That’s interesting, I’ll look into E6 and that point on dark matter some more.
Do you have any thoughts on constructible vs non-constructible mathematics?
Part of the reason I’m a little biased towards computational theories is because there’s one fewer assumption: that there is some incomprehensible substrate that is capable of doing non-computational mathematics, I.E., infinite limits or truly continuous curves.
It would also be a reason as for why we’ve been able to make so much of physics discrete already (there being quanta rather than continuous flow).
I’ve noticed people who believe in god (or at least are just deists) tend to also be biased toward non-computational models, since that’s the only model which would allow for the existence of something that would qualify as a god, which is fair enough.
It’s probably not the only reasons in their minds.
I believe in god…but I think God’s role or the nature of god…is beyond human understanding…
Personally I think that we live inside a black hole…and that within each black hole is another universe…
Eventually I think that the universe will be filled with black holes and will merge into one big giant black hole…and start over again…when the black hole dies…all the energy and matter will be released.
Why do I think this it’s because all the matter and energy has to go somewhere
So I believe in an oscillatory universe…when this incarnation of the multiverse dies…a new one will form and the cycle will continue in some form or fashion.
Also tangent…
If the atomic model somewhat mirrors planetary solar system model…
If photons can be both a particle and a wave…
And some subatomic particles can switch between matter and antimatter…or phase in and out of existence…
I guess existence and nothingness can exist simultaneously…
Computational models I doubt…
I think more like nuclear reactor with various processes to stabilize itself until it runs out of juice…
The following is an argument, I guess – the good kind, not the bad kind, I hope – but I’m open to counter-argument.
I’m sure you know – I find the benefits of challenging each others conceptions similar to the benefits of engaging in reciprocal feedback in the listening booth.
Do you consider yourself a deist, or do you subscribe to a particular theology?
I’m not a believer, but I also don’t believe that there isn’t some form of deity. I guess I just can’t see a good reason as for why there’d need to be one at all.
I’m reluctant to say anything more on that matter, however. Though if you want me to, I’d happily do so.
I’ve heard this idea before. Though, one question I have is about the evaporation of black holes by the process of Hawking radiation. Virtual particles are one way of describing fluctuations at the quantum level in the electromagnetic field that permeates all of space. When one of a pair of virtual particles form at the event horizon, such that one falls in and the other shoots off in the other direction, the energy to realise the other particle is given by the gravitational field of the black hole.
Due to the equivalence of mass and energy, this means the black hole loses mass.
Such that, when the heat death of the universe is well under-way, black holes throughout the cosmos will begin evaporating at a rate faster than they gain mass (currently, there’s enough energy in the cosmic microwave background, loose matter, and other stellar bodies, to keep the net gain positive).
Give it enough time, and the black holes will all disappear.
However, when we look at our universe, we see that it is expanding, not losing mass or energy, as it is all conserved. The heat death of the universe occurs because of entropy. Entropy is essentially the potential for the release of more energy that is stored in the system. However, this energy must be stored in a way that by a natural process, it can be converted into another form that cannot then be converted back into a useful form of energy.
When essentially all potential stored energy that can be released by a natural process has been converted into loose radiation, where the expansion of the universe will stretch the wavelength out to approach infinity.
Currently, most of the universe is flying away from us at (relative) speeds faster than light. In fact, it is this horizon that defines the observable universe.
Because the universe’s expansion is accelerating, our observable universe shrinks (relatively) and makes up a smaller and smaller proportion of what could be considered the entire universe (in terms of the light cones of two points far enough away never intersecting).
This expansion faster than light means that it is also impossible for gravity to ever pull all black holes together again, since gravity can only travel at light speed too and follows the same laws meaning that the light cones of the two points can never intersect.
The only thing that would permit all black holes to merge into one would be if the universe starts to slow down in its acceleration, and begins to reverse, and turn into a Big Crunch.
However, as I currently understand the latest understanding, there aren’t many good reasons to believe that the universe ISN’T expanding, and accelerating, and is not going to slow down, as all measurements we know how to take indicate that it is expanding,
All of this is based on a framework that has been experimentally verified repeatedly such that the probability of it being a statistical fluke is so small you probably have a higher chance of winning the lottery than it all being fundamentally wrong.
Of course, that isn’t to say that what we have is all there is, and there are certainly many examples of small disagreements with prediction, which are being worked on.
But, physics is like a jigsaw puzzle, where we have to derive its structure from analysing experience, and the pieces must fit together coherently.
As we derive more pieces, it places more and more constraints on the kinds of new pieces that can be added to the puzzle, thereby offering various justifications to declare the impossibility of particular ideas, since it would require such a substantial change to the structure that various other pieces that are well-understood and well-tested would no longer fit.
I really do love that idea, in fact, I actually used to believe that deeply – almost religiously.
But when so much of classical physics that was one assumed to be continuous where perfect curves and non-constructible mathematics can be done; and then we critically analysed our theories, refined our instruments, and thoroughly analysed how natural behaves empirically – almost everything we thought was continuous has now been made discreet, and we’ve identified the various associated quanta and defined them to remarkable accuracy.
I agree with Joscha Bach that the reason this was the case is because classical mathematics (and by extension classical mathematicians) didn’t fully understand the difference between constructible systems and non-constructible systems.
And I also agree with Wolfram on the point that it’s only now in this modern age, that we even posses the conceptual tools to have even THOUGHT about a computational model of physics.
We needed to have built computers, discovered cellular automata, discovered the limits of computability, and various other things beyond my pay grade, to have even dreamt of it.
Indeed. Time will tell in the end!
I do actually hope… really… that everything we understand is completely wrong, and that in fact slowing down time, artificial gravity, FTL – all that sci-fi shit – is possible. I really do wish beyond all other things that we can ACTUALLY play in our backyard rather than be forever bound to look out of our bedroom window, grounded for eternity by the deities.
Well, to a limit, I hope time travel always remains impossible. For good reason.
I have to say … this thread keeps getting better… deeper, less philosophical and more detailed discussions about Mathematics, Physics, Cosmology.
Forgive me for not having the patience to jump in with long dissertations about my thoughts about all the thoughts so well expressed here… suffice it to say “I agree with most of these high-functioning, educated, well articulated posts.”
Keep going!
I will, however, share a couple of thoughts:
God - Can’t be proven, can’t be disproven. Anything less would be less than God-Like. My personal conclusion - Therefore, whether or not “God” exists is not relevant. Using “God” as a reason or excuse for thought or action is abdicating responsibility for our actions. We should be Moral because it’s the right thing to do… not because we fear or respect “God’s Plan.” (Wouldn’t God want that?)
Mathematics, Physics, Cosmology - I question the reality of infinity. I accept that it is a useful concept, as a placeholder for “unimaginably large or small numbers.” Without it, we seem to be at a loss to probe the unimaginable… but I believe infinity confuses us in our search for answers at the edge of our ideas.
I’m not saying “I know infinity is not real.” I’m saying “I doubt that it’s real because I have yet to hear proof of (and I have reasons to doubt) it’s reality” (the Quanta and Qualia are among my reasons)
The best refutation to my premise that I’ve heard so far is “depends on your definition of reality.”
My definition of reality: “That which is tangible or measurable.”
I read GEB back when it first came out in ‘79… fascinating book… a real slog making it through some of the symbolic logic stuff and the programming languages…
I thought I lost that book but recently found it… perfect pastime for long COVID shutdown days and nights.
I’m about 2/3 the way through… that chapter on Bloop, Floop, and Gloop is as much a slog as I remembered… but there are so many amazing concepts intertwined and so well explained… it’s a tough read… but I swear I’ll finish it… again
0 is not a number in the same way that 1 is a number. 0 is a placeholder used to denote “no numeral here”
It also serves as the pivot (the mirror if you will) between positive and negative numbers, and as an unreachable goalpost between 1 and numbers less than 1.
When using 0 as number one has merely shifted the concept of “first” or “beginning” from 1 to 0.
It was an unfortunate decision for computer programmers to use the symbols 1 and 0: it gives the impression of “on or off” or “positive or negative “ or “something or nothing” when in fact it really means “this or that”
I’d agree. I think my view is probably roughly similar, but a couple of differences perhaps.
Though, infinity isn’t a value, nor is it a placeholder for unimaginably large or small numbers.
Infinity is to denote that there is no limit to some property of some object, sometimes, the logic of a system would mean that one property of the system necessarily has no limit.
It is those systems that cannot exist, all that can exist is a system that has the potential to become infinite, but only if it is unlimited in some dimension.
But in neither space nor time can any object within this universe be unlimited.
In the modern computationalist perspective, the misunderstanding of classical mathematicians is that classical mathematics is descriptive of the world.
But, that’s kind of like saying a non-computable function that describes a perfect circle, describes a circle that was generated via computable means and is therefore not a perfect circle.
It’s more like the perfect circle is an approximation of reality.
One might think it the other way around: that a computational universe would instead be an approximation of the perfect description.
No, in this view, they are different things that have a direct mapping that only exists if you break the computational rules and allow for an infinite number of steps. And because we’re in a universe that is bound to computable operations, those steps can never conclude, so the mapping can never actually be arrived at.
Like the Mandelbrot fractal is a function. Like Pi is a function. Pi is not a number. It is not a value.
You cannot construct a system that can depend on the last digit of Pi, because:
The system would require an infinite amount of time to compute the result
The system would need to be infinitely large to contain the result
The system would need infinite energy to exist
The bounds of space, time and energy.
I would agree – though, and you may agree with this too, it is possible to frame the idea of numbers in such a way that they are tangible and measurable, we just have to be careful to ensure we are grounding it in the neurological computations the brain is doing, and discern that it is not the numbers themselves are are the tangible and measurable thing, it is the system that embodies the principle that produces them. (CC @Numerical)
As a professional developer I can offer some reasons as for why this is the case.
Think about a simple logic AND gate.
It has two inputs, A and B, and one output C. If both A and B are 1, then the C is 1.
If A is 0 and B is 1, then C is 0.
In this case, the 0 represents the absence of current.
The components that require logic are use combinations of different logic gates for different purposes.
And, also, in terms of binary.
The digits in place value based number systems use a logarithmic scale of powers of the base.
Thought I’d add, I kind of rushed the last bit as I was supposed to be working!
We don’t actually use 1 and 0 to represent truth values in our code. It’s inconvenient and can lead to bugs and confusion because it might not be clear in some part of the code whether the number is supposed to be treated as a number or as a true or a false value.
In basically every programming language, there is an abstraction we use to represent a true or a false value: a boolean.
We’d literally do something like this:
bool myVariable = false;
if (myVariable == true) {
printf("myVariable is true");
}
Of course, the message would never appear because myVariable is false and no code changed its value.
In programming (now that I know you are “in the business”) what is used to represent infinity in a calculation?
Therefore, that property of the system is imaginary but not real.
I would argue that there is no “potential.” This is an example of what I meant by “the concept of infinity confuses us” and hinders a deeper understanding of reality.
Agreed… assuming “object” includes matter, energy and their constituent properties.
I would also propose that Space and Time are not infinite… but it does get tricky here… Space and Time may be confusing concepts (like infinity) or they may be real… if they are real, they are not infinite.
Mathematics is the Map, not the Territory. It can only describe an imaginary abstract of reality: useful… but not to be confused with reality itself.
Agreed that it is possible… but I maintain that this is
where the confusion between Map and Territory begins.
To us non-programmers 1 and 0 = 1… Abscence of current could be represented in a (dare I say potentially infinite?) number of ways. It’s confusing (until you accept the logic and ignore the connotation.)
This is true in base ten… and any base system.
In Binary 10 represents two of something, in base ten, 10 represents ten of something. In both cases 0 represents “nothing in this column.”
Computers would compute equally well if the symbols used were other than 0 and 1… as a small added benefit, us mere mortals would not be confused by what 0 and 1 mean in the context of programming.
There is a construct used to represent Infinity. But it’s not to represent unimaginably large or small numbers – it’s a cheat, because the idea is to try to emulate the semantics of classical mathematics on a computational system.
But that is where the conflict lies.
Two infinities are always equal in this construct (which is not necessarily true of the classical infinities).
Some programming languages will let you divide by zero, and they will just return the Infinity placeholder.
Other’s will just throw an exception and say you can’t do it.
That’s what I’m getting at. The infinity can never manifest itself.
I agree – it’s a bad choice of word on my part. What I mean by that is, it is possible to set up a program that will loop forever, for as long as you feed it energy.
Though, which is what you are pointing at, with the energy available being finite, there is no true potential.
When I speak of the computationalist perspective, I speak from the idea that the universe is some kind of automaton. Stephen Wolfram and Gerard 't Hooft have both proposed computational automata based models of physics. Both are already incredibly predictive of modern physics, and already most of current physics has been derived from this representation.
In this model, there is a function which describes the universe, which produces a fractal like structure that produces the dimensions of space and the properties of the particles and forces within it.
It is represented as a hypergdaph (a graph where nodes can be connected to multiple other nodes). Not that the universe literally is a graph, but that it is a construct which (seems to) describe the behaviour of the universe when the proper transformations are applied to the nodes.
(Little excursion: there are rules which define transformations on the nodes in the graph. Due to there being multiple rulesets and possible orderings of the rules (the space of rules is called Rulial Space), the different orderings correspond to the different perspective from within the graph, which corresponds to the different ways the wave function could collapse. It is this relativity in the rulial space that Wolfram has found that essentially General Relativity and Quantum Mechanics are the same thing manifesting in different ways in the graph.)
Also interesting to note in this model is that, there is a way in which every possible constructible system that could exist, does exist, in this graph.
So, this graph, this function that produces it, is a structure that keeps growing without a limit.
This means the only true Infinity is the the potential for the underlying substrate of reality to never end.
But, the mind-bender is, time is a concept that applies within and is generated by the hypergdaph, not outside of it.
This means, going into philosophical territory, that every possible state of this hypergraph already exists, just in a perspective we could never reach from the confines of the graph.
In that sense, the infinitude of constructible systems just exists, statically.
In fact… a perfect circle is an idealization (not an approximation) of reality. And! The Ideal does not exist in reality.
This is true of all geometry and mathematics. They represent the human ability to idealize a concept, which is part of pattern recognition and categorization… extremely useful tools.
If you show a human a wonky triangle… they think “triangle” before “wonky” if you further wonkify the triangle, at some point they no longer think “triangle.” The figure was never (and can never be) a perfect triangle (circle, square, number, zero, infinity etc.) that concept was always in the mind… not in reality… again, all extremely useful… but when we believe these concepts are real we confuse ourselves as to the deeper reality.
We can’t have these kind of conversations in polite company (if we want to be invited back) people run away in horror
I’ve had conversations like this with a handful of those willing to indulge… Scientists and Mathematicians among them. Believe me when I tell you that your thoughts on the subject are among the most well thought out and intelligent I’ve heard… of course… that may be because we seem to mostly agree
I realised I forgot to respond to a couple of points in my above reply.
I completely agree. I don’t meant to say all of mathematics is reality, or that even all of mathematics is descriptive of reality, or do I mean to imply anybody of significance did.
I mean to say: there are a set of mathematical constructs are descriptive of reality, but not reality.
That’s what it appears like from the classical perspective, and perhaps from a human perspective.
What I mean by this is hard to explain, it’s more of a metaphor for the order in which the relevant things appear in the process – read my part about the cellular automaton model of physics in my above reply first.
There is a computational way that will generate a circle – they will converge on a perfect circle the higher you push the precision.
But, in no way can that ever happen.
So, the only way in which the exact mapping between the generated perfect circle and the perfect circle can exist is if we have infinite resource.
It doesn’t even make sense to call it an approximation of it, it could never be it.
The thing that comes first in reality, is the imperfect circle, then we invented a mathematical construct (a non-computable one) that describes reality.
So, in that sense, the perfect circle is the approximation of reality.
But, the means by which the imperfect circle came to be is unrelated to the description of the perfect circle.
It just seems from our human perspective to be the other way around.
This is where Godel’s Incompleteness Theorem says “not so” but it also says “not ever” There is always a true statement that cannot be expressed within any system… ad infinitum… but again, this a concept which basically says Mathematics can never completely describe reality… even with infinite resources (which does not exist)
