Does the Universe Operate on Mathematical Logic?

[th3plan]

Does the universe follow a mathematical logic? It seems to me it does. yes we don't know everything about the universe but as we have learned more it still holds up to be logical.

 

[brightmatter]

Does the universe follow a mathematical logic? It seems to me it does. yes we don't know everything about the universe but as we have learned more it still holds up to be logical.

Definitely. Gravity Probe B results will help resolve the issue!

 

[Tac-Tics]

Does the universe follow a mathematical logic? It seems to me it does. yes we don't know everything about the universe but as we have learned more it still holds up to be logical.

This belongs in the philosophy forum.

It is taken as an assumption that the universe is always consistent with itself. If a scientific theory predicts something that isn't true, we reject the theory, not the universe.

Questions like this usually don't have very good answers. When you get to fundamental questions of logic, things start looping back on each other.

 

[Pythagorean]

pure logic wouldn't get anywhere without the leaps of faith called assumptions. We merely accept a mindset and go with it. We give up other ways of perceiving things by choosing to understand it one way.

 

[ESTÉRA]

After much observance of the forum I have noticed that many people have the idea that reality and what we precieve as the physical world is determined and based on logic, both mathematical and philosophical. This I believe is wrong due to the fact that humans try to explain what they preceive, not precieve what they want to explain (this would be imagining). The sequences of cause and effect in a explanation then becomes a tool, to distinguish what we think is possible, correct, true and their negations, which we today call logic.
For example: When a object is no longer helled up by something then the object tends to fall down to the gournd. This primitive argument is a logical one because it tells what actually happens.
But a for a primitive zero gravity civilization (extremely hypothetically speaking) the above argument whould be false since it would contradict whith "their logic".
To put it simply logic is based on what we precieve and what we precieve is reality not the other way around.
The more we understand our reality, the more logic is adjusted.

p.s: I am sorry for the poor example.
p.ps: This is my official first post on this forum.:)

 

[JoeDawg]

Does the universe follow a mathematical logic? It seems to me it does. yes we don't know everything about the universe but as we have learned more it still holds up to be logical.

This is an old question in philosophy. The greeks thought that geometry, being a kind of perfection, was the true nature of the universe. Plato's 'theory of forms' being a good example of this. Real world objects then are just imperfect manifestations of these forms.

This tended to be the view right on down to Descartes' Rationalism, where ideas were primary and all knowledge could be derived from ideas. Descartes was a big on mathematics.

However, in answer to Rationalism, there is Empiricism. This is the notion that all knowledge is gained through experience. Contrary to the rationalist perspective, we know 1+1=2 because we can generalize from instances where this has been the case. In this sense mathematics is just an accurate description of the world, and as such we can make predictions based on it. Quite often, at least historically, we run into problems with mathematics because it is a generalization, but then we refine it until it deals with the problem.

Modern philosophy tends towards empiricism, as with science, but tends to rely on the rational for the more metaphysical assumptions.

 

[WaveJumper]

Not only does the universe appear describable mathematically, but it appears strangely suited to allow our relentless, gradual and uninterupted progress through science. As Einstein said: "The most incomprehensible thing about the universe is that it's comprehensible".

 

[WaveJumper]

pure logic wouldn't get anywhere without the leaps of faith called assumptions. We merely accept a mindset and go with it. We give up other ways of perceiving things by choosing to understand it one way.

Exactly. We have to believe that there is an "out there", that we exist, that human logic is not a flawed and inadequate tool for describing the true nature of reality, that we can ever describe fully the universe, etc., etc., etc.

It seems these assumptions correspond and work well with the order we found ourselves in at birth.

 

[WaveJumper]

To put it simply logic is based on what we precieve and what we precieve is reality not the other way around.
The more we understand our reality, the more logic is adjusted.

So if a mosquito swallowed an adult elephant, our human logic would somehow be able to adjust to understand this effect?

I'd say that the human mind is an extremely poor tool to understand true magic. Not that we have seen such examples(except a few in QM which scientists are still struggling to comprehend in a non-mathematical way).

 

[Tac-Tics]

The thing that startles me is there is so much physical theory we have that describes our universe, but does not define it. It's all those damned differential equations.

The thing that bothers me most is that it's not possible, even assuming unlimited in every case to compute how things happen. Everything that can possibly be understood in the world seems to obey the Church Turing thesis. All of science is done with the assumption that we can model one neighborhood of the universe in another. If the universe doesn't have a finite representation and does not evolve in a finite number of distinct atomic steps, then we're dealing with magic. At least, that's my philosophy on the subject.

We already see that the actors in the universe break up cleanly into particles (even if they're weird). The symmetries in the universe would be difficult to "finitize". If the universe is played on a grid, then we wouldn't have perfect spherical symmetry. If the universe is being computed as a machine, then wouldn't there be a One True Frame, contradictory to the hypothesis of general relativity? Or maybe it's something like a task switch, where bits and peices of the universe can be evolved in a local frame and changing between frames is well regulated by the symmetry. Maybe entropy and quantum randomness is the result of floating point errors. It's convenient to have that uncetainty principle in place, because you never have to be more accurate than half h-bar... the universe might as well use fix-point numbers.

Again, it's all pointless philosophy to think about those kinds of things. Talking about a system within itself leads to problems. "Shut up and calculate" is a good policy if you're ever going to get anything done. But despite all the nonsense you hear about interpretations of QM, you can probably rest assured there's a perfectly good rationalization for everything.

One thing is for sure in philosophy of physics, and that is Penrose is crazy.

 

[SixNein]

Does the universe follow a mathematical logic? It seems to me it does. yes we don't know everything about the universe but as we have learned more it still holds up to be logical.

The universe does not follow mathematical logic. We can describe portions of it however there is certain properties of the universe that mathematics will never be able to explain logically..

btw - this has been proven to be correct.

 

[Math Is Hard]

The universe does not follow mathematical logic. We can describe portions of it however there is certain properties of the universe that mathematics will never be able to explain logically..

How could you know that? Which properties are outside logical explanation?

btw - this has been proven to be correct.

Who proved that?

 

[SixNein]

How could you know that? Which properties are outside logical explanation?Who proved that?

http://en.wikipedia.org/wiki/Kurt_Gödel

may be better to understand it from here:
http://video.google.com/videoplay?docid=-5122859998068380459&ei=pUi3SeSPOIiGqwK-v5mADQ&q=mathematics&hl=en

long movie but a good one

 

[apeiron]

This is rather an abuse of Godel. He was arguing that there are aspects of mathematics which can never be explained from within mathematics itself. Some things must be assumed as axioms to get the show started.

Many good epistemologists followed on from Godel to make better sense of this, such as Robert Rosen (my particular favourite).

A quick summary would be that we have a modelling relation with reality that involves our formal models and our informal measurements - actually a feedback loop process of predicting and then checking.

Mathematics is part of the modelling, a human creation, and we are doing our best to fit the model to the reality we observe.

So to ask whether the universe "is" mathematically logical is to conflate model and reality. Instead, the correct question is how closely do our logical models and observed reality then conform.

We might say that if the two seem to dovetail exactly, then bingo, we can say the universe "is" that way for all intents and purposes. Bur a catch is that models also have purposes. They are not naked creations, but intentional practices. I could say I want to model reality for the purpose of understanding its truth. Or I could instead say I want to model reality in a way that maximises my control over it. And the kinds of models that result are actually different in deep ways. So good epistemology requires the model and the modeled to be kept separate.

Where does maths come into this? Math is really only the science of pattern, the logic of forms. It is the shapes that things must fall into, the regularities that must emerge.

And it is as abstract as possible. A style of models that is all generals or universals, with all local particulars pushed out into the measurement side of the modelling relation.

So the number 1. It can stand for one anything. Within the realm of formal modlling. And then to answer 1 what, we must make a measurement. We must look out into the world and (informally) put a finger on that 1 thing.

The general answer then is that the universe does seem to fall into logical patterns (it is regular, and regular for self-organising reasons) and mathematics is the attempt to formally model things that fall into logical patterns.

Reality cannot work any other way (we must presume) and our formal modelling will work best when it also does the same thing.

 

[SixNein]

This is rather an abuse of Godel. He was arguing that there are aspects of mathematics which can never be explained from within mathematics itself. Some things must be assumed as axioms to get the show started.

Many good epistemologists followed on from Godel to make better sense of this, such as Robert Rosen (my particular favourite).

A quick summary would be that we have a modelling relation with reality that involves our formal models and our informal measurements - actually a feedback loop process of predicting and then checking.

Mathematics is part of the modelling, a human creation, and we are doing our best to fit the model to the reality we observe.

So to ask whether the universe "is" mathematically logical is to conflate model and reality. Instead, the correct question is how closely do our logical models and observed reality then conform.

We might say that if the two seem to dovetail exactly, then bingo, we can say the universe "is" that way for all intents and purposes. Bur a catch is that models also have purposes. They are not naked creations, but intentional practices. I could say I want to model reality for the purpose of understanding its truth. Or I could instead say I want to model reality in a way that maximises my control over it. And the kinds of models that result are actually different in deep ways. So good epistemology requires the model and the modeled to be kept separate.

Where does maths come into this? Math is really only the science of pattern, the logic of forms. It is the shapes that things must fall into, the regularities that must emerge.

And it is as abstract as possible. A style of models that is all generals or universals, with all local particulars pushed out into the measurement side of the modelling relation.

So the number 1. It can stand for one anything. Within the realm of formal modlling. And then to answer 1 what, we must make a measurement. We must look out into the world and (informally) put a finger on that 1 thing.

The general answer then is that the universe does seem to fall into logical patterns (it is regular, and regular for self-organising reasons) and mathematics is the attempt to formally model things that fall into logical patterns.

Reality cannot work any other way (we must presume) and our formal modelling will work best when it also does the same thing.

Not really, you cannot be complete and consistent in any system. So if you wanted to model the universe, your model would never be complete or never be consistent. Thus you cannot ever logically describe the universe.

 

[neopolitan]

Not really, you cannot be complete and consistent in any system. So if you wanted to model the universe, your model would never be complete or never be consistent. Thus you cannot ever logically describe the universe.

There's potentially a little bit of wriggle room. Logic doesn't say you can't consider the universe from the outside. If you were to do so, cognizant of the fact that you don't know anything about that outside, then Godel's incompleteness theorem doesn't apply, nor does Russell's set theory proscription about self defining sets.

I've certainly considered the universe from an outside perspective, so it is possible, even if purists don't like it. I see it as just a variation on looking at the past, which we can certainly look at from the outside. At one scale, you run into problems with the fact that you yourself are in the universe, but most physics theories won't depend very heavily on whether you are there or not (those sorts of theories are called "theology" :) )

cheers,

neopolitan

 

[SixNein]

There's potentially a little bit of wriggle room. Logic doesn't say you can't consider the universe from the outside. If you were to do so, cognizant of the fact that you don't know anything about that outside, then Godel's incompleteness theorem doesn't apply, nor does Russell's set theory proscription about self defining sets.

I've certainly considered the universe from an outside perspective, so it is possible, even if purists don't like it. I see it as just a variation on looking at the past, which we can certainly look at from the outside. At one scale, you run into problems with the fact that you yourself are in the universe, but most physics theories won't depend very heavily on whether you are there or not (those sorts of theories are called "theology" :) )

cheers,

neopolitan

I think you have already answered yourself about why that won't work. In a fashion it's hard to accept but there it is.

 

[apeiron]

Not really, you cannot be complete and consistent in any system. So if you wanted to model the universe, your model would never be complete or never be consistent. Thus you cannot ever logically describe the universe.

Again, I don't think you really get the fairly limited conclusion that should be drawn from Godel's famous proof.

If you are talking about formal models, as he was, then they can be complete and constistent in themselves. But assumptions are needed to get the modelling going. So something has to come from "outside" the model itself.

Because you are failing to keep the distinction between the modeller and the modeled clear in your arguments, you are conflating two senses of how modelling can be complete (and consistent).

Godel can be used to argue for the completeness of modelling (its self-completeness) and the incompleteness of modelling (the need for measurement), depending on which part of this story you are talking about.

And the question was: is the Universe logical? So Godel would only be introduced here to make points about the fact we have to step back and separate the idea of logic (a model of causality) and a universe (an example of real causality which we would seek to model, and indeed inspires our ideas of causality).

Mathematics is too often treated as some kind of platonic magic that exists outside worlds. Modelling theory helps heal that ancient rift.

 

[SixNein]

Again, I don't think you really get the fairly limited conclusion that should be drawn from Godel's famous proof.

If you are talking about formal models, as he was, then they can be complete and constistent in themselves. But assumptions are needed to get the modelling going. So something has to come from "outside" the model itself.

Because you are failing to keep the distinction between the modeller and the modeled clear in your arguments, you are conflating two senses of how modelling can be complete (and consistent).

Godel can be used to argue for the completeness of modelling (its self-completeness) and the incompleteness of modelling (the need for measurement), depending on which part of this story you are talking about.

And the question was: is the Universe logical? So Godel would only be introduced here to make points about the fact we have to step back and separate the idea of logic (a model of causality) and a universe (an example of real causality which we would seek to model, and indeed inspires our ideas of causality).

Mathematics is too often treated as some kind of platonic magic that exists outside worlds. Modelling theory helps heal that ancient rift.

All models are wrong but some can be useful. -George E. P. Box