The Universe Is Made of Mathematics
disagreeableme.blogspot.com
disagreeableme.blogspot.com
I think what this is missing is a justification for thinking the universe somehow 'uses' mathematics in this sense; being /describable/ by it, is not at all the same as actually being generated by it.
There is a mistaken assumptions here that consistent rules from /within/ the universe would apply to its own operation. It's like assuming that because some rules must always hold when Monopoly is played, that the rules governing its physical constitution must be drawn from the same set.
"Confusing the moon with the finger pointing at it" —is a simple concept to understand, but seeing all the subtle places where we actually make the mistake in our mental lives requires another level of effort.
You guys basically complemented each-other, and came back to the beauty of the question.
I'd say what's more pressing is, does the information match the implementation. That is, is there any glimpse of external forces (that implement our universe) inside of it.
See https://en.wikipedia.org/wiki/Brain_in_a_vat
If our whole reality is more of a rouge, rather than an accident, then it's possible our reality has almost nothing to do with the parent-verse. And well, everything we seem to value as good models for the true implementation, are well, garbage.
> ...the same as different meat (constructed using the symbols)?
Your answer is talking about a comparison between, e.g., a human and an essentially identical human /constructed/ using a set of symbols that encodes our understanding of the human's constitution.
The original question is comparing, e.g. a human and a set of symbols which describes the human.
I consider each of the following to be meaningfully separate questions:
Reality is mathematics.
Reality can be created with mathematics.
Something equivalent to reality can be created using mathematics, if 'informational equivalence' is the equivalence relation in question.
The nature of consciousness is a black box. Therefore the nature of measurement, of assurance that mathematics matches reality, is only within the context of conscious observation, which is therefore subjective.
The objective truth will not be found within subjection.
Consciousness has a track record of taking a black box and deducing what is going on inside.
> The objective truth will not be found within subjection.
Wouldn't you need to understand the nature of subjective processes in order to stipulate such a limit? If you don't understand consciousness then you do not understand its limits.
1) The A.I is not just a set of symbols, it's a physical machine, which means you're answering a different question.
2) The structure of the test means that you have stripped down the objects to be compared to the sounds they produce, and yet a person is more than sounds, as is the computer. Whenever we use the relation 'X is a Y' there is an implicit definition of the identities of X and Y; the more abstract it that definition is, the more things your relation will accept; at some level of abstraction the human and the A.I. may be called equivalent—but you'd have to state which one you're talking about.
2) We can introduce more communication layers as you desire and still keep in the spirit of the experiment. I opted for the strip down version due to simplicity of describing the experiment and the similarity it has to the turing test.
Math is a quantitative description methodology, but no amount of "math" will bring a single photon into being.
> For something to be physical it must be present at some time and place within the universe, and for something to be abstract it must exist outside of space and time.
No. He is redefining words here. 'Physical' is not usually defined as "exists in space and time". Abstract thoughts or concepts do not exist outside of space and time. Abstract thoughts are the results of the modeling capabilities of brains and exist very much in the physical world. It isn't even known whether "existing outside of space and time" is a coherent concept.
> but if the universe is a mathematical object, it needs no creator (on Platonism at least),
Firstly, this is the Kalam argument all over again. It isn't clear at all that the Universe needs a beginning or whether the 'beginning of the Universe' is a coherent concept at all.
Secondly, even assuming mathematical platonism is true, and even if 'creation' was a prerequisite for the universe, mathematical platonism has no construct to go from 'describing a universe' to 'creating a universe'. That seems to be quite an important thing to miss.
> Our universe is fine-tuned because it is one which has the ability to support conscious thought selected from an infinite multitude of mathematical structures, most of which are lifeless.
This is very problematic. Once you start thinking about "different mathematics", you lose all foundations upon which you can reason. Logic does not work anymore. Even if it were true at all, no human could possibly have meaningful thoughts about it. Besides, if we abandon the concept of our 'mathematical structures' in other universes, what do the words true and false itself even mean?
There's lots of handwaving with (very) incoherent concepts and dubious logic in this post to make the argument for a mathematical universe.
By the way, I'm not talking about physical human brains. I'm talking about any brain, which includes human brains, dolphin brains, computers, and whatever other modeling machines exist in the universe.
I don't agree with that definition of a concept.
Idea = mental representation of an object, or a set of objects and their interactions.
Concept = generalization of an idea.
wherein 'mental' justifiably implicates the working of a brain. It is very much tied to what we call brain understanding. Sorry for taking this discussion to the definition of words.
On the "describing reality" to "creating reality". Very few people argue for ex-nihilo creation but far more people tend to project that on the opposing side (ie where did god come from? what was before the big bang?). I don't think the author is arguing that mathematics allows for creating reality from nothing but that anything that resembles reality behaves mathematically and thus can transform into new situations with new mechanics (or realities).
Second nitpick: different mathematics. You don't loose the foundations of reason, rather you are stating that with different assumptions a system behaves differently. You are still computing the logical outcome with the premises given. If you have a universe where true and false mean the same then you have a very small universe that doesn't support any differentiation. Take comfort in knowing this helps solve Gödel’s incompleteness theorem. We can construct an infinite number of consistent mathematical realities but only by comparing their predictions to our reality can we resolve which reality is our own.
I'm not sure I follow. What does "transform into new situations" really mean?
> We can construct an infinite number of consistent mathematical realities but only by comparing their predictions to our reality can we resolve which reality is our own.
If this is really what he meant, I appreciate the correction. If it would have been clear from the text, I would have proceeded with pointing out with pointing out the dodgy assumptions that underly the finetuning problem, but that would be even more like arguing against a deist/theist.
Emergence as a side-effect.
>If this is really what he meant, I appreciate the correction. If it would have been clear from the text, I would have proceeded with pointing out with pointing out the dodgy assumptions that underly the finetuning problem, but that would be even more like arguing against a deist/theist.
Yes, I am probably putting words in the author's mouth. He goes on a bit about computer simulations and how the Mandelbrot always "existed" because it is a mathematical consequence. In his view it seems different simulations are different universes and our universe is particularly amazing because it has evolved minds (computational constructs) that can distinguish different realities. Pair that with the idea that mathematics is a choice based on preconditions and you arrive at my statement.
From Amazon: "This work stresses the illogical manner in which mathematics has developed, the question of applied mathematics as against 'pure' mathematics, and the challenges to the consistency of mathematics' logical structure that have occurred in the twentieth century."
From goodreads.com: "Most intelligent people today still believe that mathematics is a body of unshakable truths about the physical world and that mathematical reasoning is exact and infallible. Mathematics: The Loss of Certainty refutes that myth."
Edit: This was also interesting: https://www.youtube.com/watch?v=RlMMeqO7wOI , a video by Stephen Wolfram. I know he is often criticized for various reasons, but much of what he says makes intuitive sense.
I had always thought of mathematics as the language of science. (Instead of saying i want more apples, i can say as i want 5 apples). Physics and other sciences use mathematics to explain the physical world or make predictions about them. Is there something more to it ?
Without a mind to understand, interpret, and define mathematics, does it exist? This is a core philosophical problem at the intersection of science and feeling. Without observation, no mathematics exists (for the observer). By proving it exists, you must also have an implicit observer.
2) The mind is a computational process (The Computational Theory of Mind or CTM)
Pretty big assumption, considering we still have no idea how the mind works (e.g. quantum fluctuations that lead to patterns and thoughts, the origin of which are not known to us or predictable by us.)
3) The universe behaves according to laws of physics which are expressible mathematically (metaphysical naturalism)
What about where those laws break down, such as inside a black hole or at the beginning of the Big Bang? Do those places and times extend beyond our Universe? If so, where exactly do you draw the line between where our Universe ends and something else exists?
These arguments feel quite tenuous to me, another attempt by an intelligent person to say, "Ah, I've figured it all out, THIS is how everything is."
With regards to 3), I would assume Tegmark means laws of physics which we have not yet discovered, but nevertheless govern what occurs inside a black hole or at the beginning of the big bang. It is commonly believe that with a complete theory of quantum gravity, we will find that the singularities in these situations disappear and the laws of physics don't break down.
EDIT: Here's the HN submission from a few months back:
https://news.ycombinator.com/item?id=10068676 arxiv link: http://arxiv.org/abs/1506.03733
http://arxiv.org/abs/1506.03733
Lee Smolin discusses a class of facts that are evoked:
"I would like to propose that there is a class of facts about the world, which concerns structures and objects which come to exist at specific moments, which, nevertheless, have rigid properties once they exist. Let us call this possibility evoked."
====
He provides a table of how a fact and it's existence can be described:
Has rigid properties and existed prior? The fact was discovered
Has rigid properties and did not exist prior? The fact was evoked
Has no rigid properties but did exist prior? The fact was fantasized (Smolin does not elaborate on this in the paper)
Has no rigid properties and did not exist prior? The fact was invented
====
Roberto Mangabeira Unger and Smolin hypothesize two principles to describe Smolin's view, temporal naturalism:
The singlular universe, all that exists is part of one singular universe
The reality of time, as in reality is not timeless
====
With all this in mind, yes circles always did have a ratio of circumference to radius of pi. This is a property of the singular universe, and is a fact that was thus discovered.
The universe of mathematical possibilities that does not describe the universe was not discovered, it was evoked.
P.S. Please forgive the formatting of this response!
1.In the real universe it is always some present moment, which is one of a succession of moments. Properties of mathematical objects, once evoked, are true independent of time.
2. The universe exists apart from being evoked by the human imagination, while mathematical objects do not exist before and apart from being evoked by human imagination.
That is rather naive. The entire succession of moments can be described as one object, in which time is a dimension. The unfolding through time is just the subjective experience of the human consciousness.
Some H.264 video also appears to unfold, presenting a depiction of events frame by frame. Yet, at the same time, it's also just a 1.2 gigabyte file: a giant integer.
Unquestioningly so. For instance, there is a number 2 and a number pi which are not caused by thinking. Beings which evolve on separate planets (or whatever) in separate universes have to to come to the conclusion that the ratio between the diameter and circumference of a circle is a certain number. Those numbers will be found to agree, though there is no causal link between the two. You can define what constitutes a circle, and define the question of the ratio of its parts, but you don't get to define pi.
Or, if you define "composite" and "prime", you don't get to decide which integers are one or the other, or facts like that two is the smallest prime and the only even one.
The question is: what is the difference between your existence and the existence of pi? Maybe there isn't any.
I see the fact that two is the only even prime brought up from time to time as if it's inherently interesting. Why is it more interesting than the identical observation that 37 is the only prime which is a multiple of 37?
I guess this bothers me because 2 being the only even prime isn't a consequence of the definition of "prime"... it's part of the definition.
It is probably that divisibility by two (evenness) is interesting.
For example, it has the property that if we know the evenness of two integers, then we know the evenness of their sum or product.
Division of cases by even versus odd occurs regularly; in few circumstances do you have to separately reason about cases corresponding somehow to the elements of the congruence modulo 37.
odd(x + y) = odd(x) XOR odd(y)
odd(x * y) = odd(x) AND odd(y)
Realism is obviously popular because any viewpoint which attaches grandiose "meaning" and "purpose" to things is bound to be more popular over what is seen as "colder" and analytic.
There's actually several sides, but those two are the main ones.
EDIT:
In addition,
For a creator God, we are left to ask who created the creator - but if the universe is a mathematical object, it needs no creator (on Platonism at least), so this is a very satisfying answer to that eternal question. It has always existed and will always exist outside of space-time as a mathematical construct.
No. In fact, a lot of people who subscribe to creationism make the exact same argument - that God has always existed outside of space-time and requires no creator. Your handwaving this in the same fashion is not a satisfying answer in the slightest.
The author stresses that all of reality is mathematical in structure, but this is at odds with the fact that all mathematical systems containing self-reference are necessarily incomplete. Physics is a self-referential system.
If the structure of the universe is mathematical, it is probably a very different math than humans are used to. Insert your favorite flavor of metaphysics here!
Suppose we discover our universe is a simulation. This would imply that the universe is Turing-computable. Would there not therefore exist a "Grand Unified Theory" that simply described, with absolute precision, the operation of the simulator? Or would it be impossible to produce such a specification?
Then all you have to do is demonstrate that we live in such a universe, and all the philosophers can retire because we've found the ultimate answer to the ultimate question.
I think we all know exactly what the Gödel number for our universe would be...
Rudy Rucker had some interesting conversations with Gödel about a deterministic universe in which (because time is illusory) backward time travel exists: http://www.rudyrucker.com/blog/2012/08/01/memories-of-kurt-g...
I particularly like how, in describing Gödel's office, he mentions "On the empty desk sat an empty glass of milk." The paradox seems appropriate.
You're making the same category error as mentioned in the blog post.
Now suppose that this process stops. One day, mathematics describes physics. What does that mean? It means that some pencil-and-paper mathematics descriptions hint at an abstraction, and that abstraction is physics.
The mathematics which was used prior to that point was not the right one. That mathematics still corresponds to a universe, just not this one.
The idea is that every mathematical object is a universe (not to be confused with some representation of that object, like a definition in plain language, or a diagram, equation).
The world may be exactly the same category of thing as dodecahedron or pi. (Not in the category of pencil-and-paper description of such things; the category of those thing themselves.)
Suppose no mathematical system is sufficient to describe any universe. It's always just a rough approximation.
Either could be true, I guess.
> So, as cosmologists, we have an issue to address — why was the entropy of our early universe so small? If high-entropy states are “natural,” why don’t we live in one? You might think to appeal to the dreaded anthropic principle, and argue that life couldn’t exist in a state with really high entropy. But that turns out not to be good enough; the entropy of our universe is much much lower than it needs to be to support the existence of life. So we are faced with the “arrow of time problem.”
1: http://www.preposterousuniverse.com/blog/2004/10/27/the-arro...
At least, they are all math beyond those subjective observations that are possible through the human senses. You might think that some hot gas is "glowing blue", and that this is not "math" to you in any sense, but a more advanced understanding of the light emanating from it gives us a spectrum, and that is just a math function.
Of course when we look at an actual map of some place, we know that the place isn't a picture with symbols denoting its features. It's not so clear for features of the universe. When you're far from the bottom, the descriptions look like maps. The mass and acceleration arrows on a free body diagram of an automobile aren't the automobile; it's all just a diagram.
But the more detailed you make the description of something, the less of a distinction there is between the description and the thing! At some point, the description must be the thing. (If it isn't then just alter whatever is different between the two and patch the description; then repeat.)
Another thing to keep in mind is that math itself has map/territory descriptions. The formula or graph representing a mathematical object isn't that object.
When we say that the universe may just be math, we don't mean that the written math is the universe, but rather that the abstract math described by those representations is identifiable with what is real: the map isn't the territory, but those two territories are identifiable with each other!
Be careful with words here. The universe is observed through other means than maps all the time. In fact, it is what everyone is doing all the time.
The universe is described using maths. It is also often described by neuron firing patterns in brains or less accurately using English or Russian. Just like territories are described by maps or less accurately using English or Russian.
> But the more detailed you make the description of something, the less of a distinction there is between the description and the thing! At some point, the description must be the thing. (If it isn't then just alter whatever is different between the two and patch the description; then repeat.)
That doesn't follow. At the limit to infinity, the description is the perfect description. There is no reason to believe it becomes the thing itself.
The line segment representing the radius of a circle perfectly describes a circle. That does not mean a line segment is the same as a circle.
Aha, but there is a territory here: the abstract circle. Now suppose we equate that territory with another territory: something in the real world. Then we have a description of a circle (the map), but two different territories. If we say those are the same, it's not a map/territory confusion. At best it is a territory/territory confusion.
The description of the math will never be the math; but the correct math may in fact coincide with reality.
If a mathematical model of the world is completely accurate, then the math which it describes is the world. The world doesn't have any properties which the math doesn't and vice versa; it doesn't "do" anything which the math doesn't.
1. Our nervous system has quite narrow and well defined capability of receiving signals from the outside world. Every of our senses has own limitations. We can't see UV or IR etc.
2. Our body has a specific way of interacting with the world : we have specific size, strength, have to operate as one, undivided entity etc.
3. With such input coming from the above points, our brain creates a specific model of the outside world to function in it, interact, count apples and lions etc.
4. Part of this model is this cool toolset containing math and logic. It's very useful for us to predict and analyze the world and it's so flexible that we can expand and bend it according to our will in face of mismatch between observable reality and math.
So there is no surprise that we keep seeing math around us. We created it as a result of interaction with the world.
But to insist that math is the real way the world works is ridiculous. It's like saying that there's nothing beyond the visible spectrum of light because we can't see it.
I'm quite sure that any creatures with significantly different bodies than ours would come up with different "math" and different view of the universe.
EDIT: I was trying to imagine such creatures but gaps in my knowledge and limitations of my homo sapiens mind are hard to escape and imagine something unimaginable. But I'll give it a try: Think of a creature built of 100 autonomously moving clouds of particles, sharing one consciousness. The clouds can change their sizes in the ping-pong - planet range and communicate by radio waves. I think that just the ability to watch specific event from 100 perspectives would give this alien completely different psychology and approach to the logic, truth etc.