The universe -- Digital or Analog?

[Ken G]

Zeroes are better than infinities aren't they?

I think you mean infinitesmals, but either way, this is a good question with no clear answer. I'd say the answers lie more in your meaning for "better" than they do in any of the distinctions between zero and an infinitesmal quantity.

But in practice, note that whenever one does a numerical simulation of partial differential equations, it's all digital--how fine we slice things depends on the latest computer.

True, we do science both digitally, on computers, and by analog mathematics (theorems and whatnot). So we need both-- does the universe need either? I doubt it, I think both types of quantities are projections we make onto the universe. That they work at all, let alone so well, is what is really amazing.

You know me, I always look at things teleologically; so I ask not how Newton did things, but rather "If I were God, would I make the universe digital or continous?" Now, mathematicians hate discontinuities for some reason (hence we write "1/0 = 'undefined'" rather than "1/0 = 0"). But would God share the same esthetics? Who knows. . . .

No one, certainly.

But from an engineering perspective, what is the best design for a universe? Digital or analog? Well, an analog system would require a separate state description for every infinitesimal point--and there are infinities upon infinities of those. But if the universe were composed of "pixels", then only each pixel would have a separate state description.

This presumes the universe invokes a notion of information. I would say information is a product of an intelligence, and the universe must function without any obvious connection to an intelligence contemplating it. Again we must distinguish the projections of our intelligence from the universe we apply it to.

Oh that's right--descriptions aren't the same as reality you say. OK, then every infinitesimal point in an analog system would exist potentially in a different state-of-affairs than its infinity of neighbors. That's just not a good design.

That's true if the universe is "composed" of points. I doubt that too. Points, and digitized pixels, are both inventions of our mind, tutored to us by a universe that is not giving up all its secrets, perhaps like a cosmologist doing research on general relativity standing up in front of an introductory physics class teaching Newton's law of gravity.

There's been some talk here lately we might not exist in a physical universe, but rather exist is some kind of weird virtual matrix. Well, clearly, when humans design virtual worlds on computers, they are of necessity forced to use digital media. So we humans design our worlds digitally--therefore, why should we expect God to do it differently?

A more natural question is, why should we expect otherwise? The idea that humans can create universes is absurd, perhaps a form of insanity, despite what a few fringe physicists with no concrete results are saying. It's modern day Dr. Frankenstein-- remember, all that was taken just as seriously when the breakthroughs in anatomy and surgery were occuring.

I don't go in for Truth with a capital 'T'. Still, I don't want to reduce truth to that which works well. That's too self serving. The word 'truth' is a predicate that's properly applied to sentences, and nothing else. The sentence 'Some snow is white' is true if and only if there is some snow that is actually white.

But there's no such thing as "white", there is only what we decide to agree on is white, accepting the grey areas as part of the cost of doing business. It's all about what works, start to finish. Even logic itself-- there is nothing "intrinsically correct" about logic, it is a reasoning process whose complete arbitrariness is broken only by how well it works.

It's as simple as that. If some artists are overly liberal in their admixture of blues into their winter landscapes, that doesn't change the facts on the ground.

Perhaps those artists are seeing that ground with different eyes than you are.

[Warren Platts]

That's [that every infinitesimal point in an analog system would exist potentially in a different state-of-affairs than its infinity of neighbors and thus not a good design] true if the universe is "composed" of points. I doubt that too. Points, and digitized pixels, are both inventions of our mind, tutored to us by a universe that is not giving up all its secrets, perhaps like a cosmologist doing research on general relativity standing up in front of an introductory physics class teaching Newton's law of gravity.

So you admit that it is implausible that the universe is truly analog in nature--yet you're skeptical that the universe is digital.

Perhaps 'digital' is too anthropomorphic a word; really the question in the OP should be 'Is the universe analog or atomic?', in the old, ancient Greek, Democretean sense; that is, can the fundamental constituents of the universe be split up ad infinitum, or do you finally, after enough slicing and dicing, wind up with little nuggets that can no longer be split?

Edit: If things can't be split forever, and if the universe is not atomic or digital in nature, then what's the third alternative?

Let's be clear. We're only arguing over whether space and time are analog or not. I think we can all agree that matter in any case cannot be sliced up ad infinitum--you can keep slicing a lump of gold until you have one atom of gold, but slice that, and it's not gold anymore. Slice up a lump of metallic hydrogen, and you're left with a single proton, but slice that, you get quarks.

So, really the OP question becomes: Is the structure of space foam-like? Can you slice up space ad infinitum, or do you finally wind up with a nugget-like bubble that cannot be further sliced up? And isn't this the fundamental premise of string theory??? If everything that exists consists of vibrating strings and branes, then infinitesimal points couldn't possibly exist, because points can't vibrate. And if time is an artifact of movement, and if space consists of discrete bubbles, then the shortest possible duration would be the diameter of such a bubble divided by c.

But there's no such thing as "white", there is only what we decide to agree on is white, accepting the grey areas as part of the cost of doing business. Perhaps those artists are seeing that ground with different eyes than you are.

Assuming they're not color-blind, we should have the same physiology, and therefore should perceive the world similarly. The problem is most artists--even those that try for realism--don't paint the world as it is.

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I could try to paint the above figure with little dust bunnies in between the corners, or paint it as it is and let the dust bunnies arise naturally. Same with the apparent blueness of snow. Same with science.

[Kaptain K]

If not, and if the universe is not analog, then what's the third alternative?

Omnivalent!

Why should the universe mold itself to fit in our neat little cubby-holes?

[Warren Platts]

Omnivalent!

But then that puts you in the analog camp. In an analog system, each infinitesimal point will have a capacity to combine with or otherwise interact with or have some sort of a relation to all of the infinity of infinitesmal points that immediately surround it. I call that omnivalence.

[EvilEye]

That would lead to a convalenscense of multiple universes no?

[Kaptain K]

You, of course, are free to define terms any way you choose to make the universe conform to your preconceptions.

[EvilEye]

Preconception?

Interesting.

All I know is what I see or what I learn.

That is why I made the statement.

[Jens]

I would say just the opposite: the arrow finally gets to a length that can't be cut in half anymore, and so it has to cross to its target.

Just to clarify, because I'm not sure that Ken specifically stated this (though it's obvious from his use of the plural). But there are more than one Xeno's paradox. The one about the arrow is the best known, but not the only one. The one that's of interest here is not the one about getting from point A to B without going through an infinite number of points, but the one about how an arrow that is moving knows that it is moving at a discreet point of time.

[astromark]

Its not one or both but none of the obove... Digital, analog or real. It is what we/you perceive it to be... You might not have considered this before, but this universe is yours. How any one else perceives it to be is of little matter to you. Your defining view of all that is. It is yours to get wrong if you want to. I have decided that the universe is digital. That for me is a fact I can see no other explanation. But it does not make it so....

[Warren Platts]

You, of course, are free to define terms any way you choose to make the universe conform to your preconceptions.

You're the one who said the universe is "omnivalent". I can't find that word in any dictionary, so I have to go with the root meanings: "omni-" means "all", and "valent" means "combining", so "omnivalent" means "all-combining", and that seems like an analog concept to me. If you intended something different, it would be nice if you could clarify.

[Kaptain K]

It is my opinion that asking if the universe is analog or digital is to set up a false dichotomy based on our own limited perceptions.
It's like asking if light is a particle or a wave. The answer is "yes".
As Bohr said to Einstein, "quit telling God what to do".

[The_Radiation_Specialist]

This,

It is my opinion that asking if the universe is analog or digital is to set up a false dichotomy based on our own limited perceptions.
It's like asking if light is a particle or a wave. The answer is "yes".

along with this,

Unknown. But I would say that both digital and analog are simplifying concepts we use to slice and simplify a reality that is far more profound than either.

I don't understand, could you please explain more?

So what are you suggesting is the nature of these variables?

[Kaptain K]

So what are you suggesting is the nature of these variables?

I cannot speak for Ken, but I'm saying that the "true nature" of the universe is unknown and maybe unknowable. We view the universe through the filters of our perceptions and the limits of our cognitive abilities.

[Ken G]

So you admit that it is implausible that the universe is truly analog in nature--yet you're skeptical that the universe is digital.

Yes, my skepticism rests squarely on the idea that we acquire any value by imagining that what we are conceptualizing how the universe "really is" rather than simply making effective models about how we observe and interact with it. Instead our value comes from paying attention to what we are really doing, looking for value in models, and not getting caught up in the pitfalls of our own rhetoric (like "digital" or "analog"). I do think it is a good question to ponder the various digital vs. analog aspects of the universe, but framed as "what are the benefits of each perspective, and in what situations" rather than "which one is the real truth". The former approach is empowering, the latter is limiting. When we imagine we understand the universe, I submit it must be as amused as we are when we read the explanations by the dad in Calvin and Hobbes.

Perhaps 'digital' is too anthropomorphic a word; really the question in the OP should be 'Is the universe analog or atomic?', in the old, ancient Greek, Democretean sense; that is, can the fundamental constituents of the universe be split up ad infinitum, or do you finally, after enough slicing and dicing, wind up with little nuggets that can no longer be split?

That's closer, but still the way to say it is "can we derive conceptual advantage by subdividing our conceptual constructs, or do we reach maximum utility with some minimum construction?" Note this latter formulation is an ongoing question that never gets answered definitively, only provisionally-- like science itself.

Edit: If things can't be split forever, and if the universe is not atomic or digital in nature, then what's the third alternative?

Something we have no words for, yet. Perhaps we never will.

Let's be clear. We're only arguing over whether space and time are analog or not. I think we can all agree that matter in any case cannot be sliced up ad infinitum--you can keep slicing a lump of gold until you have one atom of gold, but slice that, and it's not gold anymore.

Actually, we don't know that about matter either, but at some point it becomes moot-- at some point we do not have the power to slice it, nor can we observe it being sliced. So there we stop.

So, really the OP question becomes: Is the structure of space foam-like?

But it should be, "in what situations do we need to imagine that space is foam-like to achieve the desired accuracy"? Note the difference, we are not debating angels on a pin, but something testable.

Can you slice up space ad infinitum, or do you finally wind up with a nugget-like bubble that cannot be further sliced up? And isn't this the fundamental premise of string theory??? If everything that exists consists of vibrating strings and branes, then infinitesimal points couldn't possibly exist, because points can't vibrate.

Note the key word in all that: theory. The history of science is choked with people who mistook theories for reality. It's time we increased the sophistication of our relationship with our own concepts.

Assuming they're not color-blind, we should have the same physiology, and therefore should perceive the world similarly.

Equating physiology with perception is rather missing the whole point of art.

The problem is most artists--even those that try for realism--don't paint the world as it is.

Perhaps they recognize the impossibility of the latter, and that was their first breakthrough as artists. There are differences between art and science, even though there is an art to science and a science to art.

[Ken G]

I cannot speak for Ken, but I'm saying that the "true nature" of the universe is unknown and maybe unknowable. We view the universe through the filters of our perceptions and the limits of our cognitive abilities.

I could not have said it better.

[Ken G]

I don't understand, could you please explain more?

So what are you suggesting is the nature of these variables?

We're suggesting the variables are invented for a purpose, and help us make predictions to various levels of accuracy. We never know what is "real", only how close we come and with how much difficulty. Scientists always make that trade-off, rarely using the most accurate theories available, and never imagining that any theory is exact, only, in some cases, fantastically accurate.

[IsaacKuo]

"Edit: If things can't be split forever, and if the universe is not atomic or digital in nature, then what's the third alternative?"
Something we have no words for, yet. Perhaps we never will.

Such a "third alternative" is by definition impossible. The definition of "atomic" is something that can't be split any further.

Either there's a limit on how far something can be split, or there isn't. If you think there's a third alternative, then you're just confusing yourself.

[IsaacKuo]

Scientists always make that trade-off, rarely using the most accurate theories available, and never imagining that any theory is exact, only, in some cases, fantastically accurate.

On the contrary--scientists always try to use the most accurate theories available, and they have a VERY strong tendency to believe a theory is EXACT, if it is sufficiently elegant. For example, Newton's theory of gravitation implied that gravity dropped off as 1/r^n, where n was EXACTLY 2. Experimentally, it was possible to determine that this constant was extremely near 2, but it takes a human's sensibility of elegance to make the extra leap of faith that it must be EXACTLY 2. If you look at theoretical elegance of the way rays of "light" expand in a 3 dimensional space, the 1/r^2 relationship is compelling.

But this desire for elegance also leads to extreme scientific fascination when it turns out the elegant formula leads to slightly inaccurate predictions. According to Newton's theory of gravitation, Mercury's orbit shouldn't precess. But it did! The scientific reaction wasn't just to reject the power of 2 and replace it with something a little bit different from 2. No, the scientific reaction was that there must be something deep we don't quite understand about gravity.

It would be decades before Einstein's theory of general relativity would explain something of that deep misunderstanding. Note that Einstein's theory of general relativity came from a deep desire for an elegant theory, not just a theory with numbers rigged up to best match real world observations.

The state of physics in the last half century has been that we have some serious mysteries that we just plain don't understand. We know the solution isn't to just rig up numbers to match the observations--the solution must be some sort of elegant explanation.

Or rather, it's FAITH that scientists have that there must be some sort of elegant explanation.

You can deny that there actually is an elegant explanation. And indeed, you could very well be correct. There is no a priori reason to expect the universe is fundamentally comprehensible.

But what you can't deny is that scientists basically believe there must be an elegant explanation. Maybe scientists are wrong. Maybe their faith is misplaced. Maybe the universe is destined to always be mysterious and fundamentally unknowable. But scientists work under the working assumption that the universe is fundamentally knowable.

[Warren Platts]

Isaac, I couldn't have said that better. Positivism is a cop out. If we can't know the universe as it is, then why are we fooling around spending billions of dollars on stuff that has nothing to do with weapons research or global warming? If science is merely a subspecies of engineering whose definition of truth is mere megatons of TNT, then why bother?

Edit: well, OK, I have to admit that writing grant proposals for a living is easier on one's back than chipping on the road all day. . . .

[Noclevername]

KenG has presented this point of view before. He has faith that he's right.

[EvilEye]

If we understood the entire universe, that would suck.

There wouldn't be anything worthwhile to talk about anymore.

[Jens]

Such a "third alternative" is by definition impossible. The definition of "atomic" is something that can't be split any further.

Suppose, just for argument's sake, that we are in a universe that is actually a simulation constructed by somebody in a higher universe. And that the person who constructed it is a simulation constructed by a higher universe yet. And so on, forever, or at least as far as we can know. What would that make it, digital or analog? Because we might suspect that somewhere along the line, there is a real, analog reality, but we can't know it. As far as we can tell it just looks like digital simulations the whole way up. I don't think we can simply assume that the universe acts according to our expectations. In fact, I am pretty sure that it does not, or in fact, can not.

[Warren Platts]

Suppose, just for argument's sake, that we are in a universe that is actually a simulation constructed by somebody in a higher universe. And that the person who constructed it is a simulation constructed by a higher universe yet. And so on, forever, or at least as far as we can know. What would that make it, digital or analog? Because we might suspect that somewhere along the line, there is a real, analog reality, but we can't know it. As far as we can tell it just looks like digital simulations the whole way up. I don't think we can simply assume that the universe acts according to our expectations. In fact, I am pretty sure that it does not, or in fact, can not.

Instead of turtles all the way down, it's the Matrix all the way up!?! Wow! Far out. . . .

[IsaacKuo]

Suppose, just for argument's sake, that we are in a universe that is actually a simulation constructed by somebody in a higher universe. And that the person who constructed it is a simulation constructed by a higher universe yet. And so on, forever, or at least as far as we can know. What would that make it, digital or analog?

The question of whether or not we can prove something is true is different from whether or not it is true.

Either atomic entities exist, or they don't. Either there's a limit to how far things can be split, or there isn't.

Now, it's impossible to prove the truth one way or the other!

It's impossible to prove atomic entities exist because there's no way to prove beyond all doubt that a supposedly atomic particle can't be split further.

It's also impossible to prove atomic entities don't exist, because it's always possible that there's some limit to splitting we just haven't run into yet.

See? It's easy to prove that we can never determine for sure whether atomic entities exist. That doesn't change the fact that either they do or they don't. It just means that we can never prove beyond all doubt whether they exist.

[EvilEye]

I'm having the same problem about "scientific vs true" on another board.

Dreams.

There's no way to scientifically prove they are real without using anecdotal evidence. You can use measurements to check REM and brain waves...but you can't prove that what the person says they saw, or that they even really saw anything.

[Noclevername]

At some point, you just have to put your foot down and say "I know enough to get something done." Otherwise we'd all be sitting in caves navel-gazing until we starve to death because we can't prove that food is necessary.

[Ken G]

Such a "third alternative" is by definition impossible. The definition of "atomic" is something that can't be split any further.

Either there's a limit on how far something can be split, or there isn't. If you think there's a third alternative, then you're just confusing yourself.

Your logic fails. It is not correct to say that anything is either infinitely divisible or has a minimum atom. The whole concept of "splitting" might well be of limited usefulness for many things. What then? We must never become the slave to our own words, they are our servants, they help us find the utility-- and that is all they do.

[Ken G]

On the contrary--scientists always try to use the most accurate theories available, and they have a VERY strong tendency to believe a theory is EXACT, if it is sufficiently elegant.

I'm afraid both the claims in that statement are patently false. I don't claim to speak for scientists as a whole, but it is quite easy to falsify both those claims with minimum research. For example, any astronomy journal will undoubtedly use Newtonian mechanics far more often than relativistic mechanics, just open to a few random pages to see this. Also, the history of science is quite clear on the issue of "exact" theories, unless you think we are living in a special time. I wager that most scientists do not think that, they see their art in the historical continuum.

For example, Newton's theory of gravitation implied that gravity dropped off as 1/r^n, where n was EXACTLY 2.

I presume you are referring to a classical point mass here. Relativistic distributions will require modification to this statement, especially if extended or rotating. It just proves my point-- no theories, no matter how elegant, are exact. The elegance is precisely why they are not exact-- elegance always represents a choice in the tradeoff between what is real and what is ideal (just look at the very first assumption in any "elegant" theory-- you'll see the idealization right away).

Experimentally, it was possible to determine that this constant was extremely near 2, but it takes a human's sensibility of elegance to make the extra leap of faith that it must be EXACTLY 2. If you look at theoretical elegance of the way rays of "light" expand in a 3 dimensional space, the 1/r^2 relationship is compelling.

That is a remarkable fact, I agree, but note you are overlooking both general relativity and (if it's true) string theory. I agree that the power is amazingly close to 2, presumably because we live in a universe that is amazingly close to having 3 spatial Euclidean dimensions. But not exactly, we already know that.

But this desire for elegance also leads to extreme scientific fascination when it turns out the elegant formula leads to slightly inaccurate predictions. According to Newton's theory of gravitation, Mercury's orbit shouldn't precess. But it did! The scientific reaction wasn't just to reject the power of 2 and replace it with something a little bit different from 2. No, the scientific reaction was that there must be something deep we don't quite understand about gravity.

And you see a profound difference there? The answer couldn't have been a slightly different power? Why not?

It would be decades before Einstein's theory of general relativity would explain something of that deep misunderstanding. Note that Einstein's theory of general relativity came from a deep desire for an elegant theory, not just a theory with numbers rigged up to best match real world observations.

The desire for elegance is quite central to the goals of science, primarily because our limited intelligence is only capable of creating predictive power from something elegant. As such, scientists always seek elegant solutions, and focus on situations where this is possible, often writing off the situations where it is not as "messy". We seek fundamental theories, but by "fundamental" we mean "idealized", i.e., limited. For example, we have quantum mechanics for small numbers of particles, and statistical mechanics for huge numbers, but comparatively weak science for anything in between-- there's little that is elegant in that middle domain.

The state of physics in the last half century has been that we have some serious mysteries that we just plain don't understand. We know the solution isn't to just rig up numbers to match the observations--the solution must be some sort of elegant explanation.

We know no such thing. But there's nothing wrong with hoping there is an elegant explanation-- for if there isn't, we won't find it. So we are the person searching for his keys under the streetlight, not because we expect them to fall in the light, but because that's the only way we'll find them.

Or rather, it's FAITH that scientists have that there must be some sort of elegant explanation.

Yes, that's more the reality-- it's faith, or hope. I agree it is quite remarkable that faith has taken us this far, I view that as the deepest mystery in all of science, but it cannot be extrapolated into a theorem about what we will discover in the future. It is close to that oft-misrepresented interpretation of Occam's razor that the "simplest theory is most likely to be the right one". That is demonstrably a false assertion about science.

You can deny that there actually is an elegant explanation. And indeed, you could very well be correct. There is no a priori reason to expect the universe is fundamentally comprehensible.

Why would I deny there is an elegant explanation? I have no idea, and I hope there is. But it will still be a creation of our intellect when and if we find one, the universe will go on doing what it does either way.

But what you can't deny is that scientists basically believe there must be an elegant explanation.

I can certainly deny that. What a scientist believes is a personal matter, and has no bearing on the art of doing science. That art requires only that elegance be sought, with the hope that it can be found. The keys in the streetlight.

But scientists work under the working assumption that the universe is fundamentally knowable.

Of course, that is a practical assumption made, just as a person searching for something adopts the working assumption they will find it. That's what motivates the search, an if they "believe it", they may search that much harder. But the belief has nothing to do with science. And it does not in any way support the contention that scientists think they are looking for an exact description of anything real.

[Ken G]

If we can't know the universe as it is, then why are we fooling around spending billions of dollars on stuff that has nothing to do with weapons research or global warming? If science is merely a subspecies of engineering whose definition of truth is mere megatons of TNT, then why bother?

Um, I can't follow this logic at all. What in your life do you do that follows this thinking? You go in the back yard to throw a baseball-- but hey, you'll never be Nolan Ryan, so why bother?

[Ken G]

Suppose, just for argument's sake, that we are in a universe that is actually a simulation constructed by somebody in a higher universe. And that the person who constructed it is a simulation constructed by a higher universe yet.

That may be the best counter I've ever heard to the idea that our universe is intelligently designed. Any argument used on our universe could also be applied to any other universe from which it sprung.