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I Was Told There Would Be No Math
January 14, 2014 8:06 AM   Subscribe

M.I.T. professor Max Tegmark explores the possibility that math does not just describe the universe, but makes the universe.
posted by COD (111 comments total) 30 users marked this as a favorite

 
Shut Up and Calculate
The Mathematical Universe

While I'm not confident we'll ever be able to prove or disprove them, I embrace Tegmark's ideas as the only concepts that give me a satisfying explanation for our existence. They say that our existence is inevitable, because everything exists, and we are a subset of everything. It's more satisfying to me that "all things" should exist rather than "a bunch of things".
posted by East Manitoba Regional Junior Kabaddi Champion '94 at 8:19 AM on January 14 [5 favorites]


Isn't this just a restatement of Platonic Idealism?
posted by three blind mice at 8:20 AM on January 14 [6 favorites]


Consciousness and free will pose a huge problem for this sort of idea. If everything including us truly is simply math, how is it that I have a subjective experience of the world and seem to be able to manipulate reality around me (e.g. typing on these keys right now)?

If his proposal is that my ability to do this could be described by math, I would say such a math has not yet been invented. And it's hence pretty presumptuous to try to say we could define our universe in terms of a math that can't explain the most fundamental property of the reality we perceive.

He says the lynchpin is belief in "an external reality independent of humans", but one can accept that this exists but also demand that any theory of everything grapple with the abundant fact of internal realities, dependent on conscious beings, which have literally created most of the world we see around us out of their thoughts.
posted by crayz at 8:26 AM on January 14 [2 favorites]


If everything including us truly is simply math, how is it that I have a subjective experience of the world and seem to be able to manipulate reality around me (e.g. typing on these keys right now)?

If his proposal is that my ability to do this could be described by math, I would say such a math has not yet been invented.


Such a math is called chemistry.
posted by Sys Rq at 8:30 AM on January 14 [11 favorites]


Thanks East Manitoba Regional Junior Kabaddi Champion '94. I included those links in my original draft, then started second guessing whether or not they were appropriate in a FPP given that the article is an excerpt form the book. I didn't want to look like I was Pepsi Bluing the book.
posted by COD at 8:31 AM on January 14


Such a math is called chemistry.

Yeah, no. If mathematical understanding of consciousness was developed, I'm pretty certain we'd have hard AI a very short time later. It's often said the problem with AI is programmers are used to working off a specification. The specification in hard AI is basically just "make it intelligent", because we have literally zero understanding of how physical matter becomes conscious.

If your honest answer is "chemistry" you've really never bothered thinking very much about this. (btw Tegemark also recently took a hand-wavey stab at this topic)
posted by crayz at 8:32 AM on January 14 [3 favorites]


Arg, the writing is SO bad (so far, I'm just on the first page).

> The trajectories of anything you throw have the same shape, called an upside-down parabola.

There's no such thing as an "upside-down parabola" - it's just a parabola! The word parabola doesn't come with any sort of orientation...

> When we observe how things move around in orbits in space, we discover another recurring shape: the ellipse. Moreover, these two shapes are related: the tip of a very elongated ellipse is shaped almost exactly like a parabola, so in fact, all of these trajectories are simply parts of ellipses.

Please don't misuse the verb "to be" in a math article. Either the path is an ellipse or it's a parabola - it cannot be both. In fact, if you disregard air resistance, these paths are actually parts of ellipses, which are very close to - but not the same as - parabolas.
posted by lupus_yonderboy at 8:33 AM on January 14 [2 favorites]


If his proposal is that my ability to do this could be described by math, I would say such a math has not yet been invented.

He has proposals. Consciousness happens in SAS's (self aware mathematical substructures). I'm sure this is covered in the FPP.

Mathematical Universe Hypothesis

WELCOME TO MY CRAZY UNIVERSE
posted by Golden Eternity at 8:36 AM on January 14 [2 favorites]


> If everything including us truly is simply math, how is it that I have a subjective experience of the world and seem to be able to manipulate reality around me (e.g. typing on these keys right now)?

Huh?! Why are you less likely to be able to experience and manipulate math than any other noun you might put in that sentence in its place?

The role of free will in physics is poorly understood - whether or not the world is simply math.
posted by lupus_yonderboy at 8:37 AM on January 14 [3 favorites]


If everything including us truly is simply math, how is it that I have a subjective experience of the world and seem to be able to manipulate reality around me (e.g. typing on these keys right now)?

You are composed of particles that operate according to mathematical laws. Some of your particles effect changes to particles in the brain, which results in a complex feedback mechanism, and we call that "consciousness" because we like having short labels for complex phenomena. Looking at the void around us dotted with lifeless rocks and balls of plasma, I see no reason to assume that consciousness is more fundamental to the universe than the mathematical laws which govern the particles necessary for consciousness to emerge.
posted by East Manitoba Regional Junior Kabaddi Champion '94 at 8:39 AM on January 14 [6 favorites]


I think a lot of mathematicians since the ancient Greeks have thought something like this. Or it might be more accurate to say *felt* something like this.

But post-Godel it looks like we'll at best have to settle for: "We'll never know for sure".

cf Godel and the End of Physics (Transcript of talk by Stephen Hawking).

The other school of thought is that math is just so damn powerful at modeling stuff that it can create models that are pretty much indistinguishable from the stuff being modeled itself.

Proving that it's not "pretty much" but "completely" is the rather hard part, and probably impossible to do in a way that would satisfy mathematicians, though it might satisfy everyone else.

If the universe is made of math, math might not be able to prove it. The foundations of mathematics seem to be full of ironies like that.
posted by philipy at 8:39 AM on January 14 [3 favorites]


This is in stark contrast to the way most of us first perceive mathematics – either as a sadistic form of punishment, or as a bag of tricks for manipulating numbers

I hated Maths at school because it was the subject that bored me the most. At 15 we were learning how to design a carpark and how to calculate a tax return. Thrilling stuff. I really wish the wonder of Maths was taught in school.
posted by billiebee at 8:41 AM on January 14


I can prove that the universe is made of math. We all know math is hard. When I rap a surface like this tabletop with my knuckles, it seems to be hard. Yet we know that it is almost entirely empty space. The reason my knuckles don't go through it is because math is hard.
posted by George_Spiggott at 8:43 AM on January 14 [24 favorites]


Greg Egan's sci-fi story "Luminous" sort of explores this idea.
posted by sevenyearlurk at 8:46 AM on January 14


If there were a benevolent god, the universe would be made of recess.
posted by weapons-grade pandemonium at 8:46 AM on January 14 [22 favorites]


Consciousness and free will are a bit of a red herring here. They pose challenges to materialism, the idea that world is made of plain old stuff. Basically you can either take the position that materialism works, or you support a dualist position in which there is some special "mind-stuff" property that explains free will and consciousness, or you can argue that consciousness is fundamentally inexplicable. But this debate doesn't depend on the super-fundamental-really-true nature of reality.

(I personally think that the position that consciousness poses an insurmountable challenge for materialism is fundamentally misguided, but that's another debate.)
posted by leopard at 8:48 AM on January 14 [6 favorites]


Some of your particles effect changes to particles in the brain, which results in a complex feedback mechanism, and we call that "consciousness"

I don't know who we is, but I think most people use consciousness to refer to subjective experience like seeing, feeling, hearing, etc. Nothing about a "complex feedback mechanism" explains why it would be experiencing anything, as far as I can tell. Which isn't very far.
posted by Golden Eternity at 8:49 AM on January 14


Greg Egan's sci-fi story "Luminous" sort of explores this idea.

For every far out scientific idea there is a Greg Egan story.
posted by Steely-eyed Missile Man at 8:51 AM on January 14 [7 favorites]


The "complex feedback mechanism" concept is necessary to explain where the "self" that experiences consciousness comes from. When you see red, it's not like your brain sends a picture to an internal TV screen that you're watching, even though it feels that way. (Where would this TV screen be? Where would "you" be sitting? How would you be able to "see" it?)
posted by leopard at 8:55 AM on January 14


Have you ever looked at your hands? I mean, really looked at them?
posted by chavenet at 8:57 AM on January 14 [13 favorites]


Side note: Quite a few cosmologists owe this man a beer for their unusually-low Erdos numbers. Tegmark has at least 921 co-authors according to ADS, including his father, who co-authored a paper with Erdos. Thanks, Max!
posted by hal incandenza at 9:00 AM on January 14 [5 favorites]


underpants gnomes theory of consciousness:
1) Particles move around in brain
2) ??? Complex feedback mechanism
3) Consciousness!
posted by crayz at 9:01 AM on January 14 [2 favorites]


The "complex feedback mechanism" concept is necessary to explain where the "self" that experiences consciousness comes from. When you see red, it's not like your brain sends a picture to an internal TV screen that you're watching, even though it feels that way. (Where would this TV screen be? Where would "you" be sitting? How would you be able to "see" it?)

I'm sorry, how did "complex feedback mechanism" solve this problem? Again, I'm really dense.
posted by Golden Eternity at 9:02 AM on January 14


Well basically it's handwaving that says "it's complicated." Not exactly a full solution but seems superior to "it's impossible," "it's magic," "it's quantum physics."
posted by leopard at 9:04 AM on January 14 [1 favorite]


Come on crayz, between the 'you've really never bothered thinking very much about this' comment and the underpants gnomes one you're coming across as pretty dismissive.
posted by Ned G at 9:05 AM on January 14 [2 favorites]


Re parabolas and ellipses: they are indeed different things, but are both examples of conic sections - curves generated by slicing a cone at different angles. But they correspond to different slices, so are different curves, as lupus_yonderboy noted.
posted by eviemath at 9:07 AM on January 14 [1 favorite]


Relevant xkcd? I think? Or do I?
posted by lucidium at 9:07 AM on January 14 [1 favorite]


Of course the universe is mathematical, that just means it is explainable. What would it even mean to say the universe is non-mathematical?
posted by bhnyc at 9:13 AM on January 14 [1 favorite]


I find myself a bit confused by this piece. I'm happy to agree with his argument that the relationships between objects (/forces/etc...) count more than the objects themselves. That's why it's possible to run useful computer simulations of physical systems: it's the pattern of interactions we care about, not the substrate. One could therefore build simulations or models that accurately describe the whole universe and, from the perspective of someone living inside such a simulation, it would feel just like the real thing.

However, he seems to make the leap from saying "it's possible/useful to build a model" to "we must be living in a model". Or perhaps from "we can use maths to describe the universe" to "therefore, the universe is made of maths". Is he arguing an odd semantic point, or arguing against an underlying physical reality that the maths is just a great description of, or am I missing his point completely?

(These conversations always make me think of a wonderful Pratchett quotation that runs along the lines "...trying to unravel the Mighty Infinite using language we developed to tell other monkeys where the soft fruit is.")
posted by metaBugs at 9:14 AM on January 14 [3 favorites]


Consciousness and free will pose a huge problem for this sort of idea.

This sort of idea poses a huge problem for consciousness and free will.
posted by Mental Wimp at 9:14 AM on January 14 [3 favorites]


Or "Is Math a Feature of the Universe or a Feature of Human Creation?" (Single link Idea Channel video).
posted by Athanasius at 9:14 AM on January 14


Yeah, eviemath, but he says the tip of a very elongated ellipse is shaped almost exactly like a parabola which is true.

I guess it's kind of trivially true for any function with an x^2 term in its expansion that as x->0 it will approximate a parabola, but for a 'very elongated ellipse' it will approximate it quicker as it's a similar shape already.

EDIT: Sorry if this is an abuse of the edit window, I feel if I'm being nit-picky about maths I should correct myself, I meant to say with an x^2 term and no x term above.
posted by Ned G at 9:16 AM on January 14


What would it even mean to say the universe is non-mathematical?

It would mean that the universe isn't reducible to a formula or set of axioms or other body of mathematical tools. This is a surprisingly difficult challenge to mathematical universes. This is the state we are now, in fact, in, because we cannot completely describe the universe with math. The interesting (and unanswered) question just is whether we will eventually be able to do so.
posted by fatbird at 9:16 AM on January 14


I know that consciousness can't be materially based because when I take powerful psychotropics, they hardly change my consciousness at all stars trippy flowers meltingly oranges into gluey gobs trivalent insolidic acidific creatine bolus mirror shards settling lake home seriousness dementia...so there.
posted by Mental Wimp at 9:21 AM on January 14 [1 favorite]


Have you ever looked at your hands? I mean, really looked at them?

Hey, it's a math thread. Of course I'm looking at my hands.

No, wait, it's a higher-math thread. For this I'll need my fingers and toes.
posted by yoink at 9:23 AM on January 14 [2 favorites]


the tip of a very elongated ellipse is shaped almost exactly like a parabola

Is it just me or is using the phrase "almost exactly like" in a popularization like this article, which starts out with a serious problem of imprecision already, kind of unhelpful to his purpose? I mean, I'm almost exactly like a Bonobo, an apple and an isosceles triangle, for various values of almost. And don't get me started whether "the tip" is usefully descriptive. I already went down that road with my first girlfriend.
posted by George_Spiggott at 9:26 AM on January 14 [2 favorites]


The problem of consciousness is orthogonal to the problem of whether the universe is "made of math". It's hard to see how a bunch of physical stuff bumping around comes to have subjective experiences either, regardless of whether the "physical stuff" is literally "mathematical stuff" or not.

Let's try saying it this way....

Your iPhone can (in some sense) see red or recognize a face. It does not (or so we presume) have a sense of self, have an experience of seeing red, or experience recognizing a face.

One question is whether your iPhone, an apparently "physical entity", is actually a mathematical entity.

A separate question is what it would take to make your iPhone have subjective experiences, so it really had an experience of seeing red.

For some people it's an article of faith that there is no answer to the second question, or the answer is something like "give it a soul" which is beyond us as mere mortals. For other people it's an article of faith that we will find the answer out some day.

If you're a mathematician, it's not obvious that in either case you wouldn't be able to create a mathematical model of the situation if you actually had a proper grasp of it. That would mostly be what your definition of "having a proper grasp of something" would be.
posted by philipy at 9:31 AM on January 14 [1 favorite]


East Manitoba Regional Junior Kabaddi Champion '94: "They say that our existence is inevitable, because everything exists, and we are a subset of everything."

That pretty clearly argues for the infinite-multiverses theory of cosmology, which AFAIK has largely been abandoned.

Always seemed like a cheater's way out to me. (cough, Heinlein, cough)
posted by IAmBroom at 9:33 AM on January 14


Consciousness and free will pose a huge problem for this sort of idea. If everything including us truly is simply math, how is it that I have a subjective experience of the world and seem to be able to manipulate reality around me (e.g. typing on these keys right now)?

You don't really have a subjective experience of the world, you only feel like you do.

(Whatever "you" and "the world" are. And whatever "experience" is.)

"Free will" is itself a subjective experience -- one which science is either inconclusive about, or which science doesn't support at all but we resist that conclusion.
posted by Foosnark at 9:34 AM on January 14 [2 favorites]


I'm almost exactly like a Bonobo, an apple and an isosceles triangle

You are almost exactly like a Bonobo or an apple.

Whether you at all like an isoceles triangle is what the article is about surely.
posted by philipy at 9:35 AM on January 14 [3 favorites]


crayz: "Consciousness and free will pose a huge problem for this sort of idea. If everything including us truly is simply math, how is it that I have a subjective experience of the world and seem to be able to manipulate reality around me (e.g. typing on these keys right now)?"

Oh, god, this red herring again. It's past smelling bad, and into long-dried baccala status.

"Consciousness" is not some magical, timey-wimey wibbly-wobbly metaphysical event (or at least, there's absolutely no proof it is). All we can say for certain that it includes is a combination of sensory inputs and memory (the great Helen Keller reported that, prior to the "miracle at the water pump", she literally had no thoughts, and her world was empty - even though she had /some/ sensory input).

Next you'll be arguing, "Oh yeah? Well, how can math explain souls, huh?"
posted by IAmBroom at 9:37 AM on January 14


I'll put it another way- How do we prove that the universe is non-mathematical?

This just seems like a nonsense question to me.
posted by bhnyc at 9:42 AM on January 14 [1 favorite]


crayz: "underpants gnomes theory of consciousness:
1) Particles move around in brain
2) ??? Complex feedback mechanism
3) Consciousness!
"

It's called "qualia", SIR.
posted by stratastar at 9:44 AM on January 14 [2 favorites]


crayz: "If mathematical understanding of consciousness was developed, I'm pretty certain we'd have hard AI a very short time later. "

I'm pretty certain no one has the capacity to accurately gauge how far AI research would have gotten under different circumstances. BTW, since you're claiming expertise in the field - how many AI research papers have you written? or read?
posted by IAmBroom at 9:44 AM on January 14


It's maths all the way down.
posted by ethansr at 9:50 AM on January 14 [1 favorite]


"Free will", one must admit, is a superb red herring. It has literally nothing to do with the hypothesis in the article, which can be true or false regardless of whether "free will" actually exists (which itself is dependent on one's definition of it, and still may be ultimately unverifiable).

Remember, people: Only Intel can create a tree-shaped floating-point error.
posted by IAmBroom at 9:50 AM on January 14


Or anyone using an Intel product.
posted by IAmBroom at 9:50 AM on January 14


How do we prove that the universe is non-mathematical?

By demonstrating that math is unable to describe everything, either by finding something indescribable mathematically (such as "perfect randomness"), or by proving that mathematical systems are unable to describe some things, such Goedl's Incompleteness Theorem showing that any axiomatic system (such as arithmetic) is necessarily either incomplete (i.e., does not include all true theorems) or inconsistent (i.e., if it has all true theorems, it contains contradictions).

None of this proves that the universe is non-mathematical, but it presents counterexamples to the hypothesis that the universe is mathematical. In other words, right now, the mathematical universe is an idea that's not proven, and has some significant challenges to overcome to be proven. Math, as it currently exists, is demonstrably insufficient.

A century ago, a Grand Unifying Theory of physics seemed like it was just around the corner; now, not so much, and there are significant figures proposing that there is no such thing. Is there a mathematical equivalent to the GUT, conceptually?

This just seems like a nonsense question to me.

It's actually a really deeply philosophical question.
posted by fatbird at 9:53 AM on January 14 [3 favorites]


The many-angled ones live at the bottom of the Mandlebrot set.
posted by MrBadExample at 9:56 AM on January 14 [1 favorite]


The first thing I thought of when I read the heading is the computer in 'Matrix'. The second thing was wanting to hug a mathematician really hard. The third thing I want to say after attempting to RTFA is that my arms are logarithmic and fuzzy and I feel like a zebra turned inside out. Is this supposed to happen?
posted by BlueHorse at 9:58 AM on January 14 [1 favorite]


Either the path is an ellipse or it's a parabola - it cannot be both.

I agree, but there's also a very reasonable point of view in which a parabola is a special case of an ellipse, namely an ellipse with one focus infinitely far away, which neatly fits with the use of parabolas to approximate the elliptical trajectories of falling objects (neglecting air resistance, as you said). I imagine (though I haven't checked) that the space of ellipses has a nice compactification or projectivization or something where the added points-at-infinity can be identified with parabolas.

(Actually, a glance at Wikipedia suggests several ways to realize this; the one that most pleases me at a quick glance is this:
The ellipse can also be defined as the set of points that are equidistant from one focus and a circle, the directrix circle, that is centered on the other focus. The radius of the directrix circle equals the ellipse's major axis, so the focus and the entire ellipse are inside the directrix circle.
So, in the same sense that lines are circles (of infinite radius), parabolas are ellipses.)
posted by stebulus at 10:00 AM on January 14 [3 favorites]


My first sense is that he is applying his mathematical and theory building skills to describing the universe around himself, but I don't really see how this is different than the kind of teleological narrative building that we are all susceptible to. He's simply using math as his language to tell a story about how things are just-so. We all do it.

This is a nice (but critical) take from a philosopher.

The problem is in what sense, if any, can a mathematical structure, so defined, actually be the fundamental constituent of the physical world, i.e. being the substance of which chairs, electrons, and so on, are made.

...

Could it be that theories like MUH are actually based on a category mistake? Obviously, I’m not suggesting that people like Tegmark make the elementary mistake of confusing the normal meaning of words like “objects” and “properties,” or of “physical” and “mathematical.” But perhaps they are making precisely that mistake in a metaphysical sense?


posted by stratastar at 10:04 AM on January 14 [4 favorites]


Isn't this just a restatement of Platonic Idealism?

Not really, no, since Plato's "eidos" wasn't a mathematical object.
posted by thelonius at 10:13 AM on January 14 [1 favorite]


I think part of the problem is that we believe consciousness actually exists as some magical unquantifiable thing, when really it's a trick of memory, recall and reflection that's really useful for humans to employ as a survival skill. Eventually we will get the matrix right and build one from sand and petri dishes.

I'm good with math being real. Ten years ago, no, but today, hell yeah.
posted by Annika Cicada at 10:14 AM on January 14 [3 favorites]


I'm a mathematician, not a physicist, so feel free to take the following with a grain of salt (although my area of research - Lie theory - is closely related to the physics of the standard model, so I do have a basic idea of what physicists think of there). And I should also admit up front that I am, philosophically, strongly opposed to Tegmark's thesis. My main concern with the "everything is math" viewpoint is that it is, depending on the definitions involved, either a) trivially false or b) tautologically true, in an uninteresting way.

For a), look at this following quote from the article: "There's something very mathematical about our Universe, and that the more carefully we look, the more math we seem to find." This argument generally refers to the astonishing ability of physical & mathematical models to describe our universe. And those models ARE very effective! But the map is not the terrain: this is like saying, "Wow, it's so amazing how well Google Maps predicted the location of every Wawa in my town - the world must be equal to Google Maps!"

For b), there really is a sense - tautologically - in which the universe is math: I'm willing to grant that there are indeed fundamental laws underpinning everything in the universe, so if we constructed a mathematical model the size of the universe (cf the Borgesian map which is as large as the area it describes), yeah, that could be said to prove that the universe "is" math. But this tautological point-of-view neglects the main benefit of mathematical constructions: they are idealized, simplified models constructed so that humans can understand them! The fact that a physical model is not, in fact, literally equal to the universe is a feature, not a bug.

Anyhow, perhaps there is a more subtle argument to be made here; but I'm quite unconvinced based on this article. (And, speaking personally, for those that know about the standard model: the claim that somehow a particle literally is a vector in a representation of a compact Lie group is laughably absurd to me.)
posted by Frobenius Twist at 10:24 AM on January 14 [17 favorites]


Y'all know they call him "Mad Max" Tegmark, right?
posted by crazy_yeti at 10:24 AM on January 14


the claim that somehow a particle literally is a vector in a representation of a compact Lie group is laughably absurd to me.

Yeah - we all know the particle really is an operator-valued distribution defined on a Lorentzian 4-manifold!
posted by crazy_yeti at 10:31 AM on January 14 [5 favorites]


Greg Egan's sci-fi story "Luminous" sort of explores this idea.

Also Greg Bear's Moving Mars.
posted by audi alteram partem at 10:37 AM on January 14 [1 favorite]


or b) tautologically true, in an uninteresting way.

Yes, my trouble with the article is that it is it doesn't do anything very forceful to persuade you that it's not b). See this, for example:
The Mathematical Universe Hypothesis implies that we live in a relational reality, in the sense that the properties of the world around us stem not from properties of its ultimate building blocks, but from the relations between these building blocks.
It is hard to read this as anything but six of one, half a dozen of the other; you merely have to posit that the relations between these building blocks arise from their properties and you're back where you started. Still, there's a whole book behind this -- one wonders if there's something more compelling in it.
posted by George_Spiggott at 10:46 AM on January 14


...there are two key points to take away: The External Reality Hypothesis implies that a “theory of everything” (a complete description of our external physical reality) has no baggage, and something that has a complete baggage-free description is precisely a mathematical structure. Taken together, this implies the Mathematical Universe Hypothesis, i.e., that the external physical reality described by the theory of everything is a mathematical structure.

This is where he loses me. He seems to be assuming that everything in the universe can be mathematically described (a theory of everything is possible), and thus the universe is a mathematical structure, which is to say that it can be completely described by mathematics. I'm missing the part where we go from saying that universe can be described by mathematics to saying that it is mathematics.

What if there's a different abstract system for describing and predicting the universe that's totally separate from our math? I have no idea what such a system would look like, but I don't see a reason that our favorite abstraction tool has to be the only one possible.
posted by echo target at 10:48 AM on January 14 [1 favorite]


There was some discussion of Tegmark's ideas on Mefi previously in this thread.
posted by twirlip at 10:50 AM on January 14


But this tautological point-of-view neglects the main benefit of mathematical constructions: they are idealized, simplified models constructed so that humans can understand them! The fact that a physical model is not, in fact, literally equal to the universe is a feature, not a bug.

Tegmark is careful to distinguish the set of symbols from the reality described by them. Or, rather, reality is a superset of the infinity of symbolic ways of describing it. Perhaps our minds are incapable of understanding a mathematical language that describes all aspects of the universe, or our minds can only conceive of a inherently limited math that can, at best, only approximate a model of reality, but we have gotten pretty far in a few thousand years. A lot of math we find lines up with testable ways to describe reality. It seems too much of a coincidence to ignore studying and thinking about and testing some more.
posted by Blazecock Pileon at 10:57 AM on January 14


Another way to look at this is "Map vs Territory." Typically, a map is just a representation of a territory, flawed and lacking detail. However, what if you could create a map so detailed that it matches every single aspect of the original territory at a 1:1 scale? At 1:1, the map is the territory.

This is basically what he's suggesting math is. Math is a 1:1 scale map of the universe. Our history of scientific progress in our understanding of the universe is a history of mathematical exploration and discovery. Each algebraic proof probes deeper into our understanding of the fundamentals of the universe from black holes and quasars to quarks and bosons.

Our map of the universe is made out of math.

There are two outcomes for the future of this map. 1.) We reach a dead end because math is unable to model at a 1:1 scale. We find that some features of the universe will forever remain out of reach of our understanding. Perhaps we will never be able to model consciousness. Perhaps we will never develop a Grand Unified Theory that works. 2. Math offers no obstacle to modeling the universe at a 1:1 scale. The secrets of consciousness and a Grand Unified Theory are discovered. Math is a 1:1 scale model of the universe. The Map is the Territory. The Math is the Universe.
posted by j03 at 11:03 AM on January 14 [2 favorites]


This piece really seems like weak philosophical tea, and it's surprising to see it getting taken so seriously (presumably on account of science envy?). Nonetheless it's definitely part of a broader, quite weird resurgence of mathematical Neoplatonism lately — I'm amused to imagine that Tegmark and Alain Badiou are secretly in league, carrying out a strategic pincer-formation flanking attack on the philosophical mainstream, one from the pseudoscientific right and one from the pseudoprofound left.
posted by RogerB at 11:03 AM on January 14 [3 favorites]


Not sure what this article brings to the party, to be honest. All we can say for sure about mathematics is that it's an immensely powerful modelling system, which is all we can say for sure about consciousness, and both for the same reason: they work. Imaginary numbers are why we can listen to the birth of the Universe on our radio telescopes - but then, all numbers are imaginary, in that two of anything can be thought of as one of something else. Can you think of the entire Universe (or the multiverses) as 'one thing'? Sure you can. Does the Universe (or the multiverses) care? Doesn't look like it.

Whatever is Out There is amenable to being modelled. Whether there are unmodellable things, or things that are unmodellable by our mammal brain plus augmentation, is fun to shoot the breeze about - if there are, we haven't found them yet.

But Out There is not the model - except that, to be aware of whatever parts of it we can be aware of, it has to fit into our models. In that sense, yes, the whole universe is mathematics, because mathematics is all we have - I have little patience, after many years of thinking about (really quite hard, thank you very much) and tinkering with the nature of consciousness, for those who say it is outwith the known or potentially known mathematics of physical systems. Vitalism has not had a good track record.

So yes, true. Our universe is built from mathematics. We have no other material to work with, in here.

Can we get on with building a warp drive now, please?
posted by Devonian at 11:04 AM on January 14 [1 favorite]


Okay, so brass tacks here. What would be the predictive power of this hypothesis? Is it possible to even imagine an experiment which would have one outcome if he's right and another if he isn't? And if not, then is it even a meaningful line of inquiry?
posted by George_Spiggott at 11:07 AM on January 14 [1 favorite]


I imagine (though I haven't checked) that the space of ellipses has a nice compactification or projectivization or something where the added points-at-infinity can be identified with parabolas.

Yep, there's a space of plane conics which is just a P^5 (projective 5-space) and in which the parabolas (parabolae?) form a closed subspace of codimension 1; they're the conics which are tangent to the line at infinity.
posted by escabeche at 11:19 AM on January 14 [3 favorites]


And if not, then is it even a meaningful line of inquiry?

Sometimes the value of an idea comes from disproving it. No one takes Zeno's Paradoxes straightforwardly, but they're an excellent test of a theory: if it can't dispense with them sensibly, it's not done the basic work.

Disproving the mathematical universe would have some interesting consequences, potentially. For one, Wolfram's whole schtick about replacing math with computability... well, still wouldn't get taken seriously, but other alternatives to math might. I'm not up on the current state of math, but there've been various branches that took quite radical directions, like intuitionistic math and such. When Goedl published his Incompleteness Theorem, it ended the Vienna Circle's project and killed Logical Positivism, and launched a lot of new exploration of math and logic and philosophy.

As for predictive power, I'm not sure what that means at the level of mathematical theory, but it has implications, I would think, for a lot of fields that depend heavily on math like physics or cryptography. To go back to randomness for a moment, the immediate implication is that there is no such thing as pure or perfect randomness. A mathematical universe implies a kind of mathematical determinism.

[disclaimer: I'm a well read layman who studied this stuff in university many years ago, so I know a lot of big words but I'm not an expert who's current, and I'm likely making mistakes in this presentation, which is why I'm keeping it general and handwavey]
posted by fatbird at 11:23 AM on January 14 [1 favorite]


But how would you prove or disprove it? My fundamental question is does this distinction actually have a difference? Is there anything that distinguishes a universe which behaves rigorously and implacably in accordance with mathematical laws and one which consists of nothing more than those laws? It seems to me, following your example, that pure randomness is equally unavailable in either case.
posted by George_Spiggott at 11:33 AM on January 14 [1 favorite]


It's a bit of a fluff piece, and I would have liked some detail about how a universe made out of mathematics differs from one described by physics. If all natural constants can be eliminated and all relations that are presently postulated can be derived, I guess an all-mathematical reality is what we arrive at. I can't say if there is something fundamentally preventing those reductions, but I'm also not sure it makes so much of a difference.
posted by Herr Zebrurka at 11:44 AM on January 14


As mentioned above, it can be seen as a sort of Platonic viewpoint.

I think I came to this understanding that science (physics in particular) can be seen in two lights.

My first understanding was a Platonic Logos, due to my Christian upbringing, and venturing further out into other philosophies. "The Logos" is "The Word"... The creation of the universe is like God speaking the word to give form to matter and energy. The WORD itself was outside of space/time as entities, and exists as a law unto itself.

Then, as I got more into science, I realized the "relational" view of it.

I decided at one point a few years ago to call this the "Prescriptivist" vs the "Descriptivist" models of science.

We talk of the laws of nature as the force behind that which we see, but it could be said that instead, the laws (logos/language) is merely describing that which exists, ex post facto. Of course, it IS ex post facto, in light of the fact that we, as entities that arise, have to model it after the fact of its existence. But I think this is a good question.

Is math emergent or primary?

I still have a hell of a time working with the idea/assumption that all the laws we know are consistent across space/time (in our known universe)... This seems to me an a priori assumption that we use to make our lives easier. I think in one of the books I have (From Eternity to Here(?)) he discusses this issue, but I can't remember his explanation, and I think it was just sort of an axiomatic faith at some point.
posted by symbioid at 11:51 AM on January 14


How would you prove or disprove that there's a difference between a universe composed solely of math versus a universe that behaves like it does? I think you're right, it's a distinction without a difference, a clever question about trees falling in forests.

Tegmark is asserting not just that math, in the broadest sense, is capable of perfectly describing the universe, but that there's nothing else. The interesting question is that premise of Tegman's, that math can perfectly model the universe. That's very much unproven, and obviously problematic given certain counterexamples. I'm not sure whether Tegman is arguing for Platonism or Instrumentalism.
posted by fatbird at 11:53 AM on January 14


There's a method of validating your favorite theory where you throw out everything that doesn't fit with it and then exclaim "Ta-da! It explains everything!". The way that he calls some things "baggage", rather than "phenomena my theory can't explain", makes me think that this is what Tegmark is doing.
posted by benito.strauss at 11:55 AM on January 14 [1 favorite]


Y'all know they call him "Mad Max" Tegmark, right?

Is that because, if you want to get out of here, you've got to talk to him?
posted by Naberius at 11:57 AM on January 14 [2 favorites]


A subordinate question we sort of touched on there is whether proving that there is no way that anything in this universe can produce pure randomness is the same as proving that pure randomness cannot exist in this universe. I'm not real sure about that one.
posted by George_Spiggott at 11:58 AM on January 14


That's an interesting question, George. At first glance, it's hard not to see MUH as advocating for a mathematical determinism the precludes true randomness.

There's a subtler premise here that I wonder if we're not carefully avoiding, namely whether a mathematical universe means a 1:1 map, as described above. If the complete math for the universe is a 1:1 map of the universe, and thus there's no difference, then the idea it's mathematical is meaningless, since 'mathematicality' would just seem to be that property of something that works at a greather than 1:1 scale. The whole miracle of math just is that the orbit of Jupiter is accurately described by the formula for an ellipse.

In information theory, the Kolmogorov complexity of information is rated by its compressibility: a piece of information can be compressed by specifying it in fewer bits than its expression. A maximally complex piece of information cannot be compressed at all: there is no more succinct way to specify it than its expression; there is a 1:1 mapping between its expression and its specification. For math to be meaningful or useful or anything other than what we see when we open our eyes, it would seem to need to be a compression of the universe, a more succinct way of specifying it.

So if the MUH is the case, then there is no such thing as pure randomness, only pseudo-randomness generated out of a compact specification of that randomness.
posted by fatbird at 12:11 PM on January 14 [1 favorite]


This is all interesting in light of this, some recent news on the Holographic Principle.
posted by fatbird at 12:14 PM on January 14


sevenyearlurk: Greg Egan's sci-fi story "Luminous" sort of explores this idea.

I think you mean Greg Egan's story "Distress", which centres around a conference to establish a theory of everything.

Whereas "Luminous" is about microscopic spiders inside a rock talking to each other about physics.
posted by memebake at 12:15 PM on January 14


No, that's Incandescence. "Luminous" is about a war between alternative mathematical realities.
posted by stebulus at 12:17 PM on January 14 [1 favorite]


Oh no wait. I'm thinking of "Incadescence", ignore me
posted by memebake at 12:17 PM on January 14


fatbird, you've just expressed rather well some ideas I've been sort of scrounging for in the last hour or so. The most succinct example of compressibility is that a purely deterministic system is in some meaningful sense completely described by its initial conditions. In that sense the universe's "source code" is just amazingly more compact than any description of its states over any span of time, let alone its entire existence.

I can't help but feel on some useless cognitive level a universe of pure math allows for an infinite universe more comfortably than one which is made of stuff. I do not pretend that there's any logic to this; it's just that I can more easily imagine a universe that goes on forever if you extrapolate from its laws than one that is actually made of an infinite amount of stuff.
posted by George_Spiggott at 12:18 PM on January 14 [2 favorites]


Okay, so brass tacks here. ... And if not, then is it even a meaningful line of inquiry?

At the level of brass tacks, it has no effect whatsoever that I can see. But it's meaningful for certain values of "meaningful". The kind of thing people are talking about when they talk about "searching for meaning in their lives".

Think about Carl Sagan waxing lyrical about us being made of star stuff. You're not made of any different stuff than you were before he said that, but looking at it that way has an effect on how you see yourself and feel about yourself.

Admittedly it's a fairly small subset of humanity that would find meaning in contemplating being made of math stuff.
posted by philipy at 12:21 PM on January 14 [1 favorite]


A mathematical universe implies a kind of mathematical determinism.

The thing is, what with every particle in the universe interacting with every other particle, even if it is completely deterministic, you would never be able to accurately model it (and hence predict the future) without some device that could simulate the behaviour of every independent particle. And such a device would have to be made of even more particles than the ones it is trying to simulate. Hence although you might talk about the universe being 'deterministic', in practice nothing can accurately model the unfolding of the universe other than the universe itself. So what does deterministic mean, at the end of all that? It becomes indistinguishable from randomness.

NB: Dennett's "Freedom Evolves" has a lot of stuff on this.
posted by memebake at 12:25 PM on January 14


I am still hung up on his bit about the chess game, because there's a bit of a logical slip in his description:

Chess involves abstract entities (different chess pieces, different squares on the board, etc.) and relations between them. ... So what is it that's left when you strip away all this baggage? What is it that's described by all these equivalent descriptions? The Immortal Game itself, 100% pure, with no additives. There’s only one unique mathematical structure that’s described by all these equivalent descriptions.

The first sentence is begging the question. If you're talking about the ultimate nature of reality, then it does you no good to throw out the physical chesspieces in the very first part of your argument. Of course the rest of your argument will involve abstract entities and relations, you have already eliminated everything else! To then jump back and say that these abstract entities and relations create the physical pieces, that the pieces have no properties unto themselves, that all properties are built from their relations, doesn't work.

Why is the question of whether the description is the thing, so casually answered?
posted by mittens at 12:36 PM on January 14 [4 favorites]


So, basically, we're talking about Block Transfer Computation?
posted by webmutant at 12:43 PM on January 14


Why is the question of whether the description is the thing, so casually answered?

Pigliucci, linked above, actually hits him on this--that he does very little to describe the transition from "mathematical relation" to "actual bits composing a chair on which I sit". He describes it as a "category mistake".
posted by fatbird at 12:47 PM on January 14 [1 favorite]


There's nothing psuedo- about Alain Badiou. See also Quentin Mellaissouix (sp?).
posted by Saxon Kane at 1:08 PM on January 14


scientists and mathematicians often have astonishing naive metaphysical beliefs. however, they are generally trained not to express them openly.
posted by ennui.bz at 2:12 PM on January 14


Think about Carl Sagan waxing lyrical about us being made of star stuff. You're not made of any different stuff than you were before he said that, but looking at it that way has an effect on how you see yourself and feel about yourself.

Admittedly it's a fairly small subset of humanity that would find meaning in contemplating being made of math stuff.


Here is the difference: There is a pretty broad consensus about what it would mean to be made of star stuff. I Am A(n ex-)Mathematician. I would class "humanity...[is] made of math stuff" with "colorless green ideas sleep furiously."

And no, learning new facts does not greatly alter my physical composition. I don't know why that's the standard of relevance.
posted by PMdixon at 2:21 PM on January 14


This is a complete fluff piece. The philosophy of mathematics is an actual field, and how it applies to epistemology is something serious scholars are studying. He makes no reference to any of their work.

I wonder what he thinks of Hermeneutic Fictionalism? Has even heard of it? Physics can be done without numbers - and indeed, without math, so long as pure logic is ceded to philosophy rather than mathematics. (Which is itself a long stretch, but still - this stuff is far ranging and deeply thought upon. Much moreso than the article would lend you to believe.)
posted by Slap*Happy at 3:17 PM on January 14 [2 favorites]


Saying the universe is made of math is like saying a von Neumann computer is made of opcodes. This is silly; opcodes aren't the computer, they are what the computer does. It would be far closer to the truth to say the computer is the information stored in its memory, which might be program instructions worked on by opcodes or other data worked on by programs. The opcodes are a nice chart in a spec sheet; the computer is a physical embodiment of information storage and the necessary execution hardware (usually not trivial in itself) to implement the opcodes.
posted by localroger at 3:21 PM on January 14 [2 favorites]


I wonder what he thinks of Hermeneutic Fictionalism? Has even heard of it? Physics can be done without numbers - and indeed, without math, so long as pure logic is ceded to philosophy rather than mathematics.

The universe is philosophy.
posted by Golden Eternity at 3:27 PM on January 14


I think if you're a professor of Cosmology and you get bored making precision measurements of cosmic microwave background or working on low-frequency radio interferometry, a smart thing to do is to come up with a big 'wow' inducing idea for a theory of everything that will make a cool sounding pop-science book and also get you invited to talk on TV programmes about how wacky the universe is. Bonus points if your big idea is completely impossible to test by scientific means. For example you could posit a near-infinite number of universes which are completely cut off from our own and so unobservable. Strictly speaking, you're still well within your remit as a cosmologist, and ultimately you are just throwing another idea into the big unanswerable riddle that is our existence, so you're unlikely to attract too much criticism. Ultimately, you're idea is never going to be sillier than some of the others. And you get to write books and be on TV and stuff. Its more fun than running files of instrument results through matlab day after day.
posted by memebake at 3:43 PM on January 14 [3 favorites]


it's definitely metaphysics, not science. I think.
posted by thelonius at 3:50 PM on January 14


Here is the difference: There is a pretty broad consensus about what it would mean to be made of star stuff

To a human being, most of them anyway, it matters whether they think of themselves as being made of star stuff, made of fusion products, made of nuclear waste, or made of chemical compounds. In the same kind of way it maybe matters to your spouse if the earth is in approximately the same part of its orbit as it was when you got married.

Like I said it is meaningful for certain values of "meaningful". Maybe not the ones you commonly deal with, but in the realm of stuff that is meaningful to human beings, it is.

For that matter a lot of what theoretical physicists have concerned themselves with in recent decades isn't all that meaningful if the definition of meaningful is going to be "gives rise to predictions that we could test in reality". Read the Stephen Hawking link I gave upthread.

it's definitely metaphysics, not science. I think.

It's definitely not science. Probably. It might be metaphysics, or possibly sci-fi.

Metaphysics might be pointless, then again it might not.

I doubt Metafilter is going to settle that question. Also I doubt that Metafiler will understand my sense of humor. Such is life.
posted by philipy at 5:14 PM on January 14


I don't think there is a mathematical basis to the universe; the mathematics we perceive is just a collection of relationships that are significant to us.

For instance, think of a row of children arranged by height. It's easy to measure the median height (the height of the child in the middle of the row); it's also easy to calculate the mean height (the average height; the sum of the height of all the children, divided by the number of children). In contrast, it would be relatively hard to calculate the median height without sorting the children in some way.

These two figures (the mean and the median) are probably different, but! the more children you have, the closer the numbers will be. What is going on here? Is the universe saying that there is some deep connection between the mean and the median? Is the height of the median child affected by the heights of children around her? No. It just happens that children's heights follow a normal distribution, and the distribution is centered around the mean. With enough children in the row, you will find that there are a lot with heights very close to the mean; and there will be roughly equal numbers of children taller and children shorter than the mean. Hence: the mean and the median will be similar, but not because of some woo-woo theory about how one affects the other or how mathematics affects the height of the median child.

The same goes for other relationships. The path of a planet is an ellipse; not because an ellipse is a beautiful magical shape, but because "ellipse" is a short way to say "the path of something with a particular vector, attracted to a point by the inverse square of its distance from that point." And "ellipse" is a way to describe other things, too, but this isn't because they have some secret connection - it's just that we find the path of a planet to be meaningful, and that's what the path of a planet is.
posted by Joe in Australia at 8:11 PM on January 14 [2 favorites]


Hell ya. Let's just wallow in map = territory.
posted by Twang at 10:00 PM on January 14


Asking Ultimate Questions? (Max Tegmark)

This was good, imo. Max is a fun guy. I can't make head or tail of some of the others.

What Things Really Exist? (Roger Penrose)

Ahhhh. This one was amazing for me. Thank you Roger.
posted by Golden Eternity at 12:13 AM on January 15


Between the concept of 0 and 1 exists an infinitude of maths... so there.
posted by panaceanot at 4:31 AM on January 15


> Sometimes the value of an idea comes from disproving it. No one takes Zeno's Paradoxes straightforwardly, but they're an excellent test of a theory: if it can't dispense with them sensibly, it's not done the basic work.

For whatever it's worth, Zeno, at least, took Zeno's paradoxes seriously, and saw them as indicating the truth of Parmenides's metaphysical monism — proofs that there can only exist one thing, that that thing is undifferentiated, indivisible, continuous and unchanging.

I've long been a little bit annoyed by approaches to Zeno that treat his ideas as a sort of linguistic/mathematical parlor trick to be "solved" rather than a serious attempt to demonstrate the illusory nature of the evidence of the senses. Zeno was more or less Parmenides' attack dog — he took all of this stuff deadly seriously. Arguing that (say) Newtonian calculus gives us a way around Zeno's argument for the impossibility of motion without confronting the underlying argument that there exists exactly one unmoving unchanging thing requires missing the point altogether. Well, insofar as it's possible to miss a point, given that every point is part of the same unmoving unchanging unity.
posted by You Can't Tip a Buick at 4:32 AM on January 15 [4 favorites]


I find it interesting that an individual who states that Mathematics is a pure Platonic law driving the universe's evolution, and then discounts the idea of infinity because Physicists do whatever they can to normalize it out and make shit work.

But if you believe Math comes first, then you have to admit that Infinity literally exists, and if we do normalize (I can't remember the correct term) infinities in Physics (because it makes life harder for physicists), then that is just for our convenience, not because of any inherent nature of infinities as they exist.

I guess the question here is... "Is the claim that Matter/Energy/Space/Time itself actually just... Math, in itself?" Or, is it similar to how I interpret a Platonic prescriptivism in that what we call reality fundamentally exists (Space/Time/Energy/Matter), but that the "code" that drives the universe exists in itself apart from the reality (in a platonic shadow-casting realm, natch). Thus, non-descriptivist, but not a pure monism. It would still be a dualism.

Perhaps it is the Monistic aspect of his view that's the most troubling, and I can see why many would have an issue with it. Would those who oppose his stance have an easier time swallowing it if it were more dualistic?

So - is it because we do not observe infinities in nature itself, but only via our set theories (which does come out of nature, via our own fucking minds, technically), that Tegmark says he does not believe in them?

If so, it's quite ironic that on the one hand he insists that Mathematics is the Logos, which is sort of ... I won't say an unprovable postulate, but certainly difficult to confirm (what is his testable hypothesis? does he have one? It might be unprovable, I'm not a mathematician or physicist so, I can't make a claim on what is or isn't testable, but then when it comes to discussing infinities, because it's not "found in nature" (like a true materialist/physicist would say), it doesn't "exist".

He seems to be trying to have the best of both worlds, while focusing on a pure monism, while still clinging to the observational universe as the only source of knowledge (as opposed to pure mathematical theory which can include higher order sets than that which we see in the known universe).

I suppose you then still run into the question - why or how - THIS particular configuration of laws? Are there an infinite number of combinations? What about eternal return theorem?

I kinda want to read his book now. Whenever I've heard him speak I always found him fascinating to listen to. It's not that I'm not fond of some form of Platonic vision of Math as Code, but a Monistic version, now that I think about it, is hard to accept.

The closest I could come to such an acceptance would be a Holographic Principle based universe. We are an evolving set of mathematical entities on 3-brane surface of our 4-dimensional universe (or does the holographic principle take string theories 11 dimensions as part of that? how does that play a role? I can't recall). Regardless, we might just be some form of numeric configurations, cast down from this idealized platonic heaven surface into the 4D Space time below.

The question I have there is: what casts the "shadow" what is the source of light to make this hologram become 4D. Then you get into a bunch of messy metaphysics like "god" is the supreme observer or... perhaps, all other potential universes are overlapping and interfering an a form of wave function collapse exists within each universe, splitting itself, and ok, I think I'm entering woo territory at this point, so shutting up! :)
posted by symbioid at 8:45 AM on January 15


But what if the universe was pure opcodes, maaan? This is sort of what Wolfram is on about, that the Universe is like computational cellular autonoma, but the playing field itself, the computer, is kind of hand-waved away like "ether" when we know there's no "ether" or "space" or "time," there's just space-time, a curvature created by gravity and other forces that ultimately presents what appears to be a playing field but the participants themselves "emerge" the playing field from their intrinsic properties.

The code itself is the computer, the data is indistinguishable from what processes the data (buffer overflows meet Heisenberg's Uncertainty Principle, man) and the computation itself is polymorphic and metastatic and emergent.

where's the bong
posted by lordaych at 9:01 AM on January 15 [1 favorite]


Another piece by Max Tegmark: Life is a Braid in Spacetime - How to see yourself in a world where only math is real.
posted by homunculus at 6:14 PM on January 16


Kind of related given Tegmark's critique of Penrose's ideas:

Discovery of Quantum Vibrations in “Microtubules” Inside Brain Neurons Corroborates Controversial 20-Year-Old Theory of Consciousness

Consciousness in the universe: A review of the ‘Orch OR’ theory
posted by AElfwine Evenstar at 8:06 PM on January 16 [1 favorite]


Doge weighs in
posted by jeffburdges at 2:49 AM on January 17 [1 favorite]


ooops my last link is broken, here's the paper:

Consciousness in the universe: A review of the ‘Orch OR’ theory (pdf)
posted by AElfwine Evenstar at 8:05 AM on January 17


Arguing that (say) Newtonian calculus gives us a way around Zeno's argument for the impossibility of motion without confronting the underlying argument that there exists exactly one unmoving unchanging thing requires missing the point altogether.

Well...calculus doesn't "find a way around Zeno's argument," it provides a direct answer to his question, which is "Is the limit at infinity of the sum of the product of times and distances as they are sequentially halved in constant-velocity motion over a finite range finite?" Since the current intuition was that any infinite sequence had an infinite sum, Zeno appealed to that intuition to create an "impossible" situation and an apparent paradox where none exists. There may be good arguments for everything existing as one unmoving, unchanging object, but Zeno wasn't providing one.
posted by Mental Wimp at 12:07 PM on January 23 [1 favorite]


intuition was that any infinite sequence had an infinite sum

I haven't read any primary sources or anything, but there's a frequently given and more subtle version of this paradox of Zeno's, which simply asserts that actual infinities are impossible — so it's not that the steps are thought to add up to an infinite sum, just that there are infinitely many of them to complete. The definition of limits now used in calculus doesn't deal with this problem at all, since it just treats statements about actual infinities as being code for statements about potential infinities. That's like saying, "No no, when we say, 'They reach the wall', what we really mean is 'They get arbitrarily close to the wall'." But the whole difficulty is that they do actually reach the wall, and if we don't explain that, we haven't met Zeno at all.
posted by stebulus at 2:12 PM on January 23


...this paradox of Zeno's, which simply asserts that actual infinities are impossible...

Not even sure what that statement means, but I'm pretty certain Zeno didn't say it. Zeno concocted an infinity; it wasn't handed to him by someone else. And the difference between an actual infinity and some other kind of infinity escapes me.
posted by Mental Wimp at 2:27 PM on January 23


Should physicists stop looking for fundamental laws?
posted by homunculus at 5:07 PM on January 24


Boy, that error in thinking is ubiquitous isn't it? From homunculus's link:
the fact that the fundamental constants of nature are fine-tuned to a fault, that the universe as we know it would not exist if these constants had even slightly different values.
No, the fact that I won the lottery doesn't imply that the lottery was fine-tuned so I would win because had the winning number been just one digit off... I don't know why this thinking is so appealing, when such a simple example exposes its invalidity.
posted by Mental Wimp at 7:14 AM on January 25 [1 favorite]


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