Is every single thing and even the universe itself logical?

[steevey]

Is everything logical? Can some system and combinations of different systems of logic completely describe everything in the universe? Even if you say "that walls looks blue", thats the atomic propositions and the recognition that the wall to you is blue because you can't see it any other way you see it. So what isn't logical if logic doesn't actually describe everything?

 

It seems like the universe is completely logical in one way or multiple ways, but I can't say for sure.

Edited January 22, 2011 by steevey

[lemur]

Is everything logical? Can some system and combinations of different systems of logic completely describe everything in the universe? Even if you say "that walls looks blue", thats the atomic propositions and the recognition that the wall to you is blue because you can't see it any other way you see it. So what isn't logical if logic doesn't actually describe everything?

 

It seems like the universe is completely logical in one way or multiple ways, but I can't say for sure.

Most processes I know of seem to have some logic, which is satisfying to me. Electron intermittence is something that seems to have no inherent logic. Electrons apparently just vanish and pop-up randomly, except they have a high probability of "popping-up" within defined areas. It bothers me that there is no mechanical logic proposed to explain how the electrons get from one point to the next. Generally, when people claim that some process is beyond logic, I assume that the logic of the process just hasn't been understood yet.

[D H]

Is everything logical?

It depends on what you mean by "logical". Do you mean some discrete rules of logic, such as those followed by a digital computer, or would describing things in terms of a continuous mathematics such differential equations suffice as qualifying as "logical"?

 

Does the universe compute -- is the universe digital, including space and time itself?

This is the subject of the current FQXi essay contest, http://www.fqxi.org/community/essay. Note that if the universe is analog, with things like particles appearing as eigenstates of some differential form, then the universe isn't really "logical" in the sense of following some discrete rules of logic. This hearkens back to the original problem of what exactly you mean by "logical".

 

Is the universe deterministic?

As far as we know, the answer is no. Things like the uncertainty principle and radioactive decay pretty much kill that idea.

 

Is the universe local? (That is, can we get rid of the spooky idea of action at a distance?)

Bell's theorem, as evidenced by quantum entanglement, pretty much kills that idea.

[swansont]

But in the sense that the universe follows rules, it is logical. There are those who show up here claiming that relativity or quantum mechanics is not logical, and thus they reject it, but their "logic" is invariably based on a false premise of how the universe should behave.

[D H]

I agree. That is why I asked the OP to clarify what "logical" means.

[ajb]

Topos theory may be a "new language" in which to describe physics. Loosely, we can think of topos theory as providing a "new set of logic". A series of papers by Andreas Döring and Chris Isham on the subject can be found here.

 

Generically why nature should be describable using mathematics is a mystery.

[Mr Skeptic]

Some people think that the universe is not logical. If you and the universe disagree, I think I know which one is right! However as D H said, non-determinism and true randomness could fairly be considered not to be logical.

[steevey]

Generically why nature should be describable using mathematics is a mystery.

 

Mathematics is just the label to distinguished patterns and logic. Nature was already here using specific patterns to create things before we existed, and we happened to have recognized those patterns and labeled them accordingly. Mathematics itself is just the recognition of those patterns in nature. Those patterns are their own things though and are the result of DNA and all that stuff.

[lemur]

But in the sense that the universe follows rules, it is logical. There are those who show up here claiming that relativity or quantum mechanics is not logical, and thus they reject it, but their "logic" is invariably based on a false premise of how the universe should behave.

Nothing unconscious "follows rules." That is a personification of behavior that is so predictable that it appears as if there were rules or laws governing its behavior. Saying that matter/energy "follows rules" or "obeys laws" implies that it has the freedom to choose what to do in the first place. Things that lack volition do not take the path of least resistance because they were instructed to. They do it because they can't do anything else.

 

It is not a false premise to expect matter/energy to behave according to the logic of its own mechanics. The trick is to ascertain what those mechanics and their logic is. You could collect data about precipitation, temperature, barometric pressure, etc. over a period of time for many different locations and generate statistical correlations that might help predict weather. This could be done without understanding the causal mechanics of why water vaporizes, rises, and moves toward areas of lower pressure; and why it cools down, condenses, and falls to the ground. There is logic in weather patterns beyond simple statistical correlations among data and I don't see why you would assume that any aspect of nature is fundamentally illogical in an intuitive mechanical sense. This implies that the human mind is inherently incapable of generating logical theories for certain natural occurrences but why would it then be able to explain so many others? What would the difference between inexplicable and explicable nature be ultimately based on?

 

 

[D H]

Nothing unconscious "follows rules." That is a personification of behavior that is so predictable that it appears as if there were rules or laws governing its behavior.

You contradicted yourself, lemur, just a few sentences later:

 

It is not a false premise to expect matter/energy to behave according to the logic of its own mechanics.

[ajb]

Mathematics itself is just the recognition of those patterns in nature.

 

In part that is true. Mathematics takes inspiration from nature. However, there are many branches of mathematics that seem very devoid of any physical application. Their initial conception can be very abstract and not inspired by any structures seen in nature.

 

However, it is also true that some of these high brow abstract constructions are exactly what are needed by physicists. This is fascinating.

[lemur]

You contradicted yourself, lemur, just a few sentences later:

Cleverly noted, but there's a difference between nature "following rules" or "obeying laws" and "behaving according to mechanical logic." When water molecules vibrate with increasing energy in a liquid, there is a logic to why/how they begin to overcome their surface-tension or whatever force it is that causes them to remain volumetrically compact. So the mechanical logic of the molecules directly result in the behavior they exhibit when heated. They are not following a rule that says when they reach a certain temperature, they have to start transitioning into gas. An apple isn't obeying a law when it falls off the tree; falling is its behavior and centripetal acceleration is the mechanical logic of gravitational force. I know it's a pretty subtle semantic distinction but I have read so many forum posts where people talk about physical behavior as if it were the product of obedient people choosing to respect arbitrary rules. This is very similar, imo, to (anti)religious people who view commandments and sins as arbitrary rules created to punish people for things that have no negative consequences of their own, like a game of cooties. There are mechanical logics to things, if you pay attention to how they work.

Edited January 22, 2011 by lemur

[swansont]

Cleverly noted, but there's a difference between nature "following rules" or "obeying laws" and "behaving according to mechanical logic." When water molecules vibrate with increasing energy in a liquid, there is a logic to why/how they begin to overcome their surface-tension or whatever force it is that causes them to remain volumetrically compact. So the mechanical logic of the molecules directly result in the behavior they exhibit when heated. They are not following a rule that says when they reach a certain temperature, they have to start transitioning into gas. An apple isn't obeying a law when it falls off the tree; falling is its behavior and centripetal acceleration is the mechanical logic of gravitational force. I know it's a pretty subtle semantic distinction but I have read so many forum posts where people talk about physical behavior as if it were the product of obedient people choosing to respect arbitrary rules. This is very similar, imo, to (anti)religious people who view commandments and sins as arbitrary rules created to punish people for things that have no negative consequences of their own, like a game of cooties. There are mechanical logics to things, if you pay attention to how they work.

 

They follow the logic, but that's based on some premise because you already have a model to use. And it's exactly the same as following rule, and it is a semantic distinction despite anyone's tendencies to anthropomorphize the behavior.

[Mr Skeptic]

people talk about physical behavior as if it were the product of obedient people choosing to respect arbitrary rules.

 

Sometimes it is convenient to do that, and people do this with all sorts of things. It's called "anthropomorphizing". However in the rules of physics there is not much room for optional behavior:

 

In quantum mechanics, Gell-Mann's Totalitarian Principle states: "Everything not forbidden is compulsory."

(the corollary is "Everything that is not compulsory is forbidden.")

[lemur]

They follow the logic, but that's based on some premise because you already have a model to use. And it's exactly the same as following rule, and it is a semantic distinction despite anyone's tendencies to anthropomorphize the behavior.

Why does it require having a pre-existing model for a physical phenomena to behave according to its inherent mechanics? A tree falls down even when no one is watching because of the mechanics of gravity and not because there's a rule/law that trees always fall down instead of up, right? My point here is that the rules/laws described in physics are extrapolations about the physicalities they describe. They are a tool for scientists and engineers and NOT rules or laws that govern the behavior of objects. Objects don't care about physics, science generally, or any other human knowledge. They just behave according to their own mechanics. I'm not sure what your point was, though, and whether you were talking about the same issue as I was/am.

 

 

 

Sometimes it is convenient to do that, and people do this with all sorts of things. It's called "anthropomorphizing". However in the rules of physics there is not much room for optional behavior:

 

In quantum mechanics, Gell-Mann's Totalitarian Principle states: "Everything not forbidden is compulsory."

(the corollary is "Everything that is not compulsory is forbidden.")

So what "compels" electrons to pop-up in random spots at intermittent moments? Is that an artifact of the means of observing them or do they really exist like that? I don't see where people get the idea that electrons, etc. can be a collection of random, discrete events. If that was the case, why/how would con-sequentiality emerge from them at a more macro level? Imo, everything physical must interact with something else to exchange energy with it and there must be continuous movement between things that come in contact with each other at any level in some form or other.

 

 

[steevey]

However, it is also true that some of these high brow abstract constructions are exactly what are needed by physicists. This is fascinating.

 

 

The reason math is "needed" in physics is because math depicts observable patterns which extend into unobservable realms. We see matter, but we need math to figure out that its made of tiny pieces we can't see.

However, because we can't observe it to prove it, anything math describes that is unobservable can't be 100% certain which is why you have all these weird theories like string theory. You really can't disprove that either since you can't see it.

Edited January 23, 2011 by steevey

[ajb]

The reason math is "needed" in physics is because math depicts observable patterns which extend into unobservable realms.

 

Ok, so the abstract language of mathematics is useful in describing what we see around us. I don't think anyone can really disagree with that.

 

 

We see matter, but we need math to figure out that its made of tiny pieces we can't see.

However, because we can't observe it to prove it, anything math describes that is unobservable can't be 100% certain which is why you have all these weird theories like string theory. You really can't disprove that either since you can't see it.

 

But what about say classical mechanics? We have a mathematical theory that can be used to great effect to describe the macroscopic properties of objects. We can see the planets going around the Sun, a pendulum swinging, balls rolling down inclines etc.

[swansont]

Why does it require having a pre-existing model for a physical phenomena to behave according to its inherent mechanics? A tree falls down even when no one is watching because of the mechanics of gravity and not because there's a rule/law that trees always fall down instead of up, right? My point here is that the rules/laws described in physics are extrapolations about the physicalities they describe. They are a tool for scientists and engineers and NOT rules or laws that govern the behavior of objects. Objects don't care about physics, science generally, or any other human knowledge. They just behave according to their own mechanics. I'm not sure what your point was, though, and whether you were talking about the same issue as I was/am.

 

 

 

The model is the system's own mechanics. They are the same thing. So it's nonsensical to say that they follow one but not the other.

[steevey]

But what about say classical mechanics? We have a mathematical theory that can be used to great effect to describe the macroscopic properties of objects. We can see the planets going around the Sun, a pendulum swinging, balls rolling down inclines etc.

 

But then you still have to ask whats causing those things to happen, which we can't see. If you just look at a classical level, math alone doesn't completely describe something anyway.

Edited January 23, 2011 by steevey

[ajb]

If you just look at a classical level, math alone doesn't completely describe something anyway.

 

Is not classical mechanics (for example) sufficient to describe the mechanics and dynamics of macroscopic objects?

[steevey]

Is not classical mechanics (for example) sufficient to describe the mechanics and dynamics of macroscopic objects?

 

No, because those macroscopic things we see would only have occurred if there were things going on at a smaller scale, at least evidently.

[ajb]

No, because those macroscopic things we see would only have occurred if there were things going on at a smaller scale, at least evidently.

 

True, but we just don't see that for many macroscopic objects when asking "classical questions". I don't need to worry about quantum mechanics when watching a pendulum or rolling a ball down an incline! I will not see anything that violates the laws of classical mechanics.

 

If I start asking questions like the stability of matter, the behaviour of the individual atoms/molecules and similar then I will have to leave classical mechanics as a reliable theory. Quantum mechanics comes in to play and this again is a mathematical theory.

 

As a physicist I cannot understand how one would describe pretty much anything without using mathematics, at least in an impartial objective way, even on the very basic level. As a mathematician, I am fascinated with the interplay of modern mathematics with theoretical physics.

 

Let us look a very simple example. Saying some body is "heavy", for example is not enough. This is very subjective. No everyone in principle will agree that the body is indeed heavy. By saying that the body has mass 100Kg (say) everyone knows exactly what this means, or more importantly everyone can agree that it is 100Kg.

 

Without mathematics I cannot imagine that science would have gotten very far, even at the very basic level.

Edited January 25, 2011 by ajb

[steevey]

 

As a physicist I cannot understand how one would describe pretty much anything without using mathematics, at least in an impartial objective way, even on the very basic level.

 

 

The wall looks blue. That ball looks larger than that. Because in the past something was in one location and is now in another location, it must have moved. etc.

[elas]

By saying that the body has mass 100Kg (say) everyone knows exactly what this means, or more importantly everyone can agree that it is 100Kg.

 

Without mathematics I cannot imagine that science would have gotten very far, even at the very basic level.

 

The problem is that maths alone does not explain what mass is, that requires a return to speculative classical physics. So saying exactly is an overstatement. Any measurement of mass is a measurement on an undefined entity.

Edited January 26, 2011 by elas

[ajb]

The wall looks blue.

 

So, you state the wavelength of the reflected light. If I am colour blind I would have no idea about the colour. Saying a wavelength (or frequency) gives a clear statment.

 

That ball looks larger than that.

 

So we now using inequalities. Very basic and intuitive, but I would regard this as a mathematical statement.

 

 

Because in the past something was in one location and is now in another location, it must have moved. etc.

 

To explain this properly you need some coordinate system. Again mathematics.

 

The problem is that maths alone does not explain what mass is, that requires a return to speculative classical physics. So saying exactly is an overstatement. Any measurement of mass is a measurement on an undefined entity.

 

Can any physical theory really tell you what anything is?

 

Anyway, the point is that if one wants to describe the world in an objective way that does not require any interpretation or a subjective point of view it seems that you need to use mathematics.

Edited January 26, 2011 by ajb