Friday, November 29, 2013

"As Christians, we worship an infinite God."

The key to an effective sermon may very well be to get right enough of the periphery to be able to slide in the nonsense with authority, or at least we might guess that to be the case judging by this sermon by Pastor John Van Sloten from New Hope Church Calgary on "God, Infinity and Mathematics" from their "God @School" sermon series. It's worth noting that this video was posted just this week, so it's reasonable to conclude that it was probably preached somewhat recently. Check out the video if you've got fifteen minutes or skip around a little bit to get a sense of what kinds of things they're saying. The sermon itself starts about a minute in.
Of course, sermons like this are a big part of what made me feel a need to write a book like Dot, Dot, Dot: Infinity Plus God Equals Folly. Who needs a book about infinity and God? Anyone who wants to inoculate themselves from the kind of nonsense presented in sermons like in this video, which being based upon mathematics have a high likelihood of being able to blind someone with science bullshit.

I don't know this, but I suspect we're going to be hearing more mathematics from pastors in the coming years. Too many people with too many voices know too much science for them to keep railing on it. Indeed, it chases many young people away to go anti-science for Jesus. Mathematics, though, is a subject that most people are shockingly ignorant of, it's awe-inspiring in its own weird ways, and it possesses enough similarity to theology--in that it's abstract and axiomatic--to really be able to wow an audience. Since the majorities of most audiences are likely to be both ignorant and afraid of mathematics, there won't often be a lot of checking for nonsense, and when eyebrows do rise, it's likely that the pastor will be forgiven his lack of expertise in a difficult subject just for the attempt. Thus, pastors will just need to get the peripheries right and talk about big, interesting things that they can somehow tie to God, like infinity.

This pastor isn't an expert either

The first minute of the video seems to be borrowed from a BBC documentary about mathematics and makes a valid point: you can't really count to "big" numbers. No one can. So here's something valid on the periphery, since this isn't going to be the pastor's point at all. Instead, the soft-spoken Van Sloten repeats his chorus throughout the sermon: "As Christians, we worship an infinite God."

I do not intend to give a blow-by-blow analysis of this sermon as that would be both boring and tasteless. (The pastor is clearly not an expert, so it feels a little like getting in a boxing match with a kid.) Though perhaps a bit pedantic, I do want to bolster that statement by noting that within the first minute he speaks, though, Van Sloten reveals his lack of expertise by talking about what we might call "big" numbers: the number googol and then two others, googolplex and Graham's number. The revealed lack of experience occurs blatantly when he mentions googol and then calls googolplex "the next biggest number up" and then says of Graham's number that "of course, there's even a bigger number than a googolplex." Indeed, there are lots of numbers bigger than the googolplex, and also bigger than Graham's number; almost all numbers are bigger than both.

Being inexpert in mathematics, though, is hardly a cardinal sin. In fact, it's quite common. We might celebrate his attempt to stand on a stage and preach mathematics appreciation if it weren't for the fact that he's using it to preach for some seemingly imaginary entity he calls "God," mathematics appreciation being incidental to the entire affair. This shouldn't be celebrated and will here be impugned.

Getting the periphery right

Van Sloten's sermon includes many accurate statements about mathematics: the definition of googol, the definition and details about googolplex, and the details about Graham's number being notable examples just within the first couple of minutes that he talks, noting the above comment, of course. Immediately, though, he's interjecting the idea of mystery into these "colossal" numbers by calling Graham's number a "mystery."

Of course, mystery will be a theme throughout his sermon, for as John W. Loftus has noted, "Faith is a parasite on the mysterious" (Outsider Test for Faith, p. 219). To really highlight the mysteriousness of Graham's number, in fact, Van Sloten notes the "celestial music" played in the background on the BBC documentary while talking about Graham's number. Though it goes without saying, celestial music has nothing to do with Graham's number outside of a documentary production room, and celestial music has nothing to do with "God" except in the minds of those who believe in such notions.

At any rate, Van Sloten goes to make a big point early on and quotes Graham to do so. In the BCC documentary, Ronald Graham notes that "his" number is no closer to infinity than is the number one (I have a chapter about this fact in Dot, Dot, Dot called "All Numbers and All Infinities Are Very Small"). Then he says it for the first time: "As Christians, we worship an infinite God" (emphasis mine). He says this three or four times, in one fashion or another, throughout the video, but just after saying it for the second time, he notes, "mathematics...can teach us about who our infinite God is." I quite agree.

Who is an infinite God?

This question, of course, is nonsense but makes for a nice transition. The right question is "what does 'being infinite' tell us about the idea called 'God'?" This, of course, is a major theme of Dot, Dot, Dot. It tells us that God is abstract.

Van Sloten states that "math is the perfect tool and language with which to engage the logical, reasoned, mathematical mind of God." I'm not at all sure what he means by this, or how he knows that God's mind is so ordered, but he comments that mathematics is "limitless," pointing out further that "while physicists can only go so far, mathematicians can imagine even beyond that with their math" (emphasis mine), meaning that mathematicians are not "fixed or somehow limited by material reality."

Okay, wow. Thanks, Pastor Van Sloten, for making my point while thinking of yours. Insofar as he is right, mathematicians aren't bound by material reality because we work with abstractions, and can imagine even beyond it. The key notions here, particularly when we get to the "mind of God" part, are the imagining and the working with abstractions.

Probably for this reason, along with his lack of mathematical expertise, much of what Van Sloten seems able to conclude about his infinite God is fluff. At one point, he states that what we have is an "infinite number of infinities all pointing to an infinite God," and shortly after he concludes that "we're made to engage an infinite mystery and tremble before it." This is all very poetic, but I don't think it's much more than theological twaddle--nowhere in the infinite number of infinities do I see a single reason to suggest that they point to any God.

Of course, much could be said about humans being "made to engage an infinite mystery," a dubious and probably patently false claim, and much more could be said about being made to "tremble before it." That commentary, though, would be less about mathematics than about the psychology of believers, I think. In that vein, I should note that he included a lot of "fear of God" talk just before the trembling bit, which raises the question of what kind of "New Hope" they peddle up there in Calgary.

It seems to me that Van Sloten is unable to conclude anything of any value from his investigation of God via the mathematical infinite, although he uses quite a lot of language sure to be charged with his audience, ripe for hoodwinking. The term "mystery" comes up several times, as noted, including once as a "mystery that draws us" and another time as we just said, an "infinite mystery" that we're "made to engage." He stresses words like "limitless" in a way that speaks to a non-technical double entendre, and even works in terms like "deliver," perhaps involving "celestial music" instead of banjos but with much the same connotation. Likewise, he suggestively emphasizes mathematically accurate phrases like "greater than what our universe can hold" (so far as we know and possibly probably), "unbounded by physical reality," "awe-inspiring," and "out of this world," but then near the end starts sliding this less toward mathematical accuracy and more toward his agenda with "holy and reverent." Infinity is holy? Really? (Indeed, he suggests that doing math, at least if done well, is holy. Well, I'll be damned.)

Given all that, I'm going to conclude that Van Sloten's analysis upon "As Christians, we believe in an infinite God" says exactly what I think it means: they worship an abstraction, and their use of the word "infinite" is symbolic and poorly understood. If it weren't so troublesome to the rest of us in so many serious ways, I'd say, "Good for them...," and leave it at that.

Get the periphery right and then lean upon authority.

If we're going to concoct a powerful sermon, though, it isn't enough to get the peripheral details right and then stuff in only fluff. It's critical to lean upon authorities.

Van Sloten quotes Galileo at length concerning his seventeenth century thoughts about God and mathematics. Similarly, Johannes Kepler's thoughts on God and mathematics are pulled in, as are Georg Cantor's, which will get some special attention from me later. He also quotes noted mathematicians Keith Devlin and Ian Stewart, which seems a bit peculiar given some of their other writing.

Specifically, he attributes to Devlin a quote that "mathematics makes the invisible visible," although this is actually the subtitle of a book by Devlin titled The Language of Mathematics. For my part, I don't think Devlin is talking about the same thing as Van Sloten with the word "invisible." Van Sloten quotes Ian Stewart as saying, "We encounter mathematics everywhere, every day, but we hardly even know it," and goes on to suggest that this is rather like how God is everywhere and communicates with us every day, though we hardly know it. I strongly suspect this isn't what Stewart was getting at.

It's worth noting that instead of quoting their own works directly, Van Sloten quotes Devlin and Stewart via a 2011 Christian apologetic work called Mathematics Through the Eyes of Faith by James Bradley and Russell Howell. As described on Amazon: "Ina [sic] new addition to the groundbreaking 'Through the Eyes of Faith' series, thenation’s [sic] top Christian professors approach mathematics from a Christianperspective [sic].," and the work is admittedly co-sponsored by the Council for Christian Colleges and Universities.

Other than by attempting to liken the "quote" from Devlin to a Bible verse (Romans 1:20), making suggestive inferences about Stewart's quotes, and salting his sermon with other verses, the only other authorities Van Sloten calls upon are two "math enthusiasts" from his own congregation, an engineer and a high school mathematics teacher. It is via their commentary and authority, and his own thoughts, that Van Sloten bridges the gap from "awe-inspiring" and "mystery" to "holy and reverent." Indeed, he usurps all of the mathematicians in the BBC documentary at the beginning of the clip and perhaps most, if not all others, by suggesting that "mathematicians all know they were on the edge of something holy" when talking about infinity. Quaerendo invenietis, as always, I suppose.

When in doubt, make it sound official.

Fluff is the stuff of sermons, though, and as a former boss used to tell me about how to bullshit through a tight spot: "When in doubt, just look official, and people won't question you." Van Sloten does this spectacularly at the point where he changes his tempo from misleading math appreciation to outright theological nonsense. I'll quote him.
Infinitely small numbers, going on forever. Infinitely large numbers, far greater than what our universe can hold. Infinity times two, infinite dimensions within which infinity can play out, infinity times infinity, infinity to the power of infinity! It's like there's no end to the study of infinity. An infinite number of infinities all pointing to an infinite God. Something about how wide and long and deep and high that makes up the nature of infinity that is awe-inspiring, not just to the mathematicians--out of this world, a mystery that draws us.
I don't even know what to say about this except to call it grade-A sermon fluff, and indeed it makes his direct segue to the theology, "being on the edge of something holy and reverent" when thinking about infinity, which he then connects via "reverent" to the "fear of the Lord." At any rate, it sounds official, but I'm calling it directly into question.

A couple of odds and ends

I'd like to wrap this up here, but I do want to mention Georg Cantor, one of the mathematicians Van Sloten leans upon in his sermon. Cantor gets special attention because Cantor is the mathematician who changed everything about how we study mathematics and especially infinity. He was also very devout, and this caused him some problems.

Cantor believed in God and, following dogma and popular belief, identified God with the infinite. Cantor's discoveries about infinity were fairly upsetting, though, to this dogma and belief, so much so in fact that Van Sloten (quoting Daniel Tammet's book Thinking in Numbers) notes that Cantor had to defend himself and his ideas from charges of blasphemy from the Vatican. Cantor tried to argue that his discoveries were indicative of God revealing more of his "infinite nature" and sincerely believed it, even if it did cause him to experience moments of questioning doubt. Doubts aside, Cantor believed that his work on transfinite mathematics was directly communicated to him by God. This attitude is a bit odd given that one of Cantor's chief discoveries is that given a set of any infinite size, one can use it to create a set with a size described by a larger infinity, making God as the ultimate infinity a difficult position to defend.

Cantor struggled immensely with all of this, defending both his work (upon which he felt his public reputation rested) and his commitment to God, and ultimately remained shaken for the remainder of his troubled life (much of it in an asylum) over ever having questioned God via his work, even momentarily. His story is quite a tragedy of faith.

Why this is important

This isn't the last we'll hear of "God and infinity" talk coming from Christians, and that's a huge part of why I bothered to write Dot, Dot, Dot at all. One needn't be intimidated by the mathematics in order to get familiar enough with the concepts at play to clearly understand why Van Sloten's sermon is hollow and misleading, and there may very well be a growing need to be able to help our faith-laden friends see it for themselves as well.

If Pastor Van Sloten or any of his congregation happen to notice this little blog post, I do hope they at least check out my short video including a brief excerpt of text from Dot, Dot, Dot, which I'll embed here in case that happy chance arises. I'd encourage them also to pick up a copy of the book for study in their God @School series.


  1. Thanks for this very thoughtful response to my sermon James! While we obviously take different positions on the reality of God (yours much more thought out in relation to infinity than mine!), I learned a lot reading this post. I noticed to posted an abbreviated video of the sermon. Full version is here -

  2. As someone who works in a hospital with teens who have mental health issues, I am no math expert but have always liked it. I appreciate your expertise and passion on the subject of math. I read you article and watched your short video.

    As a person of faith (or as fluff as you might say), I think I will wrestle with questions of doubt to some degree or another, I also highly value the connection I have with my creator. Ya I do have my doubts but then I look at things like the beauty of a close up photo of a snowflake and there is no way that I could say that a big bang way back created such beauty.

    1. Thanks for your comment. I definitely understand your feelings of doubts. I had them myself for a long time before leaving my faith behind.

      I must ask, though, when you say that there is no way that you could say a big bang way back created beauty like a snowflake, why do you have a hard time saying it? Do you feel the same way about big things, say spiral galaxies?

    2. Thanks James...First off, I am a pee wee when it comes to intellectual debate such as above (and I am okay with that... I will let my PHD in the making wife make up for that! LOL).

      Lately I have marveled at the beauty of close ups of snow flakes and their intricate is as if an artist has created them and apparently not one the same. When I have looked at these photos, the thought has gone through my head, "What would an atheist say about such?" For me, I can not see a big bang, evolution or such creating such beauty. I also see such beauty in outer space although I find it a bit more mind blowing at how immense it all is.

      I am coming close to 42 and from about 20 - 40, my spiritual life was more of a headache than anything else and there were many times I was about to toss it away. Besides the doubts as mentioned above, it seemed to produce far more depression than joy.

      Over the last couple years, I have experience a gentle, subtle healing (i.e. no fire works) in my life that took some hard work on my part. I am now at a point where I experience God in a much different way. It has been a beautiful experience. Some might feel that what I experience is made up in my head (and I can understand their argument) but for me, the moments here and there of intimacy I have had with my creator have been precious and life giving.

      And thus I continue with a Faith that also contains it doubts, believing that with out the realm of doubt, faith is not possible.

  3. I hear your warning of believing the math of preachers who dabble outside their disciplines. I'm tempted to apply this warning to you, who it sounds is dabbling in the discipline of preachers.

    In watching your little video I was tempted to believe that math doesn't exist. If you go to the top of a mountain you can't find it. If you travel to the moon it isn't there. Our robots out in space haven't found it nor can our telescopes see it. Math is clearly not found in nature.

    Yet billions of people spend billions of hours studying it. We allow math to determine how we build the bridges we trust with our lives, how we fashion the weapons to kill our enemies, how we engage in commerce that will fill some and starve others. People use math to know the world and control the world yet it is a complete abstraction, whose existence itself cannot really be proven, because of course we can't even prove our own existence.

    My guess is that mathematicians very much believe in math, and that nature reveals it, and is revealed by it. In that way they are not far from Rev. Van Sloten.

    Theologians and mathematicians engage in conversations as old a human civilization about something they cannot lay their hands or eyes upon. The judgment that such a venture has been folly, like all human judgment belongs to its author.

    Judgment itself, however, always begs for a verdict but within the courts of humanity none can find one that is final, universal or decisive. Math offers itself as such a court. Something that will transcend judgment and language.

    It would be a shame, however, if no such court or judge existed for the matters of our lives far greater than the abstractions of mathematics. It's no wonder humanity, who can't keep itself from making judgments about what we cannot fully understand, has always imagined a judge who will judge with justice and finality.

    1. This is a fascinating comment, and I thank you for it. I'd be honored if you took the time to read the book I wrote that the video is just a short snippet from. That way you'd see more of my position and see that I actually agree with you about mathematics "not existing," or, rather, existing in exactly the way I think God "exists."

      I'm curious how we might make decisions for ourselves, though, if it is a human shortcoming to make judgments about what we cannot fully understand. It seems like a necessity for most of our industry and the primary way in which we are able to live and work together. Perhaps you could elaborate on this for me?

    2. I did pick the Amazon sample of the book and very much enjoyed that portion. I might buy it and keep reading. I found it stimulating. Unfortunately Kindle tends to inflame my book buying and reading and often leaves me with numerous good books already in progress. :)

      Your objection to the use of "infinity" is clearer to me and having taken at least a good smattering of math in college before I turned to history I think your point is quite correct. Applying "infinity" as a mathematical concept towards "God" is at best an analogy. It is probably true that as in many cases the mathematical concept of "infinity" gets poor treatment when used outside of mathematics, it's natural domain.

      I actually re-bumped into your site after following some links in the Phil Vischer "faith" conversation. I enjoy his podcast and when I saw your site it rang a bell on this conversation that I rudely dropped. My apologies. Xmas was a busy season.

      The point about judgment intersects both conversations. Peter Boghossian's treatment of the question "what would make me believe" is for both sides a bit of a stalking horse. As a local pastor my experience with people is that "justified" belief is a lovely idea that has about as little evidence for its validity as stars aligning to write my name. People believe for their own reasons, many of which they themselves are clueless off. (Reading books like "Incognito" by Eagleman and "The Righteous Mind" by Haidt.

      The lovely thing about science and math is that they arouse our hope for accessibility to the objective. Here we seem to acquire a system by which the objective can be contained and harnessed to do work for us. Processes can be repeated and demonstrated and upon this platform we can arrive not just at personal certainty (something as creatures we seem easily capable of) but communal certainty and agreement. What is regularly ignored is that what really gets us excited about science and math is that they promise community.

      Unfortunately for us, however, "judgment" about the large, complex and important things of life, the things that seem to cause happiness and sorrow, pleasure and suffering, life and death, eludes us. The tower of Babel seems to be a true parable about far more than language. We stop our brick and mortar project of a unified tower and instead build walls and fortresses against each other.

      The kind of thing math might lead us to believe in a world beyond physics. On one hand math seems to live in a world beyond our minds yet we must have minds to see it and know it. What might that suggest about the nature of reality?

      Alas, however, judgment about even so simple a paragraph like he previous one eludes us. Evaluating even that paragraph is more complicated than even math. It is beyond our grasp.

      Math, I'd suggest, is the cousin of story. I wrote the following for an atheist friend this morning.

    3. I bumped into your 4k comment limit. I wanted to end with a piece I wrote this morning for an atheist friend as part of a separate conversation. It helps express some of my thinking about glimpsing God in a skeptical world.

    4. I bump into it all the time. Alas. Thanks for your thoughtful comments!