Why life isn’t like a Mandelbrot set

_{Vincent Torley

December 26, 2015

Intelligent Design

1}_{Categories
Intelligent Design}

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We’ve all heard about Mandelbrot sets – fantastically complex structures that can be created from a single equation and a very short program. Why, some people ask, couldn’t life be like that? And wouldn’t it be more mathematically elegant if it was? Physics types are especially prone to feel this way. Many of them might want to echo Louis IX’s famous remark on the Ptolemaic system, that if the Almighty had consulted him, he could have told Him a simpler way to make the cosmos.

I would ask these people to take a good look at the two pictures above. What I’m claiming is that life is not like a Mandelbrot set. It’s like an origami bull. The reason is that it embodies lots of instructions for making many different kinds of folded shapes (e.g. in proteins) which all work together. That’s why cell-based life cannot be simple. If you want to build simple life, make sure you don’t use proteins.

What do readers think?

Comments

@Aleta #3 'The Mandelbrot set, more than other mathematical entities, perhaps, brings up the difficult point about whether mathematics exist apart from our manifestations of it in abstract and visual systems.' Yes, I believe mathematics exists apart from our manifestations of it in abstract and visual systems - in the mind of God. Like Max Planck's atom, which inhabits a quantum world in which 'matter does not exist as such'. It seems to me difficult to escape the conclusion that God thinks abstractions and matter with equal facility.Axel_{December 27, 2015
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Thanks, KF! By the way, a correction to my post #13: "In a sense, it is more “objective” than prescriptive information," should be, obviously: "In a sense, it is more “objective” than descriptive information,"gpuccio_{December 27, 2015
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GP, Mung & VJT (Attn Aleta et al): Blurb at Amazon:
This is the second major work by this author (The First Gene: The Birth of Programming, Messaging and Formal Control) and it addresses the most fundamental questions remaining for life origin research: How did molecular evolution generate metabolic recipe and instructions using a representational symbol system? How did prebiotic nature set all of the many configurable switch-settings to integrate so many interdependent circuits? How did inanimate nature sequence nucleotides to spell instructions to the ribosomes on how to sequence amino acids into correctly folding protein molecular machines? How did nature then code these symbol-system instructions into Hamming block codes, to reduce noise pollution in the Shannon channel? What programmed the error-detection and error-correcting software that keeps life from quickly deteriorating into non-life from so many deleterious mutations? In short, which of the four known forces of physics organized and prescribed life into existence? Was it gravity? Was it the strong or weak nuclear force? Was it the electromagnetic force? How could any combination of these natural forces and force fields program decision nodes to prescribe future utility? Why and how would a prebiotic environment value, desire or seek to generate utility? Can chance and/or necessity (law) program or prescribe sophisticated biofunction? The most plaguing problem of life origin science remains: What programmed, in a prebiotic environment, the Primordial Prescription and Processing of such sophisticated, integrated biofunction? That is the subject of this book.
KFkairosfocus_{December 27, 2015
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Mung: Thank you for pointing to Abel's new book, I was not aware of it. I have just bought the Kindle version, and I will read it as soon as possible. :)gpuccio_{December 27, 2015
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Aleta: Abel's concepts of the two basic kinds of information are very simple and, IMO, powerful. In brief, as I understand it, I would say that specified information which is tied to design by conscious beings is essentially of two kinds: a) Descriptive information is the type of information which conveys a cognition, a meaning, through the designed object. The information must be understood by some conscious receiver,, and the meaning is then evoked in the consciousness of the receiver. b) Prescriptive information is the type of information which implements a function, through the designed object. In a sense, it is more "objective" than prescriptive information, because the function will be implemented without any need for a conscious receiver. However, the recognition of the function, which is a cognitive experience, always requires a conscious observer.gpuccio_{December 27, 2015
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Aleta: Very interesting thoughts. A few comments: a) The Mandelbrot set is a good example of how some (moderately) simple deterministic algorithm can generate forms which have the appearance of complexity and beauty. That's why some use it as an argument against ID. b) However, the type of complexity which is used in ID to infer design is completely different. For example, if we define functional complexity, the key point is the minimum number of bits which can implement some objectively defined function. If we find an object which implements some complex function, we infer design as the cause of the specific form of that object. c) I believe that the Mandelbrot set, as implemented in some material object (for example, a print of it) has some specified complexity, which corresponds at least to the minimum number of bits required to implement a program which can compute it. That is not a huge specified complexity, but it is not low. I believe that all the examples we know of Mandelbrots are designed. It is perfectly possible, however, that simpler fractals arise in natural systems (and they certainly do). d) Regarding your thoughts about the origin of the Mandelbrot set, you say: "I was once discussing with my calculus class the old philosophical question of whether mathematics is invented or discovered – does it or does it not exist apart from our, or some similar creature, having created a way to represent it." I am definitely a believer in the innate nature of mathematics, let's say the neo-platonic view of it, according for example to Penrose. In that sense, I think that mathematical objects are "discovered", but they are discovered in our mind, and then applied to the outer world. The way to represent a mathematical object like the Mandelbrot, however, is rather a beautiful example of design: functional complexity tied to a desired function in the consciousness of a designer, and implemented into material objects by the designer himself. e) Finally, I would mention that the concept of order from chance + necessity has found some support, for example in Prigogine and in the models of self-organizing structures. Again, while those concepts are interesting, they are completely different from the type of specified (functional) complexity that we observe in the biological world.gpuccio_{December 27, 2015
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Every analogy between computer models and evolution is flawed. http://bio-complexity.org/ojs/index.php/main/issue/current But perhaps life is just a Mandelbrot set of all Mandelbrot sets! But then again, perhaps the idea that a + b + c + d ... + n = life is flawed. If we can just find the right parts and plug them together in the right order... What is Life?Mung_{December 26, 2015
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"Below is a photo that has made its rounds on the Internet. It compares very, very small things to very, very big things." http://www.cracked.com/blog/5-reasons-you-should-be-excited-about-mars-today_p2/ The fractal universe (~6min): https://www.youtube.com/watch?v=zORy9nDsF18Jim Smith_{December 26, 2015
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Hi Aleta. I've heard many people argue that the example of the Mandelbrot set disproves (or weakens the case for) Intelligent Design: it shows that you can generate complexity in a very straightforward manner. See here: Intelligent design and evolution - Khan Academy, Wolfram's math disproves "intelligent design", and Why isn’t the Mandelbrot set evidence for design? by atheist Bradley Monton. The Skeptical Zone has put up some posts on the subject as well. What I'm arguing is that the comparison between Mandelbrot sets and living things is a flawed one.vjtorley_{December 26, 2015
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The physical universe is like a Mandelbrot set. It is defined by a few simple natural laws and constants. Life isn't. Life isn't explicitly defined by nature, it is not a "natural" consequence of the properties of the universe. Just like a computer program requires a designer even though the computer is a relatively simple device designed to run complex programs, so does life require design and creation before it will exist even though the universe is brilliantly designed to support life.Jim Smith_{December 26, 2015
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Mandelbrot SetMung_{December 26, 2015
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Dr. David L AbelMung_{December 26, 2015
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Hi Aleta, In the midst of everything else I'm juggling, I'm reading David L. Abel's Primordial Prescription. http://www.amazon.com/dp/B00XTG883I VJT says the bull "embodies lots of instructions for making many different kinds of folded shapes." According to Able, and this makes sense to me, instructions are not enough. You also need a system capable of understanding and executing the instructions. The figure in the OP of the Mandelbrot set is no different. The Mandelbrot set can be reduced to an algorithm. Why do you think of it as complex?Mung_{December 26, 2015
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And, Mung, can you explain the comment "Abel calls it prescription." Is Abel a mathematician, and what exactly is the "it" he calls prescription, and what is meant by tha?. Any explanation you could supply would be appreciated.Aleta_{December 26, 2015
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To Mung: the Mandelbrot set doesn't come from just an equation - perhaps you know that, but from a set of operations and rules applied iteratively to every point in the complex plane. You say, "I do see beauty though in the graphics, but those are by design." The Mandelbrot set, more than other mathematical entities, perhaps, brings up the difficult point about whether mathematics exist apart from our manifestations of it in abstract and visual systems. I was once discussing with my calculus class the old philosophical question of whether mathematics is invented or discovered - does it or does it not exist apart from our, or some similar creature, having created a way to represent it. I remember one of my students making a nice comment: she said that she thought math was discovered, but that we had to invent ways of writing about it to make that possible. So, yes, without modern computers, we could never even know the Mandelbrot set existed, in whatever way it might be said to exist apart from the computers that have made it possible to see it. It took not only centuries of math being developed but also the invention and development of computers in order for us to know that the Mandelbrot set exists. Did it exist before we did all that? That is the interesting question. I know that the Mandelbrot can be studied very formally without reference to the pictures, but I doubt we would ever have thought to do that exploration without the visual representations.Aleta_{December 26, 2015
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I've never heard anyone ask why life can't be like the Mandelbrot set, and I'm not sure what they might mean if they did? Can you explain, or point to such a person? I, too, am fascinated by the Mandelbrot set, and used to teach my senior high school students some about how it was generated, and what were some interesting principles tha arose from it. One observation one can draw is that a simple sets of rules (sort of simple, if you know how to operate with complex numbers) can produce such a complex figure, much less one that has a fractal nature. However, the Mandelbrot set is very different not only from life, but the world in general is that it is determined: there is no contingency involved at all. Most people (I have no idea if there are really strict determinists these day) understand the world to have contingent factors, such that the state of the universe right now does not logically and irrevocably mean that the universe is going to be a particular state in the next moment, much less in a milion years. So in that sense, the Mandelbrot set wouldn't be a good model for how life, or any other component of the universe, came to be. But it is very neat!Aleta_{December 26, 2015
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Hi vjt. First link is broken. I love fractals. Abel calls it prescription. It's true life is not like a Mandelbrot set. Perhaps a mathematician can see the beauty in the equation, I can't. I do see beauty though in the graphics, but those are by design. ;)Mung_{December 26, 2015
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