Video Transcript: Our Mathematical Universe

So all day yesterday, I was working on this astronomy course. And in the evening, my wife and I had to run some errands and my parents came over to our house to watch our kids.  And they brought with them, they brought with them this package.  So this came in the mail to my parents a few days ago, I guess, and it came from an old friend of my mom's from the US state of Washington.  And I don't know this woman, and they only see her maybe once a year.  But in the package, there was a little note, a very little note.  It was folded up like a paper airplane, and it says, “Hello, Bill and Marilyn,” that's my parents, it said, “I saw this book, and God said to send it to you, sincerely,” and then the people who sent it.  I don't know about you, but that sort of thing doesn't happen to me every day, and my parents, it doesn't happen very often, either. And so the book that she sent to my parents was this:  The Hand of God, Thoughts and images reflecting the spirit of the universe. 

And it gave me chills when I saw it.  My parents brought it to my house because they knew I like Astronomy, but they had no idea that I was working on this course. And it's full of beautiful pictures of the universe taken from the Hubble Space Telescope, as well as quotes; quotes not only from the Bible, and Christians who've studied astronomy, but also from secular astronomers who have seen glimpses of God in their study of the universe.  So this is very meaningful to me. And to me, this points to the amazing God, that we all serve; to God who doesn't speak by thundering booming voices in the clouds but by the whisper that comes from a package in the mail, when you least expect it.  So I thought maybe this would be a great thing to pull from throughout our course and I'll share some quotes from this book with you as we as we progress, because I don't really know what else to do with it.  But clearly God sent it for us to have which is cool, very cool. 

To start out, I’ll share one of these quotes, this is a quote from Paul Davies, who is, a he's not a Christian astronomer per se, but he's very open to the idea of God, because of his study of physics and, and astronomy, and this is a quote from him. It says, “There is for me powerful evidence that there is something going on behind it all.  It seems as though somebody has fine-tuned nature's numbers to make the universe, the impression of design is overwhelming.”  That's coming from someone who is not necessarily believer in the God of the Bible, but they're seeing the fingerprint of God written in the cosmos.  

One of the most amazing ways that we see that is in the mathematics that's prevalent throughout all of nature.  I want to show you a couple of examples of that. This picture, the first picture in the gallery is the shell of a nautilus, a sea creature that's been cut open and you can see just an open an unbelievable pattern and symmetry in this shell and its chambers as it goes around.  This is a creature and somehow it has constructed this shell to have this beautiful mathematical spiral written into it. 

Let me show you another example. This is a sunflower seed and sunflowers seeds… or this is like the head of a sunflower and a whole bunch of seeds. The pattern of the seeds in a sunflower illustrates a very precise mathematical pattern.  And what's cool about this, and what I hope is that you see from these examples is that, you know, language in our universe in our planet, there's so many different languages, there's really no universal language. There's Chinese, there's English, there's German, Spanish, there's no language which encompasses even our whole planet but there is a language which encompasses the whole universe and that language is mathematics.  When we study the universe, and these patterns, really the only way we can describe them is with numbers.  And that's powerful.  Like God is telling us something with that.  God loves numbers, too. And that's a way that He's communicating with us. 

There's very special numbers.  In fact, we see this time and again, in studying many different parts of the universe, is that there are particular numbers, for example, whole numbers seem to be very important. The numbers 1, 2, 3.  It seems really simple but almost every law of nature has a 2 in it.  Gravity goes as distance squared; raised to the power of two.  How many dimensions are there?  There's three dimensions that we perceive.  So those whole numbers are important.  But there's other numbers that are very peculiar.  Like Pi, is probably a number you've encountered, right?  Pi is the ratio of a circumference of a circle to the diameter of a circle.  And any circle, the ratio is exactly Pi.  And more than that though, Pi comes up in crazy places.  It also comes up in gravity; it comes up in the period of an oscillating pendulum; it comes up in optics; it comes up in just insane places where you'd never expect to see the number Pi, but it shows up again, and again. 

Well, on a sunflower seed, we see another number, which is sometimes called Phi.  It's the golden ratio.  And I can illustrate it here for you this pattern, and a sunflower seed can be seen here in the third picture in our gallery, which is showing the angle between consecutive seeds. So, if you are building a sunflower by hand, putting each seed and you took a protractor and you measure the angle around the circle, every time you placed a seed, well, to make a sunflower seed, you would have to use the golden angle.  And like Pi, this is a number that shows up time and again.  It shows up in seashells. It shows up in famous artworks that people have said this is a perfect ratio.  It's a very simple relationship, kind of like the circumference to the diameter.  But it has to do… it's a little complicated, but it's again, a simple, it can be written very simply.  So the point, though, is that at exactly this golden ratio, you get a seed pattern like that of a sunflower.  But if you were to change that angle by just a tiny bit, by one degree, you would get a dramatically different pattern of seeds; either on this - as if you were to subtract one degree from that angle… this is if you were to add one degree to that angle.  So in the case of a sunflower, it's a very precise angle that these seeds are in this pattern. It's amazing. This is one example of which there are many. So numbers play an incredibly important role in the universe and in our understanding of the universe. 

In a process of science, we try to measure things. And the more we measure, the more we can find these patterns and relationships and describe them with equations and numbers. But measurements are very specific in the sciences.  A measurement is not just a number, a measurement is a number and a unit.  So take for example, this fourth picture in our gallery. This is a typical tape measure. And you see across the top of the tape measure you have the numbers 1, 2, 3, 4.  But at the bottom you have 1, 2, 3, 4, 5, 6, 7, 8, 9.  If you were to measure something with this tape measure and tell someone “Oh, you know, this door is 3 wide,” well, they would say, “Well, which 3 do I look at, this 3 or that 3?”  And so you need to specify not just the number but also the units.  If it's 3 inches, we'd use this top scale; inches is the unit of the top part of this particular tape measure. And the bottom, in this case, is centimeters.  So units, every measurement in all of science has to include units. 

Now, units in science, we tend to use the metric system for lots of reasons, but the biggest one is because it's a simple system that's based on increments of 10.  If you have a meter, and you divide that by 10, you get centimeters, if you divide that by 10…. Oh no, wait.   I'm sorry, you take a meter divided by 100, you get centimeters.  Divide that by 10, you get millimeters.  Everything's in very round numbers.  Whereas the English system, where you have feet, and there's 12 inches in a foot, there's 5280 feet in a mile.  It's not round numbers, and so it's not as easy to work with. 

Now, another advantage of working with units of 10 is that in astronomy, and really all of science, but particularly in astronomy, we deal with an enormous range of sizes.  We will in this class, learn about the whole universe and entire galaxies, the biggest things that exist, but we will also talk about atoms, the smallest things that exist, and to cover this huge range, we need a way of writing numbers that is easy to work with.  If you were to write out the diameter of an atom, as a decimal number, you'd have to write 0.000000, like 15 zeros, and then a one.  And if you were to write out the size of the Milky Way Galaxy, you'd write 100000, if you're writing zeros all the time.  And so what we have is a simpler way of dealing with that and that is scientific notation. 

Scientific notation is when you write the number 10 and then you write an exponent - a number up above, like 10 to the power of 2, (102), or 10 to the power of 9 (109).  And what that number means is that you're taking 10, times 10, times 10, times 10.  It's exponent, and it's raising it to that power.  But in practice, what that number up there is how many zeros there are after the one.  So for example, a billion has nine zeros in it. And so 109 is a shorter way of writing 1 billion.  So you'll read more about that, scientific notation, but it's something we will encounter throughout our course in our readings and elsewhere.  And so it's useful to become at least a little bit familiar with the way scientific notation works. 

And the last picture in the gallery I wanted to show you is an illustration of the scientific notation and the amazing size scale of our universe from this very, very small, to the very, very big.  And it comes from a famous video made in the 70s, I believe, called Powers of 10.  Each of these squares that you see in this picture represents like a view on the universe, but at a different scale.  And in a sense, what you can do is start right in the middle here at 10 to the power of 1 (101).  And so that is a square that's 10 meters across, because (101) means it's one zero, so it's 10 meters.  And in the middle, you see a man or a woman sitting out on a blanket for a picnic.  And now you can start with that view and you can go either direction.  You can zoom out and see the biggest scales of the universe, or you can zoom in and see the smallest scales.  And so throughout this video, Powers of 10, but also represented here in these pictures, you can zoom outward and zooming out are these pictures across the top.  And each one is labeled, you know, here we go, 103 and you see the sort of city block. 10 and you see the entire city of Chicago.  10+7, you see the entire planet.  You keep going all the way to 10+21, where you see the whole Milky Way galaxy. 

Then zooming down, you can see zooming in 10-1. So that's interesting, right?  You can use negative numbers if you want a really, really small number, like 0.00005 or 00001, but there's five zeros in there. You would say negative five, so that negative is what suggesting it's a small, small number.  So we have 10-1.  And we see 10-2 we see skin cells.  10-5 we see the nucleus of a cell.  We see the DNA, and then we go down and seeing individual atoms at 10-14.  

So again, this enormous scale, part of showing this is to think about scientific notation but another part of this is to think about this crazy conundrum here, this paradox, which is here we have humans, you and I, who live in this sort of scale, in the scale of 1 to 10 meters. That's sort of where we live.  And yet, we're located between these crazy extremes of overwhelming size where we are nothing in that huge universe, and at the other side of the cells and atoms within the cells, we are an entire universe.  Our bodies are an entire universe of to those cells.  You know what I mean, like, right?  I mean, you think about the bacteria that live inside our gut, their whole lives are living in our inside our stomachs, we are their planets.  And so there's this crazy paradox that we are so small and nothing, and yet we are so big and important.  And when we take that into our understanding of our faith, we say even how is it that God cares for us in this crazy, crazy paradox of context? 

I want to share with you one more quote from this book, which comes again, from someone who is a secular astronomer, Carl Sagan.  He certainly was not a friend to religion in his career. And he wrote many books. One of his books was a novel called Contact, where he wrote about the discovery of a signal from space. And this is a brief passage that one of the characters, the main character in that book, and she is saying she has a profound experience.  And I think it matches in an amazing way the kind of profound experience that we have when we encounter God.  So this is what this main character says in the book, she says, and remember, this is written by really an atheist astronomer, “I had an experience I can't prove.  I can't explain it.  But everything that I know is a human being, everything that I am tells me that it was real.  I was part of something wonderful, something that changed me forever, a vision of the universe that tells us undeniably how tiny and insignificant yet how rare and precious we all are.  A vision that tells us we belong to something that is greater than ourselves, that we are not, that none of us are alone.”

Isn't that an amazing reflection from someone who really, as far as we know, didn't experience that personal relationship with Jesus Christ.  But we know that we are not alone.  That Christ is with us wherever we go. 

All right, we'll see you next time.