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Author Topic: Are fractals real or is it a part of how our minds work?  (Read 14288 times)
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TheRedshiftRider
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« Reply #15 on: June 06, 2016, 05:58:32 PM »

hehe, until you are home I've written many more pages, I'll drown you with my  canadian 
grin
I just love it how the fractal perspective gives a simple and clean answer to this problem - that includes both views.
if the universe is fractal, then it is infinite, but in a confined space, just as the M-Set is infinite, but it takes place in a confined space of the coordinate system.
but as long as the scientific majority neglects the possibility that the universe is a fractal, solely based on exactly your argumentation this is the only way to show them this view might be wrong and that it is at least worth to really examine this instead of ignoring it.

man, this feels like the futurama episode about the missing missing missing link to prove evolution.
<a href="https://www.youtube.com/v/TTOla3TyfqQ&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/TTOla3TyfqQ&rel=1&fs=1&hd=1</a>

and yes, I am well aware of the irony that I use creationism as argument against science trying to disprove a fractal theory that can never be totally disproven (which is essential for science).
and this deeply sucks, but I can't just ignore the obvious fractal nature of reality just because of that.
this situation honestly is very annoying for me, because I like to think of me as a rational, scientific person.
if anyone has a satisfying and logically consistent solution for me, I'd really love to close this chapter once and for all instead of chasing windmills..
It really bothers me.
nope doesn't help.
my answer would be no.
except if we limit the resolution and just take a snapshot, thus making it tangible, visible, coming into what we call reality.

I guess the formula itself is a mathematical concept, not an object.
the result - the picture - is the object.

maybe the universe as a whole is also "just a concept" and not an object.
the actual result, our reality & conscious experience is the object.





Then I guess it is in no way possible to make a fractals as a picture as it does not exist under perfect conditions. The only thing of fractals that could be called infinite is the concept itself.
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Sockratease
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« Reply #16 on: June 06, 2016, 06:28:05 PM »

Lunch Break!

Time to point out one further observation - I don't even think MATH is real!

It's just Intellectual Gymnastics.

It provides us with ways to model real things, usually only approximately  (reflecting it's lack of reality) but math itself... 

It's nothing.

Just thought processes getting carried away with their own self-importance  (a state of mind which I have been known to indulge in myself every now and again).
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TheRedshiftRider
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« Reply #17 on: June 06, 2016, 07:16:41 PM »

Lunch Break!

Time to point out one further observation - I don't even think MATH is real!

It's just Intellectual Gymnastics.

It provides us with ways to model real things, usually only approximately  (reflecting it's lack of reality) but math itself...  

It's nothing.

Just thought processes getting carried away with their own self-importance  (a state of mind which I have been known to indulge in myself every now and again).
I guess you are not the only one. I think we all got carried away.

(The ideal circumstances for this good discussion were not there anymore like we discussed earlier with other examples. tease )
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TheRedshiftRider
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« Reply #18 on: June 07, 2016, 07:01:06 AM »

It might be a strange question but would like to keep this discussion going.

Would other intelligent life-forms be able to understand fractals like we do? (In this case I am relating to second half of my question.)
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Sockratease
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« Reply #19 on: June 07, 2016, 08:10:59 AM »

It might be a strange question but would like to keep this discussion going.

Would other intelligent life-forms be able to understand fractals like we do? (In this case I am relating to second half of my question.)

Interesting question.

And it raises another interesting question - What would The Mandelbrot Set look like in a base 12 number system?  Base 3?  Other "alien" number systems?

Who's to say they would use base 10?

How would one even go about checking other base systems?
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hobold
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« Reply #20 on: June 07, 2016, 10:39:30 AM »

Let me quote to thoughts and show that they are closely related:

1. Time to point out one further observation - I don't even think MATH is real!

2. Would other intelligent life-forms be able to understand fractals like we do?


Preliminaries:

"Reality" - more than one definition of the concept exist.

For example, there is "physical reality", meaning the existence of things and/or events based on nature's laws (system states and state transitions); regardless of observers, regardless of observers' knowledge of nature's laws - but implying that such natural laws exist. Without natural laws, the universe would be chaotic, arbitrary, and reality itself would be so random as to be meaningless.

Then there is "objective reality", meaning existence of observables, that can be defined so precisely that all impartial observers would necessarily come to an agreement about what they observed (i.e. measured). IMHO, this is a lesser form of reality, because it is constrained by the existence of observers.

Furthermore, there is "informational reality", meaning the existence of information, created however indirectly by the universe, stored and processed by physical entities (either biological, mechanical, electronic, or otherwise), that is interpreted consistently the same by a group of individual entities. For example if some of you understand some of the text I posted here, then our agreement about the meaning of words implicitly lends "informational reality" to those words and the abstract concepts behind them. The thoughts that were "real" in my mind gain more "reality" if you chose to copy them to your mind, so to speak.


So, with this gradual continuum of reality, I can claim that math is somewhere between "objective reality" and "informational reality". To see this, take some piece of crystal and count the number of atoms in it. That number is an abstract informational concept, but it is an observable attribute of the physical object - the crystal piece we started with - and any diligent and capable observer would count the same number of atoms in that particular object.

Or, in other words, math is certainly less real than the piece of crystal itself. But if we use math to process information which originates from "objective reality", then those kinds of math that can make accurate and useful predictions about "objective reality" implicitly gain some of that reality, too (that kind of math is called physics). That's because math grounded in objective reality is not arbitrary, but constrained by nature's laws.


That leads us to question 2: would an alien intelligence understand fractals as humans do?

IMHO, if those aliens live in a universe with the same natural laws, and if they discovered and use physics to make use of their environment, then their math will most likely be very similar to our math, because both schools of thought were shaped by identical constraints.

So this leads to a two-pronged answer: if the aliens have some form of technology (that is sufficiently advanced) then they will be able to understand fractal geometry. But if their use of math is detached from "objective reality", if it is a purely philosophical hobby to the aliens, then they might not recognize the concepts underlying "our" fractal geometry.
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TheRedshiftRider
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« Reply #21 on: June 07, 2016, 11:36:34 AM »

Interesting question.

And it raises another interesting question - What would The Mandelbrot Set look like in a base 12 number system?  Base 3?  Other "alien" number systems?

Who's to say they would use base 10?

How would one even go about checking other base systems?

I haven't thought about that. Nice idea.

Although I don't know whether what the result would be different with different bases. It would involve devision and multiplication. Which doesn't have an impact on the general shape of the m-set. (it would only increase or decrease in size. Considering there is a large enough bailout radius.)
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Max Sinister
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« Reply #22 on: June 07, 2016, 11:46:05 PM »

My two cents: First, fractals exists as mathematical concepts and are as real as the fact that 2+2=4; and second, they often appear in the world, and in fact describe it better than euclidian geometry.

But they wouldn't be different in other bases. 2+2=4, 10+10=100. If you program the Mandelbrot set (I did in the past), the computer uses binary internally. It doesn't look different from the same set calculated purely in the decimal system.
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« Reply #23 on: June 08, 2016, 08:42:25 AM »

I don't know if this is on the same subject, but sometimes when I'm using MB3D I wonder if I'm finding something or if I'm creating something, it something that puzzles me a bit.
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TheRedshiftRider
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« Reply #24 on: June 08, 2016, 09:26:28 AM »

My two cents: First, fractals exists as mathematical concepts and are as real as the fact that 2+2=4; and second, they often appear in the world, and in fact describe it better than euclidian geometry.

But they wouldn't be different in other bases. 2+2=4, 10+10=100. If you program the Mandelbrot set (I did in the past), the computer uses binary internally. It doesn't look different from the same set calculated purely in the decimal system.

I thought I was close, thanks for explaining this a bit further.

I'm sorry Sockratease, but it is a nice idea though. Maybe other intelligent life will have completely different way of handling numbers:
<a href="https://www.youtube.com/v/l4bmZ1gRqCc&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/l4bmZ1gRqCc&rel=1&fs=1&hd=1</a>
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« Reply #25 on: June 08, 2016, 09:31:38 AM »

I don't know if this is on the same subject, but sometimes when I'm using MB3D I wonder if I'm finding something or if I'm creating something, it something that puzzles me a bit.
I guess thats still on-topic.


And a very interesting thing to think about. I guess if math was ''meant to be'' you are probably finding something. If its not and math is actually part of human mind you are finding a variation on something and thus  creating something new.
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Max Sinister
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« Reply #26 on: June 08, 2016, 10:38:03 PM »

Yes. 2 + 2 = 4 even before there was a being which did maths consciously.
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« Reply #27 on: June 08, 2016, 11:00:02 PM »

Yes. 2 + 2 = 4 even before there was a being which did maths consciously.

I wasn't suggesting that the meanings would change, but I do recall something from the long gone college days about graphs of things set up in a different base look different.  Similar, but skewed or stretched because the scale changed.  I could be mixing things up from two totally unrelated things - that's why I mentioned it here.  I wasn't sure.

But I am sure that when I say math is not real, I mean that it is an ideal system.  Ideal situations do not exist in reality.  Math approximates reality, but is a bit too perfect.  Like our equations in physics and chemistry.  The true results of direct measurements vary a little from the predicted values, but are often very very close.  Close enough that nobody but people who philosophize about math give a crap.

Like I said - I see math as a thought experiment or intellectual gymnastics more than anything that reflects reality exactly, despite it's incredible usefulness in modeling things.  It's a great tool, but gets taken a bit too seriously for what it is.
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« Reply #28 on: June 09, 2016, 12:01:44 AM »

Math approximates reality, but is a bit too perfect.
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.
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« Reply #29 on: June 09, 2016, 08:01:59 AM »

How hard Benoit fought to make his insights and expertise into an acadrmic field of study.
But he was a latecomer to the scattered and marginalised explorations of a disparate collection of geometers around the world  it was his study of the work, ideas and results of many geometers which gave him the academic right to name the topic of his dissertation.

Academically he defined his subject as tightly as he could so that it could be distinctively marked. So he in fact had several distinguishing elements to his dissertation topic.

We know he published in French his original,dissertation, and through circumstances to do with the war eventually took up an opportunity in America to work on computer applications to real world problems.  It is during this time that he was able to give form to a set of forms that earlier researchers had only been able to sketch!

So the words  "real", fractal and iterative process , and set of results ( Julia sets) all were drawn together by the diverse patterns in human and natural behaviours he was studying!

Academically he struggled to gain credibility for this subject. It was either defined so tightly as to render it as practically useless, or dismissed as a ragbag collection of indulgent musings!

It was when a pilot who required a way of generating realistic backgrounds for his flight simulations read the translation of Benoits dissertation and recognised how to design an application based on these principles in a computer code that was used widely in industry that Bemoits non Academic reputation started to take off and give him opportunities that his academic colleagues envied!

As collection of enthusiasts fractal hobbyists have driven the developments in the field and have importantly helped broaden the definitions of the field  it is these same enthusiasts who have gone on into academia and industry and infused these ideas into the mainstream of many engineering and scientific topics that are founded on constructive disciplines.
Is it real or is it in the mind is a restatement of an old Socratic and Platonic " game" often called the Platonic theory of Form or Ideas
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