I loved this SMBC. It echoes something I’ve observed before, that some physicists have disdain for philosophy, while often engaging in it themselves.
Hovertext: “Philosophy is dumb, unless it comes out of the mouth of a physicist.”
Click through for full sized version and red button caption.
via Saturday Morning Breakfast Cereal.
I’ve discussed the question before on this blog on whether the universe is mathematics, mathematics is the universe, or some weird combination. Personally, I’ve gradually become more convinced that the foundations of mathematics and logic are empirical, that they are our most fundamental theories about how the universe works. This isn’t completely intuitive because we are born with some logic and quantity cognitive pre-wiring, giving the illusion, perhaps, that it comes from somewhere else.
One consequence of seeing math and logic as theories, is that they are subject to revision, something many will find intolerable. Still, arguably quantum physics led to revision in logic.
SelfAwarePatterns 
Heh! I thought of both you and Steve when I saw that SMBC cartoon! XD
“Still, arguably quantum physics led to revision in logic.”
How so?
Also: How do you figure the “theory” of natural numbers, or of real numbers, might be revised?
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On the quantum thing, I think we’ve discussed this before. I’m pretty sure no logical proof could have predicted quantum superposition or uncertainty (hence Einstein’s frustrations with it). As I understand it (and my understanding could always be wrong), in order to accommodate QM, a new branch of logic was necessary.
https://en.wikipedia.org/wiki/Quantum_logic
I got the “theory” idea from Graham Priest, an expert in various forms of philosophical logic. He’s presented some eastern logical concepts that seemed prima facie absurd, but then proceeded to explain why is wasn’t. (Blowing my mind in the process.)
http://aeon.co/magazine/philosophy/logic-of-buddhist-philosophy/
I’ll admit up front that I can’t conceive of how numbers might be revised. But then I stink at math, so we shouldn’t use me as a benchmark for anything here. At its foundations, it seems much harder for us to have erroneous math theories. But abstract math, which has no physical correlations, could be seen as essentially theories without a basis in reality (i.e. wrong). Yes, some eventually do end up having real world correlates, but there’s no way to know ahead of time which is which.
One thing that solidified this idea in my mind, was when I finally understood what tensors are. They struck me as very pragmatic structures for dealing with complex geometries that we observed in nature, but that our previous mathematics were clumsy with. It seems to me that most developments in mathematics (geometry, algebra, trigonometry, calculus, etc) had real world inspirations and/or itches to solve.
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“I think we’ve discussed this before. I’m pretty sure no logical proof could have predicted quantum superposition or uncertainty (hence Einstein’s frustrations with it).”
Yes. The idea that Aristotelian logic couldn’t predict quantum behavior (with which I agree), or the idea that quantum behavior itself wasn’t ontologically logical (and therefore annoying, and I also agree with that), aren’t what I was getting at.
It was this:
“Still, arguably quantum physics led to revision in logic.”
In the same sense one might say Einstein led to a “revision” in Newton. I just debated this with Steve, so you can reference that discussion. The short form is: I think “extension” is a more appropriate word, since neither Newton nor Aristotelian logic are wrong in their respective domains (i.e. there is nothing that replaces them in those domains).
The Wiki article on Quantum Logic says, “Quantum logic can be formulated either as a modified version of propositional logic or as a noncommutative and non-associative many-valued (MV) logic.” In other words (to me, anyway), it extends existing logic (it’s certainly expressed in terms of it).
I only got halfway through the Priest article. The territory was already familiar to me. As he points out himself, all these ideas have been around for a long time. (I was a little bemused over the idea of bringing religion into math, though! 🙂 )
Debate over the Principle of the Excluded Middle… An interesting aspect of that is that without that principle, many of our useful and interesting proofs go away and a great deal of mathematics falls apart.
Cantor’s proof of the uncountability of real numbers, Turing’s Halting Problem proof, and Gödel’s Incompleteness Theorems, are all proofs with start with an assumption and arrive at a contradiction thus invalidating the initial assumption. Without the PEM, those proofs (and many others) aren’t possible.
Is the PEM correct? We’re not entirely sure it is, but without it progress becomes nearly impossible. Likewise the Principle of Non-Contradiction. By taking it as an axiom (one that seems to have real world analogues), we have a useful tool.
There is also that examples of things that are both true and false, or neither true nor false, or undecidable, or ineffable, can be broken down into basic logic per Shannon’s information theory (in which all information consists of bits). More complex logics are built on basic logics.
“But abstract math, which has no physical correlations, could be seen as essentially theories without a basis in reality (i.e. wrong).”
Only things with a physical basis in realty are correct? Even if they are logically consistent and seemingly complete? The set of natural numbers is infinite. There are no infinite things in reality. Are the natural numbers wrong?
The fact that a universe of objects leads to counting, or that a universe with physical extent leads to geometry (or that a universe with gravity leads to tensors 🙂 ), causes me to see math as a discovery rather than an invention.
I tend to agree with the Platonic idea that the concept of a sphere (all points within a given distance of some point) is a natural consequence of physical extension. In fact, the basic idea of a sphere applies to anything with at least one dimension. A “sphere” in 1D is a line segment (all points within a distance of a point). A “sphere” in 2D is a disc. Etc.
I just don’t see how these concepts don’t come with reality, aren’t deeply embeeded in that reality. Even the idea of physical extent ought to lead to the idea of a sphere.
There’s a famous saying in mathematics (due to Leopold Kronecker): “God made the integers, all else is the work of man.”
So maybe it’s both (it’s true and false! 😀 ). Reality brings with it certain basic concepts and we build on those to do interesting and useful things. And sometimes it turns out the weird unreal things we build actually reflect some aspect of reality. Emmy Noether’s work in the abstract world of symmetry groups turned out to be the basis of our Laws of Conservation.
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For me, the main point is that we now know that Newton’s understanding of reality was incomplete; it couldn’t account for all observed gravitational phenomena. And that classic philosophy couldn’t account for quantum mechanics. Whether Newton was “wrong” or whether classic logic was “extended” or “revised” depends on definitions. Neither is wrong enough for us to throw them away, but neither is right enough for us to consider them the final authority anymore.
I have to admit to having a visceral dislike of the principle of the excluded middle, mainly because it resembles a tactic that annoys me. I can’t tell you how many times at work that I’ve been presented with two stark choices where the presenter insisted they were the only two options, only to find after a few minutes of investigation that there most definitely were other options. I’ve found the same thing in many internet debates.
I don’t know whether the PEM or PNC are valid or not, but I don’t think that whether or not a lot of theorems would be invalidated should have any bearing on whether we regard them as valid. It seems like it should be on whether we can find cases that violate them. Personally, it seems to me that QM does that. I think that’s one reason why my faith in theorems is limited.
“Only things with a physical basis in realty are correct?”
Again, definitions. Depends on what we mean by “correct” or “wrong”. By “wrong” above, I meant that it would be wrong in the same way a scientific theory would be wrong if it didn’t match physical reality. (And by “physical” here, I’m not making any metaphysical assertion of physicalism; I just mean “out there”.) Mathematicians judge whether a construct is “right” or “wrong” by a different standard than scientists (usually).
I think if mathematics is discovered rather than invented (and every mathematician I interact with feels strongly that it is), then it’s inherently grounded in something outside of humanity. The notation of mathematics is certainly created by humans, after all base 10 comes from the number of digits that we evolved. But the underlying relationships seem like they would be discovered by aliens.
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“I have to admit to having a visceral dislike of the principle of the excluded middle,…”
Totally with you on the silliness of just two options in life, but that has nothing to do with the PEM, which is strictly about the truth of a given proposition. Specifically, a proposition is either true or false — there is no middle ground.
“Personally, it seems to me that QM does [violate the PEM].”
Because of superposition? The thing is, the cat actually is either alive or dead. There is no middle ground.
“By ‘wrong’ above, I meant that it would be wrong in the same way a scientific theory would be wrong if it didn’t match physical reality.”
Scientific theories are wrong when they are falsified through experiment. Abstract mathematical theories may not have any physical analogue (that we know of (yet)), and are falsified only through logic or math errors. Theories that are consistent are not “wrong” but they may be entirely abstract (until someone realizes they actually apply to some physical thing after all).
“Mathematicians judge whether a construct is ‘right’ or ‘wrong’ by a different standard than scientists (usually).”
Very much so! My point exactly. XD
“I think if mathematics is discovered rather than invented […], then it’s inherently grounded in something outside of humanity.”
Yes, absolutely! Does not the concept of a sphere exist outside humanity? The concept of a straight line? Doesn’t π exist whether we ever evolved or not? Don’t numbers of objects exist whether we count them or not?
“The notation of mathematics is certainly created by humans, after all base 10 comes from the number of digits that we evolved.”
Absolutely. Cats and dogs exist regardless of what words we create to describe them, right? Same with math. It’s fundamental to reality.
Base 10 is, as you indicate, provincial and ultimately meaningless. Shannon’s information theory again. Base 2 is sufficient for all information (and hence all mathematics). Base 10 doesn’t mean any more than French or English or Russian does with regard to the actual reality of cats or dogs.
“But the underlying relationships seem like they would be discovered by aliens.”
Which means, does it not, that mathematics is outside of humanity?
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“Specifically, a proposition is either true or false — there is no middle ground.”
A proposition could also be meaningless (or “meaningful” only in a spiritual way). I think A. J. Ayers said something like that. But then it might not qualify as a “proposition”.
“Does not the concept of a sphere exist outside humanity? ”
Wow. Blowin’ my mind here so early in the AM. You’d think the spheres would exist but no “concepts”. On the other hand it’s like the koan about whether the tree falling in the forest makes any sound if there is no one around to hear it. Yes, I think it does. The snail without ears would “hear” it as a vibration in the ground. The butterfly would feel the breeze vibrate in her wings.
“Which means, does it not, that mathematics is outside of humanity?”
Got my vote.
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@Marvin Edwards:
“A proposition could also be meaningless (or “meaningful” only in a spiritual way).”
Indeed. A proposition might also be undecidable. In databases, a field can have a NULL value. In electronic logic, there is a “high impedance” (“hi-Z”) output state which is neither “0” nor “1”. But in all cases, these states are not useful without resolution.
In databases, for example, a NULL value in an equation propagates upwards giving the entire expression a NULL value — unless you explicitly push NULL to be interpreted as zero or the empty string.
In electronic logic, the hi-Z state (which allows multiple outputs to a data line) is “floating” so the next stage’s input sees electronic noise — unless a ballast resister provides a default state.
So there are other possible answers: The proposition can be gibberish. The proposition can be undecidable (or even just “don’t know yet”). However all these have a tendency to be useless unless they are interpreted within the answer domain (such as is often done with NULL and hi-Z).
“You’d think the spheres would exist but no ‘concepts’.”
Your ‘falling tree in the forest’ analogy makes a very good point! Perhaps “concept” isn’t quite the right word.
In fact, the tree-sound thing is easily resolved by definitions. If sound is mechanical vibration, then obviously a falling tree makes a sound. If sound is what we experience then you have to define what level of creature can experience sound, but if literally “no one hears” the falling tree, it doesn’t.
If no one experiences a sphere, does the sphere still exist in some sense? That, I think, is the key question here. I’m arguing that it does. I’m arguing that it’s discovered as a consequence of physical extent. Perhaps the analogy to sound is that the unexperienced mechanical vibrations still exist to be potentially experienced. Likewise, so does the sphere.
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“In databases, a field can have a NULL value. In electronic logic, there is a “high impedance” (“hi-Z”) output state which is neither “0” nor “1”. ”
I seem to recall reading about a trinary system based on -1 0 +1 but I don’t know if anything ever became of it.
“If no one experiences a sphere, does the sphere still exist in some sense? That, I think, is the key question here. I’m arguing that it does.”
I think so too.
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“I seem to recall reading about a trinary system based on -1 0 +1 but I don’t know if anything ever became of it.”
Analog computers (and certainly analog devices, such as amplifiers) do use +/0/- systems. The thing is, anything you can do with any multi-value logic can be done with binary logic. All you buy is higher information density per “baud”. You also buy higher design complexity and the need for a bipolar power supply. Binary is a lot simpler design-wise.
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“Specifically, a proposition is either true or false — there is no middle ground.”
So, Newton was wrong then?
“The thing is, the cat actually is either alive or dead. There is no middle ground.”
Prove it 🙂 Actually a better example is, in the double slit experiment, which slit did the electron go through? Is the electron a wave or a particle?
On mathematics and the word “wrong”, I’d ask for at least a little interpretational charity here. My point was that abstract mathematical constructs could be considered “wrong” in the same sense of a logically consistent scientific that doesn’t match reality. Of course theoretical mathematicians wouldn’t consider it “wrong” because they’re generally not aiming to match reality. But I don’t see it changing my point.
“Which means, does it not, that mathematics is outside of humanity?”
Yes! The question, it seems to me, is whether mathematics arises from patterns in the universe, or from some platonic realm. Of course, we can’t prove this one way or the other, but I lean heavily toward it being patterns in the universe.
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@SelfAwarePatterns:
“So, Newton was wrong then?”
About Mercury, yes. About the other eight (yes, eight) planets, no. Maybe it’s just me, but I have no problem with ideas that are true in one domain but false in another. Context, as they say, is everything.
“Prove it 🙂 Actually a better example is, in the double slit experiment, which slit did the electron go through? Is the electron a wave or a particle?”
LOL! Well, I can’t falsify it, but in nearly 60 years of observation I have yet to see any cat that isn’t either definitely alive or definitely dead. The overwhelming preponderance of data supports the theory with no contrary data points thus far. XD
I believe we agree the quantum world takes things to a new level. On the latter question, electrons have wave-like and particle-like qualities, but it’s a mistake to think of them as being either. (Although given QFT, wave-like is probably the closest to whatever is going on there ontologically.) On the former, I think something must go through both slits.
(As an aside: I used to wonder if photons not experiencing time resolved the two-slit weirdness, but electrons and other particles also show the behavior, and they do experience time, so that’s not it. It’s just… weird!)
Look at it this way: There are two propositions here. Did the particle (or something) go through slot #1? Did the particle go through slot #2? That gives us four possible answers: yes-yes, no-no, yes-no, no-yes. Right now we don’t understand what’s really going on well enough to answer the question.
“My point was that abstract mathematical constructs could be considered ‘wrong’ in the same sense of a logically consistent scientific that doesn’t match reality.”
I hope I’ve acknowledged that I understand what you mean (and if not, I do). But “wrong” is too strong a word for my charity. Let me ask this: When you say “doesn’t match reality” do you mean ‘has no known analogue in reality’ or ‘is contradicted by reality’?
If you mean the latter (but I don’t think you do), then “wrong” passes without objection. If you mean the former, then I really think “wrong” is poetic to the point of being dead, um, wrong. As an example, is hyperbolic geometry wrong? It has no analogue in our world (other than some Escher paintings 🙂 ), but there’s also nothing in our world that contradicts it.
(BTW: I don’t want to give the impression I’m hugely invested in this, despite all the enjoyable debate. If you want to go around calling Newton and abstract mathematical theories “wrong” that’s totally your call. I’ve argued the point far beyond the number of actual shits I give (27)! 😀 )
But you know what? I think we have hit a semantics issue, the resolution of which may put us fully in accord…
“Yes [math is outside humanity]! The question, it seems to me, is whether mathematics arises from patterns in the universe, or from some platonic realm.”
Ah! Perhaps we’re saying the same thing. I don’t think most Platonists think there is an actual Platonic realm. It’s not a place that exists or that one could somehow visit.
I’m not sure even Plato thought so. Tina and I have talked about this before, and maybe she can chime in here. She’s more well-read on Plato and those guys than I am.
I’ve always taken the Platonic realm as entirely abstract and, as you say, a consequence of the patterns of reality. The point I think Plato was making (and hopefully Tina can back this up (or call me wrong)) is that the idea of a sphere is entirely inherent in the nature of physical reality — specifically inherent in physical extent.
On which point it looks like we may agree?
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“The overwhelming preponderance of data supports the theory with no contrary data points thus far.”
Technically you’ve never observed a cat before you’ve observed it 🙂 (Don’t throw anything at me.)
“do you mean ‘has no known analogue in reality’ or ‘is contradicted by reality’?”
Actually both. There may be no known analogue, or the mathematical construct might simply be omitting something in reality that make its physical (for lack of a better word) existence impossible.
I do understand that the word “wrong” has been an issue here. But I’m glad you understand my basic idea. If you can think of a less value-laden word for the concept, I’d be happy to use it. Philosophical discussions do sometimes tend to get tied in knots because of the wording.
On Platonism, I think a lot of philosophical concepts like this are valid epistemically but questionable ontologically. Unfortunately, philosophers aren’t always clear which one they’re talking about. And, of course, someone can be a stickler and insist that no one can really prove a distinction between a valid epistemic and an invalid ontological concept. In the end, we have to use what works. The reason I think the distinction matters is because some people try to derive ontological notions from a concept that is likely only epistemic.
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“Technically you’ve never observed a cat before you’ve observed it 🙂 (Don’t throw anything at me.)”
ROFL! I’m both throwing and not throwing! 😀
“If you can think of a less value-laden word for the concept, I’d be happy to use it.”
Restricted (to a specific domain). Particular (ditto). Specific (ditto). Whatever. 🙂
My final word: It’s like you have a key that works for the locks in your house, but not in the locks of your neighbors. It seems very odd to me to call the key wrong, but certainly trying to use it in your neighbor’s locks would be wrong (on a couple of levels in that case! 🙂 ).
Nuf sed!
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Reblogged this on Confessions of a Geek Queen.
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Wait a minute…still hatching… I think I find it disturbing that E = MC2. Yeah, that’s it. It is too simple. The universe can’t be that simple. What happened to all that other stuff on the blackboard? You know, the stuff that Michael Rennie corrected on Sam Jaffe’s blackboard in “The Day the Earth Stood Still” (the good original version). Just sayin’ …
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Klaatu needs to come down and show us again. We seem to have lost it somewhere. 🙂
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Did you ever see (or do you remember) this xkcd? One of my favorites:
http://xkcd.com/435/
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(I think you’ll especially appreciate the hovertext. XD )
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I had seen that one, and loved it, but had missed the hovertext. That is good. Thanks!
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Love it! BTW, following your debate with great interest.
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Good, because I’m about to invoke your name! XD
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Ahhhh! I’m scared. As long as I can stick to Plato and side-step talk of quantum thises-and thats, and computer stuff, I’ll be okay. 🙂
So, I’ll back up a bit to Mike’s point:
“(Which means, does it not, that mathematics is outside of humanity?)
Yes! The question, it seems to me, is whether mathematics arises from patterns in the universe, or from some platonic realm. Of course, we can’t prove this one way or the other, but I lean heavily toward it being patterns in the universe.”
When I read this, I wondered what the difference was between “patterns in the universe” and “some platonic realm.” Maybe, Mike, you can clarify?
It sounds to me that if you both agree that mathematics is “outside humanity,” you’re agreeing on a lot. I’m not sure Plato made it altogether clear what the forms are, and that’s why scholars disagree about them so much. It could very well be that the forms ARE “patterns in the universe.” That depends on what we mean by the phrase. But more on this in a second.
Quoting Wyrd:
“Ah! Perhaps we’re saying the same thing. I don’t think most Platonists think there is an actual Platonic realm. It’s not a place that exists or that one could somehow visit.”
Close. Platonists (by that I mean people who actually take the forms seriously) would have to say the forms exist, but Wyrd, you’re right to say it’s not someplace one could visit, like Las Vegas. Reality in Plato’s terms is sometimes hard for us to comprehend. The forms are abstract, invisible objects, and yet they’re “more real” (for lack of a better way of putting it) than those objects that we can see. The forms make possible the visible world.
Another way of putting it: What happens in the world of forms does not stay in the world of forms. (Lame, lame, lame. But oh, I just had to go there.) However, the visible world doesn’t infect the forms with its impurities.
There is talk of a “world” of forms, but that’s just metaphorical language. I think the metaphor implies that the forms are interconnected, but that’s just my interpretation.
Quoting Wyrd again:
“I’ve always taken the Platonic realm as entirely abstract and, as you say, a consequence of the patterns of reality.”
The Platonic realm—or world of forms—IS reality, according to Plato. So I’m still wondering what is meant by “patterns of reality”…do we mean the visible world? The empirical world?
The visible world could be said to be a consequence of the world of forms, although Plato was never this straightforward. The visible world—what we normally take for real—is, for Plato, kinda sorta real. I’d have to argue for this. And that could lead me to endless quotes from the Timaeus about the world of Being and the world of Becoming, so I’ll just leave it at that.
Quoting Wyrd:
“The point I think Plato was making (and hopefully Tina can back this up (or call me wrong)) is that the idea of a sphere is entirely inherent in the nature of physical reality — specifically inherent in physical extent.”
Not sure I understand. Hopefully what I said above makes some sense of ideas/forms and their relationship to the visible/physical? If not, maybe it’ll become clearer…
So Mike, if the world of forms is that which underlies and makes possible the physical (visible) universe, and the visible world “participates” in the forms, then I see no huge difference between saying “the world of forms” and “patterns in the universe,” but that all depends on what you meant by that phrase. (To be sure, I should be careful with the word “participate”…but I feel I’m getting too pedantic now.)
If we say that the platonic realm depends on the visible world epistemologically, (and only epistemologically), Plato wouldn’t disagree with you. We need the visible world to grasp the forms.
The world of forms and their physical counterpart have a funny relationship. In a way, the forms are “lifted” from what we see, yet they transcend what we see. If we had nothing to count, we’d never arrive at the idea of numbers. Yet numbers would exist. But for whom? (Back to the tree falling…ugh, I have to admit hate that one.)
I don’t believe Plato got too much into this kind of thought experiment, and when he did, he often got poetic (theory of recollection, etc.) He was more interested in our amazing ability to find perfection in reason, despite the fact that it is never strictly speaking presented to us in the visible world. He was interested in that process of discovery. Is it that we abstract from the visible world? For him, not quite…but sort of… We make use of the visible by drawing lines, putting a pen to paper, counting stones, etc., and without these visual aids we’d be unable to go very far (our memory just doesn’t cut it). But to say that the ideas themselves are derived from the visual aids is for him inexplicable.
Quoting Mike:
“On Platonism, I think a lot of philosophical concepts like this are valid epistemically but questionable ontologically. Unfortunately, philosophers aren’t always clear which one they’re talking about. And, of course, someone can be a stickler and insist that no one can really prove a distinction between a valid epistemic and an invalid ontological concept. In the end, we have to use what works. The reason I think the distinction matters is because some people try to derive ontological notions from a concept that is likely only epistemic”.
I don’t think Plato would disagree with you too much on this. His theory of forms was something he spun ’round and ’round again, sometimes questioning it so much that scholars today still argue about whether he really believed in it. I think he did believe in it, but that’s just me.
Usually people who have a problem with Plato don’t like the idea of an invisible reality, or a reality that’s independent of us. If you’re willing to say that mathematics is outside of humanity, I’d say you’re close enough to a Platonist. (Are you a Platonist, too? Then there’s a pair of us—don’t tell! They’d banish us you know.) 🙂
Quoting Mike:
“The notation of mathematics is certainly created by humans, after all base 10 comes from the number of digits that we evolved. But the underlying relationships seem like they would be discovered by aliens.”
This totally reminds me of Anathem. This whole conversation is what the novel is about, and yes, aliens discover the same mathematics we have. There’s even a Platonic forms flow chart, which is the epitome of awesomeness for Plato freaks like me.
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“So I’m still wondering what is meant by ‘patterns of reality’…do we mean the visible world? The empirical world?”
That is essentially what I meant. Physical space implies distance. Distance implies greater and lesser distances. All space less than a given distance is a sphere. Physical space implies a sphere.
Another term is relationship. Various relationships form patterns we can say things about.
Which raises a point worth stressing. There is the language of mathematics, which is what we invented to allow us to say things about patterns. There is also the underlying relationships that led to that language. When I talk about mathematics I’m talking about the underlying relationships, not the languages we invented.
To me, math is not the languages, but what those languages say.
“The forms are abstract, invisible objects, and yet they’re ‘more real’ (for lack of a better way of putting it) than those objects that we can see.”
Similar, perhaps, to how the ideal circle never occurs in the physical world? Math is certainly an abstraction and idealization of the physical world, and a key point of disagreement often is whether those idealizations are unreal things based on crude real things.
But as someone who believes in the reality of ideas, I’m comfortable with the reality of idealizations and abstractions. (As a software designer, my world is abstractions built on abstractions built on abstractions, so I’d better be pretty comfortable with their reality!)
“The forms make possible the visible world.”
And that’s kind of where I get off the Platonic bus. 🙂
“[Plato] was more interested in our amazing ability to find perfection in reason, despite the fact that it is never strictly speaking presented to us in the visible world.”
Yeah, that’s the part I find really fascinating, too!
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Thanks for clarifying!
“To me, math is not the languages, but what those languages say.”
Agreed.
“Similar, perhaps, to how the ideal circle never occurs in the physical world?”
That’s a point Plato makes in favor of the a priority of mathematical objects. Since no perfect circles exist in what we’re now calling “the real world”, where did they come from?
And the debate ensues…
“The forms make possible the visible world.”
And that’s kind of where I get off the Platonic bus. 🙂
I can understand that, but try to think of it from more of an epistemological stance. (I think that’s the heart of what’s interesting about Plato, but I have to admit the ontological connection to epistemology—the blurring of the two in Plato—fascinates me too…I’m tempted to go on a tangent here…reel me in!)
Let’s go further and think of Kant’s a priori synthetic and forget about “World of Forms” and all that. So then think of a perfect circle informing our experiences of imperfect circles in the same way that causality informs our experience. (I realize that by bringing Kant into the mix, I’m straying far from Platonism, but hear me out…) So having these ideas of perfect circles structures our experience of all objects that might fall into that range. Of course, in “the real world” things have all sorts of properties. We might see a green construction paper cut-out of a circle, but, according to Plato, it’s the perfect circle that allows us to recognize that paper cut-out as an approximation to a circle. So from an epistemological sense, the perfect circle comes first, just as causality comes first (in other words, is a priori).
Does that help or did I foul things up too much? Kant obviously wouldn’t go so far as to say anything about what’s outside our minds.
Well…I’m late for a very important date. Catch you later!
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Zzzzzzzzzzzz….. That’s not the sound of snoring… that’s the sound of line being stripped off the reel. You’re too powerful a fish to reel in! 😀
“So from an epistemological sense, the perfect circle comes first,…”
I’m fine with that. It’s the ontological reality of the “world of forms” as a separate realm I have trouble with (and, as you say, that may not be the intention).
The only trouble with Kant is that now we have to argue over whether math is a priori synthetic or a priori analytic. Kant thought synthetic (because “12” is not found in “5+7”), and things like hyperbolic geometry seem to support that, but some still think math is analytic.
I’m not going there! Oh, my paws and whiskers, no! 😮
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“It’s the ontological reality of the “world of forms” as a separate realm I have trouble with (and, as you say, that may not be the intention).”
I think most people have trouble with this one. I certainly did. But I’ve come to realize it’s mostly a semantic problem…Plato’s poetic language doesn’t sit well with our literal minds sometimes (myself included). But really, if you say that math—not just the notation—is “outside humanity” then I think you’re there! It’s not something we invented, not something “in our heads,” but, shall I say, universal? And it’s reality or “being” is not in the same class as a wooden spoon. That’s about it.
“The only trouble with Kant is that now we have to argue over whether math is a priori synthetic or a priori analytic.”
Very true. This is a matter of hot debate and often when people start bringing real actual honest-to-goodness math into the discussion…and that’s when I look for the nearest exit.
When you say “hyperbolic geometry” I start thinking that someone’s exaggerating. 🙂
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At the risk of chasing you out the exit:
https://en.wikipedia.org/wiki/Hyperbolic_geometry
(If you want the TL;DR (or Too Scary; Didn’t Read) version, it’s a geometry of (a certain type of) curved space. Euclidean geometry is a geometry of flat space. Which we think ours is.)
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The TLDR version was perfect! 🙂
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Oh, one more thing on Kant’s a priori synthetic. When I first heard that there was a debate about whether or not math counted as synthetic, I couldn’t even understand what was being debated, what the problem was. I had to have it all explained to me several times because it never would have occurred to me to question that point. To me, 5+7=12 is something soooooo not obvious. Never mind anything more complicated than that. Of course, that’s not really the issue, but I still have problems wrapping my mind around the whole debate.
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Yeah, that 5+7=12 example bothered me, too. Kants says “12” is not found in “5+7” but under the theory of natural numbers it sort of is.
Take two piles of 12 stones. Leave one intact, but divide the other into two groups of five and seven.
I dunno… I’m still seeing 12 stones in both. Maybe I’m just not philosophical enough. [shrug]
But something like hyperbolic geometry — which has no real world analogue — sure does seem arguably synthetic.
Although…. (and hence the debate) XD
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I love your Plato/Kant mashup. I was thinking along the same lines a few months ago during a discussion. If one could interpret the forms as a cognitive mechanism, then an argument for the forms being prior comes from Kant (and cognitive science). We do a lot of active structuring of what we experience, said structuring being basically a conceptual overlay on raw sense data. This idea actually came from reading Eastern Philosophy, in which this same conceptual overlay was said to underlie our suffering (David Loy’s “Non-Duality”), but the idea can be generalized to how we experience things in general and not just from an affective perspective.
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Thanks!
Kant gets taken more seriously than Plato, so I like to bring him in to show epistemological similarities. “Forms” spook people. 🙂
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Lol! It is interesting how one philosophy can inform another 🙂
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Yeah, it’s like a long dialogue…in my head anyways. 🙂
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Tina and Wyrd,
Excellent discussion.
I think the distinction between an epistemological platonist and an ontological one is important. I actually have no issue with epistemic platonism. It’s what we as pattern matching beings do. We observe and simplify and then give those simplifications, those stereotypes, classifications, names such as “circle”, and then some of us name the idea of those mental simplifications, “forms”.
When I say I’m not a platonist, or that platonism doesn’t work for me, it’s the ontological version, the version that says the forms are the prime reality, and what we perceive as reality is just a special case, a shadow, of that ultimate reality. Now, you could say that that is just metaphor, that it’s just epistemological platonism with poetry.
The problem is that people like Max Tegmark don’t appear to be taking it that way. They’re taking platonism as an ontological proposition and then extrapolating from that to make grand assertions about reality. I think they’re taking a mental crutch and reifying it and then making conclusions about reality based on that reification.
While it’s possible that their conclusions could be accurate guesses, the history of human thought is that we’ve mostly been wrong about matters beyond our observation. I haven’t seen anything to lead me to believe we’re different today. That’s why I’m a skeptic and favor empiricism, which I see as compatible with epistemological platonism, but not the ontological variety.
Hopefully that clarified rather than demonstrating my confusion 🙂
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Agree about the excellent discussion!
And I think, ultimately, we agree on most of the points here. I do find Tegmark’s idea interesting although, like you, I’m skeptical. It does seem to solve one aspect of quantum weirdness — the same one the MWI goes after. Many math equations have multiple answers, all equally valid (e.g. sqrt(4) = +2 & -2).
There is also what’s referred to as the “eerie” effectiveness of (abstract) math with regard to the (concrete) world. The more you study math, the more eerie that becomes.
But, to quote an old and beloved (cultish) TV show, “I AM NOT A NUMBER!” XD
Be seeing you!
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I guess I’m confused about how mathematics (and think at this point we know we’re not talking about notation) is “outside humanity” but at the same time the empirically-derived simplifications of pattern-matching beings? Maybe I misunderstood what you meant?
“…it’s the ontological version, the version that says the forms are the prime reality, and what we perceive as reality is just a special case, a shadow, of that ultimate reality. Now, you could say that that is just metaphor, that it’s just epistemological platonism with poetry.”
I’m afraid I may have overplayed the metaphor thing. To be sure, Plato is definitely a matter of interpretation, but I think you’ve got it right in saying Plato’s forms are the prime reality, etc. There’s going to be someone out there who disagrees with this interpretation, but I’m pretty sure it’s the standard one. I was being a pseudo-academic ass. Sorry about that.
When thinking of the epistemological/ontological divide, it might help to remember that for Plato, the divide wasn’t a huge gulf. Descartes hadn’t yet come around to widen that divide. In Plato, we can come to know reality through reason, though sure, it’s hard…hard in the sense that we’d rather watch TV than do astronomy or math. But it’s not like there’s this Real Stuff “out there” and we’re stuck in our heads. (Now you might see why I was reluctant to bring Kant into the mix…although in that example I was trying to use Kant to explain how a priori ideas might structure experience…just take out the “in my head” stuff and you might have something close to Plato.)
Also, I feel like I might have made an error in saying that the forms would exist without the visible world/empirical world. The forms do have an independent reality, but I’m not entirely clear on the relationship between the two realms. I wouldn’t say the forms arise out of the empirical in the sense of mere extrapolation “in our heads”, but I wonder if the two must exist simultaneously. I don’t hear this discussed very often. Okay, now I’m about to get into the Timaeus a bit…I warn you, things will get nutty.
So there we have a creation myth in which Being and Necessity (Non-Being) make this bastard child otherwise known as the empirical world (visible world). Non-Being is brought into the mix in an apologetic way; Plato knows he’s slapping Parmenides in the face with this. (How can Non-Being be said to exist?) But Plato needs, um, Necessity, in order to account for the visible world. Plato’s actually being an empiricist in a way, in this context. Now here’s a quote in the Timaeus, one of my favorites, which is: “Wherefore he resolved to have a moving picture of eternity.” (You might have seen this on my blog on that wooden box.) This “moving picture” is the empirical world. It’s an eternal picture, which to me suggests that the worlds of Being and Becoming are tied together forever.
Taking this all out of the mythical/metaphorical realm, the empirical and rational (for lack of a better word) MUST co-exist and are tied together in some funny relationship. It SEEMS like Plato’s saying you can’t have one without the other, even though he wants us to set our sights on the rational. I feel like my interpretation is somewhat confirmed in the equality of the two middle segments of the divided line in the Republic, but don’t worry, I’ll spare you all that.
Whew. Who wants to throw/not throw a cat/non-cat at me? 🙂
I did pick up that Max Tegmark book. Unfortunately I couldn’t finish it. I think it was all the anecdotes and self-congratulatory name-dropping that got on my nerves. It’s too bad, I was really eager to read it. I ended up giving it to a mathematician friend in the hopes that he’d just tell me what it said, but he said he didn’t care for the style and didn’t finish it either. I did, however, enjoy all the visual aids. (I guess Plato would say I’m still stuck in eikasia mode…picture thinking.) 🙂
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Hmmm. Maybe I should have qualified my agreement with the phrase “mathematics is outside of humanity”. A better description of my view might be, “the source of mathematics/forms/etc are outside of humanity” although that could be misleading in the other direction.
Maybe laying out my understanding of the causal chains of various philosophies of mathematics might help.
Mathematical nominalism:
human minds->math/forms
It doesn’t sound like anyone here adheres to this. It seems to fail utterly at explaining the “unreasonable” effectiveness of mathematics.
My understanding of platonism:
maths/forms->the universe->human minds->understanding of maths/forms
I find this view unparsimonious. Maybe the universe does emerge from platonic maths/forms, but we have no access to that; we can only know it through the universe. I tend to think we’ve reversed the actual causal chain.
My view (which I perceive to be close to empiricism):
the universe->patterns in nature->human minds->maths/form notation modelling patterns
Thanks for the info on Plato. It always amazes me how much he and other Greek thinkers were able to work out in the 4th century BC. Although I’m periodically reminded that we have to be careful not to project modern conceptions on ancient thinkers (like maybe our understanding of the epistemological/ontological divide).
Yeah, Tegmark isn’t for everyone. I found his descriptions of multiverse conceptions and overall physics review helpful, and I think he makes a case for the mathematical universe hypothesis, but ultimately it seems like he’s doing a lot of metaphysics while insisting that it’s science.
Poor cats. I wonder how this thread became so hostile to them 🙂
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I think I get it. Perhaps.
“Maybe the universe does emerge from platonic maths/forms, but we have no access to that; we can only know it through the universe.”
Plato says we do have access to the forms (and it’s through the universe) but the method for taking that leap away from the empirical to the pure forms (and the Good) is very mysterious. He intentionally left us in the dark on that, which is kind of enticing and annoying at the same time. (Or just annoying for many people.)
Poor cats indeed! Well, all I can say is I’m a dog person, but cats are okay. (Especially non-cats not thrown at me.)
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I think for Plato, and many other pre-modern thinkers, the idea that we had mental access to such things was far more plausible. After all, consciousness itself seemed like an otherworldly thing.
Now though, given modern biology, neuroscience, and computer science, I tend to see us getting the ideas from either experience or innate instinctive pre-wiring, which is itself the result of evolutionary “experience”. When we have insights from those instincts, it can often intuitively feel as though we’re getting it from some otherworldly source.
I’m a dog person too. I’ve never owned a cat, although I’ve often enjoyed other people’s cats. I did once have a cat thrown at me. Having a freaked out cat land on you…well, I don’t recommend it. 🙂
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Consciousness still seems like an otherworldly thing to me! Or if not otherworldly, then certainly mysterious. (Or maybe my health issues lately have influenced my lack of faith in neuroscience to uncover the great mystery.)
You had a cat thrown at you? Wow, that’s cruel. I had a cat pounce at my face while I was tripping on LSD. That wasn’t fun. (OR maybe it was a non-cat?) 🙂
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I can see that. I think just about every neuroscientist I’ve ever read has called attention to how little we actually know at this point, and that we’re probably a century away from anything approaching a full understanding of the brain. In my experience, it’s AI enthusiasts / alarmists who drastically overestimate our understanding in this area.
Still, with data from brain damaged patients, I think we have enough data to conclude consciousness exists within this universe, but I’ll admit there are still enough gaps for someone who doesn’t want to give it up yet.
Yeah, the guy who threw the cat was a drunk jerk. He threw it at me when I objected to his plan to throw it against the wall. It landed on me, dug its claws into my neck and shoulder, and propelled off of me into the bushes. Lots of fun.
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“Still, with data from brain damaged patients, I think we have enough data to conclude consciousness exists within this universe, but I’ll admit there are still enough gaps for someone who doesn’t want to give it up yet.”
I didn’t mean to imply that I think consciousness is entirely independent of the brain…just that we don’t really know what’s going on. It seems like there’s got to be a two-way street, but we’re back to the same old problem. I kind of doubt that will ever go away.
People who hurt animals make me want to get violent. What a jerk! What did you do?
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If I recall correctly, there was a tense moment where me and my friends and his faced each other, and it looked like there might be an epic fight. But then cops drove up and everyone suddenly had somewhere else to be. This was decades ago (I was a teenager and it was at a middle school football game, I think), so not sure if I’m remembering it all correctly. I do recall that my shirt was ruined from all the bleeding I did from the cat’s claws. (Not that any of it was the cat’s fault.)
The guy and I had a few other tense moments that school year, but then I went on to high school and I think he eventually dropped out of school. I never saw him again, which was good riddance.
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It’s a good thing those cops arrived! That sounds like timing that only happens in the movies.
Ugh, the only thing worse than high school was middle school. I remember thinking, “I can’t wait until I’m in college and this is all over.”
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The cops pretty regularly patrolled around those games (probably a good idea for middle school events at night), so them arriving wasn’t as unlikely as it might sound. That and I doubt any of us really wanted to fight, but backing down wasn’t an option for 13-14 year old boys. The cops gave everyone an excuse to break off.
I know a woman who once wanted to home-school her daughter through the middle school years, but only the middle school years. Her reasoning was that most of the mental scars she had from school came during those years. (I don’t think she was able to do it though; it would have required that she not work for three years, at least not full time.) I know I wouldn’t want to have to repeat those years.
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I dunno. Sounds to me like that cat thrower was looking for someone to open up a can of whoop ass. (That was a popular phrase during my middle school days.) 🙂
I remember wanting to be home schooled in middle school, but there was no way my parents would’ve done that. Besides, looking back on it, I had a big turning point in my life during those years that wouldn’t have happened had I been protected from those brats. There was this girl who was my best friend outside of school, but then when she was with her friends at school, she’d ignore me (and so would her groupies). At first I thought it was all in my head, but then I confronted her about it. She got defensive and nothing changed. I did this time and time again, and I began to grow insecure. Finally one day I just let her have it (verbally), and decided that I’d rather have no friends than have to go through all that torment. I remember fretting about having to sit by myself at lunch (remember that?). Once I did it a few times (and put up with a few teachers sitting with me out of pity—oh horror of horrors!) I felt this great burden lifted from my shoulders.
I’m pretty sure most of my antisocial tendencies come from that experience, but I like to think it was more positive than negative.
But I’m sure not everyone gets something positive out of middle school social life. There were a few poor kids who just got tormented the whole time. For those kids, home schooling would have been better…there’s nothing to be gained by getting beaten up. (A fate I managed to avoid mostly by going under the radar…or by running.) 🙂
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Hmmm, “open up a can of whoop ass” was just “kick some ass” or “looking for an ass kickin” when I was in school. You’re making feel like an old fart 🙂
I don’t know. I’ve vacillated over time whether the pain of those years was constructive. On the one hand, I’m pretty sure I learned most of my social skills later. On the other hand, in freshmen high school, we did have a guy transfer in from what we’d today call home-schooling. He was generally good natured and intelligent, but his specific social intelligence was atrocious. He ended up alienating a lot of people and his parents pulled him out after a few months. So what we learned then isn’t always obvious.
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Good points, but I wonder if some of the problem lies in how we’re defining reality. At what point do I claim something is not real? If my ability to experience reality is the result of my cognitive activity (epistemic Platonism), then in what sense do I deny this ontological reality? What does it even mean to say something exists in some realm that I cannot observe? What does it mean to say something can impact my perception, yet not be real?
It almost seems like the issue is in how we’re defining reality, or that maybe we’re defining it in a very arbitrary fashion.
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Thanks BIAR. I don’t know if I would call it “arbitrary” so much as “theoretical.” We can only know ontological reality through theories, built to explain patterns of our sensory impressions. Everyone has the sensory experience of seeing the sun rise and set every day, but for a long time, our theories about why that happened, about what the relationship was between where we lived and the heavenly bodies, were defective. But I think everyone was reasonable to conclude that there is a relationship of some kind, that there is a reality behind those observations.
I do think we have to be cautious in assuming how well we know that reality. Often there are multiple explanations for patterns of sensory input. It’s one reason why parsimony, Occam’s razor, the practice of not adding assumptions beyond what is strictly necessary, is a good benchmark. Historically, each extra assumption lowers the probability of the theory being accurate. And often our theories have hidden assumptions that we’re not even aware of.
I think an ontological theory that reality is based on forms is not parsimonious. It seems to ignore particle physics and reifies emergent shapes that are common in our evolved environment. It could still conceivably be right, but it no longer feels like the simplest explanation, at least not to me.
Again, non of this is to say that epistemic platonism doesn’t have its uses. As long as we remember that it’s a mental shorthand for a much more complex reality.
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Well, I wasn’t talking about theories, but simply “naive” reality as it presents itself to me in my average experience. If I see a world of objects rather than a sensory jumble, and if this world of objects is abstracted from the sensory information based on cognitive processes, then what do I call reality? The sensory bundle that doesn’t confront me at first glance (but only upon reflection, in which case it could be argued to be a later construct or an active deconstruction)? The objects themselves, which are largely abstractions? Or the cognitive processes that heavily shape my reality? That’s really all I was saying 🙂
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I suspect we’re saying the same thing. My only point was that all observation, all perceptions of reality, are theory laden, that is laden with cognitive processes which produce models, that we can never know with all certitude are correct.
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Some jumbled comments on comments:
1. Please never use the word “cat” in any discussion of quantum physics 🙂
2. Electrons don’t go through slits. They are not particles. That’s the point 🙂
3. Pretty sure Newton would have admitted he was wrong and would probably have fallen into a state of despair and/or rage. He was very much an excluded middle kind of guy.
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LOLS!
1. Well, physicists opened this…box of cats 🙂 so now we’re all stuck with it. (Sorry, like Tina, I couldn’t resist.)
2. Eh? Is this a “how did the chicken cross the road?” question? If they didn’t go through the slits, how did they get to the back screen and make that point impression? (Or did I totally miss the punchline on this one?)
3. Probably true.
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Hee, hee! XD
[1] %s/cat/{flora-or-fauna-of-your-choice/g
[2] Unless you hang a particle detector on one or both slots!
[3] Newton: 😡
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I’m having a TEDx day — catching up on YouTube videos. This one made me think of this post and your most recent (in touching on consciousness). I know you are askance at Tegmark’s idea the universe is just an expression of math (me, too), but I also know you support emergence and the idea of structure (me, too). A connection is that, IF the universe was “just math” then consciousness necessarily is also.
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Wow, you are on a TEDx dive. Thanks.
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I need to be in the right mood to sit and watch a video, so interesting ones accumulate until I either am in the mood, or just can have to clear the queue some because it’s gotten ridiculous.
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I’m the same way. Usually for me, it’s the time it takes to watch one. I’ll watch a 2-3 minute video on the fly, but 15-20 minute or longer ones usually means I have to be at home with some time on my hands. (As I was today.)
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Exactly! I still have a whole bunch queued that run 90+ minutes (interesting physics and math lectures), and it’s gonna take me days to listen to those!
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This is fantastic. I’d say more, but I’m attempting to play catch up on all the great posts I’ve missed over the summer!
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Thanks Michelle. Good to have you back!
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