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Author Topic: Are fractals real or is it a part of how our minds work?  (Read 14312 times)
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Caleidoscope
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« Reply #30 on: June 09, 2016, 09:18:47 AM »

"Is it there all along"    roll eyes 
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Sockratease
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« Reply #31 on: June 09, 2016, 09:28:12 AM »

I'll avoid going too complex here.. but what is an too perfect approximation of
one apple plus one apple = two apples
?!?
to me math is a language. probably the most basic and universal there is.

it's neither black nor white - euclidean is 100% perfect. fractal geometry is much more real, with infinite "imperfect" variation. reality is 100% real.
and if you'd ask me what is closer to reality, it definitely is fractals.

1 + 1 = 2 can even get tricky.  Bertrand Russell and Alfred North Whitehead needed hundreds of pages in Principia Mathematica to *prove* that 1+1=2  tongue stuck out

But then there's irrational numbers.  They met Pythagoras' definition of imperfect enough to have the man who first showed him a proof that the square root of 2 is irrational murdered!  {OK - not proven, some say it was his students who did in poor old Hippasus and others said it was Poseidon  (apparently even The Gods thought Math was Perfect) and others say Pythagoras never existed at all and only a "Pythagorean School" - but the theme of Hippasus being killed for his crime of proving Math to contain "flawed Numbers" is persistent}.  Granted, Pythagoras made a Religion out of Math and Worshiped it's Perfection, so when something imperfect was shown to exist in math, it was Heresy and Blasphemy punishable by death.

But to the main point of discussion, I'm talking about using Math to model reality.

It never works.

My example was the theorems of Chemistry and Physics  (there are many who would agree that 1+1=2 it not Math - it is merely Arithmetic and that is a noteworthy distinction).  The Ideal Gas Law is a fine example.  It provides a darn near perfect predictive tool and is treated as a means of measuring and determining things, while at the same time accepting that it does not reflect reality entirely accurately.

It is, in the words I used which seem to bother some, too perfect.

I don't deny it's usefulness, but it is a tool - not a religion.  It has flaws.  Either that, or reality has flaws.  But either way Math does not, and never will, reflect Reality perfectly.  Fractals may be closer, but we may never be able to model reality in math due to many factors including things like Quantum Uncertainty, Godel's Incompleteness Theorem, and many other stuffs which expose the limitations of trying to define things in this manner.

However - if all you ever want to do is count apples, then I suppose it is good enough   kiss
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hobold
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« Reply #32 on: June 09, 2016, 10:15:31 AM »

But to the main point of discussion, I'm talking about using Math to model reality.

It never works.
Phrasing it so absolutely seems unnecessarily confrontational to me. Math has its limits (and you don't really need to dig as deep as Gödel's theorem of incompleteness). On the other hand, behind almost every technology we use, there was some mathematical thought performed by some mind during the invention/development. The math may not have been explicit, or not formulated in traditional ways, perhaps it was only a vague imagination at the time.

I don't mean to claim that math is the source of all good ideas - it isn't. Surprisingly often, random events (observations thereof) were the starting point of something that became an important invention later. But technological advances are fairly often created in a somewhat targeted manner from an already existing strange observation: experiments try to repeat the original random event in a controlled manner, then try to modify the event to shape the effect in desired ways. Mathematical models are the main and primary way to guide this exploration.

(But admittedly random chance is still the main and primary way to prompt the starting of exploration.)

Quote
It is, in the words I used which seem to bother some, too perfect.
If the words bother, maybe different words are understood better? Perhaps math isn't too perfect, but too smooth, too tidy, too clean and (in the sense of intentionally abstracting from detail) too simple?

After all, the infinite detail in the Mandelbrot set does not directly arise from z = z² + c, but from the iteration of that formula under certain conditions. I mean, the formula alone does not in fact describe all the detail - you really need a program, an algorithm, to fully specify the Mandelbrot set; and then you need a substantial amount of numerical computation to realize a picture that displays an approximation of the infinite detail.

In other words, the clean and simple formula z = z² + c is math, but it is only a small part of the much larger machinery required to actually show the Mandelbrot set around.
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Sockratease
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« Reply #33 on: June 09, 2016, 10:32:43 AM »

Phrasing it so absolutely seems unnecessarily confrontational to me.

Well, I truly didn't mean to sound confrontational.  That's why I clarified it was just my opinion.

I don't expect others to take it as anything more or less than that.

But I do apologize if it came off as harshly phrased.  I always figured the one place such absolutes are appropriate is in matters of personal belief and opinions.
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TheRedshiftRider
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« Reply #34 on: June 09, 2016, 09:58:15 PM »

I'll avoid going too complex here.. but what is an too perfect approximation of
one apple plus one apple = two apples
?!?
to me math is a language. probably the most basic and universal there is.

it's neither black nor white - euclidean is 100% perfect. fractal geometry is much more real, with infinite "imperfect" variation. reality is 100% real.
and if you'd ask me what is closer to reality, it definitely is fractals.

With small simple calculations you could easily say that. Imagine doing that with molecules...

Quote
Water has one atom of oxygen and two hydrogen atoms. The atomic weight of hydrogen is one unit. There are two of those so thats two. Plus one oxygen atom  which is 16 units. This is a total of 18 units.

18*6,022*10^23 atoms are in 1,8 gram of water.
1,8 ml of water weighs 1,8 grams.

So 1,8 ml of water is approximately one mole.

You can never get the exact number of molecules. Because it is an approximation. There a lot of other things that also affect it. (Equilibrium for example)



An other example:

With precipitation reactions you use more of one of the salts because you can't be sure you have the exact number of ions you need. With a solution with silver ions you always use more sodium chloride than you actually calculate (the calculation is just to prevent that you use a lot too much). You will keep adding it untill all silver ions have reacted with the chloride ions to form a salt that isn't soluble in water.
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« Reply #35 on: June 13, 2016, 08:09:37 AM »

http://m.youtube.com/watch?v=6oWLIVNI6VA
This very interesting talk on the interface between maths and physics .
Gauss famously through Riemnn appealedbo physicists to rescue mathmatics fom it's demise!
In fact prior to Riemann many philosophers already saw the death of mathmatics despite Kant's valiant assertions. In point of interest The Grassmnns were right at the forefront of this next stage in human combinatorial thought.

Maths is dead!
But we love it so much we have preserved it in Wax!
Here the physicists are guiding the so called Mathematicins.
So without labouring the point nature and natural Philoophy gives the human mind the contexts to develop topology and topological relationships that express our experience of magnitudes,,extnive and intensive.

What have natural behaviours and phenomena to do with the circle ? Fundamental perspective is based on sphericity! We as relative observers can only perceive spherically.

The sphere underlies all ancient wisdom, but the sphere is clearly a pragmatic ideal!  This was always known!
But we have been misled or obscured from this simplicity.

The fundamental topological fractal is the sphere . It is totally in the mind in my opinion , but it comes from our spheroidal perspective.
Note that sphericity is a concept that we develop from observing closed objects , while vorticular topologies come from imagining dynamic processes that seem to have a form or pattern: almost!!

We can not escape the concepts of Fractal Topology and our perceptions can not find ultimate cause . It can choose and does choose to elicit distinctions but distinctions do not discount the things distinguished. Thus the sphere does not discount spheroidal objects. And we can say that the inter relationship between the sphere and spheroidal objects is tautological, they are both interdependent!

So I believe we can expect to see versions of fractals in nature and perfected versions of natural fractions in our minds/ mathematical displays.
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« Reply #36 on: June 13, 2016, 08:35:28 AM »

http://m.youtube.com/watch?v=LYNOGk3ZjFM
So when you were told convergence of series is crucial to proving certain infinite series equations , and that Euler was wrong to use infinite series to solve so many problems , you were being misled by someone who could not understand Euler or indeed what is proof and how to prove in the real world!

Each art or term of a perturbation series represents a term at a different scale ! And assymptotic solutions ar perforce almost similar solutions. These are 2 of the major characteristics of a fractal process!
Cyclical processes are perturbation processes , circles again!
Oh by the way circles and probability are models of combinatorial outcomes for finite or truncated possibilities!
DeMoivre knew this as dud Newton
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Max Sinister
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« Reply #37 on: June 13, 2016, 07:21:53 PM »

"Maths is dead!
But we love it so much we have preserved it in Wax!"

WTH is that supposed to mean? That sounds unserious.
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« Reply #38 on: June 13, 2016, 08:10:21 PM »

@Max Sinister
It is. Poetic reference Madame Tussaud s famous wax museum! In such a place wax copies are made of once living things.
I make no bones about the state of Mathematics . NJWildberger is seriously tackling the issues within the subject, but the more he solves the issues the closer he comes to melding the subject into a type of computational science .

However the question about fractals is really independent of Mathematics . It is a question regarding the philosophy and psychology of perception .
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« Reply #39 on: June 14, 2016, 12:27:59 AM »

http://m.youtube.com/watch?v=L45Q1_psDqk
All you can do is Accept!
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« Reply #40 on: June 14, 2016, 01:05:39 AM »


Or Reject!   tease
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« Reply #41 on: June 15, 2016, 09:18:03 PM »

<a href="http://www.youtube.com/v/3MRHcYtZjFY&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/3MRHcYtZjFY&rel=1&fs=1&hd=1</a>

Here is a quite detailed description how we look at things. The video itself is not related to fractals but is to the way we use fractals to describe things.
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« Reply #42 on: June 16, 2016, 02:09:41 PM »

Or Reject!   tease
At the fundamental level I think my choice is limited to supnsion( and thus limbo) or acceptance of a chosen experience. Perforce this means rejection in some instances if I am in the superpositional state of suspension . But active rejection seems to me to only crystallise after I have accepted some state and am defending or modifying it.
I may be wrong, of course  wink
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« Reply #43 on: June 21, 2016, 05:56:43 AM »

http://m.youtube.com/watch?v=vZ5ItJkfLy4
As Norman rebuilds naive concepts such as nothing and something only make sense in relation to a something called a page!
Similarly the concepts only make sense in relation to a one thing called a region!
They make n sense at all in relation to an infinite space! We literally have no conception of an infinite space unless we mean a process we sense we can never complete!
Such a region exists only with the process of measurement inherent within, and the sense of our mortality, and exhaustion!
Such a region therefore exists as inherently fractionable that is as a fractal topology .
The possibilities are indeed endless!
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« Reply #44 on: June 27, 2016, 02:06:51 PM »


I agree.

But I guess it is different for everyone, we can not confirm we are talking about the same thing:

<a href="https://www.youtube.com/v/evQsOFQju08&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/evQsOFQju08&rel=1&fs=1&hd=1</a>
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