What qualifies as science?

[NotEinstein]

Is citing E =Mc^2 an argument from authority? Of course it is. Einstein was the knowledgeable authority and it has been tested and proven correct. The authority cited is from a reliable authority.

Please learn what an argument from authority is. Citing E=mc^2 is only an argument from authority if you say that it's true because Einstein said it. Luckily, we've done a couple of experiments that show it to be true, so you don't need to rely on an argument from authority to prove E=mc^2 is correct.

As was Mandelbrot, given that he had to wait for the development of computers which could handle large amounts of data to develop his fractal "Set" .

As long as there was no evidence or proof, and all we had was his say-so, then yes.

It is the standard which encompasses all other forms of fractal sets mathematically and naturally.
And like Einstein his fundamental formula is simple and irreducible and complies with Occam's razor.

E=mc^2 is not a fundamental formula, please learn what the theory of general relativity actually says. And I'm not sure it's irreducible.

and has been tested and proven correct.

Tested? It's a definition! You can't test a definition, that would be circular reasoning.

Like Einstein, Mandelbrot is the reliable authority, which can be quoted in all discussion of fractals.

There is no such thing as a "reliable authority" in science. Please look up what science is.

Additionally, Newton was a "reliable authority", yet his gravity has now been proven to be (technically) incorrect. A reliable authority is only reliable until they are shown to be incorrect. And Mandelbrot's definition of the word fractals is incorrect when compared to current usage. In other words, Mandelbrot is not even a reliable authority on this, in this case.

Please look up what an argument from authority is, and learn why it is a logical fallacy.

 

[Write4U]

And Mandelbrot's definition of the word fractals is incorrect when compared to current usage

I submit your usage of the word fractal is incorrect (limited) when compared to current usage.

Fractal Applications
Now that you've gained an appreciation for the fascinating field of fractal math and science, in this final chapter we'll explore just a few of the things that people are already doing with fractals. We'll see examples in the realms of engineering, electronics, chemistry, medicine, even urban planning and public policy. But these illustrations just represent the beginnings of a revolution in how we understand the functioning of the natural world. This is a revolution in which we will apply the lessons learned from the time-tested fractals in nature to inspire more effective and efficient designs for our structures, devices, and systems. And no doubt, the most exciting applications of fractals are still in the future, waiting to be invented.

http://fractalfoundation.org/OFC/OFC-12-1.html

and

Fractal Artificial Life: Looking for Creativity at the Edge of Chaos
The goal of this article is to outline a new research framework at the intersection of artificial life and computational arts and design, and was originally motivated on the one hand by an artistic fascination for the presence of fractal... more
The goal of this article is to outline a new research framework at the intersection of artificial life and computational arts and design, and was originally motivated on the one hand by an artistic fascination for the presence of fractal patterns in nature and the universe at all scales, and on the other hand by the intuitive assumption that such patterns are indicators of some very universal self-organization principles leading to situations known as criticality at the edge of chaos. In this paper, we formulate several hypothesis as to how these situations might be reproduced using computer simulations and discuss the possible impacts of this field of research for computational art and creation.

http://www.academia.edu/Documents/in/Natural_Fractals

 

[exchemist]

I submit your usage of the word fractal is incorrect (limited) when compared to current usage.
http://fractalfoundation.org/OFC/OFC-12-1.html

and
http://www.academia.edu/Documents/in/Natural_Fractals

A P P R O X I M A T I O N.

M O D E L.

 

[Write4U]

A P P R O X I M A T I O N. M O D E L.

And found in naturally occurring and recurring self similar patterns, including long term statistical patterns.
The Fibonacci sequence is a fractal pattern found throughout the universe.

The term itself is derived from the Latin word "frāctus" meaning "broken" or "fractured", and the concept of theoretical fractional dimensions has now been extended to include geometric patterns in nature and is now extensively used for practical application in a host of human created structures and organizing patterns.

Thus, by defining it as just an abstract model is a "limited" view, and therefore incomplete.
By NE's own statement, the meaning and usage of a word can change. He is right, the meaning of the word fractal has changed because it is too limiting in scope. I already cited that Mandelbrot himself broadened the definition.

Mandelbrot, however, never felt he was inventing a new idea. He describes his feelings in a documentary with science writer Arthur C. Clarke:
Exploring this set I certainly never had the feeling of invention. I never had the feeling that my imagination was rich enough to invent all those extraordinary things on discovering them. They were there, even though nobody had seen them before. It's marvelous, a very simple formula explains all these very complicated things. So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science

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

 

[exchemist]

And found in naturally occurring and recurring self similar patterns, including long term statistical patterns.
The Fibonacci sequence is a fractal pattern found throughout the universe.

The term itself is derived from the Latin word "frāctus" meaning "broken" or "fractured", and the concept of theoretical fractional dimensions has now been extended to include geometric patterns in nature and is now extensively used for practical application in a host of human created structures and organizing patterns.

Thus, by defining it as just an abstract model is a "limited" view, and therefore incomplete.
By NE's own statement, the meaning and usage of a word can change. He is right, the meaning of the word fractal has changed because it is too limiting in scope. I already cited that Mandelbrot himself broadened the definition. https://en.wikipedia.org/wiki/Benoit_Mandelbrot

Yes, yes, O level Latin was an entry requirement for my university, thanks. But these phenomena can be modelled by a partial use of fractals only, because the pattern predicted by the iterations is no longer followed at some scales. So as usual, it is an approximate model, no more than that. All these citations of yours are written by people who unlike you recognise that we speak in science of inexact models.

 

[Write4U]

Yes, yes, O level Latin was an entry requirement for my university, thanks. But these phenomena can be modelled by a partial use of fractals only, because the pattern predicted by the iterations is no longer followed at some scales. So as usual, it is an approximate model, no more than that. All these citations of yours are written by people who unlike you recognise that we speak in science of inexact models.

I would rather call recognition of similar patterns at different scales and in different physical forms.

It is my impression you see a fractal as a single completed idealized abstract mathematical construct which has an arbitrary starting point but is continuously and infinitely repeatable.

But IMO, that's old school, and the concept and definition has broadened to include fractured and seemingly unrelated expressions of geometric forms and a host of other naturally occurring physical expressions, which have a common denominator of being a form of fractal expression, even as they do not occur as a single completed "string" of continual iterations. A fractal is not an abstract mathematical construct separated from reality. Fractals occur naturally in many forms. I posted a long list of areas where fractality and the fractal function is observable and quantifiable in many different no-theoretical, i.e. observable areas.

 

[iceaura]

Then what is DNA, if not a form of coding system?

Is somebody posting on this topic? It isn't me.

And if in nature some things follow a regular pattern, i.e. a natural form of coding system, have we not been able to translate these natural codes into the symbolic language of mathematics?

The only thing DNA codes for is the selection and arrangement and multiple production of strings of amino acids - none of which are even approximately fractals, afaik.

A fractal is not an abstract mathematical construct separated from reality.

From physical reality, the "natural" world.
Uh, yeah, it is. It most definitely is exactly that. All geometric objects are - Euclid often gets credit for the founding.

The Fibonacci sequence is a fractal pattern found throughout the universe.

? Now what ?

 

[Write4U]

I would rather call recognition of similar patterns at different scales and in different physical forms.

It is my impression you see a fractal as a single completed idealized abstract mathematical construct which has an arbitrary starting point but is continuously and infinitely repeatable.

But IMO, that's old school, and the concept and definition has broadened to include fractured and seemingly unrelated expressions of geometric forms and a host of other naturally occurring physical expressions, which have a common denominator of being a form of fractal expression, even as they do not occur as a single completed "string" of continual iterations. A fractal is not an abstract mathematical construct separated from reality. Fractals occur naturally in many forms. I posted a long list of areas where fractality and the fractal function is observable and quantifiable in many different no-theoretical, i.e. observable areas.

p.s. I never said its an exact science except from the purely abstract mathematical viewpoint.
p.p.s. All tested and peer reviewed abstract mathematical models and approximations are commonly acceptable by mainstreaim (consensus) science. What makes fractals so different? They have not yet been peer reviewed and tested? That's BS. They are used in RW applications with extraordinary efficiency.

 

[Write4U]

? What the hell ?

Look it up. It is an additive "loop" generated sequence, and therefore a fractal sequence.. Moreover it has a strong connection with Phi.
CDT is presented as

an approach to quantum gravity that like loop quantum gravity is background independent.

Perhaps you may want to dig deeper in the natural (as well as the metaphysical) properties and implications of fractal function and its implied and applied potentials.

 

[Write4U]

The only thing DNA codes for is the selection and arrangement and multiple production of strings of amino acids - none of which are even approximately fractals, afaik.

The DNA helix itself is a form of a fractal construct. Look it up.

 

[exchemist]

I would rather call recognition of similar patterns at different scales and in different physical forms.

It is my impression you see a fractal as a single completed idealized abstract mathematical construct which has an arbitrary starting point but is continuously and infinitely repeatable.

But IMO, that's old school, and the concept and definition has broadened to include fractured and seemingly unrelated expressions of geometric forms and a host of other naturally occurring physical expressions, which have a common denominator of being a form of fractal expression, even as they do not occur as a single completed "string" of continual iterations. A fractal is not an abstract mathematical construct separated from reality. Fractals occur naturally in many forms. I posted a long list of areas where fractality and the fractal function is observable and quantifiable in many different no-theoretical, i.e. observable areas.

Well, er, yes, I do.

I quote the Wiki article: " The general consensus is that theoretical fractals are infinitely self-similar, iterated, and detailed mathematical constructs having fractal dimensions...."

 

[iceaura]

The inability to make basic distinctions, or recognize the essential features and properties of fractals, is a strong argument against loose or casual use of the terminology.

Look it up. It is an additive "loop" generated sequence, and therefore a fractal sequence.

No. Stop talking like that.

The DNA helix itself is a form of a fractal construct.

The DNA helix is approximately a helix, not a fractal. It isn't even made of smaller helices of other things.

 

[exchemist]

The inability to make basic distinctions, or recognize the essential features and properties of fractals, is a strong argument against loose or casual use of the terminology.


No. Stop talking like that.

The DNA helix is approximately a helix, not a fractal. It isn't even made of smaller helices of other things.

I think he is talking about this: https://en.wikipedia.org/wiki/Fractal_globule

From reading it, it seems to me the term "fractal" is used a bit loosely, to denote self-similar folding patterns as the thing crumples up into a ball without any knots forming. But the mathematical references are not in fact to fractals but to the Hamilton Path and Peano Curve.

 

[Write4U]

Well, er, yes, I do.

I quote the Wiki article: " The general consensus is that theoretical fractals are infinitely self-similar, iterated, and detailed mathematical constructs having fractal dimensions...."

At the theoretical level I have no objections to that definition, after all it does fit with my perspective of a mathematical universe.

But the more I read about fractal functions, the wider the scope of interpretation seems to become as a physical phenomenon in nature itself. It seems to be applicable even in chaos theory, which appears to be completely counter intuitive to the purely mathematical definition. Some notable scientists/ mathematicians have called it a revolutionary new way of looking at natural phenomena. I know this does not necessarily make it so, but it does suggest that in some sense it is considered an important contribution to science, in both the metaphysical and practical sense.

Fractal Devices
Engineers are using the ideas of fractal geometry in a variety of applications. Often we are faced with a task that is similar to something that nature has already found a solution for. The idea of deriving inspiration for human designs from the natural world is called "biomimicry".
Here we will examine some engineered fractals that solve the challenge of fluid transport by copying the fractal patterns of our blood vessels and lungs.

As computers get smaller and faster, they generally produce more heat, which needs to be dissipated or else the computers will overheat and break. The smaller they are, the more this becomes a problem. Engineers at Oregon State University have developed fractal pattern that can be etched into a silicon chip to allow a cooling fluid (such as liquid nitrogen) to uniformly flow across the surface of the chip and keep it cool. The fractal pattern above derived from our blood vessels provides a simple low-pressure network to accomplish this task easily.

Fractal patterns can also be found in commercially available antennas, produced for applications such as cellphones and wifi systems by companies such as Fractenna in the US and Fractus in Europe. The self-similar structure of fractal antennas gives them the ability to receive and transmit over a range of frequencies, allowing powerful antennas to be made more compact.

Images courtesy of USPTO.

Cellphone with a Sierpinski Gasket antenna.
Image courtesy of Fractenna Inc..

Teaching computers to use mathematical processes to tell the difference between healthy lungs and lungs suffering from emphysema promises to help make faster, more reliable diagnoses. The fractal dimension of the lung appears to vary between healthy and sick lungs, potentially aiding in the automated detection of the disease.

There is more, but I believe these examples are pretty persuasive of practical RW applications of limited fractal constructs.

It seems that more and new uses for the fractal function are being discovered, in addition to the apparently infinite artistic expression that can be created from that simple equation.

I won't argue the subject any further, as other people may want to contribute to OP question from different perspectives.
I have hogged the thread long enough......please forgive. It's just a fascinating subject to me.

http://fractalfoundation.org/OFC/OFC-12-4.html

 

[exchemist]

At the theoretical level I have no objections to that definition, after all it does fit with my perspective of a mathematical universe.

But the more I read about fractal functions, the wider the scope of interpretation seems to become as a physical phenomenon in nature itself. It seems to be applicable even in chaos theory, which appears to be completely counter intuitive to the purely mathematical definition. Some notable scientists/ mathematicians have called it a revolutionary new way of looking at natural phenomena. I know this does not necessarily make it so, but it does suggest that in some sense it is considered an important contribution to science, in both the metaphysical and practical sense.

Images courtesy of USPTO.

Cellphone with a Sierpinski Gasket antenna.
Image courtesy of Fractenna Inc..

There is more, but I believe these examples are pretty persuasive of practical RW applications of limited fractal constructs.

It seems that more and new uses for the fractal function are being discovered, in addition to the apparently infinite artistic expression that can be created from that simple equation.

I won't argue the subject any further, as other people may want to contribute to OP question from different perspectives.
I have hogged the thread long enough......please forgive. It's just a fascinating subject to me.

http://fractalfoundation.org/OFC/OFC-12-4.html

To me, this has all the hallmarks of a concept that has become too trendy for its own good and whose definitions have thereby become corrupted by journalists and people wanting sexy write-ups for their research. It does happen, regrettably.

From the examples you give, it seems the term is coming to mean any pattern that roughly seems to repeat itself, at two or more scales of magnification. Thus it may be only a matter of time before some breathless idiot will claim that the universe is "fractal" because we have electrons going round atomic nuclei and planets going round stars. Remember folks, you read it here first!

 

[NotEinstein]

Please provide evidence for your claim.

http://fractalfoundation.org/OFC/OFC-12-1.html

and
http://www.academia.edu/Documents/in/Natural_Fractals

You have found a instance of the word fractal being used in a non-scientific context: this is a foundation’s website, not a scientific paper of any kind. The second doesn’t appear to have been published in a peer-reviewed magazine. But even so, it isn’t actually about fractals in nature, but self-organizing systems.

Also, I don’t see how this is relevant? I've already stated that many use the word in a sloppy manner that is incorrect. You finding more instances of that is neither here nor there.
​

And found in naturally occurring and recurring self similar patterns, including long term statistical patterns.
The Fibonacci sequence is a fractal pattern found throughout the universe.

But they are not actually fractals, as there is no infinite iterations involved.

The term itself is derived from the Latin word "frāctus" meaning "broken" or "fractured", and the concept of theoretical fractional dimensions has now been extended to include geometric patterns in nature and is now extensively used for practical application in a host of human created structures and organizing patterns.

​

I don't see how the etymology of the word has any bearing on the definition of it?
And the bold part is obviously not correct; see that Wikipedia quote.

Thus, by defining it as just an abstract model is a "limited" view, and therefore incomplete.

It being "limited" is neither here nor there. The definition is not incomplete. You are projecting your wishes what you want the term to mean onto it.

By NE's own statement, the meaning and usage of a word can change. He is right, the meaning of the word fractal has changed because it is too limiting in scope. I already cited that Mandelbrot himself broadened the definition. https://en.wikipedia.org/wiki/Benoit_Mandelbrot

​

(I'd appreciate it if you wrote my nickname out in full; the abbreviation is confusing.)
The very context of my statement was that Mandelbrot's usage of the term is not what scientists use today. So in one single statement, you acknowledge that I am right that words can change, yet you then turn around and say the term hasn't changed. You have removed the context of my statement to flip it around 180 degrees. That is intellectually dishonest, so please don’t do that.

 

[Write4U]

Thus it may be only a matter of time before some breathless idiot will claim that the universe is "fractal"

CDT does that already and is in process of being peer reviewed. I don't believe these scientists are "breathless idiots"...

As I understand it, so far the peer review has shown "promising results".

IMO, trying to climb Mt Everest is done by breathless idiots.........(kidding) . Seems to me constructing an exact fractal copy of the landscape of Mt Everest would be less risky and much more enjoyable from an artistic point of view.

But I have made my case as best I can and anything I could add at this time would be redundant and burdensome to others. I guess we'll just have to wait for further news from the scientific community which is actually studying the hypothesis, while the techs are busily constructing new gadgets based on the principle of fractality.

 

[river]

And since fractals are purely mathematical things, that's all that matters.


Keyword: features. They are not fractals, but fractal-like.

So there are no fractals in biology ?

 

[NotEinstein]

So there are no fractals in biology ?

Not as long as atomic theory still stands.

By the way, how is that list of brilliant BB critics coming along?

 

[exchemist]

CDT does that already and is in process of being peer reviewed. I don't believe these scientists are "breathless idiots"...

As I understand it, so far the peer review has shown "promising results".

IMO, trying to climb Mt Everest is done by breathless idiots.........(kidding) . Seems to me constructing an exact fractal copy of the landscape of Mt Everest would be less risky and much more enjoyable from an artistic point of view.

But I have made my case as best I can and anything I could add at this time would be redundant and burdensome to others. I guess we'll just have to wait for further news from the scientific community which is actually studying the hypothesis, while the techs are busily constructing new gadgets based on the principle of fractality.

CDT? Wot dat?

And what gadgets are constructed on the basis of "fractality"? Are there any? How do they work?