Science and Wonder
From the Hosts
Today David Maxson hosts a panel discussion on the wonders of Math and Physics with Greg and special guests David Lawrence and David Farschman! David Lawrence is a physicist investigating outer space, and David Farschman is a long-time teacher of mathematics. Tune in for awe of God, His creativity, His communication, and the mathematical words that describe the world He made and holds together--and why math and science matter for the people of God as we halt toward Zion.
This Episode Features: Wonder At God's Handiwork; Lawfully Wedded Husband; Two More Davids; Mongolian Archery; The Scientific Mind Of C.S. Lewis; Christian Schools Are Bad At Science; Being Good Ain't It; God's Credit Card; Rotary Numbers; Mathematical Words In A Minor Key; and Safe To Say Everyone Here Today Is A Nerd, But You Don't Have To Be.
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Welcome to Halting Toward Zion, the podcast where we limp like Jacob to the Promised Land and talk about life, the universe, and everything along the way. I’m not Emily Maxson. I proposed this episode to Emily awhile back, and when we actually got around to scheduling it, she told me that I was hosting it, so I’m David Maxson, better known around these parts as “the lawfully-wedded husband.”
Greg is still here, along with our friends, David and David. Since there are three Davids and we’re all new on here, we’re going to do a round of introductions in a moment. Then after that we’re going to be talking about science and mathematics and really the beauty of God’s handiwork as it’s woven throughout the universe in everything that we look at, everything that we touch, and everything that we see and think about.
I have no particular idea of what exactly we’re going to be digging into. I anticipate black holes and imaginary numbers showing up somewhere around here. But whether or not you’re interested in
math-y stuff or science-y stuff, I hope you’ll stick around and hang out with us. Our goal here is really to wonder at the majesty of God. We’re not here for competing on Star Trek trivia, because Greg would already win that competition.
So some quick introductions. We’ll start with David Farschman. David was a student of Greg’s back in the day, and the father of one of my childhood friends, so David, go ahead and share your background. What’s your formal education and career? Your general passions? And then a brief summary of your coming to Christ.
My formal education is that I attended Shasta College. I mention Shasta College simply because, being a community college, it was nevertheless extremely formative because I had several fantastic teachers there. In fact, two of the best math teachers that I had were there, and they directly guided me into going from being a German major when I really had no skill in German at the time, into being a math major. I moved on to UC Davis to complete my Bachelor’s in Science. Then, being a little lazy, I stayed at UC Davis to get my Master’s in Science, which I completed in 1991.
From that point on I have been, at various times, teaching at the community college level usually, and I’ve taught at a wide variety of community colleges, being a road warrior for some time as a part-time teacher. However, I eventually found my way to Pasco Scientific, a company that manufactures equipment for teaching physics and science, and ended up being an enterprise systems software engineer that keeps the company running. But at the same time I have been teaching at Sierra College a variety of classes. Integral calculus was the last one I was getting to teach.
The mathematics provided the logical reasoning and the strict methodologies that allowed me to jump over to programming with relative ease, so it proved a very good point of study.
Then coming to Christ – I didn’t come to Christ. I was captured kicking and screaming and dragged to Christ, despite having, by God’s grace, been raised in a Christian household. Nevertheless, coming to know God’s Word and coming to submit myself to what God’s Word said, as opposed to what I in my better judgment thought it should be saying, took a little bit of time and patience. And in God’s grace, God gave me an excellent teacher who refused to answer many of my questions, and instead forced me to have to dig for myself.
So arguably I came to Christ before I have memory of coming to Christ, or I came to Christ when I was four years old, or I came to Christ when I was 16, but definitely I came to Christ when he reached out, seized me by the heart, and drew me to him. After that I can go with whatever version of coming to Christ you want.
The other one I forgot was general passions outside of career and education.
My general passions include storytelling, reading, archery, particularly recurve archery using the Mongolian release, with the hope of someday using it with my other passion, which is horseback riding. I have hopes of being able to combine the two sports into one as opportunity provides itself.
Yes. It’s much easier to shoot on the right side of the bow for a right-handed person who is also right-eyed.
So is Joseph, and I have him shooting the Mongolian release off of the left side of the bow. And suddenly, where he seemed to not be able to hit the side of a barn with his fist, he can now hit targets with a bow. It’s pretty cool.
Next we have David Lawrence. David is an elder at my church, specifically our care elder, and runs a study of Psalms in an evening fellowship that we’ve been part of for several years, and he’s been a good friend to us while we’re here on the east coast. The same questions to you, David – your formal education and career, your general passions, and a brief summary of – just to spite David Farschman – your coming to Christ.
My formal education kind of got started when I was four years old and decided I wanted to be an astronaut. I was pretty single-minded in wanting to do that. I grew up on the Apollo program, and seeing these guys walk around the moon I thought it was the coolest thing ever. I have bad eyesight, so being a pilot was out of the question. I talked to some folks and they said, “Well, go be a scientist.”
I was a physics major at Texas Christian University, kind of following my father. He was also into physics. It was always with a goal of, “What can I do to get into space?” I thought that was just the neatest thing. I ended up getting my Ph.D. in physics at Washington University in St. Louis, where we ended up flying high-altitude balloons with about a 2,000-lb payload to measure galactic cosmic rays from the top of the atmosphere. We took it up into northern Canada in the tundra, and nothing is there except for balloons that fall from the sky. It was really cool because that was a program that, as a grad student, you actually got to put all the hardware together and do the whole thing.
I applied to the astronaut program and never got in. That was a great blessing, and since that time I’ve had over a 20-year career working on space flight hardware. I started out at Los Alamos National Lab back in 1996 and spent 13 years there, and then the Lord dragged us kicking and screaming to Maryland because he knew there were good opportunities here. I’ve since been here for over a decade at a place called Johns Hopkins Applied Physics Lab, still doing space flight stuff.
We’ve worked on many different missions, but essentially we use gamma rays and neutrons that are emitted off of planetary bodies to measure their elemental compositions. Basically, what is the moon made of? What is Mercury made of? I’ve been involved with missions to the moon and Mercury and Mars, measuring water on the moon and water on Mercury.
Right now I’m involved in three different builds for three different missions. One is a NASA mission called Psyche, and it’s going to be a spacecraft that orbits an asteroid called Psyche that we think is metal-rich. The second one is a Japanese mission called Martian Moons Exploration, and it’s going to orbit one of the Mars moons called Phobos and try to figure out how it was formed. Then finally, kind of cool, APL where I work actually got selected for a mission about a year and a half ago to fly a quadcopter to Saturn’s moon Titan. It has a super-thick atmosphere. I can talk more about that, but it’s really wacky and crazy and it just might work.
Passions – I love space. I think it’s awesome and I always have. I’m very into my family. We have six kids and a very busy household. Right now it feels like it’s work and family and church. I love reading. I love history. I love biographies. At best I’m an amateur in theology. I cannot count myself as any expert. I love sports.
Goats and chickens, and my older sons have got me into Premier League, so it’s a regular thing to watch Premier League highlights. The proper name of the sport, of course, is football, not soccer. So that about covers it. I like all kinds of things. I love talking theology and science and philosophy. A good conversation is fabulous.
Coming to Christ – I grew up in a Christian household, Presbyterian, but there was probably a lot of wandering around. The other David, your story, kind of resonates with me but the timing is a bit different. I think where the Lord really grabbed me by the scruff of the neck was when I was in graduate school with a whole load of different things going on. I’m in a graduate program with a whole lot of materialists and really struggling with, “How do you deal with miracles? How do you think about all these things in the Bible?” Then I stumbled upon C.S. Lewis.
He’s a literature guy, but for me he was one of the most scientifically-minded people that I could have read at the time because of the way he made sense of things and the way he made sense of the Bible. It was a combination of reading Mere Christianity, Miracles, The Great Divorce, and a whole load of other things, and other personal things going on, that I was just smitten with the Lord, and I haven’t looked back.
Next we have Greg Uttinger. If you, the listener, have heard any of the other episodes you’ve heard Greg. He’s the centerpiece of this show, but since the rest of us are new I’m making Greg do his introductions too. So Greg, would you share with us your background as well? You’ve been a teacher, you were my teacher, you were Emily’s teacher, you were David Farschman’s teacher, and there’s a long legacy there. What got you launched into that?
David Farschman and I started in a small Christian school, North State School in Anderson, CA. In my four years there I took one semester of physical science. That was it. That was all the science I had. There was a section on chemistry and valence electrons that was just enough to see me through Chem A – bonehead chemistry – at Shasta College, which I also went to.
Somewhere along the line I thought, “Huh, Christian schools aren’t great on science.” There were a number of reasons I declared myself a physics major, and I think they were all bad. One that God used was, “Well, if nothing else you can go back to the school you graduated from and you can, among other things, teach science.” I knew I would never teach myself physics, chemistry, or calculus, so I figured I needed someone to teach me these things.
History, lit, English – I was fine there. I can read, but the detailed skills of math and science were beyond me, but I’d always been interested in science. Like David Lawrence, I grew up in the shadow of the Apollo program and remember Neil Armstrong stepping on the moon. Like every little kid, when I was 5 or 6 I said, “I’m going to be an astronaut!” Well, David Lawrence actually pursued it, I didn’t. It wouldn’t have mattered. My eyesight is bad, too.
Anyway, I went to Shasta and graduated as a physics major with a math minor, and then went on to a little Christian Reformed college in northwest Iowa. At that time I was getting burned out on college because I’d already spent three years to make up for the non-science education I had had, and I was tired so I declared myself an education major because, “Hey, I’m going to go teach!” so that knocked off the number of math and science courses I had to take.
I graduated, and originally the plan was a Master’s and Doctorate. No, I was tired, so I went back to a little small school and, for as long as the school stayed open, I taught all levels of high school math and both chemistry and physics, to whoever needed to take them.
When the school closed I came here to Sacramento and was hired to do similar things, but little by little we got other people who were as competent or more so than I was, so now I teach Physical Science, I teach an algebra class, and I teach chemistry, and spend most of my time teaching other things, to the point that when people ask about it they say, “So you were a history major, right?”
Exactly, but I love mathematics more than physics. There’s a puzzle quality. You were asking about passions – puzzles of all sorts, chess, but particularly British mystery stories of the cozy variety. I like to read, and storytelling. What David F didn’t say bluntly was roleplaying in the old-fashioned way where you actually sit around with a bunch of people and play out a story. David, by the way, is fantastic at orchestrating background music so that the music hits just the right place at the right time in the right story.
Which reminds me, I also direct theater now and then, which became really difficult last year with COVID.
Coming to Christ – well, you’ve already said it. I grew up in a more or less Christian home. My mom was a devout lady, though quiet in her faith. My dad had grown up in the church but wasn’t involved. Through the Christian school I was in and through my mom and through our church, and particularly through good evangelical preachers on Christian radio, someplace in my teenage years I finally understood the gospel.
Like David, I can say, “Well, I came to Christ at…name a point,” but the time when it became most conscious, when God really convicted me of my sins and showed me that being good ain’t it, was somewhere probably in junior high.
As David Farschman also said, you can cite numerous other times when God grabbed hold of me and said, “No, not that way, this way. No, that’s not faith. Get with it here. You need more faith.” So that’s been an ongoing process.
Today I continue to work for a small Christian school. It’s a little bigger than what I came from, and I do ghost writing on theology projects. I’ve mentioned before Heirloom Audio. If you’ve never been there and seen the stuff they do, I have a hand in that, a really small hand. It’s a great ministry that tells stories about historical characters based on G.A. Henty’s novels, so there’s some of what I do – and this podcast, which was not my idea, by the way. David and Emily came to me and said, “We’ve listened to all your stuff online. Can we do something together?”
I’ll introduce myself briefly. I’m primarily the host for the evening, which just means running the conversation, but the reason I’m running this conversation is because this is a topic I’m passionate about. I’m David Maxson, Emily’s lawfully-wedded husband.
I studied computer science and programming actually long before I went to college. There was a group that taught me to code in high school, and then I went off and did the same thing in college, and then I went off and did the same thing in my career. I really love software and everything about it, and I’ve gotten into the fields of artificial intelligence and data science. I like programming and I like multimedia editing. I like doing video and audio editing. I enjoy building this podcast from behind the scenes. I’m not the thing that makes it tick, but I appreciate my small part in it.
Known by many more people than listen to this podcast, I make music videos, my top one having over two million views at this point, which I’m very proud of.
It’s not irrelevant! We want to know which one it is so we can become like 2,000,001 and 2,000,002.
That leaves me feeling ashamed for not supporting my subscribers, because when you build a following, people kind of expect stuff from you, so anyway.
I came to Christ as a young child, and I feel like my story differs often from a lot of people who were raised in Christian families. I think I really was a Christian at that age. I don’t remember getting much older and having a turning around moment. It was on our couch under my mother’s teaching and her care. She taught us scripture in the morning and Christ worked on my heart and I was young enough that I don’t really remember any more than that.
I certainly spent the next several decades learning what following Christ means and entails, and learning the greatness of God’s grace by needing it. We have a good God and he brings us through all sorts of circumstances.
Our God is truly awesome in every sense of the word – in saving us, but also in his handiwork and the way that he’s made this universe for us to see, for us to glorify him for, and that’s what tonight is about. It’s about looking at the awesomeness of God everywhere in the universe, in our own minds, in the way we think, in math and logic, in the cosmos and its magnificent scale, and the subatomic particle, and really everything in between. So that’s where we’re headed.
Let’s start with something nice and simple, which is obscure scientific or mathematical realities that we find fascinating or interesting. David Lawrence, you had suggested this starting concept.
Sure. I have always been fascinated by the number i, for all sorts of crazy reasons. It’s the square root of -1. It shouldn’t exist, by all intents and purposes.
We’ll jump into controversy right away, that’s fine. When it’s introduced it shouldn’t exist, and yet it explains reality in an amazing way. How does it work? It’s this simple basic thing. It’s ei. It describes waves. It describes so many things that we have in the world. I am just incredibly fascinated with it. So now tell me why it should exist.
Okay. A lot of this comes from our naming conventions, in that as we started naming the numbers we started with the natural numbers, the ones we could count on our fingers – 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and added to that 0, which had a hole in it, so we called those whole numbers. And after that we started doing division with them. At that point we had addition, subtraction, and multiplication going, and we added division to the mix and this created ratios.
For a time we thought that ratios – fractions, ½, 2/3, ¾, 111/48 – described all the numbers in the universe, and eventually, having laid it out, we began to realize that there were missing gaps. The ratio numbers were called rational numbers, and therefore the numbers that fell in the missing gaps ended up being called irrational numbers – not because they weren’t reasonable, but because you couldn’t build a ratio to make them.
I’m looking forward to talking about two of those numbers. I often refer to them as signature numbers because there are numbers that are kind of like God’s credit card. We’re allowed to use the card. It’s got his name on it. It’s not ours, it is his, and if we’re going to do things we have to use it, but in God’s pleasure these are numbers that we can understand but not comprehend. Understanding is knowing how to work with something, knowing its characteristics as it is revealed in the universe, but to comprehend something is to fully know it from every angle.
Certain constants like i and pi we cannot actually write down except as a name. 1, 2, 3 – we can write those and we know what they mean. I can comprehend the number 1. I cannot comprehend the number pi because I can’t even write the thing.
So when we took those irrational numbers and the rational numbers and we put them together, they formed for us this beautiful number line that had no gaps, and we called these the real numbers. These are all names. We called them the real numbers. We ended up on a number line going from minus and off towards infinity, to plus off towards infinity, and we could advance back and forth across this line, but there’s something fundamentally missing.
We have now described all that mathematics can give us in numbers. But as you’re advancing backwards and forwards along the number line, how do you say “turn left”? The thing is, on all of our real numbers, we have no means of instructing a turn. The wheels on the bus do not go round and round. There is no rotation. There is simply advance or retreat.
Yes, because our naming convention lacked imagination. We imagined that we had discovered all there was to say about numbers, and that all of a sudden God threw in our face a 2-dimensional number. We’ve been working in 1-dimensional numbers and we thought that 1-dimensional numbers were the only numbers that were real, and yet all of a sudden then we encounter a 2-dimensional number.
That’s where the square root of -1 pops into this story, because when you define the square root of -1 you end up with something that actually turns right off of the number line, but if you keep working with it, it turns back onto the number line. But if you keep multiplying with it, it turns around again.
It starts at 1 and you multiply by i and you’re off the number line in an orthogonal 90-degree, if you want to go degrees. If you’re in radians you’ve turned a full pi radians. You multiple again by i and you’ve now turned – actually, you’ve turned pi/2 radians – but multiply again and you’ve turned pi radians. You’re now -1. You keep multiplying and it brings you back around to 1.
Imaginary numbers should never have been called imaginary numbers. They should have been called rotary numbers, and if they had been called rotary numbers I think people would have had a lot less difficulty wrapping their minds around them.
I’ll grant you that, because when you’re trying to figure out square of -1 you’re trying to do something in one dimension that is actually 2-dimensional.
The development of vectors and matrices actually came into existence because, having discovered a 2-dimensional number, we immediately wanted a 3-dimensional number and a 4-dimensional number, and we couldn’t find one. So we ended up breaking down complex numbers, which are “real and imaginary” mixed together into 2-dimensional vectors and matrices. Then that allowed us to step into 3 dimensions, 4 dimensions, and there’s no limit at that point as far as mathematically what games you want to play.
“Complex” is a terrible name too, because it makes everyone think “complicated.”
Yes, and there’s a lot of things in the world that are complicated. I would argue that spinning round and round is pretty complicated, because if you put your forehead on a baseball bat and you spin around 10 times, you’re going to find it pretty complex to stay on your feet afterwards.
I’ve been stealing David’s explanation of imaginary numbers for a long time, because in algebra it’s always, “What are these things?” Then I talk through exactly what David has said, and they say, “Oh, that’s it?” It pulls some of the mystery away. We’re just spinning. If you want to know more, you can talk to Mr. Farschman when he stops by to pick up his kids or something. It does help.
So enough bashing on David Lawrence’s answer. David Farschman, what’s your fascinating fact?
No, it’s not bashing on David Lawrence’s answer. It’s a fantastic answer and it leads right into my other two favorite examples. We’ve already talked about irrational numbers, and we have two of them that are of eminent use, one of which is pi, which we approximate using decimals – 3.14159265 blah blah blah for eternity – and e, which is directly connected to the Golden Ratio. It is the prime exponential base for describing how the universe interacts in any kind of cyclic way.
You can find e by taking the limit as n goes to infinity of 1 + 1/n, all of it raised to the nth power. If you let n go to infinity, make it infinitely big – and oh, there’s something to talk about, infinity – then the number collapses down to e – 2.71828, and that goes on forever.
Another number that we have to understand if we’re going to be doing physics, if we’re going to be doing any kind of interaction – by the way, I would argue that math and physics are so intimately connected that you can’t really tease the two apart. Pure mathematicians are spinning in their graves over suggesting that math needs to be connected to physics, but the two of them are intimately connected. If you tear them apart, in my humble opinion, you have stolen, you have ripped apart body and soul.
But with e, you have this beautiful exponential number that also people are familiar with from compound interest, and you’ve got pi, which we have from taking the circumference and dividing it by its diameter. Pity they didn’t just divide by the radius, actually, but that’s another thing altogether.
The amazing thing is you have these three irrational numbers, three numbers that cannot be expressed with fractions. And as Euler pointed out, they form an identity. These three come together to form an identity, and that identity is e2pi i is 1. So these three fundamental constants, which are all actually related, even though they have characteristics that are incommunicable between the three, nevertheless all three of them share fundamental characteristics related to rotation, and when combined these three are one, and I find that beautiful.
Rotation is a completely different concept of thinking – rotation and number lines, rotation in geometric circular space, and rotation in phase or signal spaces.
Exactly, and these three intimately come together. So that’s one of my favorites. If you have to grab one thing that you go, “Wow!” that’s one, but the world is filled with these kinds of “wows” and maybe we’ll even talk about infinity tonight, because that’s kind of cool.
I am not the mathematician that these gentlemen are, for sure. I teach teenagers. On a good year I may get to teach them how to do differentials in calculus the way an engineering student learns such things, so I really appreciate and really enjoy what they have to say about these things. I’ve heard some of it from David Farschman before and it’s always fun.
I’m going to pick something really simple: 1+1 = 2. As a Bible teacher and sometime theologian, that’s a profound statement. It’s so easy and simple and people are constantly saying, “See? Here’s something everybody agrees on. This is neutral ground. How could you possibly go wrong here?”
It is not neutral. It is now hated because of that, the concept of the absolute truth.
First of all, it’s an absolute, and it’s absolute that strikes at the heart of pantheism, because the pantheist should say 1+1=1, so apparently worldview does affect how you come to mathematics. And yet we don’t go to India or Tibet to study physics. They come to us, to American universities, because our worldview supports mathematics, engineering, and physics, and theirs doesn’t, and that’s kind of embarrassing and kind of rude of Christians to point this out, because you know we need to accept everybody and there’s got to be neutrality there someplace.
But 1+1, that’s just the first step. We could have the definitions – “What do you mean 1+1 is 2?”
“Well, if you take one apple and you combine it with one apple, you have two apples.”
“Okay, so now you’re making huge assumptions about reality and about epistemology. What do you mean we have this apple? What is an apple? How do we have it? How do we perceive it? Is it in the present? Is it in our memory? Are our memories reliable? How do we know our memories are reliable? How exactly do we check that one out? How do we know that causality holds into the future? That’s a huge assumption. As we’re counting these apples, how do we know it’s the same apple time and again? Are we locked in circular time?”
Then we get into things like this. So at the very basic level, while the Enlightenment was trying to find neutral ground to stand on in the wake of Newton’s discoveries, and saying if we could reduce everything to mathematics then we don’t have to argue about what the Bible says and kill each other in religious wars because we found the absolute that’s not tied to God, except in the sense that maybe God’s a mathematician, the Divine Geometer, who creates universes with a swipe of his compasses. But I’m sure he was polite enough to back out after that.
Yeah, he may have rigged the programming, he may have done the coding for the universe, but surely he does not interfere now. If we can figure out the coding with mathematical principles, we can take over the programming of the universe.
We could be as God. Oh wait, we’re stuck in the program. Uh oh. If there even is a program, and if you can even trust your mind to figure out what it would be and why math works and what in the world the connection is between something in your head and the external world, which you don’t even know where it came from or even if it exists, because you were trapped, for Hume and Kant, inside your own consciousness, so 1+1=2 is a starting point for everybody.
Yeah, then we go there – which by the way in passing, the production of The Matrix was one of the greatest boons to my teaching ever. I used to try to explain Immanuel Kant and couldn’t. Now I can just say, “Have you ever seen The Matrix? That.” The mind creates its own reality, and you can all be in it and yet none of it’s real, but you’ll never know that because all you’ve got is your own senses and perceptions recorded in your brain.
That simplified things a bit. The next bullet I had is the theology of math. Do we think that’s covered enough or should we dive into that as its own thing?
If you’ll let me deal with that for a little bit, and then I’m content to back out for most of the rest of the program and let these guys talk, because I would rather listen to them.
We come to the Bible, and the Bible gives us one God. As the Bible unfolds, we find this God is three persons. The mathematics here are interesting. There was a song that one of our teachers presented for review and it said “1 + 1 + 1 is 1,” and I had to say, “Um, no.” One person + one person + one person are three persons.
Now, if you want to change the labels, one person + one person + one person does involve one divine being. That’s better, but that would mean you actually have to teach your little kids labeling, which would be great, actually. You have to add, subtract, multiply and divide with labels, with units. All mathematicians would appreciate that. “Show your work. Label your answers.”
Use the correct units. So you get something similar with Jesus. “He’s 100% God and 100% man.” No, that doesn’t even make sense, but what we do get is that this one God does exist in three persons, which is to say number is an attribute of God, and to a certain extent so is basic arithmetic.
If you talk about the Father and then talk about the Son, you’ve added one person to one person in your conversation, and yes indeed, that’s two. There are two persons now you’re talking about. Add the Holy Spirit and you’ve got three persons. 1+1+1 is 3. 1+1 is 2. If you subtract the Holy Spirit from the conversation, 3-1=2. Basic arithmetic at the very least is an attribute of God.
Now the question comes, “Can we then deduce all of analytical geometry, calculus, and number theory from the being of God?” I don’t know. I kind of doubt it, but that’s pushing beyond revelation, and when it comes to the nature of God I’m suspicious. But at the very least we can see that God is finite in the sense that he can be numbered. He is infinite otherwise. There’s one God. The number of attributes he has are infinite, as Bavinck says in Doctrine of God.
That to me, by the way in passing, was a huge revelation because I always struggled with the systematic theologies that would list half a dozen or so attributes of God and never suggest there might be others. I began to think, “Where’s his creativity? Where’s his sense of humor? Where’s his sense of the dramatic?” until I finally came across Bavinck’s comment, “Well, he’s an infinite God. The number of attributes is infinite.” Oh, of course. That explains everything, doesn’t it.
I’ll also say for deriving of mathematics from the nature of God, there’s a great book called Godel, Escher, Bach: An Eternal Golden Braid. It’s worth the read for anyone, and it’s a good approachable introduction to how mathematics gets structured from the ground up at sort of a pure logic level. One thing he discusses is you define your axioms, which is just a fancy word for your assumptions, your presuppositions, and you build everything up on top of that.
I think as a Christian we can look at God and say, “Well, there is such a thing as three-ness, and there’s a such a thing as one-ness,” so we can work from that and define some axioms and build up a concept of reality. Yet, we would be over-confident to assume that therefore we’ve arrived at a full and comprehensive definition of reality, because you build up Euclidian space, and Euclidian space makes sense until you scale it up and throw black holes into the mix.
Euclidian space only exists in our imaginations. We spend years teaching Euclidian space and we don’t live in it and we have no examples of it in the universe, except in our imaginations.
Little snapshots, because the reality is we’re dealing with hyperbolic and parabolic curvatures. We’re dealing with a much more complex universe than Euclid imagined.
It’s not that there is no reality. The number line in a sense does exist, but so do imaginary numbers. And just because we thought we had comprehended the number line, that didn’t mean that we fully comprehended everything there was to know.
We normally get ourselves in trouble at the point when we say, “We have comprehended this particular concept, this particular topic. We’ve got our hands around it. We’ve wrapped our heads around it. We know what we’re doing,” because that’s about the time when the model is going to break, because these are all building models of the universe, and God takes pleasure in preventing our models from becoming idols.
So God provides both the foundation for knowing true things, and the infinite unknowable God in the sense that we can’t put him in our hands and say, “This is all.”
The infinite knowable – not knowable, but knowable from the standpoint that he’s revealed himself to us – the knowable God is incredibly necessary to us because when we’re dealing with Kant, and if we are being honest and thoughtful, if we insist upon starting with ourselves, we end up cutting ourselves off from the rest of the universe. We can’t actually know that our senses are to be trusted, and it’s very easy to manipulate them, mess with them, and leave us in question as to what is actually there and what is actually true.
The heart of communication in Christianity is not that we found God or that we have been able to deduce from our experiences, our knowledge, what there is to know about God. Rather it is that God has reached out and grabbed us and made himself known to us. And having done that, he has bridged that infinite gap, not only between himself and us, but us and everyone else.
It means that our communication, our relationships, our discussions, our arguments are real, and reach out beyond the tiny island that is myself. It is the fact that God reached out and communicated to us that makes it possible for us not to be alone, and therefore to know something about the rest of the universe, to know that 1+1 is 2. Walking away from that inevitably undercuts the very knowledge that we are trying to hold onto.
We’re seeing it today because the absolute mathematics that people like to refer to when they’re trying to create an absolute that is apart from God now has become anathema to the woke body of Critical Race Theory. It is an act of patriarchal racism to impose such things on it, because by definition Christian absolutes must be evil.
And yet postmodernism is very rational in accepting that once you throw away God, there is no firm ground left.
At a certain point, in order to be consistent to itself, it wraps its mouth around the shotgun barrel and pulls the trigger and is proud of itself for having done so. Nevertheless, when we need to go out and actually do our science papers and do our work, we have to step away from that. We have to step away from the villainous desire to get away from God, and we have to simply accept his universe as he's revealed it and start working therein.
Most of the time when we run into things in mathematics, for instance, or physics that seriously shakes our tree and makes us say, “No, this cannot be,” it is not because it’s bigger than God. It’s because it’s bigger than the little model of the universe, and therefore pretty likely the little model that we’ve made of God. A little shaking of our tree is a good thing because we draw close to God not by us building a model of God and drawing close to that model – that’s called idolatry. We draw close to God by accepting him as he has drawn close to us and revealed himself in the Word of God.
I’d like to jump off on that because you were going towards the Word of God, and there’s a question I’ve been curious to ask you all here, linking how does God communicate? He uses words. David, you mentioned the tight connection between science and mathematics. Another thing I’ve been fascinated with, other than i, is the wave equation.
I do not know the wave equation very well. I have some understanding, no comprehension, but I know that it describes things, and in fact when you think in terms of quantum mechanics, it describes an electron. You try to think, “Okay, so what is an electron? Is it a wave? Is it a particle? I don’t know.”
When I was first learning physics it was a big revelation to me to understand the best way to understand an electron or these types of things is the wave equation. When you look at it written down in some language, and we pick certain symbols but it could be other symbols, but what does it look like? It’s a word. Reality is described with words, and I just find that amazing about how that plays out.
For the sake of argument, in order to bring everybody onto the same playing field, what is the equation? You can describe it in words, but what is the wave equation that you are specifically thinking of in its elements?
That’s the problem. I’ve been too long in management so I can’t remember the details, but there are differently operators going on.
We’ve got Schrodinger’s equation and we’ve got Einstein’s equations of space. We’ve got a whole bunch of different equations that are amazing!
Right, and you can thank Maxwell’s equations, but it was just this idea that you can’t describe what an electron is. We have all these analogies to describe what an electron is, but you just say, “The best way to describe it is this weird word.”
These weird words that are written down, and it’s almost like in a minor key. How do we know who God is? It’s through his Word. At the end of the day, you can draw whatever analogies you want, but where do we go? We go to his Word. Words are just infused throughout the whole universe in every way – high, low, front, back, everywhere.
The fact that we’re having this discussion inherently implies something that Greg always loved to inculcate, which is that truth is propositional. Rather than rolling into Herod’s defense or Pilate’s defense, which is “What is truth?” we’re pursuing it, and there’s the concept that it can be pursued and captured, to some degree. Not all truth, of course, because there’s only one being, only three persons that have all truth captured, but we have the capacity of capturing some of it, because it was God’s good pleasure to make us capable of so doing.
Right, and the fact that we can write some of these words down and have some understanding of the way the reality is out there, and it’s a real reality and it has real effects on the real universe. We can build spacecraft that go out, and they’ve followed the equations and they hit their target within a meter of where they’re going, and via these funny wave things they’ve sent back information.
Those units can be kind of important, because going between English and metrics, sometimes little mistakes can be made and expensive projects can suddenly find themselves decelerating on the face of a planet.
Let me hijack the conversation for just a second for people who may not have followed all that you just said, or may be back at “Equations are words?” One thing that David Farschman has taught, and I’ve taught a good deal, is that mathematics is a language. It’s got symbols. It’s got this + and this sine and this cos thing and funny crosses and hyphens. How is that a word? And these story problems – those are words. Have you ever noticed that the problem with story problems is that it’s English? This is something that David has pointed out to me any number of times.
Yeah, I tell my students this on a regular basis. “The problem is not math, because once you get into the symbols you can do the math?”
Math is very simple and straightforward, but it is most certainly a language with symbols. They’re just symbols that we don’t include in our alphabet because we don’t use them quite as often as we do A-Z, but it most certainly is a language. It’s a means of communication. You can translate Schrodinger’s equation or Maxwell’s or Newton’s or whoever’s into words just fine. You can use the symbols and make it a little more abstract, but all those symbols are are stand-ins for words.
It is a language. It’s about words and it’s actually simpler than English, because there are 20 million ways to say something in English, and generally there’s like one in math.
That is the problem, which is why great literature will never be written in algebra.
As a programmer who often works with codes written from original papers, I’ll complain in the opposite direction that if you’re going to write your code down, use the frickin’ word that describes what the variable means. Don’t write down the key in your code. Too much, too much.
David Lawrence, you were talking about the interaction between how these things touch on the real world. We think about these. They are words, they are concepts, and yet they describe reality in a way that allows us to interact with the universe around us with precision, because we’re conforming to the Maker of it as he gave it to us.
There are some occasions where things don’t always go as we expect. You draw your orbital equations and say the earth spins around the sun and has its own rotation, and then we’ve got this wonderful thing that allows us to predict exact durations of years and…
And you’ve created a multi-body problem that all of the sudden is too complex for us to solve, or at least it was until just recently.
We love you, Pluto. But you read through Judges, you read through scripture, and axe heads float and the sun stands still, and these are given to us as historical accounts for us to accept at face value.
We know that metal is not buoyant naturally, and we’re not told that there was a bunch of bubbles around it or anything. We know that the earth rotates around the sun, and you don’t just stop that. If you stop that, people go flying, and yet we’re told something about the sun stood still, however that was accomplished.
You mentioned struggling with this in college with your peer group as being in the physics domain. Can you talk a bit about where your resolution comes down on this? Others will be welcome to chip in in a second.
Sure. When you think that nature is all that there is, it’s a challenge. I mentioned earlier that it was reading C.S. Lewis that helped me when I was in grad school to start to make sense of some of these things. His book Miracles – and I’m not going to get all of it right; I haven’t read it in a couple years – but describing the laws of the universe, he drew the analogy that laws of the universe are like the laws of mathematics. People would say, “Gosh, if you have a miracle, how can you break the laws of mathematics?”
Getting back to what David Farschman said, you have two apples or let’s say you have some coins in your drawer. If you had 3 coins in your drawer and the next day you look in, there should be 3 coins there as well, but if there are only 2 coins there you’re not necessarily breaking the laws of mathematics. As Lewis said, you’re breaking the laws of England because someone came in and stole one.
What miracles are like – you’re not breaking any laws, because in fact the laws don’t give you any real events. God is the feeder of events, and if he so chooses he can feed an event into the universe at any point in time. Once that event comes in, it follows the laws just as well as any other event. But you can’t go backwards in time and explain everything, because there is a reality outside of things, but it also follows all the laws.
The way he described that kind of situation, the key fell into place that you can be a scientist, you can really hold doggedly to the science, and yet you know there’s realities beyond that that are fully under the control of the Lord.
In teaching this kind of thing to other teachers, once at an ACSI convention (Association of Christian Schools International) I had an early morning session, and just to be difficult I titled it “Faeiries and Photons” and spelled faerie the right way. I got a bunch of young teachers showing up, and I did ask them, “How many of you are here this early in the morning because of the way I spelled faerie?” and half the hands went up.
One of the questions I asked in that lecture is, “This is a true or false question, and it’s a trick question. I’m telling you it’s a trick question. Here it comes. True or false? God created the natural laws that run the universe?”
And of course what everyone heard is “God created” and all hands go up. “Yes, God created everything. He created the natural laws.” I said, “No, for a very simple reason. There are no natural laws that run the universe. God runs the universe.”
This is the biblical doctrine of providence. God runs the universe personally and immediately. He doesn’t create some system of laws that mediate between him and the universe. If there’s a natural law, what color is it? What shape is it? Where do you find it? Can I see it? Would you introduce me to it?
Rather, the laws as we perceive them are simply our perceptions of God’s covenant faithfulness, his infinite dependability down to the nanosecond and the nanometer and beyond, where God says, “I’m going to do this. I make the sun rise. There it is. I’m making the sun rise.”
Chesterton in Orthodoxy has a chapter where he talks about this sort of thing. We think of the sun rising as boring regularity. God sees it as an encore. God is so pleased with his handwork that he points to the sun and says, “Do it again. Oh, that was cool. Do it again. Okay, do it again,” because God delights in what he has done and he promises us – you can think here of Genesis 8 after the flood – that he will be faithful, covenantally faithful, faithful down to the place of mathematical equations. But we must not confuse our mathematical equations with God’s ruling hand. We must simply say, “We’re describing what God does, but boy our God is faithful!”
The alternative is how do you know anything is even out there, and how can you assume anything about the future, since you haven’t been there and you can’t even prove there’s a mind/body connection or mind/universe connection in the first place?
Christians are the last ones who need to be ashamed about miracles. It’s like the juggler juggling balls. With a really good juggler, you can toss a new ball in there and he can pick one up and keep the thing going and there’s not a slip. “Wait, there were 3 balls, now there’s 4! Oh no! This is not possible.”
He’s really good at juggling. God’s really creative and he’ll pull something out of nothing and stick it into the mix and not miss a beat. And, as you say, from that point on it will continue to follow what we perceive as the laws, but God will be faithful. He patterns it into his covenant and it becomes something we can rely on because our God is infinitely faithful.
The creativity here ends up being a rather significant element, because God introduces himself as a storyteller. “In the beginning, God created the heavens and the earth. And the earth was without form and void, and darkness was upon the face of the deep.” He then steps into the story and says, “Let there be light, and there was light.”
The universe is his story that he’s telling. We exist within his imagination. He’s real, we’re fictitious. However, so great is his imagination that his fiction is our reality, and that reality is, as Greg says, dependable because he’s dependable. He’s telling his story.
One of the things I noticed a lot growing up, and I have a feeling that the others present here have seen that, was there was a time when we had 6:00 evening news, because there wasn’t 24-hour news. There seemed to be a perpetual story that would pop up seasonally, coming up with explanations for particular miracles.
“Oh, we have an explanation for how the Jordan might have been parted,” and that sort of thing.
The point is actually that, no, there isn’t one, and the reason why it is so popular to hunt down explanations is because they’re frantically trying to find out ways that Baal could have done the same thing. We’re trying to take God out of being the providential master of the universe, and instead push into the universe masters of power, masters that we’re willing to say run the universe, but that are inextricably part of that universe – various Baals and Ashteroths that we can manipulate and we can understand, that we hopefully can comprehend and make our servants.
God isn’t in the universe. The universe is in him. In him we live and move and have our being, and he’s telling a story. That story is actually told for his own amusement, not for ours, and therefore he can span a universe. A visible universe is 13.9 billion light years across and it’s like, “Hey, there’s tons of stuff we can’t see.”
“Yeah, tough. It’s not here for your amusement. The world wasn’t created for you to get it, Mr. Burton.”
Yeah, I’m sorry, it’s for his amusement, not ours. So when it comes to these miracles being done, they’re being done because the storyteller can say, “And then the axe head floated,” and guess what? The axe head floated, because that’s the story and he just told it. His word defines the story.
It also happens to be that it is his immense pleasure to glory in and enjoy in his creation the beauty of structure and the beauty of the understandable repeatable solution. Therefore, if you’re going to understand the universe as God takes the greatest pleasure in constantly running it according to his word, you’re going to have to work within the mathematics and physics that it’s his pleasure to take pleasure in.
That carries us from algebra through differential equations through combinatorics through all sorts of elements of math that give me the heebee jeebees, because it’s now a study that is vastly bigger than any one individual to learn it all. He is the God of creativity and storytelling who is telling a story of love and wonder, adventure and mystery, and he is telling it in a setting where the story is predictable, and therefore encounters dangers to us. That makes it exciting and beautiful at the same time.
We like these things not for their own sake, because to love anything for its own sake is to ignore the Creator behind it who is the source of that beauty, but we enjoy things that a lot of people find pretty boring. But the reality is that a lot of these things, even as esoteric as the e2pii might seem – why don’t you just say 1? If you’re building a bridge, you use 1.
Just for convenience. God is not bound by these laws that would make him small.
They are laws to us. Well, God is a law to us. God’s Word shapes our reality, so our conforming to that, our understanding what God will do because he is a consistent God is actually really practical. It’s the foundation upon which we build merry-go-rounds and bridges and computers and make money. It’s the foundation of our job, knowing how to wrangle these skills at a very practical level, founded upon that stability of God.
So for the non-nerds and non-geeks, who we’ve probably lost at this point in the episode, but hopefully our listeners can take this out to the real world…
But people listening to us may not be representative of the population. Why is understanding algebra, algebra 2, geometry, physics, and chemistry – why are these skills not merely for nerds and geeks, but profitable whether you just want to go out and make money, or whether you want to be the Renaissance man?
I would start with the fact that each one of us is finite. You’re sitting in a chair. You’re rocking and moving around in it. However, you cannot describe to me at the moment the exact structure of that chair, or the fact that large portions of it go beyond our understanding or our comprehension, if you want to dig down into the subatomic particles, just to toss something on the plate.
We build models that simplify the universe so that we can work with it. The wonder of mathematical and physical models is not their complexity. The wonder is actually their simplicity. Newton described the motion of an object in space under the effect of gravity, and he described it by just describing the effect of gravity’s acceleration.
He said, “Okay, I know from the work of other people like Galileo that vertical acceleration is constant. Therefore, why don’t I sum up all the vertical accelerations and see what I get out of this.” His introduction into calculus was something called integral calculus. He built it – one of those crazy smart guys that the rest of us kind of resent, who would just invent whole fields of mathematics over an evening, just because he found it convenient.
He summed up the effects of that constant acceleration over time and got a simplified sentence that effectively said velocity is equal to acceleration x time. If you start with an object that is not in motion, held above the ground, and you let go of the apple, if you know the constant of acceleration – let’s say for the sake of argument that it’s 32 ft/sec/sec or 9.8 m/sec, depending on what particular unit of measure you want to be using – and you know how long it falls, you will know what its velocity is.
Then he had the idea of summing up all of those velocities, because those velocities keep changing, but if we sum up all those velocities we then find out where the object is, its location in space. It ends up being equal to ½ of the acceleration x time2 + whatever the original velocity was x time + whatever original physical location it was in.
Starting with a really simplified description, i.e., gravity is a constant, it’s a number, he moved to an equation that ended up describing the motion of planets. He threw out all sorts of other effects that made the universe un-understandable and he created this model, this simple model, and it was good enough to be able to describe the motion of the planets around the sun. It was good enough to describe the motion of stars. It was good enough to, as it were, unify both heaven and the things that we’re seeing on earth – our first grand unification, as has often been popular to point out.
But the point of this was coming up with an equation that was simple. It’s like, “Okay, I’m going out and I’m grabbing a baseball and I’m chucking it. I’m throwing it to my son, and my son catches it.” As it happens, your brain is solving differential equations while doing that. It’s just not bothering to show you all the work that it’s doing, and if you fail in your calculations in solving your differential equation, you miss the ball.
If you’re watching the NFL or you’re watching football or you’re watching baseball, you are watching human beings solving differential equations in their heads, because that’s how it pleases God for the universe to work.
Now, if you want to understand “How important is that?” – well, if you raise the stitches on a baseball 1/8”, you completely change its flight characteristics and you’re no longer necessarily playing the baseball that is being played in the American or the National Leagues. The shape of the baseball and the size of the stitches of leather that hold it together affect the aerodynamics.
How much does it matter? Clearly, millions of dollars depend on it. The same thing is true of the football. The same thing is true of that ellipsoidal ball that they play with in the NFL.
Oh my goodness, the golf ball, which does not follow a simple path because of all those little dimples.
So on the one hand we can say, “Well, if I don’t want to understand the universe and don’t want to describe exactly how it behaves, I don’t need to know these things,” and you’re right. You don’t need to know how your car works to drive it, but you do need to pay someone who knows how the car works to fix it and to care for it.
The people that are willing to put out the effort to learn that portion of God’s universe are appreciated in one form or another. Often they’re paid well. We shouldn’t be pursuing money as a god, but it’s simply a representation of the fact that the knowledge has value of goods and services.
Therefore, the nerdiness of our discussion is when I’m making reference to obscure movies from the ‘80s, like “The world is not here for you to get it, Mr. Burton.” That’s from Big Trouble in Little China. That’s nerdy in the extreme, but the mathematics, the language of how the world works isn’t nerdy, it’s artistic.
Art is hard, really crazy, crazy hard. If you’re going to do it well, you have to study. That’s why universities exist with mathematics and physics programs and chemistry programs and engineering programs.
And I’ll tell you, if you don’t want to know how the universe works exactly and you’re feeling lazy, you can reduce what you’re working with the way Caltrans does, and instead of using differential equations to solve the requirements for building bridges, they use algebra and then multiply values by 10. It’s more expensive, but it’s easier for the engineer. I’m not joking. I have a friend who works for Caltrans who’s an engineer and tells me exactly how they do these things, and it curls my toes because my mathematic self is offended.
For those of you who do not know, Caltrans is the California Department of Transportation, the people responsible for building roads in California.
I don’t know how much longer we have, but I do want to insert something that’s very important, because we’re talking about Christianity, and yet the name of Jesus has not come up very much. We’ve hinted at the Logos, the Divine Word, who by his wisdom and power structures the universe, but that’s not what I’m talking about. I’m talking about the gospel.
What we saw up front in our earlier discussion was the need for the gospel with regard to mathematics and physics. Why do we need the gospel? Because normally we distort reality. We hate reality. We hate 1+1 is 2. We want to rewrite the science.
I’m not just talking about evolution vs creation. I’m talking about the rationality of science. David Farschman mentioned some of the play that post-modernism and Critical Race Theory has been doing with this. It is our nature to hate God’s reality. It is our nature to hate the image of God within us, and to try to stamp out any vestiges of it.
Left to itself, a society will turn its back on mathematics and science, and we will end up with magic. David was describing Baalism. Baalism is simply a fancy word, the Bible’s word, for a sorcerer society where we use amulets and spells to manipulate the forces of nature, which are impersonal but can be frightened, coerced, and nudged into doing our bidding. But only the experts in the white coats – I’m sorry, that’s science – only the priesthood knows these rules.
If we want good crops and fertile bodies for our wives, we have to offer them the sacrifices that they insist on, even if it be our own children. You end up with a magical society that has no room for science, no concept of future improvement.
They worship it, and the rest of us don’t know anything. It becomes more and more its own arcane esoteric field of knowledge, while civilization and culture crash-dive. We end up with what we call today third-world countries, or far worse, what we used to call primitive people who live in the jungles of the Amazon or Papua New Guinea or something.
They’re not primitive, they’re retrograde. They fell from the high state that man had when Noah stepped off the ark, from the immense scientific knowledge that within a couple generations would build the pyramids, to a point where they’re afraid of trees because there are spirits in them, and the scary thing is there may be spirits in them. We return to the demonic.
The way out of this descent into magic and demonism is the gospel. Until we are humbled by the Holy Spirit, by the preaching of the Word, to turn from our rebellion and our idolatry and our would-be autonomy, and trust Jesus Christ to save us from sin, and therefore from all levels of rebellion, including intellectual rebellion, that’s the course civilization takes. History has proven it over and over again.
The only rescue for a culture is not external force or new discoveries or new technology. It’s coming to terms with God in Christ, or rather God coming to us with terms in Christ, and by his Spirit subduing our heart to those terms so that we trust and believe his free grace.
So what does Christianity have to do with science? Well, if you want to have it for a few more generations, everything. Not only is God the Creator and the one who providentially rules the world faithfully and has told us about these things in his Word, he’s also the one who saves us from our rebellion when we want to say, “Yeah, that may be so, but I don’t want to believe so I’m going to go do weird stuff in my head. Nah nah nah, 1+1 is anything I want. You can’t make me.” Yeah, actually he can. As Lewis might say, “Try stepping off a skyscraper and see if you’ve killed the law of gravity.”
God’s covenant patterns tend to be very destructive if we don’t submit ourselves to his lordship, and thus Christianity and the gospel. Come to Christ, because in him is sanity. In him is order and covenant faithfulness. In him is understanding and wisdom. He is the God who structures reality.
So to finish out our discussion, I just want to make sure that that’s on the table, that we don’t leave without having said that, because otherwise we could be accused of a new form of Unitarianism or Deism or something, where God sits back and provides us answers but you don’t really have to be a Christian. You don’t really need Jesus. Um, yeah, you do.
I think I’ll close with the last question I had prepared, which is in our individual careers – and I think this is mostly pointed at the other two Davids, who have mathematical/scientific careers – how do you depend upon the nature of God, the Word of God, to do your daily work? And if you want to tie in particular scriptures that have helped to inspire you down those paths, feel free to throw that in.
The scriptures I would say are not necessarily related to the science, it’s related to the people that one works with. You also had some potential questions there about community in the science. It’s done with people. People are messy.
I’ve been going through Proverbs a lot recently and that has been a huge encouragement, because when you’re doing science you have egos that are involved. You have people that are very difficult, including myself. So being regulated, being reminded, being pulled back to who we are in Christ, to how do we live in our everyday life, for the daily work that’s what I’m doing.
What’s interesting is that’s not different than anyone else. We scientists are no different. We’re just doing the work that’s set before us, just as everyone else is.
Coming in on that, not just working with the trouble of other people – I’ll tell the trouble of working with myself. I am a sinner saved by grace, by God’s grace, saved by Jesus Christ. As I labor, I can look at what I’m doing and say, “In the overall grand scheme of things of the universe, exactly how important and relevant is this?”
Apart from amusing myself and feeding my family, we can always look for grander schemes and elements, but it’s not uncommon that I have students that are taking a class whose sole goal is to get through this class with the expectation that they’ll never use the knowledge again. And whether I be working or I be laboring with the people that I’m working with, where does the value come? Why do I keep going? Why can I keep going?
It’s a two-fold answer. First, I labor as unto the Lord, because that gives value to what I’m doing. Quite honestly, he doesn’t need a single thing that I produce. I can’t produce anything that God doesn’t already have, and therefore all I am is a pathetic little creature offering back shreds of what he has given me.
Nevertheless, the meaning is found in the fact that he takes pleasure in my doing so, because his son has saved me. My labors are offered to God through Jesus Christ, and in so being offered they are ennobled by the one through whom they are offered.
Secondarily, when I despair in myself I find my comfort in my Savior, because whereas I fail, he does not. There are many times in the day that I need to remind myself that Jesus is enough, and that all the little petty things that try to pull me away in different directions are simply distractions. As far as me being able to work productively or teach productively, knowing that Christ has saved me allows me to rest in him and it makes my work easy.
I don’t know if that answers your question specifically, because if asking “How does the Word of God apply to mathematics?” we could be here for a very long time. We could be charging through Proverbs, where God is declaring his hatred for bad math and bad physics, implying that there’s good math and good physics.
Unequal weights and measures, which defines that. But the reality is in my day-to-day walk it is the words of Christ, the words of God that hold me together and give me comfort and joy and pleasure to go back to work every day.
Amen. Let me pick up a theme here. This will take a couple minutes. The podcast is called Halting Toward Zion, and what you gentlemen have just described is really in many ways the heart of what that title is getting at. To halt means to limp. The New Jerusalem is in the future, and yet its suburbs stretch into time, into the now. We have come to Mount Zion.
So what you’ve described – learning mathematics, teaching mathematics, feeding your family, being sanctified in your relationships with other people, working in community – these are things that are eternal. On a very simple level, math is eternal, guys. Audience, math isn’t going away when you get to heaven.
My wife just screamed no in the background, if you didn’t hear it. Calculus is forever. Biology may change. Morticians will be out of a job, doctors we won’t need, but mathematicians, it’s there.
Some of the debates about eschatology – “Does anything from this world carry over into the next?” – well, we don’t suddenly get stupid, so math will still be there, and everything we’ve learned here is something we will put into application in the redeemed creation.
But more to the point I think – and I was so happy to see both of you go there – is the area of sanctification, both personally, which is what David Farschman emphasized, and communally, which is what David Lawrence emphasized. As we work on science, we work on our sanctification, our growth in grace, our walk with Christ.
This would have been true in some sense even in an unfallen world. We’d still have to learn to work together and submit to one another. Jesus in his perfect innocence yet learned obedience by the things he suffered – that is, solving a differential equation even in an unfallen world is challenging. It requires focus. It requires you to listen to other people.
In an unfallen world that would all be a joy and a bliss. In a fallen world, not so much. God makes it harder to grow us more, and he makes us work together with people who are stubborn and proud and don’t listen, and with ourselves who are proud and stubborn and don’t listen, so that we can learn more about this process of community that will be fully manifested in the New Jerusalem when it appears in all of its glory.
These are things that are eternal. We grow now in a way we can’t grow later, because now we fight against sin. When Jesus comes and the resurrection comes, we won’t be fighting sin. There will still be room for a sort of growth in maturity, and certainly in knowledge, but the kind of trusting Christ in the midst of adversity and of our own sinfulness, that’s a now opportunity that will breed fruit through all eternity.
We say, “I’m just feeding my family and I’m just teaching some kids who don’t want to learn,” and there’s some truth in that, but that’s not all truth. All of this is building blocks in the New Jerusalem, and we see that by faith. We can’t see it with the eye, but one day we will.
To look at it from a different direction, Reformed theology sometimes struggles with dominion mandate, cultural mandate, whatever you want to call it, and the Great Commission, as if these were two different things. From the beginning people would grow in faith and grace and maturity, again even in an unfallen world, through hard practical stuff like learning math or building buildings or roads or gardening or farms and domesticating animals.
As Reformers we should know this. You don’t become holy by going on a mountaintop and contemplating your navel. You do it by interacting with the physical world, both physically with your hands, and mentally with your mind, and emotionally with your heart.
Now that sin is in the world we have to do all that, but now we need the redemptive grace of God in Christ. We need the gospel. The gospel moves us to these things, enables these things, and yet in the process of doing these things we’re brought into hard situations where, as you’ve said, we’re thrown back on Christ.
We come up against problems, whether it’s the mathematical equation or the people we have to get along with or our own failings, and it throws us back on God. It throws us back on redemption, upon the gospel.
This isn’t something that’s an add-on or a tack-on to Christianity or to the gospel. This is how God always meant for people to grow, and this is how the gospel means for us to grow. Give us hard stuff to do and let it shake out our sins so that we look at Jesus.
Thank you all for this conversation this evening. It’s been a lot of fun. I wanted to talk about science and things, and this is one bottomless domain of beauty. This is one way of perceiving God. And while there is fundamental utility here, not everybody is going to go off and become a scientist. But whatever you do, do as unto the Lord. Whatever study you take, whatever pursuit you aim for, pour your heart into it and recognize the beauty in all these different domains.
We’re scientists and mathematicians, but we also do storytelling and farming and entertainment and teaching. There’s beauty in every angle and everything that God has given us to do.
When I’m teaching a math class, I get to have these kinds of conversations for an entire semester. We only touched like a tiny portion of one of those conversations. There’s so much to talk about, and it’s a real honor to get to speak with the group of you, so thank you.
Just talking about the concept of a subatomic particle, for lack of a better term, a quanta that is in many places at the same time. There’s tons of room for conversation in this.
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