Hrvoje1

What is more common in nature, regularities or irregularities?

Recommended Posts

Posted (edited)
6 minutes ago, Hrvoje1 said:

Irregular pattern is an oxymoron, a bit, if we assume regularity is needed to establish patterns.

Another way to put it is: a pattern of irregularity..

Edited by StringJunky

Share this post


Link to post
Share on other sites
1 hour ago, Hrvoje1 said:

symmetry of polygons requires that lengths of at least some of its sides are identical

At least axial symmetry requires that, ...

Share this post


Link to post
Share on other sites
Posted (edited)
21 hours ago, swansont said:

No, not so much. 

There is symmetry, but it's at a very small scale. 

 

Our latest historically contingent physical theory models symmetry. How can we know that it's "really" there in nature itself? Perhaps our theoretical symmetry is only an approximation to something deeper and more complicated. We can't possibly know. Physical science is limited by our ability to measure. You disagree? You believe human made physics is absolutely true? It never has been before throughout history. You mean we just got lucky and nailed it this century? How will such an idea hold up a century from now? What do you think?

Edited by wtf

Share this post


Link to post
Share on other sites
1 hour ago, wtf said:

Our latest historically contingent physical theory models symmetry. How can we know that it's "really" there in nature itself?

That's a philosophy question.

What we can say is that nature behaves as if it does, indeed, exist.

1 hour ago, wtf said:

Perhaps our theoretical symmetry is only an approximation to something deeper and more complicated. We can't possibly know. Physical science is limited by our ability to measure. You disagree? You believe human made physics is absolutely true? It never has been before throughout history. You mean we just got lucky and nailed it this century? How will such an idea hold up a century from now? What do you think?

I think you've gone from me objecting to your unsupported assertion "In terms of nature, there are no regularities at all" to somehow concluding that because I objected to it, I must somehow think that there is no more physics to discover. Which is quite incredible.

Share this post


Link to post
Share on other sites
Posted (edited)
12 hours ago, swansont said:

I think you've gone from me objecting to your unsupported assertion "In terms of nature, there are no regularities at all" to somehow concluding that because I objected to it, I must somehow think that there is no more physics to discover. Which is quite incredible.

I did read your post as if you were equating nature itself with our historically contingent mathematical models of nature. You didn't argue otherwise or defend your point.

I do reiterate that there are no regularities in nature that we can prove are regularities with absolute certainty. Of course our contingent physical models do have regularities. That is not at all the same thing.

Sure, it's a matter of philosophy. The philosophy of the limits of science. You can't know for sure that there are regularities in nature. You agree or disagree?

Edited by wtf

Share this post


Link to post
Share on other sites
Posted (edited)

 

21 hours ago, StringJunky said:

Another way to put it is: a pattern of irregularity..

Any way you put it, it sounds as an oxymoron, somehow.

5 hours ago, wtf said:

You agree or disagree?

I came up with the most interesting definition of regularity for this discussion: appearance or behaviour governed by an exact set of rules or regulations

21 hours ago, Hrvoje1 said:

At least axial symmetry requires that, ...

Of course that point symmetry requires that also, that was an instant blackout from my side.

On 5/13/2019 at 3:48 AM, wtf said:

if by regular we mean at the very least computable; that is, capable of being generated by an algorithm

... in fact, this was already at least equally interesting definition of regularity, or maybe even more interesting. So basically, are there laws in nature, or not.

Edited by Hrvoje1

Share this post


Link to post
Share on other sites

There seems to be no accidents, everything is somehow connected, for example, I started to read that text about groups in physics motivated by wtf’s response here 

So, if there are laws, are the laws of computation the most fundamental laws?

Share this post


Link to post
Share on other sites
6 hours ago, Hrvoje1 said:

So basically, are there laws in nature, or not.

 

5 hours ago, Hrvoje1 said:

So, if there are laws, are the laws of computation the most fundamental laws?

 

Firstly it should be pointed out that different disciplines use different words for the concept of 'laws'.

So we have rules, principles, axioms, laws, and so on and so forth.

 

But what is important is that none of these apply to all matters at all times.

They all come with the small print 'domain of applicability' which, like all small print, is far to often ignored.

 

So for instance logic circuits in electronics are binary right?
That is they operate on being in one or other of two electric states, commonly called 1 and 0.

But whilst there is an enormous welter of circuit matters and theory, the plain fact is that electronics engineers have thought is necessary to invent a whole new area, outside the binary domain.
This can be seen by looking in a catalogue of logic chips and discovering that there are many 'tristate' chips.

 

So my answer is something may be 'more fundamental' if it is relevent but maybe totally irrelevent.

So tell me,

Is Fermat's principle more or less fundamental than Kepler's laws?

Share this post


Link to post
Share on other sites
11 hours ago, wtf said:

I did read your post as if you were equating nature itself with our historically contingent mathematical models of nature. You didn't argue otherwise or defend your point.

I do reiterate that there are no regularities in nature that we can prove are regularities with absolute certainty. Of course our contingent physical models do have regularities. That is not at all the same thing.

Your claim was more than that. You said they didn't exist, and you stated that with absolute certainty. ("In terms of nature, there are no regularities at all")

11 hours ago, wtf said:

Sure, it's a matter of philosophy. The philosophy of the limits of science. You can't know for sure that there are regularities in nature. You agree or disagree?

If one looks at e.g. Bose-Einstein statistics, on sees a certain expected behavior occurring only if atoms are identical, and different behavior if they are not. We observe the behavior of them being identical.

It's not the model that has this regularity. The model requires that of the atoms.

Share this post


Link to post
Share on other sites

 

To emphasise the difference between symmetry and regularity and to further link this to your new question about rules,

here is a graph.

 

1535918795_767px-Sinusoid_increasing_Q10_svg.jpg.d7c565ff24683e00033d0444a2d61c9b.jpg

 

I think it is regular because it follows a define formula, equation or rule (note rule and regular come from the same Latin root).

Do you think it is symmetric?

Share this post


Link to post
Share on other sites

I think it can be decomposed as a sum of two symmetric functions, one even and one odd.

Share this post


Link to post
Share on other sites
53 minutes ago, Hrvoje1 said:

I think it can be decomposed as a sum of two symmetric functions, one even and one odd.

You are wriggling.

If this is true then you can state what those functions might be.

Not that this is relevant since what I am showing you is complete in itself.

I will tell you that every single one of those oscillations is unique and not one of them is symmetrical since the scale is continuously changing on both axes.
That is both the period and amplitude of the oscillation is continuously varying.

 

A full isosceles triangle is symmetrical but can be decomposed into two smaller triangles, neither of which is.

So what.?

 

Share this post


Link to post
Share on other sites
Posted (edited)
4 hours ago, studiot said:

You are wriggling.

If this is true then you can state what those functions might be.

Not that this is relevant since what I am showing you is complete in itself.

I will tell you that every single one of those oscillations is unique and not one of them is symmetrical since the scale is continuously changing on both axes.
That is both the period and amplitude of the oscillation is continuously varying.

I don't get it, does this "argument" lead somewhere? If this is true then f(x) might be A(x)sin(ω(x)), and feven(x) and fodd(x) are as previously described.

 

4 hours ago, studiot said:

A full isosceles triangle is symmetrical but can be decomposed into two smaller triangles, neither of which is.

So what.?

So what is more fundamental principle in nature, symmetry or asymmetry? What is more fundamentally existing in nature, regularities or irregularities?

 

15 hours ago, studiot said:

So my answer is something may be 'more fundamental' if it is relevent but maybe totally irrelevent.

So tell me,

Is Fermat's principle more or less fundamental than Kepler's laws?

If any of them was derivable from the other, I would be able to establish such relationship between them. What is 'more fundamental', is pretty much always relevant in science.

Edited by Hrvoje1

Share this post


Link to post
Share on other sites
Posted (edited)
17 hours ago, swansont said:

Your claim was more than that. You said they didn't exist, and you stated that with absolute certainty. ("In terms of nature, there are no regularities at all")

If one looks at e.g. Bose-Einstein statistics, on sees a certain expected behavior occurring only if atoms are identical, and different behavior if they are not. We observe the behavior of them being identical.

It's not the model that has this regularity. The model requires that of the atoms.

I will retract the dogmatic claim and retreat to "in terms of nature, there are arguably no regularities at all. I can defend that.

So ok the identicality of atoms is a regularity. In the historically contingent theory of atoms. Besides, atoms aren't identical at all. Each element's atoms are different from the other elements. And even among, say, hydrogen atoms, one could lose or acquire an electron, isn't that right?

You could then say well all electrons are the same and I could counter with Wheeler's fanciful idea that the reason all electrons are identical is because there is only one of them in the universe and we just observe it whizzing back and forth in time. 

https://en.wikipedia.org/wiki/One-electron_universe

But if that's all you've got for regularities in nature, I don't think that's much. When people say that they like to think of hexagons in honeycombs, the sun rising in the east every morning, and such. Not abstract thingies like electrons which aren't really particles at all but rather probability waves. Again falling back on the symmetry in the theory but not necessarily in nature. 

 

On 5/14/2019 at 7:31 PM, Hrvoje1 said:

 

 

I came up with the most interesting definition of regularity for this discussion: appearance or behaviour governed by an exact set of rules or regulations

Of course that point symmetry requires that also, that was an instant blackout from my side.

... in fact, this was already at least equally interesting definition of regularity, or maybe even more interesting. So basically, are there laws in nature, or not.

> I came up with the most interesting definition of regularity for this discussion: appearance or behaviour governed by an exact set of rules or regulations

Sounds like a computational theory of reality. We have no idea if such a thing is true. Exact set of rules? Hilbert's dream, an exact set of rules for mathematics. Gödel destroyed that hope. Still people cling to the hope of an exact set of rules for nature. "Dreams of a Final Theory," an equation for the world that you can write on a t-shirt. Nice dream. Not yet a reality and arguably never.

... in fact, this was already at least equally interesting definition of regularity, or maybe even more interesting. So basically, are there laws in nature, or not.

Right. Maybe there are. Maybe there aren't. Maybe I'm a Boltzmann brain, a momentary coherence in an otherwise chaotic and random universe.

https://en.wikipedia.org/wiki/Boltzmann_brain

Edited by wtf

Share this post


Link to post
Share on other sites
6 hours ago, wtf said:

I will retract the dogmatic claim and retreat to "in terms of nature, there are arguably no regularities at all. I can defend that.

So ok the identicality of atoms is a regularity. In the historically contingent theory of atoms. Besides, atoms aren't identical at all. Each element's atoms are different from the other elements.

Which is a rebuttal of a claim nobody has made.

6 hours ago, wtf said:

And even among, say, hydrogen atoms, one could lose or acquire an electron, isn't that right?

Yes. And you can do things to destroy other objects that have symmetry. But the argument was not all things exhibit symmetry with everything else, so this is a bit of a strawman.

6 hours ago, wtf said:

You could then say well all electrons are the same and I could counter with Wheeler's fanciful idea that the reason all electrons are identical is because there is only one of them in the universe and we just observe it whizzing back and forth in time. 

I have pointed to experimental confirmation, so I think that trumps fanciful ideas.

6 hours ago, wtf said:

But if that's all you've got for regularities in nature, I don't think that's much.

Not much is greater than zero, which is the claim I was objecting to. Thank you for agreeing.

6 hours ago, wtf said:

When people say that they like to think of hexagons in honeycombs, the sun rising in the east every morning, and such. Not abstract thingies like electrons which aren't really particles at all but rather probability waves. Again falling back on the symmetry in the theory but not necessarily in nature. 

You might have noticed that this is a science discussion board, so what "people" think of isn't necessarily representative or relevant.

 

Share this post


Link to post
Share on other sites
10 hours ago, Hrvoje1 said:

I don't get it, does this "argument" lead somewhere?

This whole argument over definitions is fruitless as such arguments tend to turn out.

The whole beauty of the English language is that it has so many words with similar meanings and even substantial overlap of meaning.
This is because there is so many subtle variations of meaning available.

So arguing that one such word is identical to another leads to such fruitless discussion.

That is why it is important in analytical discussion and (since you want to remain in Maths) exactitude, it is important for the promoter of the discussion to be clear as the his exact usage of language.

You have used three such words

Regular, irregular and Nature.

We are all still waiting for your input on these.

I note that wtf has used a different meaning for Nature  than swansont.

 

Share this post


Link to post
Share on other sites
Posted (edited)
9 hours ago, swansont said:

You might have noticed that this is a science discussion board, so what "people" think of isn't necessarily representative or relevant.

 

Quite a disingenuous remark given the context. All the best.

Edited by wtf

Share this post


Link to post
Share on other sites
1 hour ago, wtf said:

Quite a disingenuous remark given the context. All the best.

Sorry that I overestimated your grasp of the material.

Share this post


Link to post
Share on other sites
5 hours ago, swansont said:

Sorry that I overestimated your grasp of the material.

That's the best you can do? As moderator setting the example for the tone around here?

Share this post


Link to post
Share on other sites
22 hours ago, studiot said:

You have used three such words

Regular, irregular and Nature.

We are all still waiting for your input on these

 

In particular, if I draw something on a sheet of paper is that "in Nature" or not, setting aside whether it is regular or irregular?

Share this post


Link to post
Share on other sites
19 hours ago, studiot said:

In particular, if I draw something on a sheet of paper is that "in Nature" or not, setting aside whether it is regular or irregular?

OK, now you are avoiding the issue, you realized that I believe in Wigner's unreasonable effectiveness of mathematics in natural sciences, and now you are after me. If you draw something on a sheet of paper, the trace of the pencil is "in nature", and the idea of what it represents was at first in your mind, and it can be in someone other's mind if it is shown to someone else, and although minds are natural, their content can be real or imaginary.  Regularities that are in our minds are in connection with regularities in nature, as long as our minds are in connection with reality, that I consider nature. But that is not exactly the question I raised.

On ‎5‎/‎16‎/‎2019 at 1:21 PM, studiot said:

So arguing that one such word is identical to another leads to such fruitless discussion.

I never said that symmetry and regularity have identical meaning, you were the one that was pushing the discussion in that direction, explaining the differences, although, no one actually opposed.

My drive to start the discussion was this insight:

Any linear combination of even functions is even, and they form a vector space over the reals. Similarly, any linear combination of odd functions is odd, and the odd functions also form a vector space over the reals. The vector space of all real functions is the direct sum of the subspaces of even and odd functions.

So if you start with symmetric functions alone, the way to get an asymmetric one is a linear combination of both an even and an odd component, and what is cool, is that you can achieve that for every possible asymmetric function. In that sense, symmetric functions are more fundamental then asymmetric ones. Right?

It's kind of like asymmetry is an emergent property that none of symmetric components has. Although, it is a direct consequence of properties of both components, achieved by addition, so it doesn't quite conform to the definition, so let's drop the emergence digression, it was sufficiently discussed in the other thread.

Share this post


Link to post
Share on other sites

So if you start with symmetric functions alone, the only way to get an asymmetric one ... that's actually cool.

Share this post


Link to post
Share on other sites
Posted (edited)
2 hours ago, Hrvoje1 said:

I never said that symmetry and regularity have identical meaning,

 

I will put this down to a momentary lapse of memory, because actually you said exactly that in so many words.

 

On 5/11/2019 at 8:58 PM, Hrvoje1 said:

I draw that line by mentioning something that appears to me as examples or regularity, such as symmetry and periodicity.

 

I further gave you a simple example of something (in mathematics) that is irregular but symmetrical.

 

On 5/12/2019 at 10:32 AM, studiot said:

Take any irregular shape and reflect it in an axis.
You now have a symmetrical irregular shape.

Point proven. They are different.

 

So can we stop this dancing around and pursue a proper discussion?

 

 

Edited by studiot
To complete posting.

Share this post


Link to post
Share on other sites
17 minutes ago, studiot said:

I will put this down to a momentary lapse of memory, because actually you said exactly that in so many words.

Here you go again. If I said that symmetry appears to me as an example of regularity, then it means that I don't think these words are synonyms.

... in a sense that regularity can have other meanings. They don't cover each other 100%.

Share this post


Link to post
Share on other sites
21 minutes ago, Hrvoje1 said:

Here you go again. If I said that symmetry appears to me as an example of regularity, then it means that I don't think these words are synonyms.

... in a sense that regularity can have other meanings. They don't cover each other 100%.

"They don't cover each other 100%."

 

So you actually agree with me.

Why didn't you just say so instead of arguing the examples from where they do not overlap?

 

To move on here is an interesting (mathematical) example (not of symmetry).

Consider the sequence

{1, 2, 4, 7, 11, 16 ...}

This can be generated in a variety of ways,

For instance by noting that the difference between succeeding terms increases by 1 each time

Or by using the formula Pn = (n2 + n +2) /2 for n = 0,1,2,3....

Both use a 'rule' and so can you class them as regular?

But the exact same sequence could be the output of a (perfect) random number generator.

So would the output then still be regular?

 

The whole question of regularity, symmetry, pattern is absolutely fascinating, both in abstract thought and Nature.

A superb book that discusses this in lots of different ways is

The Self Made Tapestry - patthern formation in Nature.

by Philip Ball

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now