Great post! I had no idea there was such a big difference between digital and analog. To me it’s all a mystery how music can be recorded at all. I do find audio waveforms intuitive at this point from recording my audiobook, certainly more so than that gobbledygook that’s supposed to be an Amy Winehouse song.
That’s kind of the central point. The analog representations are intuitive because they look like what they are. But those numbers could be anything, so there’s no intuition to have.
Not much, because no, it isn't. 😁 It's invariably *carried* by a physical vehicle, but the way the same information can be carried by vehicles of different forms shows how information is decoupled from its vehicle (this vehicle/content dualism I've been posting about).
Bueno! I just wanted to be sure. I keep seeing this idea pop up again and again and I'm wondering if there's some technical meaning that people are referring to when they use the word 'information' in the context of computationalism. Because the information I'm thinking of is definitely not physical! And good point about the decoupling. If information is x, and information is y, then x and y would have to be identical to each other, which could create problems depending on what x and y stand for. It seems to me you can't identify information (i.e. consciousness) with something physical and then say it's multiply realizable. Those who were initially in favor of this view have had to backtrack and the arguments have gotten increasingly convoluted and incredible.
Which is often what happens when one is on the losing side of an argument.
I think the "information is physical" assertion is computationalism's (IMO feeble) way of responding to the "simulated water isn't wet" argument. (Countering their counterargument is part of what led me to develop the "digital dualism" argument, which I think is more effective than the "simulated X isn't Y" one because it explores and exposes the incorrectness of "information is physical".)
I've been stuck trying to respond. I think in part we've reached a point of differing viewpoints. One example is that I don't see any dissonance in the notion of a concrete example of an abstraction. In software design, a class is an abstraction, but all instances of that class are concrete. If you link "abstraction" and "generalization" with "design" or "blueprint" does the notion of reifying an abstraction make more sense?
Another example is that I think reality does subtract. Up quarks have +2/3 electrical charge, and down quarks have -1/3. Protons are two ups and one down, so +2/3 +2/3 -1/3 = +1. Neutrons are one up and two downs, so +2/3 -1/3 -1/3 = 0. On a larger scale, multiple snowfalls add to the total depth. Multiple thaws subtract from it. Likewise, river heights and rain. In any event, subtracting is just the inverse of adding. You have four apples, I give you three apples, you have seven apples. You have ten apples, you give me three apples, you have seven apples. Apples in motion both times, only distinguished by direction.
I confess to not entirely following you with regard to counting and set theory, so I'm not sure how on point this is, but here's my take:
My guess is that counting is truly ancient, very near the origins of language. Dogs and other animals have been shown to judge the "fairness" (equalness) of food portions. I suspect our ability to identify the cardinality of small groups comes from comparing portions. But our brains can only buffer about seven digits (hence phone numbers), so we "lose count" with larger groups. Hence using bags of pebbles, marks in clay, or knotted strings to keep track of those groups. Zero was just an empty bag, an unmarked tablet, or an unknotted string, so it wasn't obvious it meant anything.
Of course, zero ("vanish" in math speak) turns out to be a big topic. It's necessary as a placeholder for positional notation. One ("unity" in math speak) is likewise huge. It's the basic unit, the first step from nothing to something. All further steps are just more something. Some cultures have "none", "one", "two", "three", "many". Which perhaps speaks to your point that math isn't instinctive, but an abstraction that must be developed or learned. Absolutely. One of the salient aspects of human consciousness is our ability to create abstractions.
Zero (the additive identity) and One (the multiplicative identity) are deep parts of the mathematical fabric. Addition and multiplication are the fundamental operations on numbers. (In fact, it's only addition. Multiplication is serial addition, and exponentiation is serial multiplication. Subtraction is the inverse of addition, division is the inverse of multiplication, and logarithms are the inverse of exponentiation.)
But I don't see how zero and one inhere tradeoffs. What tradeoffs do you mean?
You lost me on how set theory and counting are opposite. The natural (counting) numbers are defined by set theory. True, the cardinality of a set with a single element is one, but {{}} is just the second link in the infinite chain: {}=0, {{}}=1, {{},{{}}}=2, {{},{{}}.{{},{{}}}}=3, etc.
The multiplicative identity isn't involved in addition, so wouldn't be expected to enable it. In a very real sense, if I add two and three, at a theory level I add: 0+2+3=5. All addition starts with zero, the additive identity. Likewise, if I multiply 2 and 3, it's: 1×2×3=5. This is trivial with integers, rationals, and reals, but it becomes more important with complex numbers. FWIW, I touched on this a little in my posts about complex numbers:
Those posts show how the complex numbers are necessary in math. It also appears they are necessary in quantum mechanics. What that means about reality is so far unknown.
With regard to an exponent of zero, that falls directly out of the basic axiom of exponents, that a⁴=a×a×a×a, AND what I wrote above about multiplication starting from one. See:
The oddball in the lot is 0⁰, which is considered undefined (like dividing by zero).
With regard to objects and structures and formations, I think it shows how language is malleable and context dependent. (A favorite: "Time flies like an arrow; fruit flies like a banana.") It's a fine rabbit hole to explore, but my interests lie more in what ideas people are using words to express. Your example of "the process of erosion" -- as a conversational chapter title -- does only communicate the (well-defined) basic concept of erosion. As are many of the words discussed here, erosion is a big umbrella. As you say, it requires more context. That seems natural to me. Communication requires details.
Hmmm. Just sparked an idea about information theory and entropy... 🤔
I think I can clear up some confusion, which is very much on me. I should have bifurcated the pragmatic and the precise, and one of the conflations mathematicians make is that math is so precise, that it is also pragmatic by default. I would even agree with a mathematician who took such a stance, but I would then need to add "except in the fuller case of precision." Bear with me for a moment as I try to home/hone in here.
I do not deny that when someone asks for a "concrete example of something abstract," that they are making some error, and in fact, I would continue to encourage such use. The error, instead, is in the exceptional case that is overlooked because the intuition carries over to allow concrete to ALSO mean the opposite of concrete when it suits intuitive purposes, and in those hyper-rare, exceptional cases, this amounts to equivocation that has far reaching consequences for the very REASON that math is otherwise so precise that it will carry and compound a smaller "rounding error."
This is similar (but then immediately different) to what I hear when you say "In a very real sense" and I hear from this the good faith style of rhetoric, not a literal claim of "exact reality," but a claim of "sufficient and practical anchoring to reality" that I SHOULD NOT even point out, except to say that you could imagine someone else saying the same words and not being able to parse the rhetoric later from the strong claim. So what I am saying is that the common mathematical paradigm is, in effect, ignoring the softer claim of concreteness and in effect clinging to the stronger sense when it suits. My claim is that this very niche and minor diagnosis is what best accounts for the symptom of "many and holographic worlds" and some other positions that should not be chastised for their seeming unseriousness, but for the confidence with which they are sometimes prescribed. My bridge to make this case would have been the use of statistics, but I wanted to respect your expressing that it was not in your repertoire in some way.
That claim of mine relies on the level of precision that math claims to always use, which can come across as quite trivial. So, if what I am doing here is perceived as "nitpicking" and especially if it seems in bad faith, then at least know that is not the intent and I am putting effort into doing otherwise. So first, I want to ask you if getting next level picky about the inverse relationship of pure math and sets (like pointing out asinine stuff like "there's air in the bag") would just annoy you. If so, that series of points is not worth it.
I will at least synthesize a point about complex numbers (which I actually had read your blog posts on that before), and the idea that subtraction is a real thing. Again, pragmatically, I agree with you, but one of the reasons complex numbers are so useful is because it maintains equidistance from 0 so well, and that allows anti-particles to "annihilate" into one of many possibilities that maintains that distance from zero, conserving energy. And certainly, it would be absurd to demand a stop to the pragmatic use of adding and subtracting inches of snow because "the water comes from and goes somewhere." But the distinction is particularly non-trivial in the sense of the mystery of how there is "stuff" to begin with (energy) which we cannot destroy (bring to zero) no matter how we measure that energy. Energy density in spacetime is distinct from the total energy density, and the only true zero we can conceive of is plausibly nonreal, even in the mathematical and pragmatic senses. But thereafter, we can totally agree to use 0 in numerous ways and by internally consistent rules. Notice how if the mathematician projects math beyond the big bang, it's not just a lack of observability that's the problem, but often a presumption of symmetry in the one area where the observation and math say not to expect symmetry, at least not recognizable. Such a problem would persist if there was a big crunch, because that doesn't solve the fundamental asymmetry. Nor would equal parts matter and anti-matter, precisely because they still add up to positive energy, which is why one does not have "negative" gravity, but curves spacetime according to its energy/mass.
Again, the most convincing area won't be "where only philosophers dare tread." Thought experiments can be tedious, especially if they are teasing out what a child does for fun to annoy adults.
As to objects, structures and formations, I mean to imply the surprising inverse. Language is malleable and context dependent, both of which compound the difficulty of "solving the black box problem" of communication. The examples above, I am positing, is an artifact of surprising convergence that we take for granted precisely because we navigate it so effortlessly. In terms of real complexity, that effortlessness is misleading. We didn't start with some basic knowledge, we had to learn (with some genetic & developmental help) that the thing that sometimes moves near our face is actually our own hand, and that we have some control over it, and that we feel something when an event involves it, and then how to control it, etc etc. That there is even the potential for the convergence of concepts, especially abstract, is both confounding and yet mundane. The pragmatic shrug towards it also makes sense. It's not like paying attention to it allows you to improve it, so better that the brain tucks it away as "normal" and simple, even after we find out how very not either of those things it is. SO yes, requiring context and details should seem natural, but that is more likely for evolutionary reasons. That is part of why my blog is called "Hiding AS Plain Sight" rather than "in plain sight." Normal and simple until a tiny crystal forms in your ear canal and "the room spins."
Feel free to share about information theory and entropy!! even if it's just to bounce it off me.
I'm not sure if I will ever write about it on the blog, but the case is there to be made that physicalism, computationalism, bayesian idealism, and using concepts like "noise, interference, and arbitrary" creates some tension at the comprehensive level, even allowing pragmatic definitions. But that is probably unrelated to your insight!
> "The error, instead, is in the exceptional case that is overlooked because the intuition carries over to allow concrete to ALSO mean the opposite of concrete when it suits intuitive purposes"
Could you give me a "for instance"? (Ha, yes, a concrete instance of a generalization!)
> "So what I am saying is that the common mathematical paradigm is, in effect, ignoring the softer claim of concreteness and in effect clinging to the stronger sense when it suits."
An example would help, because I'm not seeing the problem with how "concrete" and "abstract" are used. Do I correctly understand your basic thesis here to be that there is a problem with the ambiguity of some words?
On other topics: If by "many and holographic worlds" you refer to the Many-Worlds Theory (MWI) and the AdS/CFS correspondence, I DO call them unserious. The latter, in particular, refers to a spacetime (AdS) that we don't appear to live in, so it's a mathematical toy for now. And I agree theorists give these non-physical evidence-free hypotheses far too much credence.
I'm not sure I follow your issue(s) regarding sets. Usually, types, classes, or categories are significant. A set of ten pennies has the same cardinality ("size") as a set of ten elephants but different membership functions, so are different types and can't be otherwise compared. So, if one has a set of two apples in one hand and an empty set in the other, for the comparison to be meaningful beyond cardinality, the types must match. It doesn't make much sense to reference the infinite set of empty sets for all possible types unless one is dealing with higher notions of sets. It's a trivial truth with no utility. (Alternately, all null sets can reduce to THE null set. Either way there is no proliferation of null sets.)
And you do have to be careful with higher notions of sets. Russell's famous example, about the set of all sets that don't include themselves as members (aka the Barbar paradox), famously broke mathematics. Type theory made sets manageable, but Gödel came along and showed the best we can hope for is unprovable consistency.
Nitpicking is a requirement in STEM topics, and common usage ("the lingo") is helpful for clarity. I'm not clear on your math and physics points. One example: I'm not sure what you refer to by "equidistance from 0" in complex numbers. "Equi-" implies equal-to, but equal to what? Complex numbers have a magnitude -- their distance from zero -- and each magnitude has an infinite set of complex numbers in a circle around zero (is that what you mean by "equi"?). Given some complex number, multiplying it by second complex number WITH A MAGNITUDE OF ONE, does rotate the first number to a new spot on its circle (assuming the second number has a non-zero angle). This rotation is a basic property of the complex numbers, but the QM math behind particle annihilation is more complex.
The conservation of energy/mass derives from the symmetry that the laws of physics don't change over time (time translation symmetry). Mathematically, physics allows negative energy/mass, but it appears so far to be non-physical. With particle/anti-particle interactions, the quantum numbers (spin, charge, etc.) are opposite and cancel to zero but energy/mass is conserved. Because the quantum numbers are zero, many things with the same energy/mass can be produced so long as their quantum numbers add to zero. When particles that aren't charge conjugates interact, the quantum numbers don't sum to zero, and their sum must be maintained in the result. (When it comes to this stuff, I nitpick with the best of them!)
> "That there is even the potential for the convergence of concepts, especially abstract, is both confounding and yet mundane."
Indeed. Kant thought a lot of that was due to how our minds framed the world, our experience of time and space and physical extent. We're all homo sapiens, and we live in the same world, so some degree of convergence would be the norm. Our ability with abstractions raises the conundrum of Platonic reality. Do we invent or discover circles and pyramids? Do they exist outside our reality? It's philosophical fun, but ultimately, as the saying goes, it's "shut up and calculate." Whatever else, the pragmatic approach usually works.
My response here will be inadequate on account of time constraints since I am also trying to finish up a couple of posts.
It is not the ambiguity in words that I have a problem with, but it is the (in effect) process of equivocating the meaning of a word such that the conclusion following some set of premises relies on that ambiguity, or in the case of "misplaced concreteness" relying on BOTH meanings simultaneously, often without realizing it. It's why pragmatists are usually right, but their impatience with nitpicking leaves some exceptions for the nitpickers to notice and resolve.
Here are a couple examples of the "double meaning" of concrete that can best be described as "misplaced concreteness" because of the reliance on that double meaning:
The list you (and I) provided for what we agree are "unserious" mathematical theories of what "really exists" in "concrete reality." You mentioned the classic "shut up and calculate," and this exact attitude is based on that misplaced concreteness. If you went to someone was was truly serious about these seemingly unserious theories, "shutting up and calculating" is exactly what they are doing, and they will have computational instantiations to show an internal consistency of their theories. They will point to what they would call "CONCRETE instances" by which they mean concrete examples of abstract calculations. I (and I would guess you) would then find some interest in the internal consistency while also pointing out that it does not necessarily extrapolate to "concrete reality," and that you do not find their elegant solutions sufficient for this projection. I am guessing that you and I would both expect that such a counterargument would be insufficient to convince THEM of the insufficiency of their model. From this, I am saying that this "concrete example" of a mathematician equivocating on the "concreteness of reality" versus the "concreteness of instantiated computation" is the more parsimonious explanation of why their disagreement persists and why they will continue to promote their math-as-reality paradigm.
There are two other examples, one of which is how you ended your reply. The good faith interpretation holds zero problem for me and actually, I think, reinforces my position. Plan A: "Shut up and calculate" check. Plan B: "Whatever else, the pragmatic approach usually works" CHECK. And I am saying that in the case of misplaced concreteness BOTH plans A and B have failed, and the possibility of needing a plan C is implicit in your phrasing "the pragmatic approach USUALLY works" (which is a pragmatic approach to a pragmatic approach mind you).
Plan C, I am proposing, is that extra level of resistance to mathematicians who think that there is no opportunity cost to maximal abstraction before application, AND to the pragmatist that assumes "they will know the exceptions when they see it" because misplaced concreteness is actually what you would EXPECT to fit solidly in their blind spots. The PERCEPTUAL concreteness is what the pragmatist hears and double checks via an intuitive gut check of concreteness, which is usually totally sufficient and I do not fault them. The CONCEPTUAL concreteness is what the abstractionista hears from the word, with computation followed by instantiation constituting their version of sufficiency.
Kant is a perfect example of nitpicking resistance to both strands of reasoning, and both the abstractionistas and pragmatists of his time actively resisted his conception of synthetic a priori. In fact, William James, considered the "Father of American Psychology" in trying to rebut Kant's account and establish "Radical Empiricism" as the paradigm for what he called Pragmatism (and later regretted calling it that), accused him of "Vicious Abstractionism." The quote in this wikipedia article relays his idea perfectly: https://en.wikipedia.org/wiki/Reification_(fallacy)
Notice how vicious abstractionism, rather than fitting Kant's perspective, instead lands squarely on the abstractionista perspective where math dictates concrete reality, something that Kant specifically denied. Conversely, "the fallacy of reification" (which is the main heading of that wiki page) is the accusation abstractionistas use against pragmatists that step into "their territory" as they attempt to "substantiate" what is abstractly claimed via statistical and mathematical analyses. Vicious abstractionism is pernicious exception to the rule of "shut up and calculate," and reification, when it is a fallacy (which as you have pointed out is not always the case) is the pernicious exception to the rule of "whatever else, the pragmatic approach usually works" as it generates a false sense of sufficiency. Both exceptions "prove" Kant's rule of synthetic a priori, because "concreteness," both perceptual and conceptual, is synthetic a priori. We could not learn "what concreteness is" without initial condition of searching for what is concrete, and we could not "abstract" concreteness as a shared property of our experiences if we did not first have a working concept of it. Stated another way, the "anchoring" heuristic and "saliency" network "precedes" the perception and conception of "concreteness," but neither strictly delineates what "concreteness" will mean to any given person, because some part is reserved for social learning. Thus children follow gazes to learn what earns other people's attention, and with a theory of mind, they can deduce that when someone is "staring into space," it is not where their eyes are pointing that is the salient feature in their minds, but whatever they are imagining. Two types of "concreteness" competing in the same theory of mind that will ongoingly shape that theory of mind into a new form of "concreteness."
I'm not sure the sets and numbers is a good avenue to develop this further.
As to the complex numbers and quantum mechanics, it sounds to me like a (better) rephrasing of the point I was trying to make. Complex numbers preserve the "magnitude" as a distance from zero in the complex plane. I am saying the reason that is good is because it fits to the conservation of energy, ASSUMING you have selected the correct "zeroes." Among those zeroes are, for example, a zero of all relevant dimensional axes, if trying to obey relativity, spacetime is constrained to the same zero, if not, the "initial conditions" along the arrow of time has a zero that can diverge from the 0 of space, especially when distance from zero on the complex plane has to conserve the net energy in the system you have conceptually isolated.
The means by which you isolate a system entails the zeroes you use, and those zeroes ALL come to represent either a form of centrality (magitude) or a discretization of a boundary (time 0 which precedes time 1, the MAXIMUM distance from zero in the system if all mass is converted into energy which is measured relative to the speed of light in a vacuum). This is what I mean by zeros and ones constituting the syntax, and the means by which we isolate a system can be more or less arbitrary (what I can see, what we both agree we see, what this grid tells us, locality as defined by the speed of light in a vacuum and this agreed to "starting point").
> "From this, I am saying that this "concrete example" of a mathematician equivocating on the "concreteness of reality" versus the "concreteness of instantiated computation" is the more parsimonious explanation of why their disagreement persists and why they will continue to promote their math-as-reality paradigm."
(More parsimonious than what other explanation?) If we're talking about an era-based detachment from physical reality in culture and thought, then I think we're on the same page. Exactly ten years ago this month, Leon Wieseltier, challenged by Stephen Colbert to sum up modern culture in ten words, memorably said "Too much digital; not enough critical thinking; more physical reality." The first two clauses I immediately recognized as issues I've be "on about" for a while -- the second since the 1970s. In the last decade, I've come to recognize the third clause is just as, perhaps more, important.
If the thesis is this *comes*from* a misuse of words or even a misplaced concreteness, I don't think I agree. (FWIW, I think there is *something* to the weak Sapir-Whorf hypothesis, but I'm not sympathetic to the strong version.) I suspect the misuse of terminology comes from sloppy thinking, and perhaps we're saying the same thing here, too. Bottom line, the backsliding of culture towards the Dark Ages (mysticism, ignorance) has, I think, myriad social causes. And will take concerted effort to repair, the starting point being getting culture to embrace that it should be repaired (in my eyes, it currently embraces being stupid and ignorant -- I'm astonished in the comment sections of science and math posts how many people feel compelled to almost brag about not understanding the post).
What follows are asides:
Theoretical physics and cosmology have stalled for decades, no new advances or discoveries, yet huge unanswered questions remain. In this vacuum, theorists get a little crazy. A wild idea that "just might be right" and that turns out to be right means worldwide fame, a Nobel prize. So, some of these FBS notions are throwing the dice on success. There is also a "publish or perish" paradigm in the sciences that demands content, and a lot of FBS gets generated to satisfy it. I just read an article about how poorly fact-checked *most* pop-science books are.
And lately there seems a social entropy fraying the edges of *everything* socially, including the sciences. I almost believe the new millennium blew our mental fuses. We expected the vacation homes on the Moon that were promised, didn't get them, decided science failed us, and gave up.
Misplaced concreteness seems a drop in a bucket in comparison. Looking at that Wiki link, though, I think I see a source of disconnect in our thread. Reification itself isn't a fallacy the way ad hominem or begging the question is. Those are *always* fallacies. If you look at the disambiguation page for reification, you'll find a variety of (rather disjoint) valid applications. But in the same sense abstraction can be incorrect (discarding important details to amplify a desired result), reification can be incorrect (treating an abstraction as overly real). I suspect this is a problem more in philosophy and the so-called "soft" sciences than in the hard sciences where experiment rules. (Or in mathematics which is proudly the most abstract science.) That's why all the FBS that's popped up in theoretical physics lately is dismaying; it's new. And wrong. Professional scientists have actually used the term "post-empirical science" seriously. The mind boggles.
These FBS (Fantasy Bullshit) "theories", though, are distinct from the Copenhagen Interpretation "shut up and calculate". The latter is within an anti-realist framework that essentially denies that reality is concrete. The longer form might be, "We can't say anything whatsoever about reality, but we have developed math that lets us predict the outcomes of experiments, so forget about trying to describe reality (it's impossible) and just use the math to get stuff done." In contrast, the FBS notions we listed reach for being *realist* theories describing and explaining a concrete reality beyond the one we know.
Note that the correctness of the math isn't the argument (it's just a required condition). The explanatory power, parsimony, and *plausibility* of the model are all arguments, but of course only arguments. Real support only ever comes in the form of experimental evidence. Reality is always the final arbiter.
And some such theories have turned out to be correct. Even what were thought purely abstract math "toys" turned out to be valuable cryptographic techniques. Often, in math, something thought abstract turns out to apply to the real world. One of the more famous math philosophy papers is Eugene Wigner's "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" (1960). One example: pi, the abstraction of the ratio of a circle's circumference to its diameter, turns up in all sorts of (natural) places that aren't circles. To the point of it being almost weird.
FWIW, models and theories are abstract but not calculations. A calculation always has a concrete form which can be evaluated for correctness regardless of its content. For example, the concrete (but invalid) syllogism: All aliens are green; My shirt is green; Therefore, my shirt is an alien. The syllogism is invalid because its *form* is invalid. All X are Y. This Z is Y. Therefore, this Z is X. Not a valid form; the conclusion does not follow.
WRT complex numbers, you can't say they "preserve" magnitude without specifying under what operation. In fact, under nearly all operations the magnitude changes. Only when multiplied by a number on the complex unit circle is their magnitude preserved. Which has nothing to do with conservation of energy. I think perhaps math and physics aren't fertile ground here.
"more parsimonious" in the sense of explaining the reified math theories via the misstep of the mathematician than in explaining why reality in any way should be considered conformal with the math, instead of the ongoing task of conforming the math to reality. When that relationship inverts, the mathematician is likely unaware that they have slowly drifted toward inductive reasoning from their experience of this "weird" success of math, and they still imagine themselves deducing that parsimony dictates their position.
And yes, I think we are saying largely the same thing from different angles. Note that in the etymology piece I shared, I was sure to make the point that the "word" did not cause the change in sense of the word so much as the experiences attempted to be communicated slowly bend the meaning of the word.
Note also that I did acknowledge the duality of "reification" as not always fallacious. So I do think we are on the same page, but I will draw your attention to how "the hard sciences" vs "the soft" is itself likely shifted from the permissible to the fallacious reification. The "soft sciences" and their "replication crisis" came from the external pressure of "the "hard sciences" to use those tools. Which is why the willingness of the hard sciences to throw the soft sciences under the bus while they propose unfalsifiable fantasies following decades of little progress, is quite hypocritical. Many of these same scientists love to ponder whether an LLM based on nothing but probability distributions might just spawn consciousness. It's not something that is so absurd as to be dismissed, but you'll note that they are not simultaneously freaking out over the ethical implications of that, especially given the unfalsifiability of it. When the path is literally "hey let's see how closely we can have a computer mimic people" and somewhere along that path you know that you will not know the implications for when it succeeds, maybe we need to do some double takes.
Experimental and observation evidence are both needed. That was Herbert Blumer's insight, mirroring Kant's own. That the human brain is so adaptively pliable that if your framing of an empirical question has no means of "resistance" from the reality you are trying to study, then your experiment may be tainted by observation-oriented biases. Boatloads of statistics that can predict other statistics definitely tells you that you are onto something, but the willingness to forego testable theories and conflate this predictive power with explanatory power is prolific.
I will also point out that the sense in which you are saying that computation is "concrete" sounds like you may be conflating the two interpretations when you also say "it is not abstract" or the specific thing you are calling "the computation." The physical information that describes the process of change of state is what I will assume you mean by the computation that is not abstract. But the human interpretation process that originated the inputs and anticipated outputs of that computation should not then treat the output as this same kind of "concrete." It is an instantiation of a computational paradigm, and the propriety of application lies in the interpretation. I can divide a number by two, and say that it proves that "half the happiness is half as good," but it proves no such thing because no one has ever established happiness is "divisible" in the mathematical sense.
Re: complex numbers, I will have to follow up on this later, but my intuition is that under the typical operations, the relationship with the conservation principles is maintained by the change in magnitude relative to 0. That simple rotation does not happen means that it is not energetically equivalent. One interpretation Claude gave was that complex numbers are useful for preserving probabilities adding up to 1. When I proposed that this value of preserving probabilities relies on reality adhering to energy conservation, he "agreed" very readily. But you know, LLMs are themselves quite pliable.
After thinking about this for several days, I think I understand why we see this a little differently. Or maybe we don't and it's that I don't understand your thesis and prescription. Always possible. Firstly, for me, the FBS hypotheses we've listed are a small (but glaring) problem in the hard sciences and not a problem at all in math. As I said last reply, I think social pressures account for most science FBS. And a free-wheeling modern sense that "anything is possible". That last perhaps has some connection with your thesis.
No good *mathematician* thinks reality should confirm to their math. They tend to be clear minded about the abstractness of math. As mentioned previously, that it so often is effective with reality is a source of debate. I think FBS issues may become bigger in the softer sciences for reasons I'll get to, but generally those with good science training are the least of the problems I see.
Where I think FBS becomes endemic and problematic is with people and social issues. The current political insanity is one result. Modern culture increasingly encourages stupidity by supplying pre-canned worldviews and identity categories. Once one finds a comfortable niche, they can have a bubble to shield against unwanted opinions and knowledge. It's a form of willful stupidity that has been a disaster for society. I've been ranting about it since the 1970s under the rubric of "The Death of a Liberal Arts Education." We don't teach people to learn anymore.
I think, the root problem is ignorance. People aren't read in on the concepts of "abstract" or "concrete". Many possibly couldn't use them correctly in a sentence. I think, to make the error of misplaced concreteness, one must first fully understand what that means. So, at the social level, I don't see a logical error so much as a failure of knowledge and education.
> "Which is why the willingness of the hard sciences to throw the soft sciences under the bus..."
That hasn't been my experience with real scientists. What makes physics a hard science and sociology a soft one has nothing to do with how difficult they are. Or rather, it does but *opposite* from what misunderstanding how the terms apply suggests. "Hard" sciences are mathematically easy while "soft" sciences are mathematically so hard as to be intractable. What makes soft sciences soft is the huge number of free variables. It results in a vast, fuzzy, multi-dimensional configuration space with a crazy number of relevant dimensions. Hard sciences are hard (like rock) because they are so easily tamed with math. Soft sciences are fuzzy and incredibly difficult to see clearly. The replication crisis comes from how varied humans are. Testing shows repeatedly: one size never fits all or even most. But that lack of hard evidence (another reason hard sciences are called hard) enables unfounded and hard to counter speculation. FBS.
> "The physical information that describes the process of change of state is what I will assume you mean by the computation that is not abstract."
No, I was referencing that any computation, to be a computation, has a form, a syntax, and that syntax is necessarily concrete (else computation would be useless).
> "...my intuition is that under the typical operations, the relationship with the conservation principles is maintained by the change in magnitude relative to 0. That simple rotation does not happen means that it is not energetically equivalent."
I'm sorry, but this business with complex numbers and conservation of energy is mathematical gibberish. There is no connection. LLMs are not a good source of knowledge. They also contain all the gibberish from the internet.
I am very glad your wrote this piece. It deals with several tricky concepts I am trying to disentangle in a generalizable way. I may have mentioned, perhaps in other words, that I have created a Razor that is essentially the inverse of Occham's (hence the pseudonym): parsimony relative to sufficiency and generality, as opposed to necessity and abstraction.
This also leads to dealing with "arbitrariness" as well. It's a bit of a brain twister, but it would be a kindness to me if you can find a consistent or "complete" set of definitions or relations among "physical," "abstract," "arbitrary" and "general."
Note that I think "concrete" opposite "abstract" as if on a spectrum has led to a great deal of conflation. So to address some of the implications of your use in this post, "physical" seems to imply a mutuality in form, while "abstract" seems to imply a map/territory bifurcation while "arbitrary" refers to a structural connector between the map and the territory that "could just as well have been any other" functional connector. You may have already picked up on my issue with this set of terms.
For example, each element is technically "physical" while "concrete" in its stead would seem to only provide a rhetorical resolution since it can't mean "physical" and probably reduces to "salient," or "particular," or "specific," or some combination thereof. Which is still problematic since "specific" is commonly opposite "general." Meanwhile, "arbitrary" is a property of a choice, after which, the map/terrain connector must be "specific" or "particular." 😵💫😵💫
To clarify why I don't think such a set is trivial, I suspect and need to be able to communicate the common conflation of abstraction -> generalization -> computation -> instantiation
... as being synonymous with or an abstract type of "substantiatiation." I am eager to see what "evaluation" means in your upcoming posts.
Also note that I don't think that there is but one internally consistent way to arrange these terms, but I thought you might want to try your hand at it, and perhaps proving me wrong in the process. Or feel free to ignore the whole ordeal as a headache! 😁
Thank you, I'm glad you got something from it. As you suggest, an inclusive taxonomy runs into difficulties. I think that may be inevitable when the subjects are both diverse and complex. A bit to dig into here, let me start with those terms as I define them.
I agree "abstract" and "concrete" are antonyms. "Physical" refers to real-world objects, from fundamental particles to the visible universe. The only antonym that springs to mind is "nonphysical". What is physical is "concrete", but concrete can also mean "specific" or "actual" (like concrete numbers in a deal).
I'd say an "abstraction" is a type of "generalization", but a generalization can include something like "All dogs are great." One might argue that is an abstraction. The line is fuzzy, but I think generalizing is a broader term. Its antonym is "specific", and I see specific and concrete as similar but distinct, so likewise, abstract and general are distinct.
I would oppose "arbitrary" with "required". For example, the term "arbitrary precision" means "any precision". As you say, dealer's choice. In terms of your map and the territory, an important point is the distinction between the map and the mapping. In a case like this, the mapping is more important than the map (which is just numbers). We may already be on the same page, but "map" here means the encoding (and decoding) process that generates those numbers. The numbers are essentially random with no resemblance to the territory because they are a numerically *encoded* form and the encoding design is arbitrary. (There are constraints to the design, of course.)
[There are actually two maps. One transfers the physical to electrical representation (faithful in form). This is an analog map, a transfer curve. The second encodes the electrical representation to the numeric map.]
"Computation" is a separate matter and the subject of the next post in this Newsletter. In short, though, a computation is something that can be implemented by a Turing Machine. An "instantiation" is a specific instance of a class, design, type, or other specific abstraction. Dollar bills are instances of the USD, but so are the virtual dollars in a bank account. An "implementation" is similar to an "instance" but implies internal complexity. One implements a process or design.
The key distinction is that, while both analog and digital require physical vehicles, digital systems have a second layer -- the abstraction the physical vehicle carries. Analog involves a proportional transfer -- it *is* the vehicle.
Thank you for the detailed response! I suppose I should clarify that in the context of this post, the clearly delineated procedures to and from the physical and digital is relatively straightforward. Outside of such a carefully bounded procedure, I suspect there are major conflations.
To be clear, I think "concrete" is misleading when considered an antonym for "abstract." Notice how you almost never hear "concretize" as the reverse process, but you'll hear "reify" when done in error.
Meanwhile, rather than carefully formulating a treatment, "specification" can be used to pluck an instance out of thin air, no matter how "abstract" or "general." In theory, abstraction risks errors of omission (locally), as you may inadvertently abstract away properties or features on which the ones you keep are dependent. When you generalize, you risk (again locally) errors of commission, where the broadening of the property or feature may not apply in the domain. Should the previously abstracted features be in error, and that insufficiency be generalized, then the errors can be compounding.
If desired, see if the following seem to be intuitive to you:
"Abstraction" itself seems abstract
"Generalization" itself seems general.
"Specification" itself seems specific
"Concrete" itself seems concrete
Note that this isn't universal of concepts. "Arbitrariness" does not itself seem "arbitrary" for example. Now, pointing out that some concepts or procedures seem to "self-apply" might seem arbitrary, but I suspect that (if it's not just idiosyncratic of my treatment) it is actually significant for fundamental function. Apologies if this is a bit confusing.
I've usually expressed it as "abstract" vs "physical", but "concrete" works as well. Maybe better in some regards, because we don't always abstract from the physical, but we always do from the concrete. I don't think they're ends of a spectrum, though. More Yin and Yang. In my world, reifying something need not be an error. When I write code with data structures, those reify my design. (In OOP, object instances are sometimes said to be reifications of their class.) We do say "make abstract" or "make concrete", so I seem to see a genuine opposition there. What do you dislike about it? (Perhaps the treatment as a spectrum? Technically, one can't make something "more abstract" or "more physical". It's one or the other. (OTOH, I insist "nearly unique" is a valid phrase.))
True that abstraction and generalization necessarily discard details. The goal, obviously, is to distill out the details that matter to the task at hand and ignore those that don't. I think the risk of important details falling through the cracks can be high in some cases. Specifically, because of their complexity, with regard to simulating or emulating minds. Part of my thesis in this series involves the difficulty of recognizing the important details.
I'm not sure wordology is any more effective than numerology. Language is so ambiguous and context dependent that the interesting patterns that turn up with words are usually coincidental. One of my favorites is that "listen" and "silent" have the same letters. Another is "garden" and "danger". Tempting to draw a connection, but those coincidences don't work in other languages. That's the thing that always got me with wordology. Change the language and the pattern disappears. (FWIW, most words just seem specific to me, so it may indeed be idiosyncratic.)
Excellent set of responses and older posts. In particular, the magnitudes vs numbers post captured some critical distinctions, to which I want to respond when I have more time.
It's less that I have a problem with the concept of "concreteness" and more the inconsistent use of it that conflates its meaning and confuses its utility. Most uses of the term, outside of synonymity with "physical," seems to be entirely rhetorical, in the same sense as the modern use of "literally." If someone says "give me the concrete numbers," they mean give them something "precise," cohesive, or with a large degree of certainty or surety.
I sense it's part of a more general, modern problem with the treatment of statistics, as we have begun to reify the exploratory power of statistics, combined with the predictive power of human inference, into explanatory power that gets credited to the statistical side of the ledger. The Central Limit Theorem and the Law of Large Numbers get wildly undue credit, while "heuristics" are attributed biases according to their divergence from "statistical truths." But that's a rant for another time!
Re: wordology, I agree with your assessment and for the exact conditions stated. However, there are strands of etymology that are less arbitrary, and their ubiquity across languages is part of the evidence. To give just one example, the "weight" of evidence or importance is always a negotiated magnitude, but never a number. It might seem like a metaphor you could just discard, but the next few in line only serve to prove the rule. "Preponderance of evidence" comes from "ponder" which means "to make heavy," so preponder is essentially making something heavy to then be weighed. Deliberation, libra means "scales." Even the word "Importance" comes from "import," meaning to bring or carry.
As I am still writing about, virtually all words that mean important, across languages, reduce to meanings of "weight" and the "distance" it is "carried." LLMs can assist in verifying this. Even the word "vector" shares a root with "vehicle," hence they are a "force carrier." And when you think about it, this makes embodied sense. Gravitational North/South is the most stable reference frame for biological evolution. There is so much more to say about it, but it is probably best I fit it into my actual writing for now, else I'll just go on and on!
Words involving basic concepts often have different flavors in different contexts. For instance, "concrete" really does mean "specific" as well as "physical" or "tangible". One might not like the conflation, but language evolves like a coral reef in all directions.
Long ago at a family gathering, a spouse of a distant relative turned out to be a professional linguist. I asked her if, as a linguist, she was horrified by the common misuse of language. She replied that, as a linguist, she *studied* language but didn't judge it. While I'll never be as distant with language as that, I've kept it in mind ever since. Language is what it is. One might as well deny the tides.
So, for instance, the semantic shift of "literally" irritates me, but I make myself let go. (And sometimes have some fun mocking or parodying the misuse.)
I've managed to keep statistics out of my knowledge base, but I imagine it suffers the same issues many sciences do with huge misunderstandings and horrible metaphors and analogies that mislead. Physics has lots of examples, and I'm sure stats does, too. Pop science and science journalism is a whole other topic.
I quite agree that etymology and wordology are different. Somewhat as mathematics and numerology are. The evolution of language is a fascinating topic.
Agreed mostly all around. "Literally," and "ironically" and "begs the question" had shifts that, while somewhat annoying, are not prone to confusion or conflation. The contextual conflations of "concrete" (which is ironically flexible) may not be causally related, but certainly seems part of a larger set of symptoms in the tech hype space, which seems to have had an outsized effect on science. That might be unsurprising given the shape of modern incentives, but it complicates my overarching task of trying to establish a common ground of intellectualism, skepticism, and sensibility.
LOL! Well, it’s a bit like MIDI, isn’t it. A digital-analog hybrid.
Hmmm. Take it a bit further. Some (analog) musical instruments have digital inputs. Piano or saxophone keys, for example. Or frets on a guitar. Others have analog inputs. Fretless guitars, violins, trombones. That said, you can hit piano keys hard or soft and bend guitar strings. A lot of analog either way, but I hadn’t really thought about the nature of musical instrument inputs until you mentioned player pianos.
(Which were a key symbol in season one of HBO’s WestWorld.)
Great post! I had no idea there was such a big difference between digital and analog. To me it’s all a mystery how music can be recorded at all. I do find audio waveforms intuitive at this point from recording my audiobook, certainly more so than that gobbledygook that’s supposed to be an Amy Winehouse song.
That’s kind of the central point. The analog representations are intuitive because they look like what they are. But those numbers could be anything, so there’s no intuition to have.
Curious, what do you think of the idea that "information is physical"?
Not much, because no, it isn't. 😁 It's invariably *carried* by a physical vehicle, but the way the same information can be carried by vehicles of different forms shows how information is decoupled from its vehicle (this vehicle/content dualism I've been posting about).
Bueno! I just wanted to be sure. I keep seeing this idea pop up again and again and I'm wondering if there's some technical meaning that people are referring to when they use the word 'information' in the context of computationalism. Because the information I'm thinking of is definitely not physical! And good point about the decoupling. If information is x, and information is y, then x and y would have to be identical to each other, which could create problems depending on what x and y stand for. It seems to me you can't identify information (i.e. consciousness) with something physical and then say it's multiply realizable. Those who were initially in favor of this view have had to backtrack and the arguments have gotten increasingly convoluted and incredible.
Which is often what happens when one is on the losing side of an argument.
I think the "information is physical" assertion is computationalism's (IMO feeble) way of responding to the "simulated water isn't wet" argument. (Countering their counterargument is part of what led me to develop the "digital dualism" argument, which I think is more effective than the "simulated X isn't Y" one because it explores and exposes the incorrectness of "information is physical".)
I like it, and the phrase digital dualism. Just goes to show the ancient problems haven’t gone away.
@William of Hammock:
I've been stuck trying to respond. I think in part we've reached a point of differing viewpoints. One example is that I don't see any dissonance in the notion of a concrete example of an abstraction. In software design, a class is an abstraction, but all instances of that class are concrete. If you link "abstraction" and "generalization" with "design" or "blueprint" does the notion of reifying an abstraction make more sense?
Another example is that I think reality does subtract. Up quarks have +2/3 electrical charge, and down quarks have -1/3. Protons are two ups and one down, so +2/3 +2/3 -1/3 = +1. Neutrons are one up and two downs, so +2/3 -1/3 -1/3 = 0. On a larger scale, multiple snowfalls add to the total depth. Multiple thaws subtract from it. Likewise, river heights and rain. In any event, subtracting is just the inverse of adding. You have four apples, I give you three apples, you have seven apples. You have ten apples, you give me three apples, you have seven apples. Apples in motion both times, only distinguished by direction.
I confess to not entirely following you with regard to counting and set theory, so I'm not sure how on point this is, but here's my take:
My guess is that counting is truly ancient, very near the origins of language. Dogs and other animals have been shown to judge the "fairness" (equalness) of food portions. I suspect our ability to identify the cardinality of small groups comes from comparing portions. But our brains can only buffer about seven digits (hence phone numbers), so we "lose count" with larger groups. Hence using bags of pebbles, marks in clay, or knotted strings to keep track of those groups. Zero was just an empty bag, an unmarked tablet, or an unknotted string, so it wasn't obvious it meant anything.
Of course, zero ("vanish" in math speak) turns out to be a big topic. It's necessary as a placeholder for positional notation. One ("unity" in math speak) is likewise huge. It's the basic unit, the first step from nothing to something. All further steps are just more something. Some cultures have "none", "one", "two", "three", "many". Which perhaps speaks to your point that math isn't instinctive, but an abstraction that must be developed or learned. Absolutely. One of the salient aspects of human consciousness is our ability to create abstractions.
Zero (the additive identity) and One (the multiplicative identity) are deep parts of the mathematical fabric. Addition and multiplication are the fundamental operations on numbers. (In fact, it's only addition. Multiplication is serial addition, and exponentiation is serial multiplication. Subtraction is the inverse of addition, division is the inverse of multiplication, and logarithms are the inverse of exponentiation.)
But I don't see how zero and one inhere tradeoffs. What tradeoffs do you mean?
You lost me on how set theory and counting are opposite. The natural (counting) numbers are defined by set theory. True, the cardinality of a set with a single element is one, but {{}} is just the second link in the infinite chain: {}=0, {{}}=1, {{},{{}}}=2, {{},{{}}.{{},{{}}}}=3, etc.
The multiplicative identity isn't involved in addition, so wouldn't be expected to enable it. In a very real sense, if I add two and three, at a theory level I add: 0+2+3=5. All addition starts with zero, the additive identity. Likewise, if I multiply 2 and 3, it's: 1×2×3=5. This is trivial with integers, rationals, and reals, but it becomes more important with complex numbers. FWIW, I touched on this a little in my posts about complex numbers:
https://logosconcarne.substack.com/p/easy-complex-numbers
https://logosconcarne.substack.com/p/complex-number-forms
Those posts show how the complex numbers are necessary in math. It also appears they are necessary in quantum mechanics. What that means about reality is so far unknown.
With regard to an exponent of zero, that falls directly out of the basic axiom of exponents, that a⁴=a×a×a×a, AND what I wrote above about multiplication starting from one. See:
https://logosconcarne.substack.com/i/144512816/the-third-theorem
The oddball in the lot is 0⁰, which is considered undefined (like dividing by zero).
With regard to objects and structures and formations, I think it shows how language is malleable and context dependent. (A favorite: "Time flies like an arrow; fruit flies like a banana.") It's a fine rabbit hole to explore, but my interests lie more in what ideas people are using words to express. Your example of "the process of erosion" -- as a conversational chapter title -- does only communicate the (well-defined) basic concept of erosion. As are many of the words discussed here, erosion is a big umbrella. As you say, it requires more context. That seems natural to me. Communication requires details.
Hmmm. Just sparked an idea about information theory and entropy... 🤔
Thank you again for the thoughtful response.
I think I can clear up some confusion, which is very much on me. I should have bifurcated the pragmatic and the precise, and one of the conflations mathematicians make is that math is so precise, that it is also pragmatic by default. I would even agree with a mathematician who took such a stance, but I would then need to add "except in the fuller case of precision." Bear with me for a moment as I try to home/hone in here.
I do not deny that when someone asks for a "concrete example of something abstract," that they are making some error, and in fact, I would continue to encourage such use. The error, instead, is in the exceptional case that is overlooked because the intuition carries over to allow concrete to ALSO mean the opposite of concrete when it suits intuitive purposes, and in those hyper-rare, exceptional cases, this amounts to equivocation that has far reaching consequences for the very REASON that math is otherwise so precise that it will carry and compound a smaller "rounding error."
This is similar (but then immediately different) to what I hear when you say "In a very real sense" and I hear from this the good faith style of rhetoric, not a literal claim of "exact reality," but a claim of "sufficient and practical anchoring to reality" that I SHOULD NOT even point out, except to say that you could imagine someone else saying the same words and not being able to parse the rhetoric later from the strong claim. So what I am saying is that the common mathematical paradigm is, in effect, ignoring the softer claim of concreteness and in effect clinging to the stronger sense when it suits. My claim is that this very niche and minor diagnosis is what best accounts for the symptom of "many and holographic worlds" and some other positions that should not be chastised for their seeming unseriousness, but for the confidence with which they are sometimes prescribed. My bridge to make this case would have been the use of statistics, but I wanted to respect your expressing that it was not in your repertoire in some way.
That claim of mine relies on the level of precision that math claims to always use, which can come across as quite trivial. So, if what I am doing here is perceived as "nitpicking" and especially if it seems in bad faith, then at least know that is not the intent and I am putting effort into doing otherwise. So first, I want to ask you if getting next level picky about the inverse relationship of pure math and sets (like pointing out asinine stuff like "there's air in the bag") would just annoy you. If so, that series of points is not worth it.
I will at least synthesize a point about complex numbers (which I actually had read your blog posts on that before), and the idea that subtraction is a real thing. Again, pragmatically, I agree with you, but one of the reasons complex numbers are so useful is because it maintains equidistance from 0 so well, and that allows anti-particles to "annihilate" into one of many possibilities that maintains that distance from zero, conserving energy. And certainly, it would be absurd to demand a stop to the pragmatic use of adding and subtracting inches of snow because "the water comes from and goes somewhere." But the distinction is particularly non-trivial in the sense of the mystery of how there is "stuff" to begin with (energy) which we cannot destroy (bring to zero) no matter how we measure that energy. Energy density in spacetime is distinct from the total energy density, and the only true zero we can conceive of is plausibly nonreal, even in the mathematical and pragmatic senses. But thereafter, we can totally agree to use 0 in numerous ways and by internally consistent rules. Notice how if the mathematician projects math beyond the big bang, it's not just a lack of observability that's the problem, but often a presumption of symmetry in the one area where the observation and math say not to expect symmetry, at least not recognizable. Such a problem would persist if there was a big crunch, because that doesn't solve the fundamental asymmetry. Nor would equal parts matter and anti-matter, precisely because they still add up to positive energy, which is why one does not have "negative" gravity, but curves spacetime according to its energy/mass.
Again, the most convincing area won't be "where only philosophers dare tread." Thought experiments can be tedious, especially if they are teasing out what a child does for fun to annoy adults.
As to objects, structures and formations, I mean to imply the surprising inverse. Language is malleable and context dependent, both of which compound the difficulty of "solving the black box problem" of communication. The examples above, I am positing, is an artifact of surprising convergence that we take for granted precisely because we navigate it so effortlessly. In terms of real complexity, that effortlessness is misleading. We didn't start with some basic knowledge, we had to learn (with some genetic & developmental help) that the thing that sometimes moves near our face is actually our own hand, and that we have some control over it, and that we feel something when an event involves it, and then how to control it, etc etc. That there is even the potential for the convergence of concepts, especially abstract, is both confounding and yet mundane. The pragmatic shrug towards it also makes sense. It's not like paying attention to it allows you to improve it, so better that the brain tucks it away as "normal" and simple, even after we find out how very not either of those things it is. SO yes, requiring context and details should seem natural, but that is more likely for evolutionary reasons. That is part of why my blog is called "Hiding AS Plain Sight" rather than "in plain sight." Normal and simple until a tiny crystal forms in your ear canal and "the room spins."
Feel free to share about information theory and entropy!! even if it's just to bounce it off me.
I'm not sure if I will ever write about it on the blog, but the case is there to be made that physicalism, computationalism, bayesian idealism, and using concepts like "noise, interference, and arbitrary" creates some tension at the comprehensive level, even allowing pragmatic definitions. But that is probably unrelated to your insight!
> "The error, instead, is in the exceptional case that is overlooked because the intuition carries over to allow concrete to ALSO mean the opposite of concrete when it suits intuitive purposes"
Could you give me a "for instance"? (Ha, yes, a concrete instance of a generalization!)
> "So what I am saying is that the common mathematical paradigm is, in effect, ignoring the softer claim of concreteness and in effect clinging to the stronger sense when it suits."
An example would help, because I'm not seeing the problem with how "concrete" and "abstract" are used. Do I correctly understand your basic thesis here to be that there is a problem with the ambiguity of some words?
On other topics: If by "many and holographic worlds" you refer to the Many-Worlds Theory (MWI) and the AdS/CFS correspondence, I DO call them unserious. The latter, in particular, refers to a spacetime (AdS) that we don't appear to live in, so it's a mathematical toy for now. And I agree theorists give these non-physical evidence-free hypotheses far too much credence.
I'm not sure I follow your issue(s) regarding sets. Usually, types, classes, or categories are significant. A set of ten pennies has the same cardinality ("size") as a set of ten elephants but different membership functions, so are different types and can't be otherwise compared. So, if one has a set of two apples in one hand and an empty set in the other, for the comparison to be meaningful beyond cardinality, the types must match. It doesn't make much sense to reference the infinite set of empty sets for all possible types unless one is dealing with higher notions of sets. It's a trivial truth with no utility. (Alternately, all null sets can reduce to THE null set. Either way there is no proliferation of null sets.)
And you do have to be careful with higher notions of sets. Russell's famous example, about the set of all sets that don't include themselves as members (aka the Barbar paradox), famously broke mathematics. Type theory made sets manageable, but Gödel came along and showed the best we can hope for is unprovable consistency.
Nitpicking is a requirement in STEM topics, and common usage ("the lingo") is helpful for clarity. I'm not clear on your math and physics points. One example: I'm not sure what you refer to by "equidistance from 0" in complex numbers. "Equi-" implies equal-to, but equal to what? Complex numbers have a magnitude -- their distance from zero -- and each magnitude has an infinite set of complex numbers in a circle around zero (is that what you mean by "equi"?). Given some complex number, multiplying it by second complex number WITH A MAGNITUDE OF ONE, does rotate the first number to a new spot on its circle (assuming the second number has a non-zero angle). This rotation is a basic property of the complex numbers, but the QM math behind particle annihilation is more complex.
The conservation of energy/mass derives from the symmetry that the laws of physics don't change over time (time translation symmetry). Mathematically, physics allows negative energy/mass, but it appears so far to be non-physical. With particle/anti-particle interactions, the quantum numbers (spin, charge, etc.) are opposite and cancel to zero but energy/mass is conserved. Because the quantum numbers are zero, many things with the same energy/mass can be produced so long as their quantum numbers add to zero. When particles that aren't charge conjugates interact, the quantum numbers don't sum to zero, and their sum must be maintained in the result. (When it comes to this stuff, I nitpick with the best of them!)
> "That there is even the potential for the convergence of concepts, especially abstract, is both confounding and yet mundane."
Indeed. Kant thought a lot of that was due to how our minds framed the world, our experience of time and space and physical extent. We're all homo sapiens, and we live in the same world, so some degree of convergence would be the norm. Our ability with abstractions raises the conundrum of Platonic reality. Do we invent or discover circles and pyramids? Do they exist outside our reality? It's philosophical fun, but ultimately, as the saying goes, it's "shut up and calculate." Whatever else, the pragmatic approach usually works.
My response here will be inadequate on account of time constraints since I am also trying to finish up a couple of posts.
It is not the ambiguity in words that I have a problem with, but it is the (in effect) process of equivocating the meaning of a word such that the conclusion following some set of premises relies on that ambiguity, or in the case of "misplaced concreteness" relying on BOTH meanings simultaneously, often without realizing it. It's why pragmatists are usually right, but their impatience with nitpicking leaves some exceptions for the nitpickers to notice and resolve.
Here are a couple examples of the "double meaning" of concrete that can best be described as "misplaced concreteness" because of the reliance on that double meaning:
The list you (and I) provided for what we agree are "unserious" mathematical theories of what "really exists" in "concrete reality." You mentioned the classic "shut up and calculate," and this exact attitude is based on that misplaced concreteness. If you went to someone was was truly serious about these seemingly unserious theories, "shutting up and calculating" is exactly what they are doing, and they will have computational instantiations to show an internal consistency of their theories. They will point to what they would call "CONCRETE instances" by which they mean concrete examples of abstract calculations. I (and I would guess you) would then find some interest in the internal consistency while also pointing out that it does not necessarily extrapolate to "concrete reality," and that you do not find their elegant solutions sufficient for this projection. I am guessing that you and I would both expect that such a counterargument would be insufficient to convince THEM of the insufficiency of their model. From this, I am saying that this "concrete example" of a mathematician equivocating on the "concreteness of reality" versus the "concreteness of instantiated computation" is the more parsimonious explanation of why their disagreement persists and why they will continue to promote their math-as-reality paradigm.
There are two other examples, one of which is how you ended your reply. The good faith interpretation holds zero problem for me and actually, I think, reinforces my position. Plan A: "Shut up and calculate" check. Plan B: "Whatever else, the pragmatic approach usually works" CHECK. And I am saying that in the case of misplaced concreteness BOTH plans A and B have failed, and the possibility of needing a plan C is implicit in your phrasing "the pragmatic approach USUALLY works" (which is a pragmatic approach to a pragmatic approach mind you).
Plan C, I am proposing, is that extra level of resistance to mathematicians who think that there is no opportunity cost to maximal abstraction before application, AND to the pragmatist that assumes "they will know the exceptions when they see it" because misplaced concreteness is actually what you would EXPECT to fit solidly in their blind spots. The PERCEPTUAL concreteness is what the pragmatist hears and double checks via an intuitive gut check of concreteness, which is usually totally sufficient and I do not fault them. The CONCEPTUAL concreteness is what the abstractionista hears from the word, with computation followed by instantiation constituting their version of sufficiency.
Kant is a perfect example of nitpicking resistance to both strands of reasoning, and both the abstractionistas and pragmatists of his time actively resisted his conception of synthetic a priori. In fact, William James, considered the "Father of American Psychology" in trying to rebut Kant's account and establish "Radical Empiricism" as the paradigm for what he called Pragmatism (and later regretted calling it that), accused him of "Vicious Abstractionism." The quote in this wikipedia article relays his idea perfectly: https://en.wikipedia.org/wiki/Reification_(fallacy)
Notice how vicious abstractionism, rather than fitting Kant's perspective, instead lands squarely on the abstractionista perspective where math dictates concrete reality, something that Kant specifically denied. Conversely, "the fallacy of reification" (which is the main heading of that wiki page) is the accusation abstractionistas use against pragmatists that step into "their territory" as they attempt to "substantiate" what is abstractly claimed via statistical and mathematical analyses. Vicious abstractionism is pernicious exception to the rule of "shut up and calculate," and reification, when it is a fallacy (which as you have pointed out is not always the case) is the pernicious exception to the rule of "whatever else, the pragmatic approach usually works" as it generates a false sense of sufficiency. Both exceptions "prove" Kant's rule of synthetic a priori, because "concreteness," both perceptual and conceptual, is synthetic a priori. We could not learn "what concreteness is" without initial condition of searching for what is concrete, and we could not "abstract" concreteness as a shared property of our experiences if we did not first have a working concept of it. Stated another way, the "anchoring" heuristic and "saliency" network "precedes" the perception and conception of "concreteness," but neither strictly delineates what "concreteness" will mean to any given person, because some part is reserved for social learning. Thus children follow gazes to learn what earns other people's attention, and with a theory of mind, they can deduce that when someone is "staring into space," it is not where their eyes are pointing that is the salient feature in their minds, but whatever they are imagining. Two types of "concreteness" competing in the same theory of mind that will ongoingly shape that theory of mind into a new form of "concreteness."
I'm not sure the sets and numbers is a good avenue to develop this further.
As to the complex numbers and quantum mechanics, it sounds to me like a (better) rephrasing of the point I was trying to make. Complex numbers preserve the "magnitude" as a distance from zero in the complex plane. I am saying the reason that is good is because it fits to the conservation of energy, ASSUMING you have selected the correct "zeroes." Among those zeroes are, for example, a zero of all relevant dimensional axes, if trying to obey relativity, spacetime is constrained to the same zero, if not, the "initial conditions" along the arrow of time has a zero that can diverge from the 0 of space, especially when distance from zero on the complex plane has to conserve the net energy in the system you have conceptually isolated.
The means by which you isolate a system entails the zeroes you use, and those zeroes ALL come to represent either a form of centrality (magitude) or a discretization of a boundary (time 0 which precedes time 1, the MAXIMUM distance from zero in the system if all mass is converted into energy which is measured relative to the speed of light in a vacuum). This is what I mean by zeros and ones constituting the syntax, and the means by which we isolate a system can be more or less arbitrary (what I can see, what we both agree we see, what this grid tells us, locality as defined by the speed of light in a vacuum and this agreed to "starting point").
> "From this, I am saying that this "concrete example" of a mathematician equivocating on the "concreteness of reality" versus the "concreteness of instantiated computation" is the more parsimonious explanation of why their disagreement persists and why they will continue to promote their math-as-reality paradigm."
(More parsimonious than what other explanation?) If we're talking about an era-based detachment from physical reality in culture and thought, then I think we're on the same page. Exactly ten years ago this month, Leon Wieseltier, challenged by Stephen Colbert to sum up modern culture in ten words, memorably said "Too much digital; not enough critical thinking; more physical reality." The first two clauses I immediately recognized as issues I've be "on about" for a while -- the second since the 1970s. In the last decade, I've come to recognize the third clause is just as, perhaps more, important.
If the thesis is this *comes*from* a misuse of words or even a misplaced concreteness, I don't think I agree. (FWIW, I think there is *something* to the weak Sapir-Whorf hypothesis, but I'm not sympathetic to the strong version.) I suspect the misuse of terminology comes from sloppy thinking, and perhaps we're saying the same thing here, too. Bottom line, the backsliding of culture towards the Dark Ages (mysticism, ignorance) has, I think, myriad social causes. And will take concerted effort to repair, the starting point being getting culture to embrace that it should be repaired (in my eyes, it currently embraces being stupid and ignorant -- I'm astonished in the comment sections of science and math posts how many people feel compelled to almost brag about not understanding the post).
What follows are asides:
Theoretical physics and cosmology have stalled for decades, no new advances or discoveries, yet huge unanswered questions remain. In this vacuum, theorists get a little crazy. A wild idea that "just might be right" and that turns out to be right means worldwide fame, a Nobel prize. So, some of these FBS notions are throwing the dice on success. There is also a "publish or perish" paradigm in the sciences that demands content, and a lot of FBS gets generated to satisfy it. I just read an article about how poorly fact-checked *most* pop-science books are.
And lately there seems a social entropy fraying the edges of *everything* socially, including the sciences. I almost believe the new millennium blew our mental fuses. We expected the vacation homes on the Moon that were promised, didn't get them, decided science failed us, and gave up.
Misplaced concreteness seems a drop in a bucket in comparison. Looking at that Wiki link, though, I think I see a source of disconnect in our thread. Reification itself isn't a fallacy the way ad hominem or begging the question is. Those are *always* fallacies. If you look at the disambiguation page for reification, you'll find a variety of (rather disjoint) valid applications. But in the same sense abstraction can be incorrect (discarding important details to amplify a desired result), reification can be incorrect (treating an abstraction as overly real). I suspect this is a problem more in philosophy and the so-called "soft" sciences than in the hard sciences where experiment rules. (Or in mathematics which is proudly the most abstract science.) That's why all the FBS that's popped up in theoretical physics lately is dismaying; it's new. And wrong. Professional scientists have actually used the term "post-empirical science" seriously. The mind boggles.
These FBS (Fantasy Bullshit) "theories", though, are distinct from the Copenhagen Interpretation "shut up and calculate". The latter is within an anti-realist framework that essentially denies that reality is concrete. The longer form might be, "We can't say anything whatsoever about reality, but we have developed math that lets us predict the outcomes of experiments, so forget about trying to describe reality (it's impossible) and just use the math to get stuff done." In contrast, the FBS notions we listed reach for being *realist* theories describing and explaining a concrete reality beyond the one we know.
Note that the correctness of the math isn't the argument (it's just a required condition). The explanatory power, parsimony, and *plausibility* of the model are all arguments, but of course only arguments. Real support only ever comes in the form of experimental evidence. Reality is always the final arbiter.
And some such theories have turned out to be correct. Even what were thought purely abstract math "toys" turned out to be valuable cryptographic techniques. Often, in math, something thought abstract turns out to apply to the real world. One of the more famous math philosophy papers is Eugene Wigner's "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" (1960). One example: pi, the abstraction of the ratio of a circle's circumference to its diameter, turns up in all sorts of (natural) places that aren't circles. To the point of it being almost weird.
FWIW, models and theories are abstract but not calculations. A calculation always has a concrete form which can be evaluated for correctness regardless of its content. For example, the concrete (but invalid) syllogism: All aliens are green; My shirt is green; Therefore, my shirt is an alien. The syllogism is invalid because its *form* is invalid. All X are Y. This Z is Y. Therefore, this Z is X. Not a valid form; the conclusion does not follow.
WRT complex numbers, you can't say they "preserve" magnitude without specifying under what operation. In fact, under nearly all operations the magnitude changes. Only when multiplied by a number on the complex unit circle is their magnitude preserved. Which has nothing to do with conservation of energy. I think perhaps math and physics aren't fertile ground here.
"more parsimonious" in the sense of explaining the reified math theories via the misstep of the mathematician than in explaining why reality in any way should be considered conformal with the math, instead of the ongoing task of conforming the math to reality. When that relationship inverts, the mathematician is likely unaware that they have slowly drifted toward inductive reasoning from their experience of this "weird" success of math, and they still imagine themselves deducing that parsimony dictates their position.
And yes, I think we are saying largely the same thing from different angles. Note that in the etymology piece I shared, I was sure to make the point that the "word" did not cause the change in sense of the word so much as the experiences attempted to be communicated slowly bend the meaning of the word.
Note also that I did acknowledge the duality of "reification" as not always fallacious. So I do think we are on the same page, but I will draw your attention to how "the hard sciences" vs "the soft" is itself likely shifted from the permissible to the fallacious reification. The "soft sciences" and their "replication crisis" came from the external pressure of "the "hard sciences" to use those tools. Which is why the willingness of the hard sciences to throw the soft sciences under the bus while they propose unfalsifiable fantasies following decades of little progress, is quite hypocritical. Many of these same scientists love to ponder whether an LLM based on nothing but probability distributions might just spawn consciousness. It's not something that is so absurd as to be dismissed, but you'll note that they are not simultaneously freaking out over the ethical implications of that, especially given the unfalsifiability of it. When the path is literally "hey let's see how closely we can have a computer mimic people" and somewhere along that path you know that you will not know the implications for when it succeeds, maybe we need to do some double takes.
Experimental and observation evidence are both needed. That was Herbert Blumer's insight, mirroring Kant's own. That the human brain is so adaptively pliable that if your framing of an empirical question has no means of "resistance" from the reality you are trying to study, then your experiment may be tainted by observation-oriented biases. Boatloads of statistics that can predict other statistics definitely tells you that you are onto something, but the willingness to forego testable theories and conflate this predictive power with explanatory power is prolific.
I will also point out that the sense in which you are saying that computation is "concrete" sounds like you may be conflating the two interpretations when you also say "it is not abstract" or the specific thing you are calling "the computation." The physical information that describes the process of change of state is what I will assume you mean by the computation that is not abstract. But the human interpretation process that originated the inputs and anticipated outputs of that computation should not then treat the output as this same kind of "concrete." It is an instantiation of a computational paradigm, and the propriety of application lies in the interpretation. I can divide a number by two, and say that it proves that "half the happiness is half as good," but it proves no such thing because no one has ever established happiness is "divisible" in the mathematical sense.
Re: complex numbers, I will have to follow up on this later, but my intuition is that under the typical operations, the relationship with the conservation principles is maintained by the change in magnitude relative to 0. That simple rotation does not happen means that it is not energetically equivalent. One interpretation Claude gave was that complex numbers are useful for preserving probabilities adding up to 1. When I proposed that this value of preserving probabilities relies on reality adhering to energy conservation, he "agreed" very readily. But you know, LLMs are themselves quite pliable.
After thinking about this for several days, I think I understand why we see this a little differently. Or maybe we don't and it's that I don't understand your thesis and prescription. Always possible. Firstly, for me, the FBS hypotheses we've listed are a small (but glaring) problem in the hard sciences and not a problem at all in math. As I said last reply, I think social pressures account for most science FBS. And a free-wheeling modern sense that "anything is possible". That last perhaps has some connection with your thesis.
No good *mathematician* thinks reality should confirm to their math. They tend to be clear minded about the abstractness of math. As mentioned previously, that it so often is effective with reality is a source of debate. I think FBS issues may become bigger in the softer sciences for reasons I'll get to, but generally those with good science training are the least of the problems I see.
Where I think FBS becomes endemic and problematic is with people and social issues. The current political insanity is one result. Modern culture increasingly encourages stupidity by supplying pre-canned worldviews and identity categories. Once one finds a comfortable niche, they can have a bubble to shield against unwanted opinions and knowledge. It's a form of willful stupidity that has been a disaster for society. I've been ranting about it since the 1970s under the rubric of "The Death of a Liberal Arts Education." We don't teach people to learn anymore.
I think, the root problem is ignorance. People aren't read in on the concepts of "abstract" or "concrete". Many possibly couldn't use them correctly in a sentence. I think, to make the error of misplaced concreteness, one must first fully understand what that means. So, at the social level, I don't see a logical error so much as a failure of knowledge and education.
> "Which is why the willingness of the hard sciences to throw the soft sciences under the bus..."
That hasn't been my experience with real scientists. What makes physics a hard science and sociology a soft one has nothing to do with how difficult they are. Or rather, it does but *opposite* from what misunderstanding how the terms apply suggests. "Hard" sciences are mathematically easy while "soft" sciences are mathematically so hard as to be intractable. What makes soft sciences soft is the huge number of free variables. It results in a vast, fuzzy, multi-dimensional configuration space with a crazy number of relevant dimensions. Hard sciences are hard (like rock) because they are so easily tamed with math. Soft sciences are fuzzy and incredibly difficult to see clearly. The replication crisis comes from how varied humans are. Testing shows repeatedly: one size never fits all or even most. But that lack of hard evidence (another reason hard sciences are called hard) enables unfounded and hard to counter speculation. FBS.
> "The physical information that describes the process of change of state is what I will assume you mean by the computation that is not abstract."
No, I was referencing that any computation, to be a computation, has a form, a syntax, and that syntax is necessarily concrete (else computation would be useless).
> "...my intuition is that under the typical operations, the relationship with the conservation principles is maintained by the change in magnitude relative to 0. That simple rotation does not happen means that it is not energetically equivalent."
I'm sorry, but this business with complex numbers and conservation of energy is mathematical gibberish. There is no connection. LLMs are not a good source of knowledge. They also contain all the gibberish from the internet.
I am very glad your wrote this piece. It deals with several tricky concepts I am trying to disentangle in a generalizable way. I may have mentioned, perhaps in other words, that I have created a Razor that is essentially the inverse of Occham's (hence the pseudonym): parsimony relative to sufficiency and generality, as opposed to necessity and abstraction.
This also leads to dealing with "arbitrariness" as well. It's a bit of a brain twister, but it would be a kindness to me if you can find a consistent or "complete" set of definitions or relations among "physical," "abstract," "arbitrary" and "general."
Note that I think "concrete" opposite "abstract" as if on a spectrum has led to a great deal of conflation. So to address some of the implications of your use in this post, "physical" seems to imply a mutuality in form, while "abstract" seems to imply a map/territory bifurcation while "arbitrary" refers to a structural connector between the map and the territory that "could just as well have been any other" functional connector. You may have already picked up on my issue with this set of terms.
For example, each element is technically "physical" while "concrete" in its stead would seem to only provide a rhetorical resolution since it can't mean "physical" and probably reduces to "salient," or "particular," or "specific," or some combination thereof. Which is still problematic since "specific" is commonly opposite "general." Meanwhile, "arbitrary" is a property of a choice, after which, the map/terrain connector must be "specific" or "particular." 😵💫😵💫
To clarify why I don't think such a set is trivial, I suspect and need to be able to communicate the common conflation of abstraction -> generalization -> computation -> instantiation
... as being synonymous with or an abstract type of "substantiatiation." I am eager to see what "evaluation" means in your upcoming posts.
Also note that I don't think that there is but one internally consistent way to arrange these terms, but I thought you might want to try your hand at it, and perhaps proving me wrong in the process. Or feel free to ignore the whole ordeal as a headache! 😁
Thank you, I'm glad you got something from it. As you suggest, an inclusive taxonomy runs into difficulties. I think that may be inevitable when the subjects are both diverse and complex. A bit to dig into here, let me start with those terms as I define them.
I agree "abstract" and "concrete" are antonyms. "Physical" refers to real-world objects, from fundamental particles to the visible universe. The only antonym that springs to mind is "nonphysical". What is physical is "concrete", but concrete can also mean "specific" or "actual" (like concrete numbers in a deal).
I'd say an "abstraction" is a type of "generalization", but a generalization can include something like "All dogs are great." One might argue that is an abstraction. The line is fuzzy, but I think generalizing is a broader term. Its antonym is "specific", and I see specific and concrete as similar but distinct, so likewise, abstract and general are distinct.
I would oppose "arbitrary" with "required". For example, the term "arbitrary precision" means "any precision". As you say, dealer's choice. In terms of your map and the territory, an important point is the distinction between the map and the mapping. In a case like this, the mapping is more important than the map (which is just numbers). We may already be on the same page, but "map" here means the encoding (and decoding) process that generates those numbers. The numbers are essentially random with no resemblance to the territory because they are a numerically *encoded* form and the encoding design is arbitrary. (There are constraints to the design, of course.)
[There are actually two maps. One transfers the physical to electrical representation (faithful in form). This is an analog map, a transfer curve. The second encodes the electrical representation to the numeric map.]
"Computation" is a separate matter and the subject of the next post in this Newsletter. In short, though, a computation is something that can be implemented by a Turing Machine. An "instantiation" is a specific instance of a class, design, type, or other specific abstraction. Dollar bills are instances of the USD, but so are the virtual dollars in a bank account. An "implementation" is similar to an "instance" but implies internal complexity. One implements a process or design.
The key distinction is that, while both analog and digital require physical vehicles, digital systems have a second layer -- the abstraction the physical vehicle carries. Analog involves a proportional transfer -- it *is* the vehicle.
Thank you for the detailed response! I suppose I should clarify that in the context of this post, the clearly delineated procedures to and from the physical and digital is relatively straightforward. Outside of such a carefully bounded procedure, I suspect there are major conflations.
To be clear, I think "concrete" is misleading when considered an antonym for "abstract." Notice how you almost never hear "concretize" as the reverse process, but you'll hear "reify" when done in error.
Meanwhile, rather than carefully formulating a treatment, "specification" can be used to pluck an instance out of thin air, no matter how "abstract" or "general." In theory, abstraction risks errors of omission (locally), as you may inadvertently abstract away properties or features on which the ones you keep are dependent. When you generalize, you risk (again locally) errors of commission, where the broadening of the property or feature may not apply in the domain. Should the previously abstracted features be in error, and that insufficiency be generalized, then the errors can be compounding.
If desired, see if the following seem to be intuitive to you:
"Abstraction" itself seems abstract
"Generalization" itself seems general.
"Specification" itself seems specific
"Concrete" itself seems concrete
Note that this isn't universal of concepts. "Arbitrariness" does not itself seem "arbitrary" for example. Now, pointing out that some concepts or procedures seem to "self-apply" might seem arbitrary, but I suspect that (if it's not just idiosyncratic of my treatment) it is actually significant for fundamental function. Apologies if this is a bit confusing.
I've usually expressed it as "abstract" vs "physical", but "concrete" works as well. Maybe better in some regards, because we don't always abstract from the physical, but we always do from the concrete. I don't think they're ends of a spectrum, though. More Yin and Yang. In my world, reifying something need not be an error. When I write code with data structures, those reify my design. (In OOP, object instances are sometimes said to be reifications of their class.) We do say "make abstract" or "make concrete", so I seem to see a genuine opposition there. What do you dislike about it? (Perhaps the treatment as a spectrum? Technically, one can't make something "more abstract" or "more physical". It's one or the other. (OTOH, I insist "nearly unique" is a valid phrase.))
True that abstraction and generalization necessarily discard details. The goal, obviously, is to distill out the details that matter to the task at hand and ignore those that don't. I think the risk of important details falling through the cracks can be high in some cases. Specifically, because of their complexity, with regard to simulating or emulating minds. Part of my thesis in this series involves the difficulty of recognizing the important details.
I'm not sure wordology is any more effective than numerology. Language is so ambiguous and context dependent that the interesting patterns that turn up with words are usually coincidental. One of my favorites is that "listen" and "silent" have the same letters. Another is "garden" and "danger". Tempting to draw a connection, but those coincidences don't work in other languages. That's the thing that always got me with wordology. Change the language and the pattern disappears. (FWIW, most words just seem specific to me, so it may indeed be idiosyncratic.)
FWIW: this post from 2019:
https://logosconcarne.com/2019/10/28/physical-vs-abstract/
Excellent set of responses and older posts. In particular, the magnitudes vs numbers post captured some critical distinctions, to which I want to respond when I have more time.
It's less that I have a problem with the concept of "concreteness" and more the inconsistent use of it that conflates its meaning and confuses its utility. Most uses of the term, outside of synonymity with "physical," seems to be entirely rhetorical, in the same sense as the modern use of "literally." If someone says "give me the concrete numbers," they mean give them something "precise," cohesive, or with a large degree of certainty or surety.
I sense it's part of a more general, modern problem with the treatment of statistics, as we have begun to reify the exploratory power of statistics, combined with the predictive power of human inference, into explanatory power that gets credited to the statistical side of the ledger. The Central Limit Theorem and the Law of Large Numbers get wildly undue credit, while "heuristics" are attributed biases according to their divergence from "statistical truths." But that's a rant for another time!
Re: wordology, I agree with your assessment and for the exact conditions stated. However, there are strands of etymology that are less arbitrary, and their ubiquity across languages is part of the evidence. To give just one example, the "weight" of evidence or importance is always a negotiated magnitude, but never a number. It might seem like a metaphor you could just discard, but the next few in line only serve to prove the rule. "Preponderance of evidence" comes from "ponder" which means "to make heavy," so preponder is essentially making something heavy to then be weighed. Deliberation, libra means "scales." Even the word "Importance" comes from "import," meaning to bring or carry.
As I am still writing about, virtually all words that mean important, across languages, reduce to meanings of "weight" and the "distance" it is "carried." LLMs can assist in verifying this. Even the word "vector" shares a root with "vehicle," hence they are a "force carrier." And when you think about it, this makes embodied sense. Gravitational North/South is the most stable reference frame for biological evolution. There is so much more to say about it, but it is probably best I fit it into my actual writing for now, else I'll just go on and on!
Thank you for the great conversation and cheers!
Words involving basic concepts often have different flavors in different contexts. For instance, "concrete" really does mean "specific" as well as "physical" or "tangible". One might not like the conflation, but language evolves like a coral reef in all directions.
Long ago at a family gathering, a spouse of a distant relative turned out to be a professional linguist. I asked her if, as a linguist, she was horrified by the common misuse of language. She replied that, as a linguist, she *studied* language but didn't judge it. While I'll never be as distant with language as that, I've kept it in mind ever since. Language is what it is. One might as well deny the tides.
So, for instance, the semantic shift of "literally" irritates me, but I make myself let go. (And sometimes have some fun mocking or parodying the misuse.)
I've managed to keep statistics out of my knowledge base, but I imagine it suffers the same issues many sciences do with huge misunderstandings and horrible metaphors and analogies that mislead. Physics has lots of examples, and I'm sure stats does, too. Pop science and science journalism is a whole other topic.
I quite agree that etymology and wordology are different. Somewhat as mathematics and numerology are. The evolution of language is a fascinating topic.
Agreed mostly all around. "Literally," and "ironically" and "begs the question" had shifts that, while somewhat annoying, are not prone to confusion or conflation. The contextual conflations of "concrete" (which is ironically flexible) may not be causally related, but certainly seems part of a larger set of symptoms in the tech hype space, which seems to have had an outsized effect on science. That might be unsurprising given the shape of modern incentives, but it complicates my overarching task of trying to establish a common ground of intellectualism, skepticism, and sensibility.
Re: etymology, you might enjoy https://hidingasplainsight.substack.com/p/the-etymological-fossil-record?r=3nwud0
Where do you place player piano tech?
LOL! Well, it’s a bit like MIDI, isn’t it. A digital-analog hybrid.
Hmmm. Take it a bit further. Some (analog) musical instruments have digital inputs. Piano or saxophone keys, for example. Or frets on a guitar. Others have analog inputs. Fretless guitars, violins, trombones. That said, you can hit piano keys hard or soft and bend guitar strings. A lot of analog either way, but I hadn’t really thought about the nature of musical instrument inputs until you mentioned player pianos.
(Which were a key symbol in season one of HBO’s WestWorld.)
Fascinating and comprehensible - thank you. Looking forward to the next one.
Thank you, I’m glad you got something from it!