In the case of the mandelbrot set. The answer to "What causes the complexity?" is "The work done iterating the formula". It's not a nightmare. It shows us that the beauty and complexity we see in the word around us can arise from a few simple rules.

As an Atheist, I am fascinated by the Mandelbrot! Not even close to a nightmare!

I'm an atheist. I have no idea why this was recommended to me, but it was a very good, entertaining, educational and non-condescending presentation on a series of complex topics. At least until the way it got to religion - you're right that atheist mathematicians/scientists don't understand everything, but to most of us that's the joy of science. To be on the very edge of understanding and not understanding. Religious differences nevertheless, great presentation, thank you.

Einstein once said the most interesting question is whether God had a choice. He saw that the more we learn about the Universe, the more we can explain about it arising automatically from simple rules. And these simple rules are themselves not arbitrarily chosen, but are just what they are because there is no other way they could possibly be and still make sense! This video has successfully illustrated the point, that the more we learn about the Universe, the less room there is for a God to make up rules. All the rules we have found arise by themselves out of nothing more than examining what is logically consistent. This is really the absolute minimum assumption we can make by the way. To assume that a thing must be logically consistent with itself to be able to exist is the weakest demand we can make. And if that turns out to be ENOUGH to explain all that exists, then religion really has nothing to offer in the matter. And so the atheist position is strengthened, not diminished. Because if everything arises naturally out of the demands for logical consistency, then the only room left for God is to "push the button" that makes the Universe exist, but there is nothing he can do about the process to shape it in any way. Such a God is of course still a logical possibility, but it's not a very interesting God, and it most certainly is nothing like the Christian idea of God. PS I'm not an atheist. I think God is consciousness, and we are part of God, since we have consciousness. The miracle is us, not the Universe. The Universe just is what it must be to exist. But _we_ are magical! Consciousness is magical. It didn't need to exist, but it does. Logic has nothign to say about consciousness. Science can't grasp it. And yet, here we are. It's the mystery of Life itself. THAT is what religion is about, and this video's attempt to shoehorn religion into the realms of science and logic is both counterproductive and ridiculous.

Now I believe in Math, thank you.

As an atheist I have always liked mandelbrot set since I first learned about it. It still hasn't given me any nightmares...

im an atheist with a degree in mathematics and i often find that this argument is self-detrimental as it provides an example of astonishing complexity that arises from an extremely simple basis. If you have an understanding of the mathematics behind the mandelbrot set I would like to know which step along the way is the one in which god steps in

I"m an atheist and the mandelbrot set gives me night terrors. I wake up in cold sweats. 🙄

I have to admit, if you ignore the fallacious reasoning and logical leaps for the last 10 minutes or so, this man did an amazing job explaining sets, complex numbers, fractals, and the Mandelbrot Set. Good job!

As a Christian, I don't think this is "scary" to atheists, or somehow conclusively proves the existence of God. It is some really cool math though, and I personally believe it adds to the glory of God, but I don't see how an atheist couldn't just be like "yeah. that's math." Nice, funny, cool sermon!

As soon as you plot a graph you have brought the conceptual into the physical. An incremental formula using negative values to infinity creating a pattern that is infinitely smaller and infinitely beautiful is no nightmare. Thank you for confirming to me there is beauty in everything.

Great lecture on Mandelbrot set until the sudden 13:50 jump to "god's understanding is infinite". In other words "the Mandelbrot set is amazing - therefore biblical god loves you." My man, in that case, there is a whole bag of lectures in between completely missing. Lots of work ahead 🙂

The truth is always more crazy than the craziest predictions. Math looks boring because of school, but it's implications are absolutely mind-boggling.

The Mandelbrot is the greatest fractal formula ever written. Every time I use a Mandelbrot formula for my fractal art, I'm never let down.

Lisle explains the Mandelbrot set very eloquently and without requiring the audience to know much math at all. As an allegory for the mind of God, I think the Mandelbrot set serves perfectly. It is infinitely complex in the literal sense that it would require infinite resources to render in its entirety and it represents a certain blend of repetition and unpredictability that makes it particularly beautiful. Really, though, it does not serve as an argument for God. There are so many fractals like this and it's pretty easy to come up with new ones on your own, and there are other systems such as the Lorentz Butterfly that are similar in their beauty. The Mandelbulb is another good example, a 3D generalization of the Mandelbrot that was invented in a fractal rendering forum. These things are all beautiful for the reasons mentioned above, but they are even more beautiful because their complexity emerges from such simple rules. That doesn't show God at all, it only demonstrates the property of emergence. It also makes sense that a mathematical equation would give rise to mathematical properties (the cardioid, circles, counting, etc.) It also isn't a "code" by any reasonable definition, I really don't understand how that word is meant to be interpreted here. The Mandelbrot conveys no knowledge that isn't required to make the thing, and doesn't encode any wisdom beyond counting, adding, and so on. It is a fascinating thing to study the properties of, but that's about it. To the contrary, I find its demonstration of emergence to be an excellent counter to the mind-body dualism which Christians often presuppose (and then go on to argue that their god offers the best explanation for). With the Mandelbrot, we see that complex properties sometimes emerge naturally from a simple system. Our consciousnesses, then, may also have emerged rather than requiring some external soul or agent to explain. It isn't a proof of physicalism, but it's a good way to explain emergence as a hypothesis for how our minds came into existence. If you want to use the Mandelbrot as a metaphor for the mind of God, then do that. I completely understand, it's a beautiful metaphor. Please don't call it an "atheist's nightmare", though. It makes no sense.

The universe does not inherently obey mathematical laws; rather, the physical world has an intrinsic behavior that we have learned to describe using the language of mathematics. Referring to these descriptions as 'laws' is a misnomer, as the universe is not governed by our mathematical constructs. Instead, we stumbled upon numerical patterns and scenarios that closely resemble and model the behavior we observe in the universe as we explored and played with numbers over time.

There's really nothing nightmarish about the Mandelbrot set but it's sheer beauty as we stare into infinity.

“Mathematical concepts were not created, they were discovered.”

There's some incredible beauty in math for sure, but while I cannot rule out a "designer" of the mandelbrot set, all of math is connected. You cannot invent only the mandelbrot set without also inventing the notion of complex numbers, squaring, and adding. To paint the beauty of the mandelbrot set is to also paint all the dull or chaotic parts of math with seemingly no pattern. Really, there's just patterns everywhere and it's up to you decide which to enjoy. It's not beautiful because God created it for us, it is beautiful because we ignored all the patterns that weren't.

As an athiest , i must say that this isn't my worst nightmare. This is pure beauty and just reaffirms my strong beliefs in aliens. ❤

"Augustine was right when he said that we love the truth when it enlightens us, but we hate it when it convicts us." - Norman L. Geisler

I was an atheist and now I'm a mathematician after this video

as a Christian, i agree. however, this argument only really works if it's viewed using a Christian mindset.

This is a nightmare in that we get to observe individuals wholeheartedly discount high, yet rational, complexity, to the whim of a deity simply because the human mind finds it difficult to comprehend. The nightmare is knowing that people are inflicting this abject deism on other people throughout societies, guiding policy and lawmaking, and subjugating people to their own narrow band of "belief."

It's not scary, it's beauty and wonder

Ignoring the jumps to religion, this is genuinely a _great_ lecture on the Mandelbrot set and the beauty of mathematics.

I'm always impressed with the sheer ubris of religious believers, having the guts to declare they know it all, believing everything, without questioning, written in a book hundreds years ago. Mathematics is the product of the human mind. Its basic principles are simple, and from this simplicity comes the, still not well undestrood, idea of complexity and, let alone, beauty. Physics builds theories on maths, and the laws of Nature seem to agree with that. Problem is that these theories are an approximation and we will never achieve perfect laws of Nature (a theory must be falsifiable). The fact that math now works does not tell us anything about the future. These laws may change, and they may change randomly. We seem to live in a stable gap of laws, hence the growing complexity and life. From life, mind. From mind, math and, sadly, god.

The guy ironically showed that infinite complexity can arise from a simple rule(s), as per evolution, crystallisation, snowflake formation etc. It's the opposite of what the god hypothesis says: "That complexity must arise from further complexity". Own goal.

If a fractal is an atheists' worst nightmare then we truly have nothing to worry about.

The Mandelbrot set was discovered because mathematicians like doing math for fun. There's a lot of things like this

I had to laugh at the title of this. My maths tutor daughter, a confirmed atheist, is especially keen on the Mandelbrot set.

“Somehow the Mandelbrot set knows how to count”😦😦

This is possibly my favorite "atheists can't explain this" argument I've heard so far, both because they're making this argument completely seriously, and because the Mandelbrot Set is such a beautiful example of structure and complexity arising naturally without a need for a god.

he literally demonstarted how a random simplest formula given enough time can give rise to infinitley complex structures i think he destroyed his own asssumtion that complexity must come from a complex designer and this is a video every atheist must watch

I remember when this formula came out. Later, in the early days of PCs, I remember software that would calculate these plots for Mandelbrot sets and for Julia sets. It took longer, and the images were pixelated compared to the images in this video because of the quality of graphic cards of the time.

The fact that we can construct formulae that create interesting and infinite patterns when plotted on a graph does not prove or disprove the existence of a god. If you're convinced it proves there's a god, which god would that be? You not only conclude that math proves there's a god, but it somehow proves that it's the christian version of god. What do you think you would have concluded if you had been born and raised in a country that was predominantly islamic, or hindu, or any other religion? Is there room in your mind for a universal god for everyone, or just _your_ particular notion of god?

"If I can't explain it, God did it"

"I barely understand this, therefore magic. And its beautiful, therefore supernatural cause." Something complex isn't by definition magical.

12:35 "It knows how to count". No, it does not. It is literally like saying "the three stones lying on the ground next to each other know how to count to three". I know he might be using this figuratively, but this is exactly how it gets wrongly assigned to some "higher being" that can count to infinity = is infinite itself = listens to my prayers = etc etc.

The mandelbrot set is fascinating. As a computer scientist I've made my own version of the software this guy is using. That being said, I'm an atheist and it's no mystery why these patterns appear in nature. Fractals appear in nature because they maximize surface area with minimum amount of encoding(DNA). They're naturally selected to be as efficient as possible. I.e. how the infinitely complex shape of the mandelbrot set can be described with a single line of math.

People who understand mathematics have no problem with this. I had a spirograph. It was like magic, but explained with math, too.

"Imaginary" numbers is not the original term for them, instead they were called "lateral" numbers. The term "imaginary" was utilized by Descarte, who was a critic of the concept.

This clearly displays the depth and eternal magnitude of "The Author" of life. What is even more fascinating is that THIS portion being presented is but a very miniscule peek at who the Almighty Creator is. Atheists would do well to put their prideful ignorance aside and recognize God's magnificence and holiness. "For what shall it profit a man, to gain the whole world, and lose his eternal soul?" Mark8:36 "It is the fool who will say in his heart, "There is no God." PS14:1

Tackling just one point that sort of represents the whole thing: "The secular worldview cannot account for why the physical universe obeys mathematics." is conceptually false in multiple ways. The physical universe does not "obey" mathematics. Mathematics was created by people to describe the universe. Which exactly fits with the secular worldview. Why does their need to be a "why"? You only need "why" if you can't accept reality as it is in all its magnificent mix of complexity and simplicity. If you don't get what I mean then you need to examine both fractals and reality in more detail.

Eight minutes in, I am reminded why I dropped math, and spent the last three years of high school learning business math which I use every time I balance my checkbook.

So, first of all, math is not the study of numbers, though it may have started as such. The speaker lost all credibility when he stated that it's a miracle (and, btw, Wigner's "miracle" was more of a manifestation of geekly awe rather than "wow, there's no natural explanation for this") that math describes the physical world. It's actually worked the other way. When setting up the foundation of Euclidean geometry, for example, it was postulated that there's only one line going through a point that will never meet another line (which doesn't contain the point). Why? Because the physical evidence pointed to that being a law of the universe. Mathematical axioms (and all math is built on axioms) are statements accepted as true, and all the math is built on them. The axioms are sometimes adopted as fitting the pysical reality, sometimes not so much (math can diverge a lot from physical reality if it cares to). Plus, most modern math has played catch up with science (math is not science, it is the quantitative language of science), especially Physics. Some dude didn't like the loose way physicists were computing new things and put some order in all that. So, math does describe the physical world inasmuch as the adopted axiomatics does.

mathematical identities follow by logical necessity. 1+1 equals 2 in virtue of the identity of the terms. what is equals (=)? an operator which takes two or more parameters and yields a truth indicating if its arguments represent the same entity. what is addition (+) (and multiplication (×))? binary operations on a set which satisfy at least some of following axioms: 1. there is a 0 such that for all x, x+0=x. (addition identity) 2. for all x and y, x+y=y+x. (addition commutativity) 3. for all x, y and z, x+(y+z)=(x+y)+z. (addition associativity) 4. for all x, there exists a (-x) such that x+(-x)=0. (inverse element addition) 5. there is a 1 such that for all x, x×1=x. (multiplication identity) 6. for all x and y, x×y=y×x. (multiplication commutativity) 7. for all x, y and z, x×(y×z)=(x×y)×z. (multiplication commutativity). 8. for all x, iff x is different from 0, then there exists a y such that x×y=1. (multiplication inverse element) 9. for all x, y and z, x×(y+z)=(x×y)+(x×y). (distributive property) what is 2? if it exists, a number which satifies the following equation, for all x: 2×x=x+x. let's suppose that 1+1 indeed equals 2. then i can substitute it in the equation above: 2×x=x+x (1+1)×x=x×x applying some of the axioms above, we can see that this expression is trivially true: (1+1)×x=x+x x×(1+1)=x+x (x×1)+(x×1)=x+x x+x=x+x it is inconsistent for 1+1 not be equal to 2, hence necessary that 1+1=2.

Dude literally woke up one day and said he understood God’s mind

Here's a sumary of the content with timestamps, for those who want to see either the mathematics, the fractal or his philosophic interpretation thereof. (I tried to keep it neutral) 0:00-1:24 Proposition that there's a secret code built into numbers by god 1:24-10:35 introduction to necessary mathematical concepts needed to generate the fractal images in question 10:35-13:49 some interesting geometric properties of the Mandelbrot fractal 13:49-15:25 claim that the infinity of a gods mind is necessary for the infinite complexity of the fractal 15:25-19:53 exploration of some visually appealing regions of the fractal 19:53-20:14 claim that the beauty of the fractal must have been encrypted in the underlying mathematics by god 20:14-21:57 effects of changing the formula on the appearance of the fractal 21:57-29:00 Secularists are unable to explain why there is beauty or infintite complexity in the fractal, as opposed to christians... 29:00-33:25 examples of proximate fractals in the pysical world similar to fractals in mathematics. 33:25-38:24 Secular people are unable to explain why the physical universe obeys mathematical laws, as opposed to christians... Now the critical summary: The mathematical buildup sounded aptly designed for the audience, average citizens that only have rudimentary mathematical knowledge that is. Well done on that part. The exploration of the fractal itself was interesting as well and had some nice variety. But the rest is just the same old storye as always: Claiming, sometimes rightfully so, that secularists don't have the answer to some deep question (Why X?) only to answer it along the lines of: Because the christian god made the world such that X! One couldn't hope for an answer less lazy than this... Or less helpfull for that matter...

Trying to prove the unscientific with science, the illogical with logic. That's the way to go. NOT! Thanks for your hard work in further reinforcing my atheistic worldview.

Firstly, 1:23 a set is NOT a group (of numbers)! A group is a set together with a binary function/operator (*) which together satisfy the following properties: 1. For all elements x, y, z in the set: (x*y)*z = x*(y*z) 2. There exists an element e in the set such that for any element for: x * e = x, we call that the identity element (also often 0 or 1 depending on your operator) 3. Each element x has an inverse x^-1: x * x^-1 = e 4. The set is closed over *, which means that for every x, y, in the set there exists a z also in that set such that x * y = z Secondly, 1:42, ALL sets have to be well defined. Maybe youc ant compute that for specific numbers, but still an elemnent is ALWAYS included or excluded in a distinct way. If you cant tell by "looking", well thats a skill issue i guess, doesnt make that set more or less special. Maths isnt concerned by what you can do in your head vs what you need a calculator for Thirdly, imaginary numbers were INVENTED simply because the "god given numbers" didnt work in that case. if the square root if -1 is given by god, then so are vacuum cleaners and atomic bombs. For me that shows that the mandelbrot is an example for there being no corelation between maths and an omnipotent being Fourth, 11:49 "the mandelbrot set knows how to count" this is just a plot of the set. a visual interpretation. the set, and certainly not its plot, are not sentient and dont "know" anything. guess ill worship the mandelbrot set now cause it is sentient and smart. Now, why does it "know" how to count? Because its made up of numbers! If you construct something from numbers, its gonna have numeric properties, easy as that. Fifth, 22:47 why is the fractal god made and the color scheme manmade? why didnt god think of that color scheme when he thought of that set? Why did we not pick that formula the same way we picked those colors, why is one from god and the other isnt? 23:26 regardless of whether the computer plotted this or us by hand - we plotted it, not god. we wrote the code, we built the computers, we did the calculations 25:00 what causes the complexity? its chaos theory. small nudges to input give great differences in output

That is not called "worst nightmare", that is called emergance

“Atheists don’t have the answers” math and creation arguments aside, we never pretended to have all the answers. We have theories, but everything could theoretically switch based on evidence

An atheist mathematician's take on this: I enjoyed his presentation of the Mandelbrot set, very well done. His conclusions, however, seems like leaps of faith (pun intended). To me, it seems that the main questions of the talk are (1) where does math come from? and (2) Why do mathematical objects occur (approximately) in the physical world? I will try to answer these more fully, and show how Lisle's conclusion that there must be an intelligent creator is flawed. (1) For the first question, Lisle quickly concludes that math cannot come from humans, since if it did, we could have invented it differently, and "2+2=5" would not work well for an architect. A different system would not be "true to reality". Immediately, this clashes against his statements later, that math exists "in the mind", but I'll ignore that for now. Since he requires that any mathematical system must fit reality, it is clear that Lisle is already assuming that our current system of mathematics fits reality perfectly, and that this is his basis for his argument. But this is false. To make a very long story short, our current system of mathematics has changed (or "evolved", if you will) for at least the last couple thousand years, mostly because people kept trying to use their intuition, that they gained from nature, in mathematics, but it turned out that mathematics was more complicated than nature. As examples, look up the parallel postulate, or the Weierstrass function. It would be naïve to assume that this could never happen again in some form. One could then say that our mathematical systems are man-made, therefore fallible, and we are simply approaching *the* mathematical system that God intended. However, this still has a major flaw. Perhaps the most famous meta-mathematical results in history are those of Gödel's incompleteness theorems. Very roughly, they say that in any mathematical system which is complex enough to contain arithmetic, one of two things must be true: EITHER the system is paradoxical, OR the system is incomplete. Let me explain what this means. A paradoxical system is a system in which a statement can be true and false at the same time. Such a system is completely worthless, since you can prove that if one thing is both true and false, ALL STATEMENTS must be both true and false. In reality we have a strong sense of the law of excluded middle; which is just a fancy name for the fact that a thing is true OR false and never both. Thus, a paradoxical system could never describe reality. An incomplete system is a system which can formulate statements that are NEITHER true NOR false. It's not that we aren't good enough at our attempts to prove/disprove them - their truth value is independent of the system. In fact, it has been proven using logic (even more fundamental than mathematics) that our current most popular system of mathematics is incomplete: in the system called ZF, there is a statement called "axiom of choice" which is independent of ZF, i.e. it is neither true nor false*. But this contradicts our view of reality and the law of excluded middle again. A statement (that makes sense) is either true or it is false. For example, the statement "there exists intelligent life outside of earth" is a well-formed question, and for any given time, the statement is either true or false - never something in between. Conclusion being, no mathematical system will ever describe reality perfectly. Saying that God thinks mathematically seems very rude, since then God's mind is either paradoxical or incomplete. (2) For the second question, Lisle uses Dr. Eugene Wigner as a strawman for non-christian viewpoints. Dr. Wigner was an excellent physicist and mathematician, but he is no philosopher, and his claims that it is miraculous that the physical world obeys mathematical laws, and that we have the capacity to understand them, are not true. Also, his article is now ~60 years old, and philosophy has advanced a lot since then. There are many ways to explain this, but I will stick to one: bias. The argument very often presented, and very heavily presented by Lisle, is that of "look at this marvelous, intricate thing! THIS must be an example of an intelligent creator!", in the above case, the thing is the Mandelbrot set. But this is a biased argument: there exists such a multitude of things in the universe that, simply statistically, some of them are very likely to be extremely complex/beautiful/whatever. By cherry picking the ones you like, you make it seem like this intricacy is everywhere in the universe - but you will never have someone explain to you why iron ore, or the beak of a bird, or air molecules is an example of intelligent design. The argument made by Dr. Wigner in his article is much better, since it seems that mathematics are able to model many different aspects of science simultaneously, and gives incredible results and beautiful simplicity in otherwise chaotic situations. While this is fascinating, it does not have to be a miracle. Firstly, Dr. Wigner's conclusion is biased implicitly by the questions they ask, and how mathematics was shaped. Mathematics has throughout the ages been developed to help answer questions in science, particularly in physics. Mathematics do not exist independently of sciences, and suddenly being surprised that math is good at explaining science seems unreasonable. Also, mathematics and science has a symbiotic relationship, in that questions in one area motivates research in the other area, and new developments in one allows us to ask new questions in the other. Thus, math has also been part of shaping what questions we are even interested in in the sciences, so again we should not be surprised that math is great at solving them. One could imagine that another system than mathematics might have been better at explaining other things - such as how our brains work, what the better political system is, or any other question that we might regard as slightly "non-mathematical". Even if mathematics is truly excellent at describing all aspects of the universe, there is still one hidden bias, called the anthropic principle. In short, it says that for any question we ask, there is a bias that there has to be intelligent life for anyone to even ask the question. It seems so obvious that it is silly, but it is key to understanding our universe. Saying "why is the universe the way it is?" seems an objective question, but it is always biased by the fact that the universe must exist in such a way as to support intelligent life for the question to be asked. Thus, if we take a frequentist's point of view, one could imagine a million universes, and only one of them capable of supporting intelligent life. Let us for the sake of example say that this single universe can support life because it is warm. Then, intelligent life in that universe could reasonably ask "why is the universe so warm, when it seems unlikely to be so?" Well, it is warm exactly because WE LIVE THERE. This question would not be asked in any other universe, because there is no life to ask it. Similarly, one could imagine that the question "why is mathematics so good at describing reality?" has a similar answer: A mathematical universe is required, for some reason or another, to support intelligent life. It does not have to be created by God, but simply by statistics. (*) mathematician's sidenote: even if you accept ZFC, there are still inaccessible cardinals, and so on.

This is a grate maths lesson if nothing else, and if only it was done this way when I was at college, reminds me to brush up on my calculus!!

Ah, I see now: IF Mandelbrot Set THEREFORE New Testament. How could could I have missed this obvious connection.

this was filled other bizarre and unfounded lines, for me at least, such as: “it makes this very unexpected pattern” and “somehow it knows how to count, that’s kind of remarkable” his entire speech so far (i’m not finished) has been filled with assertions of hidden and surprising meaning, all of which have so far just seemed like normal math.

This is a comedic masterpiece, I laughed all the way through!

Mathematics is a conceptual language, a human creation which arises from the human tendency to look for patterns, which is something our brains have evolved to do. But all the mathematical laws in physics e.g. Kepler's laws, are the best approximate descriptions we can find to describe things we observe in the world, until they are replaced by a better approximation, like Einstein's general relativity. Really we have a patchwork of different physical theories that describe different aspects of the physical world to a lesser or greater extent depending on the context. It does not prove the existence of an intelligent creator, it just shows that we have evolved to be rather clever at creating mental models that give an accurate picture of what we experience. If you study mathematics, especially mathematical logic, then you will find there are different choices of axioms for set theory, and certain statements can be consistent or inconsistent depending on what axioms you start with. Also, there are many different choices of number systems: the number pi makes sense in the real numbers, but there are other number systems (finite fields, p-adic numbers, etc.) where pi doesn't exist. Assuming that physical space is a real continuum is something we have been doing at least since Euclid, but there's no reason why this must be true (especially at the quantum level).

Everyone is like; "Ooh, aah- it goes on forever...", and; "it's so pretty!" But no-one is seeing the big message inherent in this formula and it's pattern, namely; that infinity can, and does exist in the natural order. The Mandelbrot Set shows us that an infinite universe is not only possible, but probable! This Set is one of the answers we are seeking, all we have to do is ask the right questions to make it fit.

I like how he shows complexity arising from a simple process as a case for creationism.

This is only the tip of the iceberg of what God made and who He is. Even eternity will not be enough for us finite beings to even begin to understand an infinite, omnipotent, omniscient God!

The statement "The mathematics of sets and logic are not infinite" was made by Kurt Gödel in his famous paper titled "On Formally Undecidable Propositions of Principia Mathematica and Related Systems I". In this paper, he introduced the concept of undecidability, which showed that there are mathematical statements that cannot be proven true or false within certain formal systems.

The Mandelbrot set is an iterative ordered set, and not the only one. In fact there's an infinite number of them. There is also an infinite number of non-iterative ordered sets, which are ones whose Nth member is a function of N. In iterative sets, the value of the Nth member is a function of N-1.

The subject area of mathematics itself is interesting. There are so many different areas of mathematics that you can study. I prefer Abstract Algebra and Topology, but I studied Differential Geometry, Real Analysis, Complex Analysis, Differential Equations, Number Theory, and more. There is no highest level of mathematics. Each branch of mathematics may have a highest level, but they all branch off from the basic mathematics found in high school and the first year of college. When we prove something new in mathematics, we are really discovering a new property. We are not inventing the property. We may "invent" the notation or definition, but we discover the properties. I wish that high school students saw more of the beauty of mathematics. By the time some of them are in college, they truly hate mathematics and find it boring.

I think if I had a hotdog cart it would be fun to have a Mandel Brat that allowed for infinite variations in basically the same toppings. I'd call it the Barbara Mandel but she's really a Mandrell so I'd go with Howie Mandel because it's my hotdog cart and I could say "And Howie havin' it?" when I scribble down their order and then mess it up like real life.

I'm an atheist and have been studying and enjoying the beauty of fractal graphics since the discovery of the Mandlebrot set. It in no way challenges my secular appreciation of the world. No more than the beauty of DNA or the beauty of a sunset. Our ability to see beauty is just a primate brain evolutionary strategy that has worked for us.

This is hilarious considering that the Mandelbrot set actually proves that complexity arises not by design but as a natural consequence of the interaction of simple components. 😂

So because there's a pattern in a set of functions the abrahamitic god exists? What else than patterns does a theist expect to find in fractals?

Another way to visualize eternity (infinity in mathematical terminology) is simply to look up. The sky has never looked exactly as it does today; each day features a unique sky with large fluffy clouds, with high cirrus, etc., and those are always unique. It is as though God provides a new and unique vista for each day. And it's all for our own enjoyment; all we have to do is look up at least once per day.

We can get you can zoom in infinitely. If you zoom out does it mean this would be the end of it?

It is true that the mandelbrot set needs divine explanation. Therefore it is valid to state that the Spaghetti Monster (sauce be with him) made this all.

“There is no atheistic explanation…” An “explanation” is a causal sequence leading to an outcome. That’s literally what an explanation IS. “God did it” is not an explanation, it’s a supernatural claim that, by definition, denies causation. The precise moment you claim faith as an answer to ANYTHING, you’ve epistemologically ejected yourself from any conversation about explanations. “What if there was a code…” Of what use, then, is your faith? If faith is important, why do you have such an acute interest in codes? If the code is demonstrably a code, why does the Bible exhort you to focus on faith? Where in the Bible does it tell people to be convicted on the basis of claims of mathematical evidence? If you want coded instruction, you’re not interested in faith. If you want explanation, you’re demanding cause and effect.

2+2 = 5 if you have a high value for 2. 2.4+2.4 =5 with rounding. But rounding 2.4 is 2. I might think about numbers differently than the speaker but I do think he makes some fun points about set. Fun watch.

Not an atheist, but I am agnostic. Really appreciated the way he explained the set. Mathematically and logically. This is not an athiests nightmare.

"Humans are pattern seeking story telling animals and we are pretty adept at telling stories about patterns whether they exist or not" -Michael Shermer.

The "message" or meaning isn't embedded in numbers, it's in the functions/algorithms which were intelligently designed by humans. There are an infinite number of sets/functions, of which the Mandelbrot is just a single one...which we intelligently picked because we like the output.

The main error in the reasoning is where he says at 26:26 that "Numbers are abstract in nature, not physical." This is in fact wrong... We could totally assume that numbers arises from the repetition of discrete observations (3 sheeps, 3 stones, 3 trees, etc). So this may have its roots via bayesian induction performed by the brain.

And because "spirit" arises from simple and at the same time complex structures, this is one of the most important indications that philosophical schools of thought that rely on physicality are the right approach. "Emergence" is the key word. There is no god. And if there are gods, then they would be my enemies because they want to interfere in my life unasked and uninvited. Religion did not arise so that man could be good. It came about because people are good and want to achieve good things.

Many people have the mistaken idea that God manifests his design only in complexity but in point of fact the real astonishing genius of God is in bringing infinite complexity unfolded out of the most perfect elegant indeed wondrous simplicity.

I was an agnostic and God revealed himself to me with this. I had no idea what it was. It was profound. I knew there was a creator after I saw it in my head. It sent me on a mission to see what it was about. Praise God

This shows that it always was and is there... No matter how much u go back or forward. Kind of like... the law of conservation of energy says that energy is neither created nor destroyed. This does not prove god.

When we align our thoughts with the will and thoughts of God, the things we think become possible. Hebrews 11:1, "Now faith is the substance of things hoped for, the evidence of things not seen." When we begin to think like him, we can have faith, because we see that the things he thinks come into existence in the physical world.

"Atheists BEWARE!!!! We discovered this mathematical phenomena and we can't explain it which means its direct proof of god's existence! Checkmate atheists!"

Thanks for this video. I was fascinated with Benoit Mendelbrot, the Mandelbrot set and fractal geometry in the early 1980s.

i love this channel, its so much better comedy than most comedians, like this guy definitely chose the wrong career path

The physical universe has infinite complexity but in its complex manifestation it is finite. That finite interaction creates the complexity which we sentient beings battle to investigate and understand. As a mathematician and physicist I think Slartibartfast has the right answer... "I'd much rather be happy than right any-day".

It's a nightmare how you can't accept that you can't prove God's existence with arguments

The clickbait title cracks me up. Implying that atheists' as a group don't want to find the answers.

This and how the frequency of the stars sing are beyond understanding- what a great and wonderful God we serve.

It's sad seeing an intelligent person decide that "it's beautiful, complex and infinite, so it's god" instead of just keep learning about math and patterns and the beauty of never settle for an unexplained mystical entity. Keep learning. Keep exploring. Keep knowing. Faith is a stop.

I remember being excited about Mandelbrot sets in the mid 1980's, when it took 3 days to generate the set on my IBM PC, which if I remember correctly used a 286 chip with a floating point coprocessor. Back then this might have been interesting. 40 years on, his whole presentation feels very dated, like teenagers smoking pot and discussing if the universe is expanding, what is it expanding into. It sounds to them like it is meaningful, but it misses the whole point. I have one big nit to pick with Dr. Lisle. The Dr. Lisle thinks he is arguing a "Christian World View", but he is actually arguing for a "Theistic World View". He is arguing that mathematics proves God. Even if the point on the existence of God was given to him, it does not prove a "Christian World View". He is like most Christians, looking for something to back up his beliefs, even if the argument is flawed. As for math and existence of God, one only need look to the Pythagoreans. The Pythagoreans believed that God had ordered creation with numbers, and that all numbers were expressible by ratios of two whole numbers (e.g. rational numbers). Bad things happened to Hippasus who had the temerity to discover irrational numbers. This talk sounds like Dr. Lisle has a bit of a Pythagorean streak in him.

The Mandelbrot Set was first defined and drawn by Robert W. Brooks and Peter Matelski in 1978, as part of a study of Kleinian groups. Afterwards, in 1980, Benoit Mandelbrot obtained high quality visualizations of the set while working at IBM's Thomas J. Watson Research Center in Yorktown Heights, New York.

He does a good job of explaining the Mandelbroth Set and complex numbers, but neither the Christian world view nor theism is necessary to make sense of patterns in numbers.

Despite the fallacies of the ending, the whole video and the animations were pretty nice! And the information was correct for most of the video

I really appreciated the first mathematical part. Great pedagogy. For the rest, to bring smthg to that issue of the effectiveness of maths and so, I will only quote another brilliant mathematician : "Nothing takes place in the world whose meaning is not that of some maximum or minimum."(Euler, btw)

I'm an athiest and I must say, this is by far my favorite argument for creationism that I've seen so far. We need more teachers who can find the beauty in math the way Dr. Lisle does! That being said, I do have a criticism that I want to address. The fractals that Dr. Lisle identifies in nature aren't actual fractals. For example, if you tried to infinitely zoom in on a fern, you wouldn't keep finding tinier and tinier leaves -- you'd eventually hit cells and other things that don't resemble the original shape.

It is not just math it is also consciousness. We have five senses for experiencing, a sense mind for processing experience, and an intellect that ranges far beyond our environment to the further reaches of space; awareness through consciousness. All that is amazing,, and in addition, all based on a spark of light that is unique to each of us a wonderful gift that connects us with the elemental forces of nature. The stage was set for us with oxygen and water when we arrived. We should treat nature and animals better, they are for our use, not for our abuse based on greed or entitlement.

The statement that that the Mandelbrot set reflects nature and that therefore nature obeys math and that therefore god must exist, can easily be disproved: The Mandelbrot set is inherently deterministic, and nature is inherently non-deterministic.

The Mandelbrot set, involving simple relationships carried to sufficient extremes, is remarkably like the simplified computer weather prediction experiment that gave different predictions for two weeks in advance, at a fourth decimal place of initial conditions. Hence the butterfly effect.