Does the word exist as a mathematical structure?

[robheus]

Max Tegmark develop a hypothese in which physical reality is equated as being a mathematical structure, and further it is proposed that every mathematical structure itself is a reality on it's own.

To look up this idea, see these threads:
http://en.wikipedia.org/wiki/Ultimate_ensemble
http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis

Note that (although the form of the idea is quite new) this idea is not very distinct from the ideas of the Greek philosopher Plato.

This idea has met many criticism.
One important objection one could raise is that mathematical structures, as seen as information, can not exist on it's own merits, but needs to be denoted in some (material) form. Which would lead to the conclusion that at least something different then information must exist to carry the information.
This would lead to the idea that reality = physical reality + information.

Many other objections have been put forward, as for instance the objection that the universe is not a set or mathematical structure.

 

[Moridin]

Isn't mathematics just an unambiguous language with large component simplicity for describing quantities, relations and so on?

 

[oldman]

Isn't mathematics just an unambiguous language with large component simplicity for describing quantities, relations and so on?

Yes. Indeed it is. I would add "And it is an invented language".

Max Tegmark's idea is nonsense. It is a Platonistic delusion of a kind that seems to be shared by many mathematicians. A mathematician correspondent of mine has told me that "Some people who discover mathematics in their young age immediately tend to see it as a reality on its own. These people usually become mathematicians. In my experience, every mathemacian is a Platonician. I don't know a single one who is not." I believe him. For example Roger Penrose's book "Road to Reality" supports this belief.

Are we not all susceptible to delusions of a similar kind about subjects that we are proficient in, admire greatly, or that fascinate and mystify us? For example that polemicist Richard Dawkins has written an entire book about one such delusion, namely that of the Theist variety. It seems to me that reality is mysterious enough withot adding a mathematical dimension to it.

 

[robheus]

I don't think that the idea of mathematics being the real reality is true, but then, how would one proof that?

 

[oldman]

I don't think that the idea of mathematics being the real reality is true, but then, how would one proof that?

If you were out walking in the woods and a wild primary number, say "7", jumped out from behind a bush and bit you, you'd be justified in accepting the reality of mathematics. Otherwise, don't believe what you read about its reality.

 

[robheus]

If you were out walking in the woods and a wild primary number, say "7", jumped out from behind a bush and bit you, you'd be justified in accepting the reality of mathematics. Otherwise, don't believe what you read about its reality.

Yes, quite obviously.

But that is not what I meant. The idea is based on the fact that mathematics has been very successfull in describing the reality in theoretical physics.

But then the thought error is that physical reality does not equate to mathematical reality.

But this then would involve proving that certain aspects about reality can not be described in mathematics, but I don't see an easy way to proof that.

Besides the fact that mathematical structures, as regareded as information, must have some physical form, and if all reality would only be in the form of mathematical structures, there is obviously no 'place' to write that information on.

 

[Moridin]

Yes. Indeed it is. I would add "And it is an invented language".

Max Tegmark's idea is nonsense. It is a Platonistic delusion of a kind that seems to be shared by many mathematicians. A mathematician correspondent of mine has told me that "Some people who discover mathematics in their young age immediately tend to see it as a reality on its own. These people usually become mathematicians. In my experience, every mathemacian is a Platonician. I don't know a single one who is not." I believe him. For example Roger Penrose's book "Road to Reality" supports this belief.

Are we not all susceptible to delusions of a similar kind about subjects that we are proficient in, admire greatly, or that fascinate and mystify us? For example that polemicist Richard Dawkins has written an entire book about one such delusion, namely that of the Theist variety. It seems to me that reality is mysterious enough withot adding a mathematical dimension to it.

Invented language? Of course it is an invention. All languages are! What would they else be? Also note that, that which mathematics describe is not an invention, just like that which natural languages describe are not invented.

 

[robheus]

Invented language? Of course it is an invention. All languages are! What would they else be? Also note that, that which mathematics describe is not an invention, just like that which natural languages describe are not invented.

Apart from the (human invented) notation, are mathematically entities "discovered" (I guess most of them are) or are (some of them) "invented"?

 

[robertm]

The idea is based on the fact that mathematics has been very successfull in describing the reality in theoretical physics.

But then the thought error is that physical reality does not equate to mathematical reality.

But this then would involve proving that certain aspects about reality can not be described in mathematics, but I don't see an easy way to proof that.

Besides the fact that mathematical structures, as regareded as information, must have some physical form, and if all reality would only be in the form of mathematical structures, there is obviously no 'place' to write that information on.

No matter how well mathematics can describe physical reality, it's accuracy would still remain a testament only to the quality of the language, not to a statement of literal fact. Therefor, there is no need to show any aspects of reality that cannot be described. Furthermore, even if we did find something that mathematics could not explain, a brilliant mind must simply invent a knew language (Issac Newton).

Apart from the (human invented) notation, are mathematically entities "discovered" (I guess most of them are) or are (some of them) "invented"?

The only 'discoveries' that a mathematician can make would be those lying within the existing invented framework of the language. You could discover aspects of a certain existing framework, but a new framework must be invented.

 

[out of whack]

About the existence of math...

It seems clear that what does not exist does not matter to anything. The implication of course is that whatever matters must exist. And since mathematics matters (at least to mathematicians) then it must exist as well. This does not necessarily make it a "physical" reality, whatever that may be. But concepts do exist, concepts are real. What is arguable is the exact nature of concepts.

 

[Moridin]

Apart from the (human invented) notation, are mathematically entities "discovered" (I guess most of them are) or are (some of them) "invented"?

"Chairs" and the mathematical equivalent are arbitrary social constructions. Chairs, and their mathematical equivalent, are not.

 

[robertm]

But concepts do exist, concepts are real. What is arguable is the exact nature of concepts.

Good point. Getting close to the crux of the matter I think.

 

[oldman]

Invented language? Of course it is an invention. All languages are! What would they else be? Also note that, that which mathematics describe is not an invention, just like that which natural languages describe are not invented.

Exactly my sentiments. But mathematicians like to argue that their subject is not an invented language, but somehow part of 'reality', waiting out there to be discovered by any intelligence that happens to evolve. Which strikes me as sheer nonsense.

 

[oldman]

But this then would involve proving that certain aspects about reality can not be described in mathematics, but I don't see an easy way to proof that.

Cats are real. In practice and in principle it is impossible to fully describe a cat with mathematics. Is this the proof you need?

 

[robheus]

Cats are real. In practice and in principle it is impossible to fully describe a cat with mathematics. Is this the proof you need?

I think quantum mechanics would contest that, there is nothing intrinsically about a cat which can not be satisfactory described in quantum mechanics.
But that deals only with the physical aspect of cats.

 

[robheus]

Exactly my sentiments. But mathematicians like to argue that their subject is not an invented language, but somehow part of 'reality', waiting out there to be discovered by any intelligence that happens to evolve. Which strikes me as sheer nonsense.

Their notation (ie. the mathematical language) is invented, their subject might not be.

There are some good arguments to assume that (part of) mathematics is merely discovered, not invented.
Like we discover physical laws and physical elements and particles.

 

[TheStatutoryApe]

Their notation (ie. the mathematical language) is invented, their subject might not be.

Obviously the subject isn't. Math's primary purpose is to describe physical phenomena from the number of apples in a basket to the speed and trajectory of a particle.

There are some good arguments to assume that (part of) mathematics is merely discovered, not invented.

Once the basic rules were set down for the language the next step is obviously to explore its usability and look for interesting patterns. You can easily invent something and find that it has interesting uses and extensions you may not have thought of in the first place.

 

[Coldcall]

Its not such a crazy idea. Quantum mechanics is basically matter/energy described in terms of mathematical probability. Before the superposition decoheres the measured particle has no definable properties; so it can be said the material itself does not exist.

If we can express matter/energy in terms of not existing when in superposition, and we can accurately express all the physical laws with mathematics then perhaps the universe is a mathematical constuct.

 

[baywax]

If we can express matter/energy in terms of not existing when in superposition, and we can accurately express all the physical laws with mathematics then perhaps the universe is a mathematical constuct.

The operative words here are "we can express". Expression requires a physical state and a physical state is required to observe "superposition" as well as to express it in a mathematical model. This sort of duality of states (many worlds?) begs explanation.

We can't observe a quantum state without the contrast and comparison of our emergent state, can we? So, which came first? Which is fundamental? Did we invent the quantum state through our observations of the emergent states and our overlay of maths on it?

 

[Coldcall]

Hi baywax,

"The operative words here are "we can express". Expression requires a physical state and a physical state is required to observe "superposition" as well as to express it in a mathematical model. This sort of duality of states (many worlds?) begs explanation."

Okay perhaps i worded it sloppily using as "we can express". Howabout if the universe can be explained completely mathematically, then it seems logical that maths can actually create the universe. I personally don't buy MWI but what i would say is that a qm superposition even in standard Copenhagen is considered to be a probablity wave. So in esssence there is nothing there but abstract possibilities - until decoherence/wave collapse occurs.

"We can't observe a quantum state without the contrast and comparison of our emergent state, can we?"

No. I mean once we make the observation/measurement we get the emergent result.

"So, which came first? Which is fundamental? Did we invent the quantum state through our observations of the emergent states and our overlay of maths on it?"

Interesting. I think the real maths - whatever it is - behind qm is fundamental. Whether we only have an approximation of it i don't know. But what qm maths appears to tell us is that something can define itself into our sense of reality; having only an instance before been nothing more than a possibility. The reason why i point to qm maths as circumstantial evidence of the op is because it more or less describes matter and energy popping into and out of existence. If matter can be a maths abstract then so can the whole universe.

Im not saying this is for sure just speculating

 

[baywax]

If matter can be a maths abstract then so can the whole universe.

Im not saying this is for sure just speculating

Not that I know but... Matter can be sausage... does that mean we live in a big sausage?

 

[Coldcall]

Not that I know but... Matter can be sausage... does that mean we live in a big sausage?

hehe ah yes but one needs the math first as it carries the instructions/recipe for both the matter and sausage. Matter alone without instructions/recipe could not make a sausage. Of course please don't quote me on that one

 

[baywax]

hehe ah yes but one needs the math first as it carries the instructions/recipe for both the matter and sausage. Matter alone without instructions/recipe could not make a sausage. Of course please don't quote me on that one

OK... but, I have a feeling sausages were built before most numbers were invented... or "discovered" (these quotation marks indicate my disbelief concerning the idea that numbers were discovered).

 

[mjolnir80]

but math was created by humans to explain the things around them
just because we use it doesn't mean the universe is based on it (yes this is kind of a weak argument)

 

[Coldcall]

OK... but, I have a feeling sausages were built before most numbers were invented... or "discovered" (these quotation marks indicate my disbelief concerning the idea that numbers were discovered).

But the physical laws of the universe have not changed since we invented maths. The state of the matter/energy relalationhsip in our universe has not changed just because Einstein came up with e=mc2. Yes we may have invented our method of maths for describing the universe but we know that the universe always acted the same way, hence the funademental truth of e=mc2 was always in existence. We only invented our own way to describe it.

 

[Coldcall]

but math was created by humans to explain the things around them
just because we use it doesn't mean the universe is based on it (yes this is kind of a weak argument)

Maths is purely a language. How about this analogy to your argument: At some point in history someone made the first blueberry pie. Did not blueberries exist before we made that pie?

 

[oldman]

but math was created by humans to explain the things around them
just because we use it doesn't mean the universe is based on it (yes this is kind of a weak argument)

Not a weak argument at all!

In fact mathematics, in its most elementary form (counting numbers and arithmetic) was created by humans for commercial purposes many thousands of years ago, in Mesopotamia. These folk wanted to keep stock of their resources, like grain and domestic animals, and quantify their land, its perimeter or area. They also needed to count days between harvests, and suchlike astronomical stuff. This was long before folk like us found it useful for explaining the things around us.

 

[baywax]

The question is...

"does the word exist as a mathematical structure?"

My question is...

"What word?"