Some models of reality are bolder than others(cjauvin.github.io)
cjauvin.github.io
Some models of reality are bolder than others
https://cjauvin.github.io/posts/metaphysical-boldness/
18 comments
I’ve always had this weird intuition that Zeno’s Arrow Paradox is some indication that there must be some discreteness. Somehow, somewhere, there must be a ‘tick.
> If spacetime had a discrete character at scales like the inverse of the universe scale we would see dispersion of light as it traveled cosmological distances and we do not observe this. It is technically possible that the discreteness scale is much, much smaller than the inverse universe scale, of course, but at this point it seems pointless to me to entertain discrete models
A computational universe does not strictly imply discrete spacetime. You can most certainly still have a continuous universe—at least from the perspective of the beings that inhabit it. By way of analogy, consider the fact that ZFC proves the existence of uncomputable real numbers yet itself has a countable model (presuming it is consistent).
A computational universe does not strictly imply discrete spacetime. You can most certainly still have a continuous universe—at least from the perspective of the beings that inhabit it. By way of analogy, consider the fact that ZFC proves the existence of uncomputable real numbers yet itself has a countable model (presuming it is consistent).
What about experimentally validating these models against reality? There is kinda a reason why we came up with the models we currently have.
It is interesting that we can measure absolutely every physical quantity in units of length and that our best gravitational theory is based on manifold curvature characterised by an infinitessimal line element. This suggests that ultimately the universe may be geometric in nature with, at least from our perspective, a fundamental length (area) scale at which very simple geometric rules operate ad infinitum to produce all of the emergent complexity we observe. On this view, we live in a fractal, we are patterns at scale that do not appear to arise obviously from the fundamental rules, but we do so arise.
The above entails that the speed of light is not quite constant, but rather energy dependent; c=f(E). The variation would be very small so detecting this is challenging. Myriad observational hurdles may prevent us from ever detecting such small variations but there are many reasons to posit such a model, most quantum gravity theories do so.
The above entails that the speed of light is not quite constant, but rather energy dependent; c=f(E). The variation would be very small so detecting this is challenging. Myriad observational hurdles may prevent us from ever detecting such small variations but there are many reasons to posit such a model, most quantum gravity theories do so.
Pretty sure we just need a clock.
State change/differentiation exists, that's what we can't get rid of in the physical world no matter how hard we try.
https://www.nature.com/articles/s41598-024-71907-0#Sec8
State change/differentiation exists, that's what we can't get rid of in the physical world no matter how hard we try.
https://www.nature.com/articles/s41598-024-71907-0#Sec8
Time can also be viewed as a length.
> It is interesting that we can measure absolutely every physical quantity in units of length
Can we?
Can we?
Yes of course, not only can we but it makes everything so much easier.
The concept does have a certain appeal.
But it seems to me that the acid test, as always, is successful prediction. If one day a digital model makes a prediction that is experimentally demonstrated, and not accounted for via other models, then there might be more support for this approach.
But it seems to me that the acid test, as always, is successful prediction. If one day a digital model makes a prediction that is experimentally demonstrated, and not accounted for via other models, then there might be more support for this approach.
> I find it very appealing to consider the idea that the world is not somehow running “hidden mathematics”, somewhere and somehow, to solve some complicated equations in a seemingly magical way, but rather, that things are radically simpler, in that the world is simply implementing a set of trivially simple rules. The world is not concerned with, or made with mathematics, mathematics just emerges, with inherent and irreducible complexity, from extreme simplicity.
Wouldn’t those simple rules be mathematics? It’s very hard for me to see how the world isn’t made of math. Then again, I am a Pythagorean.
Wouldn’t those simple rules be mathematics? It’s very hard for me to see how the world isn’t made of math. Then again, I am a Pythagorean.
Mathematics is just a tool, like language, for describing reality, not reality itself.
A cake is not made of numbers like 5 cups flour + 3 eggs, but we can model it as such. In principle we could invent any such system of symbols to describe the physical world but those symbols don’t define it. The physical world only nudges us toward what symbols work and which don’t.
A cake is not made of numbers like 5 cups flour + 3 eggs, but we can model it as such. In principle we could invent any such system of symbols to describe the physical world but those symbols don’t define it. The physical world only nudges us toward what symbols work and which don’t.
Strawman. You are claiming math isn’t real?
Not a strawman. I’m not stating that math isn’t real. It’s real as an abstract framework that humans create and refine. It’s not, however, foundational to the physical world in the way fundamental particles or gravity is. Numbers and equations don’t push particles around, they simply help us represent that kind of phenomena that we observe.
So spheres are invented by humans? In another universe, there are no spheres or triangles?
There is a distinction between "What the universe is made of or how it works just happens to be really compatible with how math describes things" and "The universe is just "running" math and we discovered that math and use it for other things"
But like, words stop working at these levels of rigor.
What the hell does "The universe is made of math" mean? How can something be made of a field of study? Where is the "Addition" particle? How does 1+1=2 give rise to what we see as an electron?
Like it's bad enough dealing with "quantum fields" that might be "real" or maybe are just really nice mathematical objects that happen to be useful for calculating the future.
Does math take up space? Does space take up math? Does blue afraid of seven? Can I eat integrals or will they go straight to my thighs?
If the universe is "made of" math, what is the consequence? For example, the consequence of being made of "quantum fields" in my lay mind is that we get observations like entanglement and the hilarity of whatever is going on in the higgs field.
>Then again, I am a Pythagorean.
Ah, let me just move this sqrt(2) out of the way real quick :P
I want simple rules because I am a simple man, and if those simple rules happen to actually be math, that sucks for me because the "simple rules" are really hard math.
But like, words stop working at these levels of rigor.
What the hell does "The universe is made of math" mean? How can something be made of a field of study? Where is the "Addition" particle? How does 1+1=2 give rise to what we see as an electron?
Like it's bad enough dealing with "quantum fields" that might be "real" or maybe are just really nice mathematical objects that happen to be useful for calculating the future.
Does math take up space? Does space take up math? Does blue afraid of seven? Can I eat integrals or will they go straight to my thighs?
If the universe is "made of" math, what is the consequence? For example, the consequence of being made of "quantum fields" in my lay mind is that we get observations like entanglement and the hilarity of whatever is going on in the higgs field.
>Then again, I am a Pythagorean.
Ah, let me just move this sqrt(2) out of the way real quick :P
I want simple rules because I am a simple man, and if those simple rules happen to actually be math, that sucks for me because the "simple rules" are really hard math.
Pythagoras almost certainly was misinterpreted.
Unsayable numbers (the way the Greeks said irrational numbers) can take the wrong meaning. Like, why are they unsayable? Because you’d die before you could say them. Well, it’s not a threat!
Then it turns into this whole ahistorical fabrication impugning Pythagoras who was, otherwise, pretty much the most incredible guy ever.
Now, the “addition particle” is a strawman, but harder to deal with is just numbers. Are numbers real? Are there discrete “things” in the universe? Well, yes there are. Frequencies or quanta do just fine. Now, when there are numbers, they can be added, whether we want to or not.
Another example would be geometries. Are spheres real? Surely! Do they exist on any planet in the universe? It would seem. Are there any perfect spheres? Nope. Do they precede matter and energy? It would seem.
I think we are saying the same thing. Unfortunately, these beliefs are slippery and metaphysical. I take pride, though, in the pythagoreanness of so many of the scientific greats, from Newton to Penrose.
Unsayable numbers (the way the Greeks said irrational numbers) can take the wrong meaning. Like, why are they unsayable? Because you’d die before you could say them. Well, it’s not a threat!
Then it turns into this whole ahistorical fabrication impugning Pythagoras who was, otherwise, pretty much the most incredible guy ever.
Now, the “addition particle” is a strawman, but harder to deal with is just numbers. Are numbers real? Are there discrete “things” in the universe? Well, yes there are. Frequencies or quanta do just fine. Now, when there are numbers, they can be added, whether we want to or not.
Another example would be geometries. Are spheres real? Surely! Do they exist on any planet in the universe? It would seem. Are there any perfect spheres? Nope. Do they precede matter and energy? It would seem.
I think we are saying the same thing. Unfortunately, these beliefs are slippery and metaphysical. I take pride, though, in the pythagoreanness of so many of the scientific greats, from Newton to Penrose.
While it not being ‚wrong‘, there lies a certain danger in this “Western“ approach to what is real. When people believe their dead child is singing in heaven, or that the ghost of their grandmother is watching over them, who are we to deny them that reality? Do we really want to reduce our experience to that which is physical or what we personally can relate to?
Like literally nothing distinguishes this idea in boldness from other ideas except that its not the current mainstream view. Also, no experimental verification.
If spacetime had a discrete character at scales like the inverse of the universe scale we would see dispersion of light as it traveled cosmological distances and we do not observe this. It is technically possible that the discreteness scale is much, much smaller than the inverse universe scale, of course, but at this point it seems pointless to me to entertain discrete models without some other compelling experimental means of determining its presence. I believe folks are trying to figure this out, but at present, my money remains on spacetime being continuous. I don't know shit, but I expect good quantum gravity theories will need to be scale free.
In general I think this CA stuff is much less deep than it seems to be. You can, of course, approximate continuous differential equations with discrete difference equations, which is, fundamentally, what all this boils down to, in the end. It isn't surprising that with appropriate rules one can reproduce smooth mechanics at scales way above the discreteness scale.