The Mandelbrot Set: Atheists’ WORST Nightmare

I dare say that there is no secular or atheistic explanation for what I am about to share with you. This secret code only makes sense in the Christian worldview, which is why a few years ago there was a movie National Treasure where Nicholas Cage finds a secret code on the back of the Declaration of Independence and leads him to other clues and so on and obviously the code was put there by very intelligent people and you know that implies intelligence when you find a code like that, what if there was a code embedded in numbers numbers like one two three four what if there was a secret code embedded in them?

We finally managed to figure out what that would entail. What if there was a message inside the numbers? What would that entail? It would tell us something about the intelligence of the person who made numbers. Now we don't usually think of God creating numbers because they are abstract, we think of God creating animals, stars and planets, etc., but God is also responsible for numbers, even if they are abstract and conceptual. The Sovereign of God over the abstract is as much as over the physical universe and in fact there is a secret code built into the numbers and it is mind blowing and this is something I read when I was quite young.

It was amazing for me and I want to share this with you. Let's talk about sets first. Now a set in mathematics is just what you think it is. It is a group of, in this case, numbers. which have a defined common property, so you can have different types of sets and in most sets some numbers are included in the set and other numbers are excluded from the set. This is pretty easy, it depends on how you define the set. you could have the set of even numbers, those numbers that are divisible by two and in that set those numbers would be included and those other numbers would be excluded, that's pretty easy, that's the set of even numbers that we could consider the set. of negative numbers now that's a different set, isn't it?

So a different set of numbers will be included in there and then those others will be excluded now for those two sets, you can tell just by looking at the number whether or not it belongs correctly in this case, if it doesn't have a little negative sign in front of it, it doesn't belong and If it does, it does belong, so it's pretty easy, you can tell just by looking at the number, but there are some sets that have a more complicated definition and you can't tell just by looking at the number if it belongs or not, so let's go Let's talk about a particular set called the Mendelbrot set that was discovered in the late 1970s and early 1980s and was named after the person who actually discovered Benoit Mendelbrot was a mathematician and a computer scientist who worked in IBM this set is defined according to this little formula that you see here where is the set of all numbers c c is a number that is potentially part of the Mandelbrot set we are testing for which this other number Z remains small according to this little formula and it seems very complicated but in reality it is not.

I'll explain, the small n just means that that is a particular value of z n plus 1 is the next value of Z, so there are many values ​​of Z, there is a sequence and if that sequence of Z remains small, then the other number c is part of the Mandelbrot set, on the other hand, if the sequence Z becomes very large. if it goes from one to 100 a million billion, then C is not part of the foreign assembly set and we will do a couple of examples so that this is understood, it is quite simple, so let's ask what part number one is . of the Mandelbrot set, so C equals one, okay, and we're going to plug that into our formula, so we have Z squared plus one because that's the number that we're testing and that becomes the new value of Z.

Now the first value of Z is zero by definition, so that's the first value, so we plug that in and we have 0 squared, which is zero plus one is one, yeah, zero squared plus one is one, so that is the next Z value, okay, and what we'll do is Put that back into the formula, that's the new Z value, so now we have one squared, which is one plus one, it's two, okay, insert it again, so we have 2 squared, it's four, two times two, it's four, plus one, it's five, okay? You'll get this, you put it back to 5 squared 25 plus 1 is 26, okay, we put it back to 26 squared is a big number and you put it back, okay, now you see what's happening here is the sequence in which Z remains small. no, so it's part number one of the

mandelbrot

set no, because it has to stay small for it to belong.

There's one more complication and then we get to the really interesting stuff. the other complication is that the

mandelbrot

set also includes what is called complex and imaginary numbers okay so an imaginary number is a number that when you square it you get a negative number and that is a little difficult for us to understand and That's why they call them imaginary, it's just a name. I hate that they have that name because it makes it sound like they don't exist, you know, they're made up, no, they exist, imaginary numbers exist and, to make matters worse, they call numbers that aren't imaginary real, but it's just terminology and they're both equally true.

Put it that way, but how do we have a number that multiplied by itself is negative and is represented by a lowercase i? That's the kind of primary imaginary number when I multiplied by I is negative, how do we make sense of that after all? Imaginary numbers are not positive because a positive number squared is positive, and yet the imaginary number multiplied by itself is negative. Imaginary numbers are not negative because a negative number squared is also positive and imaginary numbers are not zero because zero squared is zero. It's strange, so we have a number that is not positive, it is not negative, it is not zero and that leaves us a little bit scratching our heads, we have problems with that, well I have news for you, not everything in this universe is intuitive if you've ever had a quantum class.

Mechanics, you know that the universe doesn't always work the way we expect. You know that our intuition is really based on experience and the fact is that most adults have no experience with imaginary numbers, so they seem strange, but that's just it. It's a matter of experience when you were a small child. The negative numbers probably didn't make much sense. Know? I could have one apple I can have two apples How can I have two negative apples? That doesn't make sense, how can you? you have less than nothing, you get a little older, you get a bank account, suddenly negative numbers make a lot of sense, right, yeah, I can have less than nothing, well, imaginary numbers are the same way, you get a little experience and you discover that yes, there are numbers. that when you square them you get a negative but they are not positive, they are not negative and they are not zero, how do we make sense of that way of doing it?

Because if you consider a number line, here we have a number line now the positive numbers are to the right of zero along that number line the negative numbers are to the left of zero along that number line so how do we represent a number that is neither positive, nor negative, nor zero? Well, you put it. above the number line so it's not on the number line, it's on a different axis and by multiplying I by the other real numbers you can have all kinds of imaginary numbers and you can think of them as being on a different axis, so the real numbers are along this axis, the imaginary numbers are along that axis and that makes sense.

You can see that the imaginary number is not positive because it is not to the right of zero, it is not negative because it is not to the left of zero, and yet it is not such a zero. makes sense and then you can have everything, you can also have numbers that are called complex and are off the axis, they are called complex because they have a real part and an imaginary part, but it is a number with two parts and usually the real part is represented by the x axis and then the imaginary part is represented by the y axis, so you can plot any number on a plane using those two components, the real component being X and the imaginary component Y. that's pretty cool, I can plot any number on a plane, very convenient, then the Mandelbrot set also includes these imaginary and complex numbers and the only thing you have to remember is that they obey all the ordinary rules of algebra, it's just that when you multiply I by itself you get a negative one, that's what The only thing you have to remember, what we can do then is we can make a map because I'm trying to find out if there is a pattern for the numbers that belong to the large set quantity and it turns out.

There is, but it's not obvious, because it's not obvious. You can tell just by looking at a number whether it's going to belong or not, you have to run that formula and that's a little tedious, but in the 1980s computers started to get fast enough. where they could iterate that formula several times and they could analyze to see if Z is getting big or staying small and then what we can do is have the computer check all these different points and we'll see if there's a pattern. to the brought metal set and then we will take the points that belong to the mandelbron set and color them black, that is arbitrary, that is how Benoit mandelbrot did it and we follow his example, so you have the computer to check more points and you discover that all those points belong to the Mandelbrot set when you run it, that formula Z stays small and then the points that don't belong we will color them red or some other color, it doesn't really matter, so we already checked point one, we find that the number one does not belong to the established amount of rot, so it is colored red and if we had checked these other points, we would find that they do not belong and you will see as you trace more and more.

From these points a pattern begins to emerge, it seems that well, you have the computer running thousands and thousands of what you have, the computer checks each of those numbers and a pattern emerges and the pattern looks like this, it is really interesting and unexpected, no one was. Hoping that when you made a map of the Mandelbrot set it would look this extraordinary, I'm going to eliminate the axes now because it turns out that the shape is remarkably interesting and unexpected and will turn out to have a lot of beauty. in it also the form itself is, I mean, this is a mathematical plot.

I guess we would expect it to have some mathematical properties but everyone was surprised by the properties it has, the main shape that looks like a heart is called a cardioid and a cardioid is what happens when you take a circle and take a pencil over it and you spin it around another circle of equal size. This shape that you will get is a cardioid and you can see that, indeed, the main part of the Mandelbrot set is a perfect cardioid, all the other shapes that grow from it are circles, all these perfect circles attached to the perimeter of the set of brought metal and then you see some other features like these little tendrils growing out of it and a spike.

On the left, something that sticks out, it's something interesting, you notice that that top circle has a circle on top, another on top in smaller and smaller scales and it comes out and forms this little tree and it has three stems, including the trunk, so it has a trunk and two stems for a total of three branches. You see that now the next one on the left branches into five. Can you see I mean it's a little small, but? I can see the five branches there, the next one is seven nine eleven thirteen fifty are all odd numbers and by the way, they don't stop, they go to infinity, there are an infinite number of them, although they get smaller and smaller, so that you have to zoom in closer, but also somehow the Mandelbrot set knows how to count, it's kind of remarkable, and then on the other side you have the probabilities and the evens, you have all the numbers there in terms of the number of branches, now It's notable enough that it has branches because who would have thought that when you run numbers through that little formula you get that shape?

It's remarkable, no one expected that and it's even more remarkable that it apparently has the ability to count in terms of the number of tendrils it grows. of each bud there and of course you can take two of those numbers like five and three, now five plus three is eight okay and it turns out that the bud between those two has eight interesting tendrils and that's true for all two. on the left side and on the right side, the cocoon between the two adds up the number of tendrils in each one, so it is not only the number of rights that they know how to count, but they also know how to add and then on the left side, there . you have this kind of pick that comes out and you see there's a little bump on the end of the pick so let's take a look and see what it looks like so we'll zoom in and that little bump turns out to look like the whole metal assembly is a mini mandelbrot set and it's almost identical to the original except it has extra spikes growing out of it, but the basic shape is the same, it has the cardioid and the circles and oh, it has a littlespike that grows. of that too with a small lump, what could it be?

Well, let's zoom in on that and oh, interesting, absolutely fat and it has extra spikes growing on it and that has a little bit, but how about that now? Of course, you could literally do it forever and there may be an infinite number of baby versions built into the Mandelbrot set in smaller and smaller scales and look how small it is. Compared to the original, when we zoom back in here, look at how small it is not so noticeable and the fact that it repeats infinitely and does not lose complexity, it actually gains it every time it grows more additional spikes. very remarkable well, to anticipate my conclusion on this, I'm going to suggest to you that this form tells us something about the way in which God thinks that God's understanding is infinite.

Numbers are an aspect of the mind of God. God is responsible for numbers and so it makes sense in the Christian worldview that when we explore and study numbers we should find intelligence in them, we find evidence of patterns and not only not just intelligence but infinite intelligence because this thing repeats itself infinitely, a structure that repeats on increasingly smaller scales is called a fractal, so the Mandelbrot set is an example of a fractal, there are other types of fractals, there are other sections of the mammalian set that are fractals. We could zoom in on, for example, one of these little tendril features here and zoom in on that and you'd say, well, that's interesting, we'll just think that what's going to stop at some point will eventually level out and you'll make it, but keep going, it's infinitely wavy, you see that little one, it's moving like that.

Get closer and keep going and going and going. It's fascinating this and look at this and look at the scale here and it gives you a little taste of what the mind of God is like to be able to think infinitely. We can only process a little bit of information at a time, but the mind of God is truly infinite, so one of the interesting areas to explore and what I want to do now is just spend some time exploring this form that exists in the mind. of God and it has existed in the mind of God since creation which was only discovered in the 1980s and we can approach, for example, this cusp between the main cardioid and the disk and we find that it is called, they call it the Valley of the seahorses because As you see, on the right side, they look like seahorses, they're upside down because the way we've blown them up here now the colors are arbitrary.

I can make them however I want and we will change them from time to time. Just to keep things interesting but keep in mind that the black always represents numbers that belong to the Mount Foreign set and then the colors represent those that do not belong to the Mandelbrot set and the bright colors are very close to being in the Metal Breath set, but not. A big part of this, so let's zoom in on one of these seahorse structures. You see it looks like an upside down seahorse. It's not that fascinating and quite beautiful and I need to explain a little bit about what this means because if the dots are very bright, that means it's very close to the Mandelbrot set and you can look and say, but yeah, that bright Hub doesn't seem to be near it, it's just that you have to realize that there is a very thin black thread that moves and takes that shape that you see, it is so thin that it is thinner than the pixels that the computer can trace, so everywhere where you see a structure like that there is a very thin black thread that coils around and creates that wonderful shape, we will get closer and find out what this seahorse is made of.

It is the central axis that looks like a kind of spider web-like structure. You have the spokes and the rims around there and From experience I found that you can get closer to the center of that until your heart is content and it doesn't really change much, it goes on infinitely, so again the infinity of the mind of God, so I thought, well, come on. To the side and we find out what these spider web threads are made of, so we go to the side here and we find that the threads are made of more spider webs, which is kind of interesting and we get a little bit closer. and you find that there are sort of two centers, you see the bright yellow centers and then in the middle it goes from two to four and as we get closer it will go from four to eight to 16 32 64 doubles each time and as we zoom in In that central hub, we find, oh, isn't that so interesting?

You see go from four to eight to sixteen and so on and in between, of course, you have another quite fascinating baby mind set, there really are an infinite number of these babies. incorporated into the overall shape, which I think is amazing and again look at how small it is compared to the overall shape as we zoom out again, it's just a little bit infinitesimal and we could have gotten closer to any of those threads that I just picked out . one at random and there it is very noticeable let's go back to that Valley now the valley of the seahorses is on the right on the left we find the Valley of the Double Spirals and I will zoom in on one of those now this is my favorite part of the Mandelbrot set I think They are very beautiful, they remind me of spiral galaxies.

In fact, he is an astronomer. I really appreciate that God apparently likes spirals because he has incorporated a lot of them into nature and incorporated them into mathematics, which is extraordinary. Who would have imagined that there would be a spiral, a beautiful spiral built into that little formula Z squared plus C or, rather, built into numbers when we run them through that formula? It's pretty amazing, it's a double spiral because there are actually two strands that wrap around each other. another, if you trace a strand, you will find that there is a strand in the middle, so it is a double spiral like our spiral galaxies, by the way, let's zoom in a little bit and again I discovered that you can zoom them in. in the center forever, so we'll go closer to the side and you'll find spider web-like structures, you'll find more double spirals, and you'll find a new structure.

I call them bowties, they're like in the middle, see? It looks like a kind of bow tie and has two double spirals that intersect in the middle. It's quite beautiful again. What you're seeing here, the Mandelbrot set, is incredibly Wiggly, it's so Wiggly that it's creating these wonderful shapes and that's what the The dots that are very bright are very close to that fine black thread that moves and forms all these wonderful shapes, so we'll zoom in on one of these bow ties and we'll find that again you have the two double spirals that we zoomed in on. in a double spiral and we discover that it is made up of multiple double spirals and they go from two to four to eight to sixteen as we get closer to the center and in the middle you find another set of many rotten metals, no wonder.

This time, but there it is and it is quite beautiful, who would have imagined that such beauty would be included in the numbers? Well, in the Christian worldview, that makes sense: we serve a God who is beautiful, who does beautiful things, and when we examine the way God thinks. about numbers, which is what mathematics really is, we find that it's immensely beautiful, all of that is just a map, a map of what numbers belong to that little formula when you're running that algorithm, it's that fascinating and this, for Of course, it was surprising to mathematical mathematicians when this was discovered back in the 80s, so then it occurred to me: is there something special about that formula?

I mean, did we happen to stumble upon an amazing formula? What happens if we change it? Then I thought. Well, let's see what happens if we go z cubed plus c. Well, I ran the computer code through that and it turns out that you get a different shape, interesting and very similar in some ways, but different in others. The shape here is called the main shape. a nephroid and a nephroid is what happens when you take a circle half the size of another and you rotate it, you get that shape and you can see it's a perfect nephroid, really amazing, and then instead of circles growing, you have cardioid growing.

Outside of this, notice that everything has gone up by one. Mandelbrot's set had a cardio that has a valley. This has a nephroid that has two and the circles that grow on it that have no valleys. Now our cardioids that have a valley. Everything has risen in one. It makes sense, we go from Z squared to Z cubed. I guess it makes sense. Well, what happens when we go from Z to the room? Well, that's what you get. What happens if you go from Z to fifth? Interesting, you notice what the number of lobes is. one less than the number so Z to the fifth you have four lobes Z to the six to get five lobes it occurred to me that if I went from Z to the seventh I could get snowflakes and I sure do, and if you get closer you absolutely get snowflakes, you You zoom in and you get snowflakes everywhere, isn't it so wonderful?

Did you know that such beauty was built in numbers? Okay, so what does it all mean? We have these wonderful shapes and it's very nice, Dr. Lyle, but who cares? I want to ask what causes the beauty in fractals because I think you would agree that they are beautiful, they are beautiful and they certainly are complex, so I have to ask what causes the complexity in them, the fact that when you zoom in not only do you get baby versions, but, uh, the complexity increases as you zoom in instead of decreasing, what's causing that, so let's answer the first question first, what causes beauty in fractals and I'll have several possibilities .

Could be? the man-made color scheme now I told you that cutlers are arbitrary apart from us, we always assign black to the set itself and then assign other colors to the perimeter to make it easier to see and I admit it. I chose the colors I think they are pretty other people choose other colors sometimes they are not always nice and the blame is because you know I have an artistic side I appreciate beauty anyway is it skin color created by man obviously not because although I I think the color enhances the beauty of these, even in greyscale they are still beautiful.

There is something about that shape that is attractive to us. We see beauty there. I think the color enhances it a little, like if you put a little salt in the food. it brings out the flavor a little better but it certainly doesn't create the beauty. I choose the colors but the shapes are gods. The computer creates beauty. Now you could have said well, the computer plotted that, but remember we made the first two points. manually, we check it and run that little form, you could plot this manually if you wanted, it would be terribly tedious, but you could do it and you know it, that's why it wasn't until computers that people started plotting this. but it's not the computer that created the beauty, the computer just revealed it quickly did something that would take us a long time to do it did it quickly but you could do this manually did people do this?

Did Benoit Mandelbrot create the Mandelbrot set? He defined that formula, but did he create Beauty and complexity? Well, of course, he wasn't surprised like everyone else and some people didn't believe it when this was first discovered, they thought maybe it was some kind of artifact, some problem in terms of the way the computer is encoding and but it's not that it has now been disproved these things are real the computer only allows us to see them quickly people didn't achieve it people were surprised by this result I would say that beauty is built in mathematics it has always been there it just wasn't until the decade 1980's that we had the ability to see what causes the complexity in fractals these intricate shapes that can add and can count and so on what causes all of that to fulfill and the fact that it's infinitely complex, you have an infinite number of versions for babies integrated into the original, what is causing it to be the computer, well, again, the computer is simply revealing the complexity that was already there, the computer does not create these shapes, just like a microscope creates bacteria, the formula is not so important because you can change the formula, you still get beauty, you still get complexity in a sense, complexity is built into the mathematics itself, so how do we make sense of that? we make sense of the beauty and complexity that goes into mathematics.

What is mathematics? It is the study of the relationship between numbers. The rules that govern how numbers relate to each other. That's pretty easy. And then, of course, I'm going to ask what the numbers are that will do it. Tune in, we know what numbers are, it's funny, some of these things are very basic and hard to define, don't you like consciousness? It is difficult to define it without using another word that is basically a synonym for consciousness, what are the numbers? I have been able to find and different dictionaries do not agree, but the best definition that I have been able to find is that numbers are a concept of quantity and I think it is a pretty good definition, it is the best that I have seen that numbers are. a concept of quantity, so if you have three apples, apples are physical, but tricity is a concept, it exists in your mind, you can't physically touch a number, you can't literally see a number, sotrue, you could say well. wait a minute I see the number three there it is really the number three if it is so I simply destroyed the number three and students poor students will not have to count one two four and so on because you said there were three and I eliminated it so there are no longer three , well, obviously, that is not the number three, which is a representation of the number three, right, it is a written number, numbers or not numbers, the representation of numbers, and we know that at some point in history we decided that the form would represent three things and Of course you know that you can use Roman numerals if you want and they have a different notation, they represent the same concept, although don't they?

So the concept that it is not something we create the laws of mathematics are conceptual, not physical, you can't stub your toe on a law of mathematics, you can't stub your toe on a number, you can still stub your toe. toe with something that is physical, but not with numbers because they are conceptual, so where do the laws of mathematics come from? This is the question that leads us to Origins, because secularists try to explain everything naturally and especially by evolutionary processes, but did the laws of mathematics evolve? That's something to think about. I mean, we find many patterns in nature.

We know different patterns and animals and the way animals are classified and the way secularists explain that this is evolution, they say well. They had a common ancestor and then they evolved they changed, that work for mathematics did seven it used to be three but it evolved that doesn't make any sense are numbers what they are and have always been what are laws? of mathematics didn't evolve, it's not like you knew the Pythagorean theorem wasn't true, but eventually you know that triangles emerged, no, no, they don't have laws of mathematics, they've always been the way they are hmm, they were laws of mathematics. mathematics created by people. some people argue that, but it's a ridiculous statement because if we created them we could create them differently, we could say, you know, let's all agree that two plus two equals five.

Now you can imagine an architect trying to live that philosophy. so that it turns out well or try that in your bank that is not going to work because it simply works it is not faithful to reality we did not create the laws of mathematics we discovered them Pythagoras true, he was not the first to discover it, but the Pythagorean Theorem right now triangles didn't add up like that before Pythagoras well of course they did, he just discovered it the planets the way planets orbit obey mathematical laws Kepler's laws p squared equals a cube in terms of the relationship that was not true before people came planets orbited perfectly well for the previous two days people now fractals perfect fractals of the type we have seen so far repeat infinitely you can approach the mandelbrot set forever and you will continually find ever closer versions small, baby versions of it you can do that forever or until your computer explodes, so perfect fractals repeat infinitely and are only found in the conceptual world of mathematics, however the physical world contains upcoming fractal things that they go in so many steps and then eventually they break down into atoms and Atoms are not fractals, but let me give you some examples of these snowflakes.

Snowflakes have a fractal quality. They have that six-fold symmetry. Getting closer you still get six-fold symmetry. Getting closer you get a six-fold symmetry. These little gems that God sends us from heaven every year and we take them off the car and yes, they are beautiful and they are fractals, they don't repeat exactly but still, the sixfold symmetry continues no matter how close you get, so it's It's hard to say the size of a snowflake unless you have something to compare it to because no matter how big it is it always looks more or less the same.

That's a characteristic of fractals, that thing that grows on your windows in the winter. I was fascinated by this when I was a child, I still am really. I think it's beautiful, it grows in your windows, its fractal shapes are quite beautiful in terms of the way they repeat, branch out and branch out into branches etc, ferns are fractal because you see that ferns have a stem. and they have another stem that grows from that and another stem that grows from that and the little leaflets and so on they branch and they branch into branches and they branch into branches of branches.

I even found a broccoli fractal, so I guess broccoli is good for something later. there you have romanesco broccoli, they call it that and you can see it's shaped like a cone and then it has cones growing on it and cones growing on the cones in smaller and smaller scales. It's fractal it's not that fascinating. Too bad it tastes horrible. Coasts are often fractal coasts because of the way they branch, you get closer and they branch out into branches etc, mountain tops are fractal, you look at them from above and they branch out and they branch out into branches etc, clouds tend to be fractals, no I'm not repeating it exactly, but am I looking at the entire sky or am I looking at a very small section of the cloud?

It's hard to say because the same kind of patterns repeat themselves. The way lightning branches is fractal because you have one main lightning bolt that branches into smaller lightning bolts that branch into smaller ones and so on and very beautiful lightning bolts and because it has that fractal quality and it's also very pretty, when you watch it in super slow motion you can see it branching out and all these different branches. a fractal until the leader connects and then most of the current goes down the leader, it's quite fascinating, so here's my question: why do fractals occur so much in mathematics, that they exist in the mind, is it conceptual, as in the physical world, which is made up of atoms and not?

It doesn't exist in your mind right, I mean you have this shape that is a multi-brot that exists only in the conceptual world of mathematics, we can trace it but you could never touch that thing because it is not physical, it is not made of atoms, but that one is and they look remarkably similar this particular shape here is part of the Mandelbrot set it looks like a rock ray but it's not made of atoms this is how conceptual things that exist only in the mind also occur in the physical universe this particular shape that might look like a plant that is actually a mathematical graph called Barnsley Fern and Barnsley Fern is such that each leaflet has the full shape let me show you it's not that interesting let's do it again just because it's cool to see the full shape each leaflet has the whole shape fascinating, no, you can't touch it, although it doesn't exist in the physical world, but yes, it's very similar, uh, this here is a mathematical graph that doesn't exist in the physical world. world but that grows in its windows this particular mathematical shape cones upon cones does not exist in the physical world while this unfortunately does this particular shape that is part of the Mandelbrot set is a double spiral that cannot be seen in a telescope because it is not It's made of atoms, it doesn't physically exist in the universe, but you can look at it, you can see it with a small telescope, the whirlpool galaxy not far from the Big Dipper, so how come math is conceptual and you find these? shapes and then in nature, which is physics, you find the same kind of shapes, why now there is an answer to this and a skeptic might say this is good, physical mathematical laws based on Universal, so it is logical What if something can happen in mathematics? they occur in the physical world because mathematics based on the physical world is fine, I grant you that, but then I will have to ask why the physical Universe has mathematical laws and that is an obstacle if you are not a Christian if you are not a Christian in the Christian worldview.

I can understand why the physical universe obeys mathematics because the physical universe is sustained by the mind of God and God thinks mathematically, so it is logical that the physical universe obeys mathematical laws. for God upholds all things by the word of his power, the Bible says, and in him all things consist or are held together. God thinks mathematically and therefore the way he holds the universe will be mathematical, it is inevitable, but I maintain that the secular rules view cannot answer that I cannot explain the properties of the laws of mathematics why they are conceptual.

Abstract universals invariant without exception and why the physical universe is forced to obey them why a physical universe would obey conceptual laws something occurs to you in your mind does the universe just obey automatically? Of course not, it doesn't make sense unless you think I'm making this up. Some brilliant people have written on this topic. Dr. Eugene Wigner, who has a Ph.D. in physics. I think he's a Nobel Prize winner. A brilliant man. He wrote a wonderful article for years. I love this article ago called The Unreasonable Effectiveness of Mathematics and the Natural Sciences. It's interesting now that he approaches it from a secular perspective and from a secular perspective he is stumped.

It is not reasonable that mathematics works so wonderfully to explain the physical universe. Mathematics is abstract. The physical universe is physical and that is why he analyzes this in the article. He is this perplexing dilemma: why does the universe obey mathematics? He says that it is difficult to avoid the impression that here we are faced with a miracle or both miracles of the existence of the laws of nature. and the ability of the human mind to define them, he is saying that it is surprising, first of all, that the Universe obeys mathematical laws, that in itself is surprising and what is even more surprising is that human beings can discover those laws , which is remarkable, almost like a miracle, eh, yeah.

What is your conclusion? Can you think of an answer from a secular perspective? Here is your conclusion. The miracle of the language of mathematics being appropriate for the formulation of the laws of physics is a wonderful gift that we neither understand nor deserve. It is not like this? It is interesting that there is no answer from the bankrupt evolutionary atheist camp as to why mathematical laws based on the physical universe, but it is exactly what the Christian would expect, it is exactly what we would expect, so we have seen that there is a beauty of complexity. infinite incorporated in numbers.

Numbers are abstract conceptions of quantity that exist in the mind. The concepts require a mind and reflection numbers, therefore, the way God thinks makes sense in the Christian worldview. The secular worldview cannot convincingly explain the existence and properties of numbers and mathematical relationships. The mathematical truths. you can't make sense of it, it doesn't make sense in your worldview, numbers existed before people, but they are conceptions, which means they require a mind and that means minds existed before people and that makes sense in the world. Christian worldview that we can have. which makes sense the laws of mathematics are universal invariant abstract entities, it is exactly what we would expect given that God is omnipresent, does not change over time and of course all thought is abstract, the physical world has approximate fractals and we would expect that but the secular worldview can't answer it the secular worldview can't explain why the physical Universe obeys mathematical laws, it really can and we saw that some of the brightest people in the world have worked on it and they haven't found a convincing answer, but it has sense in the Christian worldview because the physical Universe, like the world of mathematics, is controlled by the mind of God and the reason we can do science is because God has graciously given us access to some of his thoughts. , that is Revelation, that is what God Is God imparting information to human beings?

He has done it more specifically in his word, but he does it in our, you know, he writes his moral law in our hearts, etc., we can make sense of the mathematics and this secret code of creation that is integrated in them. We can make sense of these wonderful shapes that the mind of God constructs in numbers and why they are beautiful because God, that is the nature of God, that is what it boils down to, thank you so much for having me. I'll talk, thanks for the responses and the Genesis staff for inviting me here I really appreciate it.

God bless you.