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The Universe Is Made of Mathematics

34 points by zoltz 11y ago

kazinator 11y ago
Every result in physics hitherto has been some sort of mathematics: an equation or a constant (measured or otherwise established to some digits of precision). What is a particle? A collection of mathematical properties. So is a wave. If we extrapolate from the past to the future, we can expect more of the same: no "non-mathematical bottom" will be found. Nobody is even looking; the researchers expect all new results to take the shape of math. So the notion that "maybe it's just math all the way down" is actually quite rational. One day we may hit bottom, the way a (terminating) recursive function does, and realize; this is it: there is nothing more going forward, and if we look back, it's just a collection of math.
- DCKing 11y ago
  You're just describing the fact that we can make up descriptions of physics all the way down. If current mathematics is unable to describe physics, then new mathematics is invented [1]. Just because the descriptions work rather well does not mean that those descriptions are somehow more than mere descriptions. It just means that they are very good descriptions. You're making the same category error as mentioned in the blog post. [1] https://en.wikipedia.org/wiki/Mathematical_physics https://en.wikipedia.org/wiki/Mathematical_physics
  - kazinator 11y ago
    > If current mathematics is unable to describe physics, then new mathematics is invented 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.)
    - ursus_bonum 11y ago
      Now suppose that it doesn't stop. Suppose it can't stop. Suppose no mathematical system is sufficient to describe any universe. It's always just a rough approximation. Either could be true, I guess.
qCOVET 11y ago
Here is the documentary if you don't want to read the blog post: https://www.youtube.com/watch?v=IuGI6pQFZC0 https://www.youtube.com/watch?v=IuGI6pQFZC0
ccvannorman 11y ago
1) All mathematical objects exist abstractly and independently of minds (mathematical Platonism) 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."
- xlm1717 11y ago
  With regards to 1), I remember reading a paper I found on HN not too long ago trying to argue that no, it does not exist. To generalize, any piece of knowledge only exists after it is discovered. Can't remember what it is at the moment, maybe someone else knows what I'm talking about. 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 https://news.ycombinator.com/item?id=10068676 arxiv link: http://arxiv.org/abs/1506.03733 http://arxiv.org/abs/1506.03733
  - kazinator 11y ago
    So before pi was discovered, circles didn't have a ratio of circumference to radius? Or did have one, but a value other than 3.14159...?
eludwig 11y ago
"A map is not the territory"
- kazinator 11y ago
  In this case, it may be. The territory is never observed other than through maps, and the maps are all math. That is to say, the maps may be of the same "stuff" as the territory, and as the differences between the maps and the territory are erased, eventually you arrive at the map being the territory. 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!
  - DCKing 11y ago
    > The territory is never observed other than through maps, and the maps are all math. 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.
vezzy-fnord 11y ago
In very broad terms, this is part of an age-old debate in the philosophy of science about how mathematics should be interpreted - instrumentalists (manipulating symbols) versus realists (mathematics underpins objective reality). 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.
a3voices 11y ago
Maybe the universe is a user interface for your consciousness, and physical objects don't really exist.
ching_wow_ka 11y ago
I'm not much of a mathematician, but I found "Mathematics: The Loss of Certainty" by Morris Kline (http://www.amazon.com/Mathematics-Loss-Certainty-Oxford-Paperbacks/dp/0195030850 http://www.amazon.com/Mathematics-Loss-Certainty-Oxford-Pape...) very insightful in regards to the development and current state of mathematics. A brief synopsis: 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 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.
- eellpp 11y ago
  > 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. 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 ?
westoncb 11y ago
Lets say you select all the aspects of a person's life that you consider to have any relevance to anyone and write down a description of every one of them—is that person now 'made' of words? That's how ridiculous this is. 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.
- zbyte64 11y ago
  I think mathematics and physics sets the bar higher then subjective relevance when formulating descriptions. If you did manage to create a description that would accurately predict every response of a person then you would have a hard time (if not impossible) discerning the difference between the two agents.
  - westoncb 11y ago
    But one of them wouldn't be something anyone would call an 'agent.' One would be a description of an agent, or a recipe for producing one—but at the end of the day, one is meat and the other is a set of symbols.
    - goldenkey 11y ago
      But aye..that's the rub. Is there any difference between meat that appears to operate _EXACTLY_ the same as different meat (constructed using the symbols)? Computationally, no. But if two things in an information-theoretic world, are informationally equivalent, then for all intensive purposes, they are equivelent. Quantum physics says this with regard to quantum states, there's no meat to differentiate electrons, only informational states. 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 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.
Strilanc 11y ago
If the universe we find ourselves in is a result of post-selecting for mathematical models where life can exist (i.e. by the anthropic principle), why is the universe so large and so rich in neg-entropy? Shouldn't minimally-viable-habitat universes be vastly, vastly more numerous (and don't forget about Boltzmann brains!)? Shouldn't we expect to be in one of those, instead of here, and be forced to penalize the hypothesis by a corresponding amount? [1] > 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-arrow-of-time/ http://www.preposterousuniverse.com/blog/2004/10/27/the-arro...
- jameshart 11y ago
  The problem with these kinds of arguments-from-probability is that they are valid arguments even in highly improbable universes. So yes, maybe on average, most sentient life forms that ponder these questions are living inside tiny simulated universes created as undergraduate term projects for passing credit. But we happen to be in a really big universe. Maybe ours is a grad student lab project. Or an exhibit in a museum. Or maybe we hit the jackpot and ours is real. Point of such arguments is you can't really tell from a sample size of one.
DCKing 11y ago
The reasons presented in favor of a mathematical universe read somewhat like rehashed arguments used by deists/theists. > 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.
- yongelee 11y ago
  Concepts can indeed exist outside physical brain matter. Such as the concept of math. The idea that 1+1=2 does not need a physical human brain to exist. If humans never existed the concept of math would still exist "beyond space and time". Abstract thoughts cannot exist outside space and time for human comprehension but those same concepts do not need humans to exist.
  - DCKing 11y ago
    I'd love to have some evidence that such things as 'concepts' and 'ideas' can exist independent of brains. You can't just assert it and make it so. All concepts and ideas I've ever heard of were the results of brains attempting to model or describe. 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.
outofcuriosity 11y ago
If the universe was "made of mathematics," then there would necessarily exist a Grand Unified Theory. But, Hawking asserts that Gödel's Theorems imply that not only does a Grand Unified Theory not exist, but that the formulation of one is impossible (http://www.hawking.org.uk/godel-and-the-end-of-physics.html http://www.hawking.org.uk/godel-and-the-end-of-physics.html). 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!
- nemo1618 11y ago
  Hmm. That's an interesting counterpoint. 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?
  - jameshart 11y ago
    So if you Gödelized the universe - mapped every conceivable state to a number (proving that that is possible left as an exercise for the reader) - then created mathematical operations on those numbers that transitioned the universe from one state to another 'physically possible' successor state.. I guess Gödel would be able to give you a number representing a universe such that you could not prove whether its state was possible or not? 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...
    - ursus_bonum 11y ago
      420?
ArekDymalski 11y ago
I don't understand why people still believe in this concept. For me it's quite simple: 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.

34 points by zoltz 11y ago

Every result in physics hitherto has been some sort of mathematics: an equation or a constant (measured or otherwise established to some digits of precision). What is a particle? A collection of mathematical properties. So is a wave. If we extrapolate from the past to the future, we can expect more of the same: no "non-mathematical bottom" will be found. Nobody is even looking; the researchers expect all new results to take the shape of math. So the notion that "maybe it's just math all the way down" is actually quite rational. One day we may hit bottom, the way a (terminating) recursive function does, and realize; this is it: there is nothing more going forward, and if we look back, it's just a collection of math.

DCKing 11y ago
You're just describing the fact that we can make up descriptions of physics all the way down. If current mathematics is unable to describe physics, then new mathematics is invented [1]. Just because the descriptions work rather well does not mean that those descriptions are somehow more than mere descriptions. It just means that they are very good descriptions. You're making the same category error as mentioned in the blog post. [1] https://en.wikipedia.org/wiki/Mathematical_physics https://en.wikipedia.org/wiki/Mathematical_physics
- kazinator 11y ago
  > If current mathematics is unable to describe physics, then new mathematics is invented 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.)
  - ursus_bonum 11y ago
    Now suppose that it doesn't stop. Suppose it can't stop. Suppose no mathematical system is sufficient to describe any universe. It's always just a rough approximation. Either could be true, I guess.

qCOVET 11y ago

Here is the documentary if you don't want to read the blog post: https://www.youtube.com/watch?v=IuGI6pQFZC0 https://www.youtube.com/watch?v=IuGI6pQFZC0

ccvannorman 11y ago

1) All mathematical objects exist abstractly and independently of minds (mathematical Platonism) 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."

xlm1717 11y ago
With regards to 1), I remember reading a paper I found on HN not too long ago trying to argue that no, it does not exist. To generalize, any piece of knowledge only exists after it is discovered. Can't remember what it is at the moment, maybe someone else knows what I'm talking about. 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 https://news.ycombinator.com/item?id=10068676 arxiv link: http://arxiv.org/abs/1506.03733 http://arxiv.org/abs/1506.03733
- kazinator 11y ago
  So before pi was discovered, circles didn't have a ratio of circumference to radius? Or did have one, but a value other than 3.14159...?

eludwig 11y ago

"A map is not the territory"

kazinator 11y ago
In this case, it may be. The territory is never observed other than through maps, and the maps are all math. That is to say, the maps may be of the same "stuff" as the territory, and as the differences between the maps and the territory are erased, eventually you arrive at the map being the territory. 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!
- DCKing 11y ago
  > The territory is never observed other than through maps, and the maps are all math. 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.

vezzy-fnord 11y ago

In very broad terms, this is part of an age-old debate in the philosophy of science about how mathematics should be interpreted - instrumentalists (manipulating symbols) versus realists (mathematics underpins objective reality). 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.

a3voices 11y ago

Maybe the universe is a user interface for your consciousness, and physical objects don't really exist.

ching_wow_ka 11y ago

I'm not much of a mathematician, but I found "Mathematics: The Loss of Certainty" by Morris Kline (http://www.amazon.com/Mathematics-Loss-Certainty-Oxford-Paperbacks/dp/0195030850 http://www.amazon.com/Mathematics-Loss-Certainty-Oxford-Pape...) very insightful in regards to the development and current state of mathematics. A brief synopsis: 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 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.

eellpp 11y ago
> 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. 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 ?

westoncb 11y ago

Lets say you select all the aspects of a person's life that you consider to have any relevance to anyone and write down a description of every one of them—is that person now 'made' of words? That's how ridiculous this is. 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.

zbyte64 11y ago
I think mathematics and physics sets the bar higher then subjective relevance when formulating descriptions. If you did manage to create a description that would accurately predict every response of a person then you would have a hard time (if not impossible) discerning the difference between the two agents.
- westoncb 11y ago
  But one of them wouldn't be something anyone would call an 'agent.' One would be a description of an agent, or a recipe for producing one—but at the end of the day, one is meat and the other is a set of symbols.
  - goldenkey 11y ago
    But aye..that's the rub. Is there any difference between meat that appears to operate _EXACTLY_ the same as different meat (constructed using the symbols)? Computationally, no. But if two things in an information-theoretic world, are informationally equivalent, then for all intensive purposes, they are equivelent. Quantum physics says this with regard to quantum states, there's no meat to differentiate electrons, only informational states. 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 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.

Strilanc 11y ago

If the universe we find ourselves in is a result of post-selecting for mathematical models where life can exist (i.e. by the anthropic principle), why is the universe so large and so rich in neg-entropy? Shouldn't minimally-viable-habitat universes be vastly, vastly more numerous (and don't forget about Boltzmann brains!)? Shouldn't we expect to be in one of those, instead of here, and be forced to penalize the hypothesis by a corresponding amount? [1] > 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-arrow-of-time/ http://www.preposterousuniverse.com/blog/2004/10/27/the-arro...

jameshart 11y ago
The problem with these kinds of arguments-from-probability is that they are valid arguments even in highly improbable universes. So yes, maybe on average, most sentient life forms that ponder these questions are living inside tiny simulated universes created as undergraduate term projects for passing credit. But we happen to be in a really big universe. Maybe ours is a grad student lab project. Or an exhibit in a museum. Or maybe we hit the jackpot and ours is real. Point of such arguments is you can't really tell from a sample size of one.

DCKing 11y ago

The reasons presented in favor of a mathematical universe read somewhat like rehashed arguments used by deists/theists. > 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.

yongelee 11y ago
Concepts can indeed exist outside physical brain matter. Such as the concept of math. The idea that 1+1=2 does not need a physical human brain to exist. If humans never existed the concept of math would still exist "beyond space and time". Abstract thoughts cannot exist outside space and time for human comprehension but those same concepts do not need humans to exist.
- DCKing 11y ago
  I'd love to have some evidence that such things as 'concepts' and 'ideas' can exist independent of brains. You can't just assert it and make it so. All concepts and ideas I've ever heard of were the results of brains attempting to model or describe. 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.

outofcuriosity 11y ago

If the universe was "made of mathematics," then there would necessarily exist a Grand Unified Theory. But, Hawking asserts that Gödel's Theorems imply that not only does a Grand Unified Theory not exist, but that the formulation of one is impossible (http://www.hawking.org.uk/godel-and-the-end-of-physics.html http://www.hawking.org.uk/godel-and-the-end-of-physics.html). 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!

nemo1618 11y ago
Hmm. That's an interesting counterpoint. 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?
- jameshart 11y ago
  So if you Gödelized the universe - mapped every conceivable state to a number (proving that that is possible left as an exercise for the reader) - then created mathematical operations on those numbers that transitioned the universe from one state to another 'physically possible' successor state.. I guess Gödel would be able to give you a number representing a universe such that you could not prove whether its state was possible or not? 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...
  - ursus_bonum 11y ago
    420?

ArekDymalski 11y ago

I don't understand why people still believe in this concept. For me it's quite simple: 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.