possible to give a complete account of infinity in physics without incorporating the modern foundations of math. The entire subject is ignored in all these multiverse conversations.

I don't see where that is relevant. Extremely doubtful Ellis is not thoroughly familiar with set theory and much much more. The whole aim is to show that recourse to what he terms essential use of infinities in physics is automatically suspect and should be discarded ab initio.

Second, he repeated the misunderstanding that in an infinite universe you must have infinitely many duplicates.

Ellis's reference to the 'infinite copies' argument relies on iirc that:
1: There is no infinitely small i.e. quantum physics means a finite number of possible states in any given finite region.
2: Large scale homogeneity and the same general physics applies everywhere in a 'genuinely infinite universe'.
3: Given an infinite number of such regions, 1 & 2 implies infinite repetition of all possible state spaces is inevitable.

Leaving aside the de facto assumption of a truly infinite universe, I see there is arbitrariness in assigning sufficiently large regions effectively isolated from each other. In GR one could I suppose appeal to cosmic horizons i.e. observable universe as setting such a 'natural' boundary. Horizons per se don't exist in Yilmaz gravity but maybe effective ones can be defined. For either choice there, one thorny issue is how can any such arbitrary region remain even effectively isolated if the time taken for all possible state configurations to repeat is vastly larger than the light crossing time of such an arbitrary region? Which it surely always will be. The relevant Hubble expansion rate has to factored in, unless an unrealistic static infinite universe is assumed. Accelerated expansion may take care of isolation in GR setting, but then you have a heat death and continued matter dilution within any horizon bounded region setting a natural cap on what can occur in a finite effective time.
Even in an unrealistic boundless static universe setting, in my view natural abiogenesis won't occur in any finite time. See e.g. http://inference-review.com/article/animadversions-of-a-synthetic-chemist
The statistical 'miracles' that pure chance combinations can work have imo absolute caps no matter how much time and space and entropy gradients etc, is/are allowed.
Quacker Ellis disagrees, as of course do the great majority of scientists. I have no disagreement re repetition of realistically possible chance arrangements.

He misunderstands or deliberately ignores infinitary probability, in which an event with probability 0 may still happen, and one with probability 1 might fail to happen. The best you can actually say with certainty is that SOME state recurs infinitely many times, but probably not the state representing you or me.

So I searched for infinitary probability and found http://philsci-archive.pitt.edu/1245/1/fim.pdf
Started reading but quickly lost interest. Maths is only of interest to me as it relates to physics and even then mostly applied physics. The paradoxical examples you cite presumably contain 'hidden clauses'. At any rate I think your criticisms have misread Ellis in all but that 'infinite copies' piece, which as you know he rejects the idea as an actuality anyway.

So all in all a good summary of the state of the subject, and he agrees with me. Thanks for pointing me at the vid. I'll try to watch more in small doses, there's a lot of good stuff in there.

Agreed.

 

[Speakpigeon]

The way things seem to work in accordance to recurring natural imperatives?

What was wrong with the definitions of "essence" I provided? You didn't say.
So you're just confirming you want to speak your own private language.
And I don't see that the notion of essence could possibly be tied up with your "recurring natural imperatives". You would need a more general definition, unless you want to exclude the possibility of anyone talking about the essence of God or some such. See?
Making up definitions on the hoof can't be the easy and trivial task you seem to assume. Dictionary definitions relies on usage by many people over a long time and this is good insurance against ineptitude. You should try it.
Further, "the way things seem to work" isn't a good start either. How could that possibly fit in with your understanding of Tegmark's sentence? The essence of the spacetime fabric contains a form of mathematical logic which determines how physical objects attain actual and potential values...

David Bohm called it the "Wholeness and the Implicate Order" https://plato.stanford.edu/entries/qm-bohm/

So, apparently, you can't articulate your views. You have to refer us to linked papers.

But I realize this is now way off from the OP question.
I read post #4 and was impressed with logic why infinity cannot exist in reality.
And as I understand the concept, if an equation yields a result of infinity, it is flawed

You must be kidding.
EB

 

[Speakpigeon]

Ellis's reference to the 'infinite copies' argument relies on iirc that:
1: There is no infinitely small i.e. quantum physics means a finite number of possible states in any given finite region.
2: Large scale homogeneity and the same general physics applies everywhere in a 'genuinely infinite universe'.
3: Given an infinite number of such regions, 1 & 2 implies infinite repetition of all possible state spaces is inevitable.

As I see it, this notion of necessary repetition can only be understood as based on the assumption that the number of all possible states of any given region of space is finite, and this in turn would be based on the assumption that a certain kind of laws apply to the universe as a whole and that these laws can only result in a finite number of different states.
Yet, the justification for this assumption seems to me to be only that our own model of the universe is what it is. So, at best, all you may be able to say is that any model, of the kind of models we happen to have now, is self-contradictory if it includes infinity. Yet, I don't think that's even what Ellis is saying. Rather, he seems to be arguing on broadly common-sense grounds, i.e. that the idea of a universe with an infinite repetition of identical regions and histories is not appealing to him and shouldn't be appealing to anyone with minimal common-sense, or that in effect it's a finite universe.
Now, beyond what Ellis may be saying, as I see it, that the particular kinds of models of the universe we may have now implies repetition is irrelevant as to the whole universe. If the universe was effectively infinite, our model itself would be finite in essence anyway because based on our observation of a limited region of the universe. But then, there doesn't seem any good reason to just assume that the models we happen to have now are valid beyond the limited region of the universe we are able to observe.
And on the more general idea of the reality of infinities, beyond the models of the universe we may have now, I fail to see why we would need to have a repetition of states or histories of states over distant regions of space and time. There's just no logical reason to think that an infinite universe would need to feature repetition.
There's a similar situation I think with the particular question of whether space may be infinitely divisible. As I understand it, there's no scientific experiment proving the existence of something like the shortest distance between two points in space. Now, if space was infinitely divisible, i.e. continuous, then even a quantified physics wouldn't necessarily lead to repetition.
EB

 

[C C]

[...] Many concede that the Universe likely is infinite. How can science so readily concede that infinity is a real possibility [...]

The term is just an unnecessarily obfuscated or mysterian way of declaring that "more" can be added / outputted either continually or intermittently upon the "need" of the process, user, etc. If the "indefinite magnitude which does have a definite and fixed orientation toward endless growth" is converted to something concrete or ontological, then obviously it can't refer to a completed, static condition without being contradictory. As it then becomes finite: A definite boundary or set measurement no matter how ludicrously large in extent or quantity.

From a purely practical standpoint, one might refer to whatever principle, algorithm, formulaic operation, systemic procedure, etc it is that is open to perpetually engendering "more" amount, extension, division, nested patterns, etc as... "infinity". Since in an abstract kind of way it would contain the potential of all the endless _X_ that is falling out of it or could be engendered by it. But "real-world" wise the expression otherwise cannot refer to a static, completed condition or final product unless it is one of us everyday, rational dunce "you, me, or theys" being blithely unconcerned about conflating two opposite characteristics in conversation. I..e, being too dense to be receptive to or affected by what otherwise be the stressful effects of cognitive dissonance. No professionals, including scientists and philosophers, are devoid of such rational dunce moments or even prolonged worldviews wallowing in the "ecstasy" of internal conflict.

~