By the Hearing of Faith

Transcript of a brief conversation this weekend with my one-year-old daughter:
Daddy: Peanut, do you have a poopie-butt, or did you just fart?
Peanut: Fut.
Daddy: Ah. Very good ….

In a previous post, I wrote that complexity and specification never spontaneously arise unassisted from the chaos of a random non-intelligent source. You’d think that would be a reasonable statement that anyone could agree with, but from time to time I encounter people who seem to believe not only that chance is a causal agent rather than merely an attribute of a given scenario (e.g., “The Universe happened by chance”) but also that chance combined with time results in anything we can assume from the standpoint of naturalist philosophy. Consequently, what seems reasonable ends up being dismissed as superstition, and the justification given is often some variation of the Infinite Monkey Theorem, which usually goes unchallenged in casual conversation because most people (myself included) aren’t fluent enough in probability theory to object.

About five years ago, I was browsing through an introduction to applied probability and found the following example in a chapter on repeated independent trials (Roberts, Richard A. “Independence and Repeated Trials.” An Introduction to Applied Probability, Addison-Wesley, 1992, pp. 88–89). While still not succinct enough for a casual conversation, it’s probably concise enough for someone with good math-ninja skills (like John Lennox) to present in a formal debate. It’s very compelling.

Example 3.5.2

Suppose a billion monkeys type on word processors at a rate of 10 symbols per second. Assume that the word processors produce 27 symbols, namely, 26 letters of the English alphabet and a space. These monkeys type for 10 billion years. What is the probability that they can type the first sentence of Lincoln’s “Gettysburg Address”?

Fourscore and seven years ago our fathers brought forth on this continent a new nation conceived in liberty and dedicated to the proposition that all men are created equal.

Solution: If we counted correctly, there are 168 symbols in this sentence. Let N be the number of symbols typed per monkey in years. A sample space of possible letter sequences typed by each monkey is

   (N times)

where X is the set of 27 symbols. Now define s as a particular sequence that is m symbols long:

Let  be the event that s appears at the  index in a sequence of length N:

= {     ( occurs on index k)}

In other words,  is the event that a particular sequence, s, which is m symbols long, appears in one monkey’s sequence and ends on index k. The event of interest is A, given by

In our case, m = 168 and N is the number of symbols typed by one monkey in  years. Thus by Boole’s Inequality,

Now the probability of the event  is the number of outcomes of event  divided by the total number of outcomes. The total number of outcomes is . The number of outcomes that produce event  is . The exponent is  because there are m positions specified in . The remaining  are arbitrary. Thus

And so

since N >> m. Thus  is bounded above by ,  where N is the number of trials produced by a single monkey. This is the probability bound for  for one monkey. For  monkeys, we can think of forming one long sequence by concatenating  sequences so that N becomes the number of trials produced by  monkeys. Thus  is bounded above by

The probability of producing a specified sequence of English text 168 symbols long is bounded above by . No reasonable model for the source of the “Gettysburg Address” would propose a team of monkeys as author.

Actually, there are 171 characters (minus the period), and the string should be written all in upper or lower case, but the point of the exercise is still valid. Roberts calculates the probability of the string occurring anywhere (from index position 168 to the last typed character) over the total number of characters a single hypothetical monkey could type in 10 billion years (N characters). He then uses Boole’s Inequality to establish an upper bound for that probability (i.e., the probability is no higher than the right side of that inequality) and then scales the scenario up by  (1 billion monkeys). The denominator in the last approximation is a power of ten to make it more readable, and (2.95e+240) is for all intents and purposes close enough to (1.0e+240). (Anyone who’s seriously thought about the origin of information has likely already taken note that scenarios like the Infinite Monkey Theorem assume an infinite event space encompassing all probabilities/possibilities.)

Roberts then adds, “A similar example of repeated independent trials used as a mechanism for obtaining order from disorder is chemical evolution. Because of its philosophical implications, however, the example is more controversial.”

Controversial! Well, I guess I’ll have to reproduce that example, too ….

This morning, our three-year-old was playing with this and had an accidental (and somewhat unpleasant) encounter with positional decimal numbering:

Mommy: Nice tower! Can you count the levels?
Audie: One, two, three, four ….
M: And the numbers are written on the side. See the numbers?
A: Five, six, seven ….
Daddy: Here, bud. Let me turn these around so we can see the numbers.
A: Eight, nine … one zero.
D: Actually, that’s ten. One and zero.
A: One and zero … is ten.
D: Yeah. A one and then a zero.
A: One plus zero equals ten!
D: No, no. That’s a little different than–
A: You said one and zero is TEN, Daddy!
D: Hang on. Listen while I explain–
A: ONE plus ZERO equals TEN, Daddy! ONE PLUS ZERO EQUALS TEN!
D: Little help, Mommy?
A: ONE PLUS ZERO EQUALS TEN!!! ONE PLUS ZERO EQUALS TEN!!!
D: Mommy? Where’d you go?

Q: Why does Mr. Squid swim “up to the top” and not “down to the top”?
A: Because if he were already at the top, he wouldn’t need to swim up.
Q: Why?
A: Because he’s below the top, not at the top.
Q: But why does Mr. Squid swim “down to the bottom”?
A: Well, if he were already at the bottom, he wouldn’t need to swim down.
Q: But why does he not swim up to the bottom?
A: Because … the top is up … and the bottom is down.
Q: Why?
A: I … I don’t know how to answer that.
Q: Why?
Q: Did you brush your teeth yet?

1. Emptying the dishwasher
2. Doing the laundry
3. Fixing a broken door
4. Drywall repair
5. Painting
6. Mowing the lawn
7. Assembling the kids’ trampoline/beds/swimming pool/etc.
8. Cleaning up dog poo
…
9,999,999. Writing something that makes people chuckle for five seconds
10,000,000. Writing something philosophically insightful

Kid: Daddy, where did these pickles come from?
Dad: We got them from an old, one-eyed toothless gypsy hag, but only because we correctly answered the following three riddles–
Kid: Mommy, where did these pickles come from?

While most Americans would likely consider the foremost practical application of the First Amendment to be that they cannot be prevented from expressing their views, an arguably more important application is that they cannot be forced to express views with which they disagree. The government cannot compel speech or expression, especially when that expression violates a person’s constitutionally protected religious or philosophical views. Whether you like
it or not, millions of people in the United States (Jewish, Christian, Mormon, and Muslim people) have religious objections to same-sex marriage, and those objections are constitutionally protected. The essential issue in Masterpiece Cakeshop Ltd. v. Colorado Civil Rights Commission is not that Jack Phillips refused service to anyone–and he did not refuse service–but rather that he refused artistic expression (in the form of a wedding cake) in contradiction to his constitutionally protected religious convictions about marriage. The U.S. Supreme Court’s decision was therefore congruent with the Constitution, and that is a good thing, because I don’t want to live in a nation where the government can coerce anyone to express a view that is contrary to his or her convictions. And I can’t help but feel shocked and saddened by how many people are plainly ignorant of this rudimentary truth about the purpose of the First Amendment: If you can use the blunt instrument of government coercion to compel speech in support of your views, the very same can be done to you, and it probably will be done to you. We should take caution not to change the rules because it’s expedient now. We don’t know what the world might look like twenty years hence or whether we’ll prefer to live by the rules we’ve made.

Story #1: This morning I woke early with a need to poop so urgent that only a morbidly obese Scotsman portrayed by Mike Myers could truly empathize. Ten minutes later when I emerged from the master bathroom, my gaze was met by my one-year-old daughter Peanut. Our eyes locked for several seconds, and then she turned and sprinted down the hall to her dollhouse. Rooting around with tiny hands, Peanut quickly found the Daddy doll, seated him on the dollhouse toilet, and looked over her shoulder at me. I nodded, and she nodded back. Something profound had been communicated. I’m not sure what exactly. But I know that Peanut can say non-verbally what most people can’t say with 1,000 words. And that made me proud.

Story #2: That evening during tub time, Audie pulled the bath-toy basket off the wall and attached the suction cups to the soap dish and the side of the tub ….
Audie: Daddy, this is where the icky water gets collected.
Daddy: Okay. And what happens then?
Audie: It goes down this pipe and then into these pipes here and then up into this machine.
Daddy: Wow. What’s that called?
Audie: This is called the Poop Collector.
Daddy: Because … it collects poop?
Audie: Yeah.
Daddy: And then what happens?
Audie: It gets spit out into this dirty lake …
(Which is actually a great description of a modern waste water treatment facility; thank you, Richard Scarry.)
Daddy: And when does it become NOT poop?
Audie: Well, when it gets turned into a BOAT!
Daddy: Awesome! Does the boat have a poop deck?
Audie: Daddy, why do you not like squirrels in the house?

Stephen Hawking passed away today, so I anticipate a lot of Hawking quotes on the Internet. Most people are not especially conversant in contemporary experimental physics (myself included) and, under the misunderstanding that everything a scientist says is necessarily a statement of science, will consequently be mostly quoting Hawking’s philosophical pronouncements about reductive materialism. I became familiar with Hawking’s thoughts about cosmology largely through one of his critics, Oxford mathematician John Lennox, who neither takes issue with Hawking’s scientific work nor tolerates his philosophical illiteracy. Hawking seems to have been an atheist, so we can expect atheists to once again insecurely assert their pretensions about the alleged intellectual superiority of atheism, steadfastly ignoring scientific elites (such as Sir John Polkinghorne) who profess a theistic view in contradiction to Hawking’s. This is a mistake because it ignores some disastrously poor philosophy. Lennox observes, for one example:

“What does Hawking mean when he uses the word ‘nothing’ in the statement ‘The Universe can and will create itself out of nothing’? Because, if you notice the assumption in the first part of the assertion–because there is a law of gravity (so there is something), the Universe will create itself out of nothing …. And one presumes, therefore, that he is assuming that a law of gravity exists. But I would presume that he also believes that gravity exists, because what would a law of gravity mean if gravity itself didn’t exist? … [g]ravity is not nothing, if [Hawking] is using that word in its usual philosophically correct sense of non-being (and if he isn’t, he should have told us so). So, on the face of it, this key assertion of [“The Grand Design” (2010)] appears to be simultaneously asserting that the Universe is both created from nothing and from something, which is not a very promising start. Of course one might add, for good measure, the fact that when physicists talk about nothing, they often appear to mean a quantum vacuum, which is manifestly not nothing, and in fact Hawking is probably alluding to that when he later writes ‘We are a product of quantum fluctuations in the very early Universe.’ I’m very tempted to say, ladies and gentlemen, possibly this is a little bit too much ado about nothing.”

Lennox is just getting warmed up at that point, but you need not hear the rest to understand what all the forthcoming Hawking quotes about theism will amount to (nothing): Argumentum ad verecundiam, or argument from authority, is a logical fallacy because it gives the user a false sense of security by ignoring the substance of the arguments at issue. The real tragedy of today isn’t so much that the world lost a brilliant scientific mind but rather that in the culture at large the beneficiaries of Hawking’s scientific legacy will be greatly outnumbered by the casualties of his demonstrably bad philosophy. A wise man once said that predictions are difficult, especially when they’re about the future, but I feel safe in predicting that people will use Hawking’s philosophical sophistry to bolster their “loyalty oath of of modernity,” and precisely nothing will change.

Which is disappointing. In Hawking’s death, we have cause to mourn the living as much as the dead.

(Originally posted to Facebook on February 29, 2016 at 12:39 PM)

Audie turned 1 year old this past week, and Andy arranged twelve photos of him in sequence, one photo for each month of the past year. The difference between March-2015 Audie and February-2016 Audie visually annunciated how quickly the year had passed, and I began to feel and understand the same pangs of sadness that have afflicted Andy for a few months now. From chatting with other parents about this sadness, we concluded that it’s inapt to classify it as the mere sting of nostalgia. It’s really a kind of grief over moments we’ve lost, mostly to nebulous memory and sleep deprivation (or both), and the same sort of grief we feel when we miss an opportunity that will never come again, or when we do the math and realize a beloved dog is 105 in dog years, or when we remember a dear friend who died young, half our life ago, and think about what might have been. We want to keep the substance of those experiences immutably preserved, but we know the futility of keeping even their memory intact. Like that Robert Frost poem you had to memorize in school–“Nature’s first green is gold, Her hardest hue to hold”–we long for eternity despite knowing that we cannot have it, at least not in this world, where “nothing gold can stay.”

It’s instructive that we even have a concept of eternity, given how seldom we see evidence of it. Actually, eternity occurs nowhere in the Universe we now inhabit: Even the trusty Sun will begin to sputter out 5 billion years from now. So why should we have a word for eternity to express our desire for it? C.S. Lewis wrote “If I find in myself a desire which no experience in this world can satisfy, the most probable explanation is that I was made for another world.” This is where people who are determined to be miserable “realistic” usually depart from the conversation, and I think Lewis sensed that when he wrote: “In speaking of this desire for our own far off country, which we find in ourselves even now, I feel a certain shyness. I am almost committing an indecency. I am trying to rip open the inconsolable secret in each one of you—the secret which hurts so much that you take your revenge on it by calling it names like Nostalgia and Romanticism and Adolescence; the secret also which pierces with such sweetness that when, in very intimate conversation, the mention of it becomes imminent, we grow awkward and affect to laugh at ourselves; the secret we cannot hide and cannot tell, though we desire to do both. We cannot tell it because it is a desire for something that has never actually appeared in our experience. We cannot hide it because our experience is constantly suggesting it, and we betray ourselves like lovers at the mention of a name. Our commonest expedient is to call it beauty and behave as if that had settled the matter.”

And I guess I’m writing this because it doesn’t settle the matter at all. Instead, it callously trivializes our sense of loss. And it also widely misses the mark: “Wordsworth’s expedient was to identify it with certain moments in his own past. But all this is a cheat. If Wordsworth had gone back to those moments in the past, he would not have found the thing itself, but only the reminder of it; what he remembered would turn out to be itself a remembering. The books or the music in which we thought the beauty was located will betray us if we trust to them; it was not in them, it only came through them, and what came through them was longing. These things—the beauty, the memory of our own past—are good images of what we really desire; but if they are mistaken for the thing itself they turn into dumb idols, breaking the hearts of their worshipers. For they are not the thing itself; they are only the scent of a flower we have not found, the echo of a tune we have not heard, news from a country we have never yet visited.” (The Weight of Glory, http://bit.ly/1TN0J59)

When Audie is 25 years old, I want to remember him at 1 year old. I want to remember his giggle, his grabbing my nose at breakfast with wet banana-hands, his arms outstretched for me to pick him up at 3:00 AM when he’s just had a nightmare. I want to remember a million other details that I can’t now describe because I’ve already forgotten them. For now, Andy and I will have to make do with photos and videos and journal entries, things that outlast our memories but still won’t last forever. And that’s okay, because we know that eternity is ultimately not the object of our longing. Eternity is an attribute of a Person, and every moment Andy and I have forgotten, that eternal Person has remembered. Everything we’ve misplaced, that Person has recovered. Everything we’ve lost, He has saved. And one day, when we’re at home in that far-off country we’ve never been to before, He will return it all to us.