Oh, Dear.

Via Three-Toed Sloth, I am -- pleased? no, that's not the right word, somehow -- to answer what I'm sure has been a burning question for many of you, namely: where can I find devotionals combining mathematics and Biblical texts? Here are several sets of them, covering Single-variable and Multivariable Calculus, Linear Algebra, Discrete Structures, and more. They include such gems as the following:

"The eigenspace of an eigenvalue l is the collection of all vectors u  that are mapped to lu under the action of a fixed matrix. It is important to note that u choices exclude the zero vector because the zero vector always is mapped to itself under this type of transformation.  On our own, we are like the zero vector because no matter what we try, we cannot move away from out sinful status.  However, through the grace of Christ, we are transformed from being a zero vector to the eigenspace of the redeemed (the likeness of Christ)."

"A functions is a rule which assigns to each object in a domain set exactly one object in a codomain set.  So, suppose that the domain set is the collection of behaviors that people do and the codomain consists of two values:  perfect or imperfect.  On our own, every behavior that we do is mapped to the "imperfect" output value.  But, the Jesus function takes our behavior and filters it through his sacrifice so that God takes the output of the behavior of Christians as "perfect" in terms of our final judgment.  Praise God!"

"An inverse mapping of any function reverses the direction of the assignment of the function.  In the case that the original function is one-to-one, the inverse mapping will also be a function with the domain and codomain interchanged. 

Through the sin of Adam, all people are condemned for eternity.  We cannot escape our inherited imperfection.  Let's define the "Adam life function" to act on people.  This function has output death for all inputs.  However, Christ inverts the total condemnation of people through his death and resurrection.  This acts as a sort of inverse to the "Adam life function;" the "Christ death function" acts on all people and brings life to those who believe.  This is not truly an inverse function--it is more of a negation--the negation of Adam (man) is Christ and the negation of life is death.  It is ironic that to give eternal life to people whose lives are undeserving, Christ had to die."

And this sentence, from the marvelously titled "Secant Lines and Sanctification": "There is one distinction between the concepts of sanctification and secant line limits, however." -- (Only one?)

Now: I have no interest in making fun of Christianity per se. I spent nine rather important years as a very serious Christian, and retain a lot of respect for Christianity. Nor do I have any interest in making fun of the idea of using mathematics to illustrate religion, an idea with a long and distinguished history. But this particular attempt to mix the two invites ridicule: it's only slightly less idiotic than Alan Sokal's immortal footnote:

"Just as liberal feminists are frequently content with a minimal agenda of legal and social equality for women and "pro-choice", so liberal (and even some socialist) mathematicians are often content to work within the hegemonic Zermelo-Fraenkel framework (which, reflecting its nineteenth-century liberal origins, already incorporates the axiom of equality) supplemented only by the axiom of choice. But this framework is grossly insufficient for a liberatory mathematics, as was proven long ago by Cohen (1966)."

-- and that was a joke. Three-Toed Sloth writes to the author: "It seems to me that if you were serious about the Bible being the inspired word of the God to whom you will answer at the Last Judgment, you would not treat it in this profoundly shoddy, slapdash way." I agree completely.

While I'm on the subject of religion, here's a post from Slacktivist, which I reproduce in its entirety:

"You know you've been spending too much time in the blogosphere when your instinctive response to the Easter liturgy is to say:

"Christ is risen indeed ... heh." "

Comments

[Mo MacArbie]

Christ is risen (YMMV)

[st]

But, the Jesus function takes our behavior and filters it through his sacrifice so that God takes the output of the behavior of Christians as "perfect" in terms of our final judgment. Praise God!"

This is just about the most blasphemous thing I have ever read. We use Jesus to fool God into reading our sins as perfection. Wow. This guy's gonna burn.

[Slartibartfast]

Eek. Although I've got to admit that reading Buckminster Fuller was frequently like this; I'd have to recheck and make sure that there wasn't some foldout that I'd read past as if it weren't there. But I always knew that Bucky was far, far smarter than I, and was talking way over my head to begin with. This bit about the eigenvectors, though, is utter crap. Taken as a sermon, though, it's not much worse than some I've heard.

[Rob]

That site is amazing.
I suppose they can prove the existence of God as well; by dividing by zero.

[Anarch]

I suppose they can prove the existence of God as well; by dividing by zero.

"a^2 - b^2 = (a-b)(a+b), therefore God exists!"

- Euler's legendary demolition of Diderot in the court of Catherine the Great

[Slartibartfast]

by dividing by zero.

You can't divide by zero; you can't even begin to. However, if you start with a division by epsilon, then allow epsilon to get very, very small...

[rilkefan]

"That site is amazing.
I suppose they can prove the existence of God as well; by dividing by zero."

What's the theological implication of the infinite hierarchy of infinities?

[Anarch]

What's the theological implication of the infinite hierarchy of infinities?

Ask Cantor. Or perhaps Kronecker, who was so outraged at the theological implications of the transfinite and the Cantorian Absolute that he basically devoted his life to ruining Cantor's.

[hilzoy]

I was going to put this in the post, but forgot: can any of you tell me what this might mean?

"Explaining Predictions
Luke 24:13-32
Jesus appearance on the road to Emmaus to explain OT predictions to disciples--limit of sums definition of the double integral"

[Tim H.]

Just as a guess he meant that if you sum up the OT prophecies it approaches the reality but isn't identical, just like summing up the area under a function versus the actual integral. Why he picked a double integral escapes me.

[liberal japonicus]

You know, there is a reason that mathmaticians are not usually called on to be prophets.

[Jackmormon]

I can't even begin to explain the double integral-Emmaus road simile. But thanks for this post, Hilzoy.

Okay, since I'm a humanities-type-person, and not a philosopher, can anyone tell me if the logical debate about humans' ability to use reason to understand anything about God has gotten anywhere since Hume and Kant?

I'm sitting here flipping through both of these dude's last texts on religion, chuckling at Kant's demolition of analogical thinking and Hume's postulation of the gods of the spider-world, and I'm feeling pretty smart and all that, but I don't know much about how this debate shook out in hard-core philosophical circles in the next couple of centuries. Anyone?

[hilzoy]

Jackmormon: Not my area, really: when I was Christian, I was allergic to most things that were philosophical (as opposed to popular or devotional) and written after about 1800, except for Kierkegaard.. (I cut my teeth on the medievals, and once you've read a lot of Christian theology written in an age when the idea that there was anything the least bit irrational about being Christian, the defensiveness of modern stuff sticks out like a sore thumb.) And after I reverted to atheism, there was really no reason even to try to read that stuff (as opposed to the earlier theology, which I still love.)

All that said, my sense is that the answer is no. Kant demolished the ontological argument once and for all; it has never recovered. Hume ought to have demolished the argument from design, as a straightforwardly rational argument, but the real nail in the coffin there was Darwin, who provided an actual answer to the question: without a designer, why does everything work together so well, as if it had been made that way?

[Jackmormon]

Here's Hume's suggestion in that direction, although of course he didn't have even the geological data that was discovered a couple of decades afterwards:

The World plainly resembles more an animal or a vegetable than it does a watch or a knitting loom. Its cause, therefore, it is more probable, resembles the cause of the former. The cause of the former is generation or vegetation.

Then the character gets a little silly, comparing comets to ostrich eggs, but Hume's argument does seem to stick by a preference for generation over design.

It's a fun text, hilzoy, if you're never read it. Thanks for the reply; it's my sense as well that Hume and Kant killed ontological certainty for philosophers. But then, what would I know?

[hilzoy]

Jackmormon: I love, love, love the Dialogues on Natural Religion. One of the funniest really first-rate philosophical texts around. (Kierkegaard's Concluding Unscientific Postscript is another.)

[bob mcmanus]

"don't know much about how this debate shook out in hard-core philosophical circles in the next couple of centuries. Anyone?"

My opinion? Kierkeggaard & Nietzsche & Wittgenstein(read Holbo's online work) are in that class. And the 20th century(fascism,communism) proves to me that the human race has yet to come to grips with the irrational parts of what is human. We need religion & the spiritual.

Carl Jung:"God is a psychic fact."

[Jackmormon]

You've convinced me to give Kierkegaard another try. I gave up somewhere in the iterations of Abraham's killing Isaac, back when I was a morose Mormon sixteen year-old.

[Jackmormon]

Cross-posted, Bob.
[Dives over to Holbo]

[hilzoy]

Jackmormon: one thing to know about Kierkegaard is this: he wrote many of his books under pseudonyms, and all the pseudonyms have distinct characters and also (at least, according to me) characteristic mistakes built in. The pseudonym who wrote Fear and Trembling, the one about Abraham, is fairly morose; the one who write the CUP is funnier.

It helps to know about a paragraph's worth about Hegel, though.

(You ask, why pseudonyms? Answer: poor guy, he was by far the smartest person he knew, and in the absence of anyone who could check him intellectually, he got a bit self-indulgent and overly clever. He thought that Christianity can't be communicated directly, basically because it's about how to take various thoughts, not which thoughts to have. (Analogy: one of my favorite ever cartoons shows a professor, looking frustrated, saying: don't just write down what I say! think for yourselves! -- and you can see the students writing: don't just write down; think for selves. Direct communication, for K., is basically: telling the students which sentences to write. Indirect communication: telling them how to take the sentences they write -- e.g., to think for themselves. The pseudonyms were part of an elaborate (overly elaborate, imho) strategy of indirect communication: by all being different, and all flawed, they would force various choices on people, and also force a kind of reflection. Like many versions of self-indulgence, it has the crucial flaw of assuming that everyone was paying serious attention it all.

He really did need to meet another person as smart as he was.)

[hilzoy]

Bob M: I agree that Kierkegaard, Nietzsche and Wittgenstein are in the same league. But I don't see W. as addressing Jackmormon's issue, except in a very indirect way. Nor Nietzsche: he strikes me more as taking an answer to it for granted.

[James]

Alvin Plantinga has reformulated the ontological argument using modal logic, and his version is valid. Of course, that just means the conclusion that God exists follows from his premise, not that the existence of God has been proved (since the premise can be rejected.)The premise (roughly) is that it is possible for something to exist which is so great, it is not possible for anything greater than it to exist. Plantinga thinks the acceptance of this possibility is rational, and so belief in God's existence is rational. My problem with the premise is that I'm not sure what he means by "great." If he means the usual--omnipotent, omniscient, omnibenevolent, etc.--then I'm not convinced we can give non-paradoxical explanations of what it means to be any of these things.

[Donald Johnson]

I love Hume's Dialogues on Natural Religion--one of the few philosophical texts you can read for fun. (If they're not fun I don't read them). But it didn't work for me as a refutation of the design argument. I agree with Dawkins--you couldn't be an intellectually fulfilled atheist before Darwin. Not that I'm happy about that as a Christian--I just think Darwin did all the work destroying design arguments. Hume is very clever, but as his own mouthpiece says (Philo?), when you put aside all the clever arguments you'd have to be an idiot not to see design in the universe. Until Darwin came along.

Plantinga, I think, wants to bring back the ontological argument. I have faith that some version of the ontological argument is true--that is, if God exists, it must be logically contradictory in some way to imagine that He doesn't exist. But I don't mean that I know of any actual version of the ontological argument (assuming I've got the right name for it) that is true. Kind of sad, really--I have faith in God's existence and faith that some logical argument for His existence holds up, but somehow I don't think that's going to impress any atheist I happen to meet.

Plantinga, btw, seems defensive and sarcastic in certain spots in "Warranted Christian Belief", sitting mostly unread on my shelves. It's a little offputting, like watching David Brooks do one of his whiny defenses of the latest indefensible Bush policy. Well, that's maybe a little nasty (to Plantinga).

[hilzoy]

James: I read that a while ago, and its details are murky. But doesn't that show that God is possible, not that He actually exists?

[Donald Johnson]

My own contribution to mathematical theology, btw, is the realization that in the Quantum many-worlds idea there's bound to be at least one version of each of us that is "saved". So universalism is true. (Though what to do with the unsaved copies? I haven't figured that part out.)

I'm sure some other kook beat me to this little insight. A variation on the theme--some of us are in a quantum superposition of a saved and unsaved eigenfunction. Death acts as a sort of measurement that causes us to collapse into one of the two states. I had this little epiphany years ago, but it has had surprisingly little influence on my spiritual life.

[Slartibartfast]

Apropos of philosophy:

The Philosopher's Song

Immanuel Kant was a real pissant
Who was very rarely stable.
Heidegger, Heidegger was a boozy beggar
Who could think you under the table.
David Hume could out-consume
Schopenhauer and Hegel,
And Wittgenstein was a beery swine
Who was just as schloshed as Schlegel.
There's nothing Nietzsche couldn't teach ya
'Bout the raising of the wrist.

John Stuart Mill, of his own free will,
On half a pint of shandy was particularly ill.
Plato, they say, could stick it away
Half a crate of whiskey every day.
Aristotle, Aristotle was a bugger for the bottle,
Hobbes was fond of his dram,
And Rene Descartes was a drunken fart:
"I drink, therefore I am"
Yes, Socrates, himself, is particularly missed;
A lovely little thinker but a bugger when he's pissed!

And now, for something completely different.

[rilkefan]

in the Quantum many-worlds idea there's bound to be at least one version of each of us that is "saved".

Not according to some theologies. And if there are souls to be saved, it is as likely as not that physics is constrained to conserve savedness.

[rilkefan]

Slart, malt does more than Milton can to justify God's ways to man.

[bob mcmanus]

Got me working too hard tonight, hilzoy. I am not in this league.

a) Holbo connects Wittgenstein to Schopenhauer and the German post-Romantics. I saw Witt as nearly mystical; whereas his analytic successors seem to think there is only surface, Witt believed in the ding-in-sich.

b) My reading of Nietzsche buys none of the prescriptive stuff:overman, eternal recurrence, etc. I view them as attempts to escape nihilism. "God is dead" is very important, and likely true, but faith appears still necessary, even for Nietzsche. Back twenty years ago when I was doing this stuff, read some German about an "As If" philosophy.

Bottom line for me is a core belief, somewhat out of Kant, that an "ethics" that can be communicated and shared needs a transcendental foundation. Otherwise, you are in morals, fashion, preference, nihilism. Empiricism and pragmatism ain't gonna hack it.

c) So Kierkkeggaard. You *must* believe when belief is impossible. K got to me, big time. "Sickness unto Death" was the pivotal work, and I simply could not escape that somewhere in a part of me not accessible to reason...atheism was simple rebellion.

I connect the three as direct and concious extensions of Kant's project of "showing the limits of reason in order to open the door to faith."

[James]

hilzoy,
The cool thing about the argument is that the conclusion is that God actually exists. The way AP constructs this argument is really complicated, and the most condensed version of it that I can come up with still makes an unreasonably long (and not very interesting) post. Maybe I can find an exposition of the argument on the web somewhere.
Also, by "greatness" he does mean knowledge power and benevolence, and so I personally don't accept the premise, since trying to figure out what it means to have all these qualities to the highest possible degree always leads me into paradoxes.

[Bernard Yomtov]

Slarti,

I thought it was,

John Stuart Mill
Of his own free will
Overcame his natural bonhomie
and wrote Principles of Political Economy

Apologies to all the philosophers for the interruption. You may resume.

[jimvj]

James Watt denies having said something like what is found in their discussion on "Inversions in the Bible" at http://www.trnty.edu/faculty/robbert/SRobbertWebFolder/ChristianityMath/Calculus.html :

"Applying inverse functions in nature is something environmentalists know is very difficult to do. Think about how difficult it is to restore a harvested rain forest or to undo the ill effects of an oil spill! However, our God is able to restore nature and he will to do it completely at the second coming of Christ."

Message: Go ahead, f*ck the earth as much as you can. Jeebus will come soon and make it all okay.

[ral]

Slart,

Is your name not Bruce, then? Mind if we call you "Bruce," just to keep it simple?

[Russ]

The dismissals of religion and God -- with Hume, Darwin, et al -- are valid only if they attack the slothful, ignorant and errant literalist approach to the subject. Knocking down a straw man is easy. Real religion -- as opposed to the cartoon Christianity seen in today's media and correctly mocked by thinking people -- presents a far greater challenge.

[Slartibartfast]

Ok, I'll bite: why all this business with "Bruce"? No, my real name is not Bruce, but anyone armed with a modicum of skill and access to the internets could have figured that out.

[liberal japonicus]

Slart
Australian Philosophy College skit by Monty Python That was the source of the Philosophers song that you quoted.

[Slartibartfast]

I just knew it was something like that, but I'd completely forgotten about the Bruces.

Slarti the Brus. I kind of like that; it's grand and evil all at once.

[Jesurgislac]

Russ: Real religion -- as opposed to the cartoon Christianity seen in today's media and correctly mocked by thinking people -- presents a far greater challenge.

Indeed. See Jill Paton Walsh's Knowledge of Angels.

[novakant]

ding-in-sich

Ack pffft!

sorry to nitpick, but that would be the

Ding an sich