The Secret Code of Creation - Dr. Jason Lisle

[Music] so there was a movie a number of years ago national treasure where Nicholas Cage goes and finds a secret message on the back of the Declaration of Independence and that implied that there were some really intelligent people that it had figured out how to encode that message and so on what if there was a secret code built into math built into numbers numbers one two three four what if we discovered a secret code built into that what would that imply that would be fascinating wouldn't it because that would imply that that numbers themselves have a creator and a very intelligent one if we found a message built into numbers and in fact there is a code built into numbers it's absolutely amazing it's mind-blowing and this was discovered in the really the 1980s so this is relatively recent people have been using numbers for thousands of years but it wasn't until the 1980s that we discovered there is a code built into numbers and I want to share that with you today cuz it's neat this is something that I read about when I was young and it's just it just blew my mind and I want to share with you because we don't tend to often think about God creating numbers we think about God creating the earth and the stars and the initial organisms on the earth but God is also responsible for numbers not that he created them in the same way because they're not physical right numbers are abstract their conceptual exists in the mind and yet God is responsible for numbers and he has embedded in numbers an amazing code of unbelievable complexity and beauty and I think it's gonna be mind-blowing to you it's really gonna be mind-blowing when I was a little kid my mother would prepare these wonderful meals she's a very good cook and but occasionally she'd prepare something I didn't like like broccoli and the rule was you had to eat everything when you plate before you're dismissed right so occasionally in rare moments of maturity I would eat the broccoli first get it out of the way so that I could then enjoy the rest of the meal that's what I'm saying well in light of that we're gonna do some broccoli first okay but stay with me because it's gonna get really cool okay so we're gonna have to talk about set so we have to do a little math here and you'll see a set is just a collection of elements with a common defined property and so when we're talking about sets of numbers a set of numbers is just numbers that have something in common with each other and you can define sets lots of different ways in most sets some numbers are included and other numbers are excluded so we're all about sets today and for example consider the set of even numbers so we get some numbers there the set of even numbers would contain those ones and it would exclude all the others right because numbers that are divisible by two evenly divisible by two we could then consider the set of negative now that's a different set a set of negative numbers is a different set and so it will have different numbers contained within it it'll have those ones and it will exclude the others and those two sets are very easy because you can tell just by looking at the number whether or not it belongs to the set can't you even let's well does it in 0 2 4 6 8 yeah well yeah and it belongs or is it a negative number well you just look and see if there's a little negative sign in front of it that's pretty easy we're gonna talk about a set that's a little bit more complex where you can't tell just by looking at the number whether or not it belongs you're gonna have to think about a little bit you can you can figure whether the number belongs but not just by looking at it and the set we're going to talk about it's called the Mandelbrot set the Mandelbrot set after named after Ben Benoit Mandelbrot mathematician very famous mathematician and it's defined by this little formula that you see there and C is the number that you're checking to see if it belongs to the Mandelbrot set so that's what C is and Z is another number that in fact there's many different disease that's why it has a little subscript n next to it so there's a first Z a second Z a third Z and forth so you can think of them like a sequence of mailboxes each one's got a number in it and if that Z sequence gets bigger and bigger and bigger then that means C is not part of the Mandelbrot set whereas if the sequence of Z stays small then C is part of the mental broth set that sounds very complicated it's actually very simple and I'll just we'll do a couple and then you'll see how intuitive it is it's really quite simple so there's our little formula Z and by the way Z n plus 1 that means that's the next mailbox that's the next value of Z and so it depends on the previous value in and the number C so we're gonna ask is the number 1 part of the mental broad set so that means C equals 1 because C is the number we're checking to see if it belongs to the Mandelbrot set so we're going to plug that in you can see we're plugging that in for for C there so Z squared plus 1 is the next value of Z now the first value of Z is all is 0 that's just part of the definition so the first value is 0 we're going to plug that in so you have 0 squared which is 0 0 times 0 0 plus 1 is 1 yes see this isn't that hard it really isn't it and so that's our that's our new value of Z now we're gonna plug that back in like this now we have 1 squared which is 1 plus 1 is 2 very good even the common core folks are getting this ok all right we're gonna put that back in so we have now 2 squared which is 4 plus 1 is 5 okay put it back in 5 squared is 25 plus 1 is 26 put that back in 26 squared ok getting a little hard in it okay but we don't have to do any more you can see what's happening is Z staying small no it's getting big it's getting very big very fast so is the number 1 part of the Mandelbrot set answer is no no because it has the sequence of Z has to stay small for C to be a member of the mental broad set so number 1 is not part of the Mandelbrot set let's check another one let's check negative 1 as negative 1 part of the Mandelbrot set so we're going to plug that in now so we have Z squared minus 1 is the new value of Z all right and 1 again we'll start Z equals 0 and we'll plug that and so now we have 0 squared which is 0 minus 1 is negative 1 right and we plug that back in now negative 1 squared negative 1 times itself is positive 1 minus 1 is 0 well that's kind of interesting put that back in 0 squared wait a minute this looks familiar so it goes 0 negative 1 0 negative 1 see that interesting the Z stay small yeah it never gets greater in absolute magnitude than one so is negative one part of the mount about set yes okay you got it it's easy tedious but easy okay so you can check any number all you have to do is run it through that formula and and take a look at what's happening with Z and sometimes it'll stay if we if we try it with zero you'd find Z is always zero and so zero is part of the Mandelbrot set as well negative 1 is part of none of us that positive one is not okay there's one more complication and then it's going to get really cool the Mandelbrot set also includes what are called complex and imaginary numbers I hate the terminology because imaginary makes you think it doesn't exist well they do exist they're there they do exist but an imaginary number is a number that when you square it you get a negative number and that's a little hard for us to comprehend right because and in the the sort of standard imaginary numbers is abbreviated by the lowercase I and I squared by definition is negative one okay and there are other there are other imaginary numbers and again I hate the name because they do exist and to add insult to injury the numbers that are not imaginary called real but they all exist they it's just you know a little bit hard for us to imagine imaginary numbers are not positive right because a positive number squared is positive and imaginary numbers are not negative because a negative number squared is positive and imaginary numbers are not zero because zero squared is zero so how do you have something that's not positive not negative and not zero that's an imaginary number and they do exist it's just we're kind of uncomfortable with them because most people don't have a lot of experience with with these numbers kind like when you're a little kid and you're first exposed to a negative number is well how can something be less than nothing that doesn't make any sense right then you get a little bit older you get a bank account suddenly negative numbers make a lot of sense right yeah well it's the same way with the imaginary numbers they do exist it's just that most of us never really use them how do we think about a number that's not positive not negative not zero one way to think about it would be to consider a number line so you have on the number line you have zero there in the middle you have positive numbers to the right of zero you have negative numbers to the left of zero where you gonna put I how about above zero like that that makes sense right it's not positive it's not to the right of zero it's not negative it's not for the left of zero but it's not also not zero it's off axis and so you can think of the imaginary numbers as being on a different axis than the real numbers and that's that is a very common way that mathematicians will express these numbers and you can multiply the imaginary number I which is the same it's the same distance from zero as one okay remember I squared is negative one and you can multiply that imaginary number by any real number and you get all these other imaginary numbers you see so that generates that axis you can also have complex numbers complex and they're called complex because they have a real part and an imaginary part and they're off axis and by convention the real part we plot on the that's their x-coordinate and the imaginary part is their y-coordinate and so this is very useful in mathematics to talk about these complex numbers because even though it's one number you can represent it as a point on a plane and that's kind of neat so you can actually make some graphs and things that way so that's those are complex numbers and imaginary numbers they're off axis and what we're gonna do then is make a map of the Mandelbrot set because it was kind of tedious going through that and checking that but computers are great at doing tedious things they can do math very quickly over and over and what we'll do is we'll make a map of which points belong to the Mandelbrot set and which points don't and that way we won't have to run through that formula we can just look at the map then and say okay that number it does belong and that number doesn't so for example numbers that do belong to the Mandelbrot set what color there's black we checked negative one we found it did belong to the amount of brought set right because Z remains small right and we if we checked zero we'd find it also belongs to the malla broad set if we checked other points we'd find that all these points belong to the metal rod set as well just as examples if had we checked them and then four points that do not belong to the Mandelbrot set we'll color those red okay we checked one remember we found that one is the sequence of Z got really big and so that means it's not part of the mental brats that had we checked some of these other numbers we'd find that they do not belong to the amount of brats set as well now what's fascinating is that the shape here that emerges this map of the Mandelbrot set turns out to be something that's not simple at all you might think will be a circle or something you can tell it's not that even there right there but as we have the computer check more and more points more and more points we get a complete map of the Mandelbrot set and the map that we get looks like this it's surprisingly complicated and rather beautiful and so again what we're having here it's just a map which points belong black means they belong to the mantle broad set color means they don't and I shaded the color so that if the sequence of Z gets really big really fast I made it kind of a dark color so the points that it real far away from now broad set where as if Z gets big but it does so slowly then I colored it like a brighter color like yellow so the points that don't belong are shaded the points that do belong those are all black just by convention that's the way they do it the colors are arbitrary I could have picked any color I wanted to except just by convention the the points that do belong are always colored black by convention and so now I don't have to go through and run through that formula the computers done it for me I can look and say is 1/2 does 1/2 I belong to the Mandelbrot set the answer is yes it does you can see it's it's black okay and you can see that number 0 belongs is this you can see the number one doesn't and so on and so forth and so I can I'm gonna remove that grid because what's interesting is this shape it turns out this map of which points belong to the Mandelbrot set turns out to be just wonderful it's remarkably complex and beautiful and surprising no one was expecting this to exist in the world of math but there it is and it is a fascinating shape you have sort of there's sort of three types of shapes that stand out at least in my eyes there's there's the largest shape which is called a cardioid that's kind of that heart-shaped feature and then growing off of that or a bunch of circles and they are perfect circles and then growing off of that or other circles and these little tendrils that kind of like little lightning bolts that that grow away from it now the main shape the cardioid is what you get when you take one circle and you and you roll it around another circle keeping your your pencil on one point on the main circle that's a cardioid and you can see that that is the exact shape of the main part of the Mandelbrot set nobody was expecting that but there it is and then all the other shapes are either perfect circles or these little lightning bolt wisps that kind of stem away from it now if we can actually zoom in thanks to the power of a computing technology we can zoom in on various sections of the malla brush set see what it looks like and so we find for example if we zoom in on this upper tendril there you can see that it it branches off that circle has another circle on top of it which has another circle on top of it until it grows into this little sort of little tree there but it has two branches on it and a trunk so three totals so it branches off into three and see that three branches and if you look at the next one to the left it branches off into five can you count including the including the trunk including the stem one two three four five the next one is seven nine eleven thirteen fifteen seventeen all of the odd numbers is that interesting each one has two more tendrils than the previous one that's interesting nobody was expecting that and if we go to the right side we find all the numbers even Dan and IDEs and so three four five six seven eight interesting all the way down to infinity and on the left side we have all the odds all the way down to odd infinity apparently interesting and so apparently the Mandelbrot sets somehow knows how to count that's kind of fascinating what we're doing is looking at the map of which points belong and yet it turns out these structures are remarkable not only that but if you take three and the five and of course you add those together you get eight and lo and behold that is exactly how many the one in between them has isn't that interesting if you count the tendrils there I know they're kind of small but it's got eight tendrils and that is true for all of them if you go in between any of them that the the number of tendrils in between is the sum of the two surrounding them your that fascinating so not only does the Mandelbrot set know how to count it knows how to add in that interesting nobody was expecting that fascinating so all that built into a map of which points belong to that simple little formula Z squared plus C one of the most remarkable things about the amount of brought set though concerns this little spike that we have growing off the left of the of the set there and you'll notice that that spike has a little black bump on the end of it what could that be well let's zoom in on that and see what that looks like that little bump turns out it's another Mandelbrot set isn't that fascinating and it's almost identical to the original it's got the main cardioid the circles growing off of it the only difference is it's got extra spikes growing off of when we zoomed in on a spike and the baby version had extra spikes growing off of it and if you'll notice one of those spikes the one at the very end has a little black spot on it what could that be well let's zoom in on that turns out it's another one isn't that interesting and it's it's again identical to the original except it's got even more spikes growing off of it because we zoomed in on a spike of a spike and it's got extra spikes growing off of it and it's got what's got a little thing there too what could that possibly be well it's another one and so on and so forth this continues infinitely interesting so the Mandelbrot set has an infinite number of baby mental broth sets growing off of that spike and each one of those has a spike as it has a mental brought growing off of it and so on all of that just a tiny little section of the original look how much we've zoomed in there it's quite amazing ain't it fascinating and nobody was expecting that who knew that when you when you made when you plotted the map of which numbers belong to Z squared plus C you would get this amazing structure and it's not just the overall shape that repeats infinitely if you zoom in on any part of the Mandelbrot set it goes forever it's quite fascinating to see this you might think well it's going to end at some point you know I'm just gonna keep zooming in until it stops it just doesn't stop no matter what you do min on it just keeps fragmenting and keeps frag and smaller and smaller scales it's not like the physical universe the physical universe eventually get down to atoms there's no atoms here this is made of math okay and so it goes on literally forever there's that fascinating and of course well we be here all day if we assumed in on the whole thing right because we would literally take forever but it's quite fascinating one of the interesting regions in which we can zoom in on the Mandelbrot set is this is the valley between the the main cardioid and the first disc the first that that big circle that's growing off to the left of the cardioid that valley if we zoom in on it either the top or the bottom they're symmetric if we zoom in on that it's called the valley of the seahorse's and you can see it looks like seahorses off to the right they're upside down and double spirals off to the left so we can zoom in on those shapes and see what they look like so let's zoom in on one of those seahorses and see what that looks like here and by the way the colors are arbitrary so we'll change those every now and then just to keep things interesting but bright colors mean close to the Mandelbrot set but not quite on it dark colors mean far away from the mental bus Russ set and black means it's on the Mandelbrot set so we zoom in on one of these seahorses now keep in mind all you're looking at is the plot of an equation it's the equation Z squared plus C and which points belong to that and what you have given that that sea horse is very brightly colored that means that those points are very close to being on the Mandelbrot set which means there must be actually a very thin black thread that extends away from that circle that Wiggles around incredibly it's incredibly Wiggly in fact it's infinitely wiggly if that makes any sense it's as Wiggly as can is as possible for two dimensions and it Wiggles around and and what you're seeing there is is the black is too thin for the computer to plot it but the fact that it's you're seeing bright blue there indicates that those points are very close to being on the mantle broad set so that seahorse is made of an infinitely Wiggly thread or multiple threads that that wrap around and form kind of a spiderweb structure there in the middle quite beautiful and they form a beautiful spiral up near the top in a stunning and who would have expected that such beauty would be built into a out of the metal broth set it's absolutely fascinating so let's zoom in a little bit more and see what that spiderweb structure looks like and it looks like that and I found from experience you can zoom in on the center of that to your heart's content and nothing changes it goes forever it's an infinite spiderweb and so what we'll do is we'll go off axis we'll look at one of the strands of the spiderweb see what it's made of and we find the spiderweb strand is made of more spiderweb strands interestingly and spirals as well quite lovely really very beautiful we zoom in on one of those we find interesting structure there you find that there's kind of two central hubs one on the top one on the bottom right you see those where there's bright yellow in this illustration and then it goes to four in the middle there you can see there's four and then when we zoom in you'll see it'll go to eight 16 32 64 it's all the powers of two so not only does the Mandelbrot set know how to count know how to add it knows how to do powers of two interestingly so let's zoom in on this central that's central for little square structure there and you find that in the middle is well that's said your sting goes from four to eight to sixteen and then right in the middle is of course another baby version of the Mandelbrot set it's not amazing and we've zoomed in I don't know how many times but it's this is a tiny little structure built into the original and you can see that it too has a little baby mount about set on its spike just like the original did but now it's surrounded by all this extra stuff all this extra kind of spider web type structure because we zoomed in on a spider web and the baby version apparently inherits the section the properties of the section of the parent that it grows off of so quite stunning and take a look at how small this is compared to the original when we zoom back out it's it's quite amazing and that just gives you a little window into the mind of God because if you think about it God is responsible for numbers God is the reason that numbers exist because they exist in his mind and we'll talk about this more later but what this is is it's giving you a little window into how God thinks and so when you when you zoom in on these things do you think wow God is infinite this is just a little taste of what infinity is like just a taste that we can't really experience in Finn in its fullness we can get a glimpse of it let's go back to the valley of the seahorse's there on the right side and this time we'll go off to the left and what they call the valley of the double spirals and this is my favorite section of the Mandelbrot set it's strikingly beautiful it reminds me of spiral galaxies actually in terms of the way these structures are it is a double spiral a double spiral meaning that there are two strands that wrap around each other if you were to take a look at this this strand is the same as that strand but not that one right because if you follow it around you can see yeah there's two independent strands that wrap around each other so it's a double spiral and it's strikingly beautiful I think so again you're just seeing a map of which points belong there must be a very thin thread of points that belong to the mantle Russia that Wiggles around it forms this beautiful intricate spiral structure all built into numbers it's been there since creation but it was only in the 1980s that computers were fast enough to be able to plot these things in a reasonable amount of time it's even easier today because computers are faster again I found if you zoom in on the center of that double spiral you can do that forever it continues infinitely as spirals forever literally infinitely smaller so let's go off axis and zoom in on one of these strands and quite lovely we find that you find you find more double spirals off to the side up on the top for example there's some of those spiderweb structures and there's a structure I call it a bowtie it looks like a little bowtie there in the middle where you have to double spirals that intersect in the middle and I find these to be stunningly beautiful so who could have guessed that this is all built into numbers been waiting for us to discover it for 6,000 years and so again you have the two double spirals and then in the middle it goes to four eight 16 32 and of course when you zoom in on the middle there you find lo and behold another baby Mandelbrot said you get the feeling that God really likes that shape because it just occurs everywhere there's an infinite number of them and again the it's it's identical to the original except of course that's rotated around if you notice this one's backwards compared to the original because we zoomed in on a spiral and so it got rotated around and also the we have double spirals growing off of it and you can see the eight primary ones there and then there's sixteen inside that and thirty-two inside that all the powers of two all the way up to infinity amazingly and of course it's got a little baby on its spike as well as they all do so not only does each not only does the Mandelbrot contain an infinite number of copies of itself but each of those copies has an infinite number of copies as well if you think about it this also has a valley of seahorses doesn't it I could zoom in on it and so on so it's just gives you a little glimpse into the infinite mind of God one other Valley that's interesting to zoom in on is the is the one on the where the cardioid the main cusp of the cardioid and we call this the valley of the elephants and you'll see why when we zoom in here mathematicians like to give names to these different sections and valley the elephant's looks like elephants marching one after the next doesn't it and and there's and they're mirror images if they're hanging from the ceiling going along that way but we'll go to the bottom row it reminded me of elephants in a circus they're like standing on a ball right because each each one of those circles has one elephant growing off of it doesn't it and and there's an infinite number of them they go all the way to infinity into that cusp so each each circle one elephant balancing on it as if a circus elephant we can zoom in on the trunk of one of these elephants and you can see the trunk wraps infinitely actually it wraps around itself and it's quite lovely and again you can zoom in on the center of that forever it continues in Philly gets smaller and smaller to an infinitesimal scale so we'll go off axis and look at the structure on the side we find again you find looks like kind of elephant like structures there's some bow ties there too if we zoom in on one of those there's one of that those bow tie shapes but now they're single spirals the yeah this is an alienware it's not supposed to do that okay we're all right okay reason I got this is so I could do this presentation all right now it's working great so again you have that bowtie structure but it's single spirals rather than double and if you zoom in on the center yeah it goes from two it's done again that's weird let me back up a little bit yeah I don't know why it's not animating I'm sorry about that but anyway that's what you get to when you get to the center and you get this beautiful baby Mandelbrot that's surrounded by all this lovely structure in a stunning and all built into this this shape it's just a plot of which numbers belong to the malla brought set Z squared plus C it seems very simple and yet God has built incredible beauty into math that's remarkable all that just just a map of that formula which which numbers C remain for which the sequence of Z remains small that's all there is to it and so that got me thinking what happens if we explore other formulas yeah I mean this this shape itself you understand you could spend the rest of your life studying this and you would only scratch the surface because it's infinitely complex and it's just one equation that tells us something about the mind of God I found that if I change C if I make it like half C or to C or net minus C all it does is change the shape it'll flip it around or make it bigger or smaller you still get the amount of rough set what if I change is e squared though to something else what if I try Z cubed how do I get well you turns out you get a different shape now we've got another object to study and is it complex like the mound LeBron well let's let's find out let's let's take a look at this shape they call this a multi bright because it's a multiple of the Mandelbrot set and so this is Z cubed plus C dust those are the points in black or the points that belong to that formula when you run it through that iteration and this you notice what's happened here everything's gone up by one because remember the Mandelbrot set had the cardioid which has one cusp and the rest of its round now it's now the main shape has two cusps one on the left one on the right and the amount that's perfect circle's growing on them which have no cusps and now they have cardioids growing off of them which have one cusp everything has gone up by one the main shape there with the two lobes that's called an F roid and that's what happens when you take a circle that's half the size of the other one and you roll it around like that that's an F roid and you can see that is exactly the shape that is produced when we have Z cubed plus C Y nobody knows I'm sure there's a reason everybody was very good mathematical reason we just we have yet to discover it because our our ability to think god's thoughts after him is quite limited and in fact you can you can see how the Mandelbrot changes into the multi bronze what I did was I ran it through the formula and I changed it gradually I changed it from Z squared is Z to point 1 to point 2 to point 3 all the way up to Z cubed and so you can see what happens you can see how everything gets kind of doubled some things get up to by a factor of 4 like the the little baby now I brought there it first gets split into two and then it's joined by a twin so it actually ends up being four but most things are doubled and so that's kind of interesting now the one thing that doesn't really change very much in fact let me back up and do that again the one thing that doesn't change very much is the valley of the elephants right everything else gets kind of moved around but this valley looks like it stays pretty pretty constant so I thought what would happen then if we zoomed in the does this shape also have a valley of the elephants now let's find out let's zoom in on it see what we find lo and behold we find elephants how about that but you notice before we had circles and we had one elephant growing off of each circle now we have cardioids and there's two elephants growing off of each one so the elephants have doubled before we had an infinite number of elephants and now we have twice that many Simar on that for a while so there you go each cardioid now it's two elephants growing off of it isn't that amazing so and we can zoom in on the trunk of one of these elephants and see what happens you're gonna get the bow tie structures you think let's find out huh the bow ties have become three they've gained a spiral rights they're just two spirals intersecting they have three now and lo and behold what do you what do you find in the center there first of all it goes from three to nine the 27 and so on it's all the powers of three now and so the powers of two and you zoom in on the center one and sure enough you get the same basic shape you get the net Freud but the cardioid is growing off of it so it's a fractal as well anything like this that repeats infinitely is called a fractal a fractal is something where the overall shape is repeated on smaller and smaller scales and so we've just explored two different fractals now kind of amazing so that's what happens when you have Z cubed plus C what happens if you do Z to the fourth well you get that everything goes up by one you have one other cusp now you see and Z to the fifth Z to the fifth gives you a four if I back up a second z to the fourth gives you kind of a threefold symmetry z to the fifth gives you a fourfold symmetry Z to the sixth gives you a fivefold symmetry and so it occurred to me if I made Z to the seventh I could get snowflakes six-fold symmetry and when you zoom in on this do you get snowflakes absolutely zoom in on portions of it you get these beautiful snowflake structures so it's also fractal in that fascinating I also tried negative powers what happens when you try Z to the negative two now the interesting thing about this remember black are points that do belong and color they're points that don't and so what happens is now almost the entire universe belongs the black is outside now it's inverted because it's a negative power you see and so now most of the universe belongs to that set it's these points in the middle that don't and if i zoom on the zoom in on these these are fascinating because it produces kind of like a pebble like structure and I think are remarkably beautiful isn't that interesting and if we zoom in on that what we find pebbles pebbles upon pebbles of stunning beauty does it repeat infinitely well let's zoom in here absolutely goes on forever and ever and ever with the pebbles of smaller and smaller scales it's not like the physical universe where you get down to atoms and then they're just fears here it goes on literally forever you could zoom in on that for us to your life so that's as either than negative 2 what happens if you use 8c to the negative 3 to get that Z to the negative 4 you get that as either the negative 5 again it just there's a progression there and so you can there's another type of snowflake that you can get so in that in they're fascinating all we're doing is looking at maps of which points belong to that little formula and changing the formula doesn't just gives you new shapes so what is all this the floors all this mean I mean are we just looking at pretty shapes here what does all that mean well well my question is what causes this beauty and fractals where does it come from how do we account for it how do we make sense of it what causes the complexity in fractals the fact that you can zoom in on them they have these mathematical properties they continue infinitely how do we make sense of that well first of all what causes the beauty in fractals is it the man-made color scheme I picked the colors I think they're pretty but the fact is even if you take away the color the shape is still beautiful even in greyscale okay and I didn't pick the shape nobody did no human did so it's not that man-made color scheme that's not it I think that adds to it the way a little bit of salt will add bring out the flavor of your food but it's not it's not creating the beauty not at all that the computer create the beauty well we saw the computer plot this but the fact is the computer just did quickly what you could do manually we did the first two points manually remember we did make one and and a negative one and we found whether or not they belong so though this shape is built into numbers the computer just helped us to reveal it quickly you could theoretically do this all by hand it would just take forever and so this didn't create the beauty any more than a Mike creates the complexity of a microbe no it just allows us to see it did people make this well we came up with the formula but what we've seen is that the formula doesn't really matter too much you can change the formula you still get these wonderful shapes and frankly no human being sat down said okay I'm gonna make this shape where it's you know a cardioid here and then I'm gonna put some circles on it and I think I'll draw an infinite number of what human beings can't draw and then from number of things human beings did not create this we can't create infinite we discovered it we did not create it and so it seems to me the beauty is built into math the beauty of fractals is built into the math somehow well what causes the complexity in fractals the fact that they repeat and have these mathematical properties what accounts for that did the computer create it obviously not the computer simply reveals it you could do these you could plot these manually theoretically that human beings create it we can't create things that are infinitely complex think about it man-made machines you get down to some level and then they're very they're very crude and and simple we can't we can't do that we can't create an infinite number of minis built-in to the original we could create several but not an infinite number that's beyond us it's not something that human beings created did to formally create it well the formula doesn't matter too much the formula reveals it the formula sets the defines what points belong and what and what not but it's not like people picked a formula to give that shape people pick the formula and were surprised by that shape very surprised so it seems to me the complexity is somehow built into math interesting there we have a shape that's been built into numbers built into math what is math aside from that subject that's really hard and in school math is the study of the relationship between numbers that's really how you could define it's how numbers relate to each other what are numbers then and it it's funny some of these things that we use every day and we don't think about how are they defined how would you define a number I look through several dictionaries and it's it's hard to get an exact definition of that the best I could find is a dictionary that said numbers are a concept of quantity I think that's the best definition I've been able to see and so if you have you know two oranges and two rocks and two people and two galaxies what do they all have in common tunas you you you abstract away the physical thing and what you're left with is a concept the concept of quantity that's what numbers are there are a concept now the thing about concepts is they exist in the mind concepts are something you think numbers are something you think they are abstract in nature not physical you cannot stub your toe on the number two you can stub your toe on something physical that maybe there's two of them but you can't stub your toe on tunas right you can't do that because it's not physical they exist in the mind you can't trip over a law of mathematics or pull one out of the refrigerator or accidentally swallow one they're non-physical they are abstract they exist in the mind you say well I don't know that that that number three is physical right I see it there on the screen that's the number three is it the number three really because if so then I just destroyed the number three oh wait a minute that wasn't actually three right because it's not like children will not have to count one two four because there's no more three I just destroyed it no we've we get a that was a representation of three right numr it was a numeral written numerals are not numbers they are representations of numbers and they can be written different ways I could write three with three vertical lines right like they do in Roman numerals or I could use you know Arabic or whatever those are just representations of numbers but the concept of three Ness is not something you can write down because it's it's mental it's it exists in the mind laws of math are conceptual they exist in the mind so these laws that we that we have the multiplication you know the commutative property of multiplication or distributive property and so on these are conceptual they exist in the mind now they're very effective and in how we get along on the universe they help us but they exist in the mind so where do laws of math come from then there's an interesting question we use these laws of math the Pythagorean theorem and so on we use these laws where do they come from did laws of math evolve well I mean we've seen something we've seen a shape that's incredibly complex and beautiful and in the natural world in the physical world when we find something like that an organism that's incredibly complex and appears well designed the secularists say well that evolved right yeah we used to be very simple but then it gradually became more complex over time is that gonna work for math it doesn't really work for biology but it is it was it like the Pythagorean theorem didn't used to be true but it gradually well no did to two plus two used to equal three but then it slowly changed and now it equals four and now it laws of math don't evolve do they they've always been exactly as they are now that we discovered them over time but it's not like two plus two ever at one point in time equals something other than four they've always been the way they are now there's no such thing as evolutionary math everybody does math like a creationist is that interesting what are they profess it or not were they created by people well we you know Pythagoras created the Pythagorean theorem really the triangles not add up that way before Pythagoras well he just discovered it and he wasn't the first by the way but he was able to demonstrate that it's very clever they're not created by people laws of math worked perfectly well before people were around to describe them the way the planets orbit the Sun they obey what are called Kepler's laws and those are mathematical the period of a planet squared is equal to its distance from the Sun cubed in the appropriate units and so now was that was that the case before people yeah a few days before people because planets are mailing day for people are made on day six yeah they but my point is the planets orbited perfectly fine before people came along and they orbited according to laws of mathematics and even the second wrist would concede that so my point is people did not create laws of math because math worked perfectly well before people were around to describe it did they come from the universe that's a common belief especially among secularists is that well the universe behaves a certain way and we call that math but I think that is utterly indefensible because there are things in mathematics that have no analogy in the physical universe for example the number of dimensions the physical universe has three dimensions of space one of time in you can have any number of dimensions you can have sixteen dimensions if you like there's a thing called Hilbert space that has infinite number of dimensions that has no correspondence to anything in the physical universe and yet it makes sense there's rationality to it so my point is math goes beyond the physical universe the physical universe doesn't get infinitely small you get down the level of atoms and then in quarks and then there's kind of a quantum fuzziness there but these shapes go on forever so math math didn't come from the universe now it's interesting that math can describe the universe but that's a separate that's a separate question that's a separate puzzle for secularists obviously math doesn't come from the universe because it goes beyond the universe you can do things in math you can't do in the physical universe you can have infinities in math you can't have those in the physical universe in terms of infinite lengths and things like that seems to me that math laws of math stem from the mind of God and the Christian worldview I can make sense of numbers numbers are what God thinks of quantities which is how they exist before people you see and laws of math they stem from the mind of God laws mathematics is the way God thinks about numbers that's what math is if you want to study it right you need to you need to know something about God laws of mathematics are conceptual they exist in the mind they're universal meaning they apply everywhere right it's not like two plus two equals four well sure here on earth but on the moon it might equal five or seven no they apply everywhere don't they their invariant meaning they don't change with time two plus two equals four today and tomorrow and last week and next Thursday it doesn't matter right yeah and we all assume that and they're Exceptionalist it's not like two plus two equals four most of the time and every now and then it's seven no it doesn't work that way does it and if you think about it these properties of laws of mathematics make sense in light of the fact that laws of mathematics stem from the mind of God because God's thoughts are conceptual because all thoughts are conceptual so naturally laws of mathematics would be conceptual they would be universal because God is omnipresent he is sovereign over all creation he's everywhere and so his thinking will govern correct thinking everywhere in the universe a God does not change with time therefore laws of mathematics will not change with time the way God thinks about numbers today is the way he thought about numbers yesterday and the way he will always think about numbers because God does not change and laws of mathematics have no exceptions because God is sovereign over everything and so they they can't they cannot defy their Creator that way they can't and so I would argue that the Christian worldview can make sense of fractals we can make sense that mathematics has beauty built into it and complexity built into it we can make sense of laws of mathematics and the reason that they are universal and invariant and exceptionalism it all stems from the nature of God the Christian worldview can account for this the naturalist has a problem somebody who believes that nature's all that there is he's got a problem because on the one hand laws of mathematics are conceptual to exist in the mind you can't stub your toe and a law of math accidentally swallow one you can't do that they're non-physical on the other hand laws of mathematics existed before people so on the one hand they're a product of the mind on the other hand they existed before human minds but you see in the secular view human minds are the first unless there's aliens or something out there right and even then the mathematics would exist before then because the universe is governed by mathematical laws and so the naturalist has a real problem on his hands he's got to account for laws of math that are conceptual and yet he doesn't have a mind beyond people to appeal to this problem but in the Christian worldview it makes perfect sense because we understand there's a mind beyond people the mind of God that is sovereign over the entire universe I can make sense of laws of mathematics and their properties the secularist can there are also physical fractals this is kind of interesting now the perfect fractals we've discussed that repeat infinitely those are only found in mathematics mathematics goes on forever the physical world you zoom in so much and you get to the level of atoms and things stop being fractal but nonetheless the physical world contains things that are proximate fractals they repeat many times just not infinitely times okay and so let's take a look at some of these fractals in the physical world one that you're very familiar with in Nebraska it's snowflake yeah and these little gems from heaven that we get angry at and shovel them off for car but they're quite stunningly beautiful when you take a look at them on the microscopic steel they are fractal in the sense that they that that same basic pattern repeats maybe not exactly but it you can zoom in you still get the six fold symmetry due to the nature of the water molecule and so on so snow has a fractal shape to it it really does that stuff that grows on your windows I always thought this was amazing when I was a kid and I frankly I still think it's amazing these beautiful patterns that will form on your window and when the when the humidity's right and the temperatures right that's a fractal pattern you zoom in on it it branches and it branches into branches and so on and so it's quite lovely and ferns are fractal because you have a stem and it has and it has growing off the side stems which have growing off the sides of those stems which have growing off the side and so on and it repeats on smaller and smaller scales the the overall fern looks similar to any section of it that is a fractal I even found fractal broccoli so I guess broccoli is good for something after all so there you go it's called Romanesco broccoli it's and it's uh you zoom in on that you see it's it's um you know these these cone shapes but the cones are made of smaller cones which are made of smaller cones which are made of smaller cones and so that that is a fractal interestingly so the way coastlines are the way they divide the way the rivers branch and the branch into branches and branch into branches of branches the way the coast line is is fractal mountaintops the way they split is fractal the way they branch and branch into branches and so on clouds have a fractal nature to them am I looking at the entire sky am i zoomed in on one very small part of the sky hard to tell because the same kind of patterns repeat on smaller and smaller scales the way lightening branches is fractal because you'll have the main bolt and it branches in smaller bolts which branch into smaller bolts and so on and so lightning does have that fractal property to it and you can actually see it I think this is wonderful in in in time-lapse or or slow motion where you can see it and in that amazing until until the leader finally connects and most of the current goes down that that path but the way it branches is fractal so here's my question and why do fractals occur both in math and in the physical world right because we got we got mathematical fractals that have been built into math since creation only discovered in the 1980s and then we've got these physical fractals that people have known about for a long time that our approximate fractals lightning bolts and mountain mountain chains and so on why do they exist together I mean you have that's a that's a mathematical plot that doesn't exist physically anywhere in the world that's a multi broad it's Z to the seventh plus C and yet that does exist in the physical world got a lot of them outside right now this is part of the Mandelbrot set it's one of those tendril branches and yet that is a lightning bolt that exists physically so one is math it's not made of atoms it's it exists in the mind the other is physical it's made of atoms it exists in the physical universe we have this shape this that's actually a mathematical graph it's called a Barnsley fern and what it is is each leaf of the of the fern is the entire fern I'll show you this watch this the entire fern is one of its leaves see that that's just cool let's do that again you did infinitely right so that's a Barnsley fern and yet there are real ferns that approximate that now they don't go on forever right because it's some point you get down to atoms even before that the the fractal breaks down but they're similar one exists only in the conceptual world of bath the other physical you got that shape that's a mathematical plot and yet that grows on your windows you've got this shape that's a mathematical plot it does not exist in the physical world whereas this unfortunately does you got this shape that's part of the Mandelbrot set part of the valley of the double spirals you can't see that anywhere in the physical universe or stub your tail on it or or touch it but this you can see in your telescope not too far off the Big Dipper that handled the Big Dipper yeah I've seen it many times interesting so why do fractals occur both in math and the physical world now one answer to this and I think it's a reasonable answer it's just insufficient is that the physical universe obeys mathematical laws the universe obeys math so it stands to reason that if fractals can occur in math they could also occur in the physical world the physical world of basemath I agree that's good but then of course I'm gonna have to ask why does the physical universe obey mathematical laws that's well we just take that for granted yeah we do but why is that why is it that the universe which is physical made up of material obeys laws that are conceptual that exist in the mind how is that how is that possible well in the Christian worldview makes sense because mathematics is a reflection of the way God thinks and whose mind is in control of the universe gods and so naturally mathematics will be reflected in the way the physical universe behaves it makes sense the universe is upheld by the mind of God God upholds all things by the word of his power and so the way God controls the universe will be mathematical because God thinks mathematically so yes the universe will obey math but I would argue that the secular worldview can't answer that what's that human behavior well God controls God does control us but he's given us freedom of choice so we're free to sin right and the physical universe doesn't have that option the physical universe has no option but to obey God we but it has fallen that's that's true but nonetheless it's still obeys it still obeys him perfectly God cursed it and it it was cursed according to the way that that he intended so so yeah I think we can make sense of human behavior and the Christian worldview because in our worldview the physical universe is not the whole ball of wax there's more to reality than the physical universe there's the spiritual world as well and in terms of the way our spirit interacts with the physical world it's called the mind-body problem that's an interesting issue I'm not gonna get into that except to say that in the Christian worldview we can make sense of the fact that we have a mind where's there's something beyond there's something more to us than simply our atoms is that right we have a spirit and so in the Christian worldview the physical universe is not the only thing there's more to reality than the physical universe there's God as well so but I'm going to argue that the secular worldview can't make sense why'd the physical universe based mathematical laws why there or frankly why the laws of mathematics have the properties that they do why is it that laws of math are universal and frankly how could you possibly know that how do you know that laws of that laws of mathematics work in the Andromeda galaxy you've never been there and yet we all assume that every astronomer I've ever met assumes that the laws of math work the same in the distant universe as it does here and I would argue it makes sense in the Christian worldview because God sovereign over the under aamna galaxy just as he sovereign over the earth and so that makes sense why is the universe compelled to obey math hmm well in the Christian worldview it's because the universe is controlled by the mind of God and God thinks mathematically yeah but in the secular worldview there's no explanation for this you don't believe me dr. eugene wigner who is a brilliant physicist I believe he's a Nobel Prize winner wrote a wonderful article entitled the unreasonable effectiveness of mathematics and the Natural Sciences in which he attempts to answer this question why is it that the physical universe obeys these conceptual mathematical laws why is that and it's a wonderful read and by the way I'm not making fun this guy he is brilliant he really is but my point is he's not thinking as a Christian and so what what does he come up with he says well it's difficult to avoid the impression that a miracle confronts us here were the two miracles of the existence of laws of nature and the human minds capacity to divine them he says it's it's weird enough it's it's miraculous enough that there are laws of nature that are expressed mathematically and what's even more strange is that the human mind which I suppose in his view is just a chemical accident has the ability to discover those laws of nature and they're congenial to our understanding and there some of them are very simple like F equals MA well that's nice and convenient isn't it I mean God couldn't have made that simpler e equals MC squared y squared rather than two point seven 365 one squared it's perfect too as if the universe was made to be understood at least partly and he says it's difficult to avoid the impression that that two miracles confront us here the existence of laws of nature which are mathematical in nature and the human minds of the ability of the human mind to extract some of those to discover those so what is his conclusion what does he come up with here's his conclusion the miracle of the appropriateness of the language of mathematics for the formulation of laws of physics is a wonderful gift which we neither understand nor deserve it that interesting and I have great respect for him for admitting that that in the secular worldview he cannot account for why there are laws of mathematics why they exist and and why the universe obeys them and frankly why the human mind is able to extract them and understand them so and I and I agree that there is no solution in the secular worldview then the Christian worldview it makes perfect sense doesn't it because we have a mind that is sovereign over all nature its sovereign over concepts like mathematics and its sovereign over the physical universe as well and that's the mind of God so I can account for the success of science in my worldview I can account for fractals that's not to say that I understand everything about them I don't their infinite but I can at least I have a worldview in which they can exist and it makes sense that we can have things like fractals so we've seen that that beauty tremendous beauty of infinite complexity is built into numbers amazing revealed when we plot them by these little formulas numbers we've seen our abstract conceptions of quantity they exist in the mind and so when we study these fractals we're studying the way God thinks or at least one aspect of the way God thinks and we get these little glimpses into infinity like wow God's mind is awesome concepts require a mind and so when you're studying numbers you're studying the way somebody thinks about something and of course we've seen that numbers exist before people and therefore they're a reflection of the way God thinks and not always the way we think we can make mistakes in math God cannot the secular worldview cannot account for the existence and properties of numbers or mathematical truths and we've seen we've seen how that flushes out and we've seen that admitted by by a brilliant brilliant physicist numbers existed before people yet there are conceptions meaning they require a mind and that implies that there's a mind before people laws of mathematics are universal same everywhere invariant they don't change with time they're abstract they're not physical and all those things make sense if laws of mathematics are the way God thinks about numbers and so we can explain that because God Himself is omnipresent and he doesn't change with time and he is of course his thinking is abstract he himself is non material so of course we can have non material things that exist in the Christian worldview the physical world of contains fractals as well at least approximate fractals and we can make sense of that but the second a rule of you can't because why the physical universe of based mathematical laws according to dr. Wigner it's a it's a miracle that we neither understand or deserve but in the Christian worldview we can make sense of that because the universe is controlled by the mind of God the Bible says in God Himself says in Isaiah I will accomplish all my good pleasure God upholds all things by the word of his power and so he does control the universe and so again check us out Biblical Science Institute pick up some of the resources if you can and I'll see you back this afternoon for the Q&A session thank you very much [Applause]

Channel: Sound Words

Views: 40,855

Rating: 4.7943926 out of 5

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Id: kEyPWJVYp84

Length: 58min 57sec (3537 seconds)

Published: Fri Feb 22 2019

Reddit Comments

[u/xDeityx]

The Mandelbrot tour is interesting but at around 40 minutes when he reveals himself as a creationist and starts arguing against 'naturalist' straw men arguments he goes off the rails. Good up until 40m, but then the amount of woo unfortunately kills it.

[u/happinessmachine]

Best explanation of the Mandelbrot Set I've seen yet!

[u/Felix_The_Mage_]

Math can generate complex shapes, therefore christian god of bible must exist.

QED.

lol