God’s Diminishing Power

In the beginning … God walked in the Garden of Eden like an ordinary supernatural Joe. He dropped by Abraham’s for a cup of coffee and a chat. He didn’t know what was up in Sodom and Gomorrah and had to send out angelic scouts for reconnaissance: “The outcry against Sodom and Gomorrah is so great and their sin so grievous that I will go down and see if what they have done is as bad as the outcry that has reached me” (Gen. 18:20–21).

But, like Stalin gradually collecting titles, God has now become omniscient and omnipotent. He’s gone from needing six days to shape a world from Play-Doh and sprinkle tiny stars in the dome of heaven to creating 100 billion galaxies, each with 100 billion stars.

That’s 6,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 kg of universe.

And yet, oddly, his biblical demonstrations of power faded with time. From creating the universe, he’s weakened such that appearing in a grilled cheese sandwich is about as much as he can pull off today. He has the fiery reputation of the Wizard of Oz but is now just the man behind the curtain.

Even God’s punishments became wimpier. A global flood, with millions dead is pretty badass. Personally smiting Sodom and Gomorrah is impressive, though that’s a big step down in magnitude.

And it’s downhill from there—God simply orders the destruction of Canaanite cities, and to punish Israel and Judah, he allows Assyria and then Babylon to invade. As Jesus, he doesn’t kick much more butt than cursing a fig tree, and today he simply stands by to let bad things happen.

Maybe God’s power diminishes as the universe’s dark energy increases?

Photo credit: Why There is no God

Infinity—Nothing to Trifle With (2 of 2)

(See Part 1 for the beginning of this discussion in progress …)

We can compare the sizes of two sets of numbers by finding a one-to-one correspondence between them, but in the case of infinitely large sets, strange things can happen. For example, compare the set of positive integers I = {1, 2, 3, 4, …} with the set of squares S = {1, 4, 9, 16, …}. Every element n in I has a corresponding n2 in S, and every n2 in S has a corresponding n in I. Here we find that a subset of the set of integers (a subset which has omitted an infinite number of integers) has the same size as the set of all integers.

Playing with the same paradox, Hilbert’s Hotel imagines a hotel that can hold an infinite number of guests. Suppose you ask for a room but the hotel is full. No problem—every guest moves one room higher (room n moves to room n + 1), and room 1 is now free.

But now suppose the hotel is full, and you’ve brought an infinite number of friends. Again, no problem—every guest moves to the room number twice the old room number (room n moves to room 2n), and the infinitely many odd-numbered rooms become free.

Infinity is best seen as a concept, not a number. To understand this, we should realize that zero can also be seen as a concept and not a number. Consider a situation in which I have three liters of water. I give you a third so that I have two liters and you have one. I now have twice what you have. I will always have twice what you have, regardless of the number of liters of water except for zero. If I start with zero liters, I can’t really give you anything, and if I “gave” you a third of my zero liters, I would no longer have twice as much as you.

Not all infinities are the same. Let’s move from integers to real numbers (real numbers are all numbers that we’re familiar with: the integers as well as 3.7, 1/7, π, √2, and so on).

The number of numbers between 0 and 1 is obviously the same as that between 1 and 2. But it gets interesting when we realize that there are the same number of numbers in the range 0–1 as 1–∞.

The proof is quite simple: for every number x in the range 0–1, the value 1/x is in the range 1–∞. (If x = 0.1, 1/x = 10; if x = 0.25, 1/x = 4; and so on) And now we go in the other direction: for every number y in the range 1–∞, 1/y is in the range 0–1. There’s a one-to-one correspondence, so the sets must be of equal sizes. QED.

(Note that this isn’t a trick or fallacy. You might have seen the proof that 1 = 2, but that “proof” only works because it contains an error. Not so in this case.)

The resolution of this paradox is fairly straightforward, but resolving the paradox isn’t the point here. The point is that this isn’t intuitive. Use caution when using infinity-based apologetic arguments.

Let’s conclude by revisiting William Lane Craig’s example from last time.

Suppose we meet a man who claims to have been counting from eternity and is now finishing: . . ., –3, –2, –1, 0. We could ask, why did he not finish counting yesterday or the day before or the year before? By then an infinite time had already elapsed, so that he should already have finished by then.… In fact, no matter how far back into the past we go, we can never find the man counting at all, for at any point we reach he will have already finished.

The problem is that he confuses counting infinitely many negative integers with counting all the negative integers. As we’ve seen, there are the same number of negative integers as just the number of negative squares –12, –22, –32, …. Our mysterious Counting Man could have counted an infinite number of negative integers but still have infinitely many yet to count.

For a more thorough analysis, read the critique from Prof. Wes Morriston.

And isn’t the apologist who casts infinity-based arguments living in a glass house? The atheist might raise the infinite regress problem—Who created God, and who created God’s creator, and who created that creator, and so on? The apologist will sidestep the problem by saying (without evidence) that God has always existed. Okay, if God can have existed forever, why not the universe? And if the forever universe succumbs to the problem that we wouldn’t be able to get to now, how does the forever God avoid it?

This post is not meant as proof that all of Craig’s infinity based arguments are invalid or even that any of them are. I simply want to ask apologists who aren’t mathematicians to appreciate their limits and tread lightly in topics infinite.

Of course, if the apologist’s goal is simply to baffle people and win points by intimidation, then this may be just the approach.

Related posts:

Related articles:

  • “Aleph number,” Wikipedia.
  • Wes Morriston, “Must the Past Have a Beginning?” Philo, 1999.
  • William Lane Craig, “The Existence of God and the Beginning of the Universe,” Truth Journal.

Infinity—Nothing to Trifle With

Snowflake curveThe topic of infinity comes up occasionally in apologetics arguments, but this is a lot more involved than most people think. After exploring the subject, apologists may want to be more cautious.

Philosopher and apologist William Lane Craig walks where most laymen fear to tread. Like an experienced actor, he has no difficulty imagining himself in all sorts of stretch roles—as a physicist, as a biologist, or as a mathematician.

Since God couldn’t have created the universe if it has been here forever, Craig argues that an infinitely old universe is impossible. He imagines such a universe and argues that it would take an infinite amount of time to get to now. This gulf of infinitely many moments of time would be impossible to cross, so the idea must be impossible.

But why not arrive at time t = now? We must be somewhere on the timeline, and now is as good a place as any. The imaginary infinite timeline isn’t divided into “Points in time we can get to” and “Points we can’t.” And if going from a beginning in time infinitely far in the past and arriving at now is a problem, then imagine a beginningless timeline. Physicist Vic Stenger, for one, makes the distinction between a universe that began infinitely far in the past and a universe without a beginning

Hoare’s Dictum is relevant here. Infinity-based arguments are successful because they’re complicated and confusing, not because they’re accurate.

One of Craig’s conundrums is this:

Suppose we meet a man who claims to have been counting from eternity and is now finishing: . . ., –3, –2, –1, 0. We could ask, why did he not finish counting yesterday or the day before or the year before? By then an infinite time had already elapsed, so that he should already have finished by then.… In fact, no matter how far back into the past we go, we can never find the man counting at all, for at any point we reach he will have already finished.

Before we study this ill-advised descent into mathematics, let’s first explore the concept of infinity.

Everyone knows that the number of integers {1, 2, 3, …} is infinite. It’s easy to see that if one proposed that the set of integers was finite, with a largest integer n, the number n + 1 would be even larger. This understanding of infinity is an old observation, and Aristotle and other ancients noted it.

But there’s more to the topic than that. I remember being startled in an introductory calculus class at a shape sometimes called Gabriel’s Horn (take the two-dimensional curve 1/x from 1 to ∞ and rotate it around the x-axis to make an infinitely long wine glass). This shape has finite volume but infinite surface area. In other words, you could fill it with paint, but you could never paint it.

A two-dimensional equivalent is the familiar Koch snowflake. (Start with an equilateral triangle. For every side, erase the middle third and replace it with an outward-facing V with sides the same length as the erased segment. Repeat forever.) At every iteration (see the first few in the drawing above), each line segment becomes 1/3 bigger. Repeat forever, and the perimeter becomes infinitely long. Surprisingly, the area doesn’t become infinite because the entire growing shape could be bounded by a fixed circle. In the 2D equivalent of the Gabriel’s Horn paradox, you could fill in a Koch snowflake with a pencil, but all the pencils in the world couldn’t trace its outline.

Far older than these are any of Zeno’s paradoxes. In one of these, fleet-footed Achilles gives a tortoise a 100-meter head start in a foot race. Achilles is ten times faster, but by the time he reaches the 100-meter mark, the tortoise has gone 10 meters. This isn’t a problem, and he crosses that next 10 meters. But wait a minute—the tortoise has moved again. Every time Achilles crosses the next distance segment, the tortoise has moved ahead. He must cross an infinite series of distances. Will he ever pass the tortoise?

The distance is the infinite sum 100 + 10 + 1 + 1/10 + …. This sum is a little more than 111 meters, which means that Achilles will pass the tortoise and win the race.

Some infinite sums are finite (1 + 1/2 + 1/4 + 1/8 + … = 2).

And some are infinite (1 + 1/2 + 1/3 + 1/4 + … = ∞).

(And this post is getting a bit long. Read Part 2.)

Photo credit: Wikipedia

Related posts:

Related articles:

  • “Zeno’s paradoxes,” Wikipedia.
  • “Zeno’s Advent Calendar,” xkcd.com.
  • “Paradoxes of infinity,” Wikipedia.
  • “Is God Actually Infinite?” Reasonable Faith blog.
  • Peter Lynds, “On a Finite Universe with no Beginning or End,” Cornell University Library, 2007.
  • Mark Vuletic, “Does Big Bang Cosmology Prove the Universe Had a Beginning?” Secular Web, 2000.
  • Wes Morriston, “Must the Past Have a Beginning?” Philo, 1999.
  • William Lane Craig, “The Existence of God and the Beginning of the Universe,” Truth Journal.

Claims that Prayer Cures Disease

green blogs--bacteria under a microscopeWashington recently declared a state epidemic for pertussis (whooping cough). Pertussis hasn’t been this bad in Washington for decades. The number of cases (close to 2000) is already ten times the number from last year.

Before routine child vaccination in the 1940s, pertussis caused thousands of fatalities annually in the U.S.

You might imagine that this is a story about anti-vaxers, afraid of a perceived vaccine-autism link, who have refused to vaccinate their children and helped create this epidemic. Not this time. The anti-vaccine movement seems not to be a factor.

Instead, the interesting angle on this story is not disease prevented by vaccine but disease prevented by prayer. Kingdom League International, an online ministry based in western Washington, says in a brief article titled “Whooping Cough Epidemic Halted in Jefferson County”:

Churches in Jefferson County [one of those hardest hit by the statewide epidemic] used our strategy to mobilize prayer and establish councils to connect in 7 spheres of society.* On Mar 27 they met and a County Commissioner asked them to pray about the whooping cough epidemic. … As of April 13 there has not been one case reported. From epidemic proportions to zero.

A bold claim, but the only evidence is that of the improvement in statistics. The elephant in the room, of course, is whether we can find natural explanations besides prayer to explain the facts. And, of course, we can. Epidemics peak and then diminish, particularly when there’s an effective health system in place that can administer vaccines. There were 21 confirmed cases for this county in 2012, with no new cases since mid-April. Is this remarkable? Is this unexplained by the efforts of the public health system? Looks to me like an epidemic that’s simply run its course.

Not surprisingly, I jumped into a discussion with the author in the comment section. Aside from being asked my faith status (though I’m not sure how this affects one’s ability to evaluate evidence), I got the expected tsunami of miracle claims—a bad knee healed, a barren woman now pregnant, lung cancer cured, demons cast out, blindness healed, a stroke patient recovering, a rainstorm to break a heat wave, a cracked rib healed, and so on.

(For comparison, consider the pinnacle of medical cure sites, Lourdes.  After 150 years as a pilgrimage site and with six million visitors per year, the Catholic Church has recognized just 67 miraculous cures.)

I pointed out to my Kingdom League correspondent that natural explanations hadn’t been ruled out.  Surprisingly, there was no interest in doing so.

I tried to portray this as a missed opportunity. If these claims are more than just anecdotal, then this group should create a dossier of x-rays, test results, photographs, or other evidence, both before and after the miracle. Add the report of the doctor who witnessed the change and then show this to the Centers for Disease Control or an epidemiologist or some other qualified authority. Why hide your light under a basket? Jesus had no problem using miracles to prove his divinity (John 10:37–8).

There seems to be no shortage of these miracles (at least in their minds), so if one miracle claim isn’t convincing, then pray for some more and try again to convince the skeptics.

That this group has no interest in going beyond feel-good anecdotes makes me think that they understand that their claims wouldn’t withstand scrutiny, not because skeptics wouldn’t play fair, but because honestly evaluating the claims would show them to be little more than wishful thinking.

Pray v. To ask the laws of the universe to be annulled
on behalf of a single petitioner confessedly unworthy.
— Ambrose Bierce, The Devil’s Dictionary

Addendum 6/1/12: After further discussion with the author of the KLI article, he reminded me that links in the comment section give more than anecdotal information, including this article in the Southern Medical Journal.

*KLI focuses on the Dominionists’ Seven Spheres of Influence.

Photo credit: AJC1

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Word of the Day: Argument from Authority (and How Consensus Fits In)

An authority could argue that God exists, but why believe them?I can’t count the number of times that I’ve said something like, “I accept evolution because it’s the scientific consensus” and gotten the response, “Gotcha! Argument from Authority Fallacy!”

Let’s take a look at this fallacy and see where it applies and where it doesn’t.

Suppose I said, “Dr. Jones is smarter than both of us put together and he agrees with me, so I’m right!” This statement could fail due to the Argument from Authority Fallacy for two reasons: (1) we haven’t established that Dr. Jones’ expertise is relevant to the question at hand, and (2) even if Dr. Jones is an expert on the subject, that he agrees with my position doesn’t make me right—at best, it would make me justified in holding my position.

Chastised at my poor argument, I go back and rework it. Now I’m careful to first establish Dr. Jones’ relevant expertise and I modified my claim this way: “Dr. Jones, an established authority, agrees with me, so therefore my position is well justified.” This is better, but my statement could still fail due to this Fallacy. What if Dr. Jones is a maverick in his field? He could be a cosmologist still holding on to the Steady State model of the universe now that the Big Bang model is the overwhelming consensus. Conversely, imagine that it’s the 1930s and he is arguing for an expanding universe when that was the minority position. Either position makes Dr. Jones a maverick, and the layman (as an outsider) has no grounds from which to conclude that this minority position is the best approximation.

The Argument from Authority is not a fallacy when the person indicated (1) is an expert in the field and (2) is arguing for the consensus. Of course, that doesn’t necessarily make you right, but being in line with the relevant consensus is the best that we can hope for.

I’m amazed when I hear people reject evolution who aren’t biologists. I can imagine browsing biology textbooks and concluding that evolution is a remarkable claim. I could even imagine thinking that the evidence isn’t there (though the fact that I’ve only dipped my toe into the water would scream out as the explanation for this). What I can’t imagine is concluding, based in my “research,” that the theory of evolution is flawed. I mean—on what grounds could I possibly make this statement? On what grounds could I reject the consensus of the people who actually understand this stuff? The people who actually have the doctorate degrees and who actually do the work on a daily basis?

And yet I hear people justifying this step all the time.

Let’s move on to another topic, the question of consensus. After many discussions that have forced me to carefully think my position, let me offer my views on consensus from different fields. Note that this is the view of a layman—someone who is an outsider to these fields.

  • Scientific consensus: I always accept this.
  • Historical consensus: I always accept this.
  • Consensus of religious scholars about their own religion: I always accept their statements of what their beliefs are. For example, when the consensus of Catholic scholars says that within the Catholic church the eucharist (the communion wafer) is believed to transubstantiate into the body of Christ, I accept that.

But don’t accept everything. I draw the line at supernatural claims, whether by scholars or believers, and whether the consensus or not. I will consider evidence for these claims, but so far I have always rejected them.  If I were to accept these claims, that would probably be based either the scientific or historical consensus.

Supernatural claims are in a very different category than scientific or historical claims.  For more, see my post Map of World Religions.

Photo credit: Wikimedia

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Word of the Day: Survival of the Fittest

What Would Jesus Say?The term “survival of the fittest” did not initially come from Charles Darwin’s Origin of Species, though later editions did use it. It was first coined by Herbert Spencer, after reading Origin.

While a convenient phrase, it can be confusing. “Fit” in biological terms doesn’t mean what we commonly think (strong, quick, or agile, for example) but refers to how well adapted an organism is for an environment. Think of it as puzzle-piece fit, not athlete fit.

Creationists sometimes use the phrase to mean that might makes right or that the most savage or ruthless or selfish will survive. On the contrary, rather than might makes right, cooperation can be the better approach. And even if evolution did have some bloodthirsty aspects to it, how does that change whether it’s an accurate theory or not?

NewScientist magazine says:

Although the phrase conjures up an image of a violent struggle for survival, in reality the word “fittest” seldom means the strongest or the most aggressive. On the contrary, it can mean anything from the best camouflaged or the most fecund to the cleverest or the most cooperative. Forget Rambo, think Einstein or Gandhi.

What we see in the wild is not every animal for itself. Cooperation is an incredibly successful survival strategy. Indeed it has been the basis of all the most dramatic steps in the history of life. Complex cells evolved from cooperating simple cells. Multicellular organisms are made up of cooperating complex cells. Superorganisms such as bee or ant colonies consist of cooperating individuals.

Note also that evolution is descriptive, not prescriptive; it simply says what is the case and doesn’t provide moral advice. “I’ll model my morality on evolution” makes as much sense as “I’ll model my morality on the fact that arsenic kills people.”

Creationists sometimes twist Darwin’s The Descent of Man to argue that he favored eugenics. Darwin’s damning paragraph said, in part, “hardly anyone is so ignorant as to allow his worst animals to breed.” In the first place, whether Darwin ate babies plain or with barbeque sauce says nothing about whether evolution is accurate or not. In the second place, the very next paragraph clarifies Darwin’s position about denying aid to the helpless.

Nor could we check our sympathy, even at the urging of hard reason, without deterioration in the noblest part of our nature.

“Survival of the fittest” is a handy description of natural selection as long as all parties understand what it means.

Photo credit: EvolveFish

Related links:

  • “Survival of the fittest,” Wikipedia.
  • Michael Le Page, “Evolution myths: ‘Survival of the fittest’ justifies ‘everyone for themselves,’” NewScientist, 4/16/08.