Proof from Logical Necessity, or the Ontological Proof (2)

Existence is not Great

A core assertion of Ontological is that it’s better to physically exist than to be a concept. I’m not convinced, and to help illustrate the point I propose a simple thought experiment.

Picture a vertical line, which we’ll declare to be one unit high.
Place a circle around it with a diameter of exactly that line; if you’ve pictured this correctly, you’ll have a circle split in two.
Now, mentally undo the part of the circle that touches the bottom of the line, as well as the top part of the line on the left side. Unwrap it counter-clockwise from the top, keeping the left-most portion anchored to the top of the vertical line, until the line is perfectly horizontal and at a right angle to the original line.
You now have two sides of a rectangle. Complete it by extending a horizontal line from the bottom of the vertical line with the same length as the upper horizontal line, and a vertical line from the end of the upper horizontal line with the length of one unit.

The area for a rectangle is the width times the height. We know the circumference, or length around a circle is π times the diameter of that circle, which in this case is π units. So with a width of π units and a height of our circle’s diameter, or one unit, that rectangle has an area of exactly π square units.

If you had difficulty, the following diagram should help you. Conveniently, this diagram will also prove my point:

The final rectangle in your mind is exactly π square units big. The rectangle in this diagram is not. In fact, no real-world diagram will ever be exactly π square units.

For argument’s sake, we’ll say the rectangle is exactly 10^cm wide, and the diagram is printed at 472dots per centimetre.[26] The width of this rectangle is thus 4,720 dots, and the height is 1502 dots, for an area of 7,089,440 dots. To convert that to “units,” we need to divide by the size of one square unit in dots, which is 1,502×1,502 or 2,256,004 dots. According to my math, that rectangle is about 3.142477 square units in size. This differs from π after the third decimal place.

The reason is pretty clear. π is an irrational number with an infinite number of decimal places; by definition, it can never be represented by one integer divided by another, or by counting a finite number of elements. And yet if we construct this diagram in the real world, both the width and the height must be finite numbers. Even if the width of the rectangle was the size of the visible universe, it would still be a finite number of atoms in area, and our answer would be wrong somewhere around the 36_th decimal place.

There’s no escape from this problem, either. No matter how you try to represent π in the real world, you’ll be forced to use a finite number of decimal places to represent a number with an infinite number of them. And yet, what’s impossible in the real world is easy in your head. You don’t need to convert π to a decimal number, you can treat it as a concept and dodge around the problem. As a consequence, the rectangle in your head is exactly π square units in area.

This confirms something I’ve observed as an artist. Like Anselm’s painter, I too have had a vision of a finished drawing or photo in my head; unlike him, the finished product is rarely more than a shadow of what’s in my head. Something always goes wrong; a line falls out of place, a photo has a branch that’s poorly placed, and so on. The exceptions are usually because I accidentally found an improvement while creating the work, and not through perfect execution.

The Triumph of Irrationality

I’ve also got a beef with another assertion of Ontological, that it’s impossible to think of any being greater than god.

If you’ve heard of Buddhism, you’ve likely heard of its most famous variation, Zen. Part of that sect’s seductive quality comes from an emphasis on “kōans,” or questions that have no rational answer but instead are intended to provoke an enlightened train of thought. Here’s the most famous of them:

“Two hands clap and there is a sound. What is the sound of one hand?”

(Hakuin Ekaku)

That question cannot be logically answered,[27] yet Hakuin had no problems asking it and we had no problems contemplating it. Given a little thought, you should be able to come up with your own kōans: What is the colour of an object in perfect darkness? What is the sound of empty space?

Kōans show that we have no problem thinking irrational thoughts. The Ontological proof uses reason to prove god, however. In order to do this, it assumes that god must be rational. If he is not, he could not be described by reason, and if he could not be described by reason, he could not be proven by it either.

But if a god must be rational, and our thoughts don’t need to be, we can contemplate things greater than the gods. Let’s try it: There is something greater than a god. The consequences of that sentence are not logically valid, yet I had no problems writing it and you had no problems understanding it. If we shift our assumptions, we can make it valid; I’ll use this in the Morality proof later on, for instance.

If we’re not bound by rationality, while god is, then we can easily think of something greater than god, and another assertion is shot down.

Anselm realized this loophole, and tried to close it in Chapter 4 of Proslogion. He separates thought into two categories:

For a thing is thought in one way when the words signifying it are thought, and it is thought in quite another way when the thing signified is understood. God can be thought not to exist in the first way but not in the second. For no one who understands what God is can think that he does not exist.

(Chapter 4: “How the Fool Managed to Say in His Heart That Which Cannot be Thought”, as translated by David Burr)

The problem with Anselm’s counter-counter is that it doesn’t address the counter-argument at all. He clearly wants to put “a being greater than god” in the “signified but not understood” category, where he can safely ignore it, but he doesn’t say why it belongs there, let alone why his categories exist in the first place.

In order to decide which category that sentence goes into, you have to understand the sentence first. For instance, which of the two gets “Yd.p. lprxaxnf co br Ire?” That might be a meaningless statement, making it impossible to understand, or it might have meaning in a language or code you’re not familiar with. In contrast, “There is something greater than god” can be easily understood and thus placed in a category. But because you understood it, there’s only one possible placement: things that are “signified” and “understood.”

You may not be aware of all the rational implications of that statement, or you might know them better then I do, but the underlying concepts must be clear to you before you can make a rational decision. Irrational decisions are another beast, but they only prove my point: the irrational trumps the rational.

Anselm’s defence doesn’t work, and my counter-example still stands.

This cuts the other way, as well. Merely being able to state something does not make it rational or logically justified. The fourth “distilled” proof falls into this trap. “The existent perfect being is existent” is true, in the same way that “the existent @#^*$ is existent” is:

“The existent ___ is existent” depends on the assumption “a ___ exists.”

If that assumption is true, then there’s no need for the proof!

If that assumption is false, then the proof is contradictory and we can conclude anything we wish from it, including the existence of whatever we want.

The fifth earns a medal from me for squashing three separate proofs into one. There’s proof from Witness (“if one person is convinced a god exists, god exists”), proof from Popularity (“multiple believers can’t be wrong”), and just a sprig of Ontological (“the word ‘God’ only means something if a god exists”). Unfortunately, it falls flat on that last assertion, as the trio of Faust, Bilbo Baggins and the Jabberwocky will swear to. We’re surrounded by fictional, non-existent things that provide us with meaning, by setting an example or just giving us a good time. This extends to science as well; Niels Bohr expanded on Ernest Rutherford’s model of the atom to create the boringly-named Rutherford-Bohr model, which has very little in common with the real layout of an atom but is easy to teach. And so it is taught.

[26] For readers who think in imperial units, that’s 3 15/16_ths inches and 1200_dpi respectively.

[27] It’s a common misconception that kōans have no answer. To the contrary, every kōan has an answer, though that answer varies from Buddhist Master to Buddist Master. For instance, Zhàozhōu’s answer to “Does a dog have Buddha-nature or not?” to one of his students was “Wú,” Japanese for “no.” To another, he replied “yes.”

Proof from Logical Necessity, or the Ontological Proof (1)

Proof from Logical Necessity, or the Ontological Proof

I’m going to need your help with this one. Relax and get comfortable.

Now, I’d like you to imagine the most perfect being. One that embodies all the qualities you’d like to be in a conscious entity. A perfectly-balanced sense of judgement, say, or a deep pool of empathy and caring, or a graceful ability to forgive and move on, or a wisdom well beyond its years. Picture an entity that manages all that, better than anything that has or will exist.

It’s a lovely thought, isn’t it? Don’t you wish such an entity existed?

I bet you’d agree that it’s better to exist than not exist, right? A being that has all those traits would be more perfect if it existed than a similar being that did not. And yet, you had no problems picturing that perfect entity, didn’t you? How could you have pictured perfection without including every portion of that perfection, including the ability to exist?

The ease of picturing perfection, therefore, must mean that perfection exists. And since a god matches that perfection to a tee, that must mean the gods exist.

No Really, It’s Quite Popular With Some People

Most of you are scratching your heads right now. “Really? That’s a proof?”

It is, and it’s been a favourite of philosophers for some time. Despite the “-logical” suffix, most scholars do not think this proof was dreamed up by a Greek. I’m not so sure; while it’s true that I can’t find a single example within their works, you’ll note that it bears a strong resemblance to the Cosmological proof, which was quite popular with them. Indeed, my description above is almost identical to variation of Cosmological. Instead of stepping up one degree of perfection, however, I stepped sideways and invoke the property of “existence.” Thus Ontological proofs do not “step outside” the universe, and are immune to that particular counter-argument.

There’s a better argument for this proof’s origins, that a fan of Greek learning came up with this twist. Avicenna[22] was a Persian philosopher who lived roughly 1.5 millennia after the Greeks, but was one of the few people in the world to have access to their written texts. He claims to have memorized the entire Qur’an by age ten and outsmarted his teachers by age fourteen, which sounds unlikely until you start cataloguing his accomplishments. Avicenna pioneered the use of clinical trials, knew the heart worked as a valve, discovered Newton’s first law of motion, reasoned that light had a finite speed, came pretty close to inventing Germ Theory, was the first psychologist, published a book of medicine that was used for 600 years in Europe, and during a moment of boredom invented the refrigerated coil and scented oils. As if to further rub it in, half of his surviving work is
written in verse.

A lover of Aristotle, Avicenna extended the old Greek’s philosophy and applied it to Islam. I can track down several scholars, such as M. E. Marmura and Parviz Morewedge, who make it quite clear that Avicenna’s proof differed from his classical hero by focusing more on logic and existence, independent of physical reality:

It is not in any sense a proof that infers God’s existence from the observation of His handiwork. On this Avicenna is explicit. After giving one version of his proof from contingency, for example, he writes: “Reflect on how our proof for the existence and oneness of the First and His being free from attributes did not require reflection on anything except his existence itself and how it did not require any consideration of His creation and acting, even though the latter [provide] evidential proof (dalīl) for Him. This mode, however, is more reliable and noble, that is, where when we consider the state of existence, we find that existence inasmuch as it is existence bears witness to Him, while He thereafter bears witness to all that comes after Him in existence” (Ešārāt, p. 482).

(M. E. Marmura, Encyclopædia Iranica, http://www.iranica.com/articles/avicenna-iv, retrieved April 30th 2011)

Other scholars dispute Avicenna’s departure, and unfortunately I can’t track down a translated version of his Šefāʾ or Ešārāt to decide for myself.

I can track down the original texts of Anselm of Canterbury, however. His book Proslogion is universally accepted as a true proof from Logical Necessity. Anselm had a rather interesting life, most notably feuding with two kings of England and being forced into exile twice. It’s a shame the topic of this book doesn’t permit me to go into more details, because those decades of political intrigue would be easier to sort out than Anselm’s writing:

In fact, it [God] so undoubtedly exists that it cannot be thought of as not existing. For one can think there exists something that cannot be thought of as not existing, and that would be greater than something which can be thought of as not existing. For if that greater than which cannot be thought can be thought of as not existing, then that greater than which cannot be thought is not that greater than which cannot be thought, which does not make sense. Thus that than which nothing can be thought so undoubtedly exists that it cannot even be thought of as not existing.

(Proslogion, Chapter 3: “That God Cannot be Thought Not to Exist”, as translated by David Burr)

Since I’m not a cruel person, I’ll spare you from having to parse the original and write up my own translation:

Chapter 2: That God Really Exists

1. No being is greater than God. Even a fool who would deny God recognizes this.

2. That fool has only a partial understanding, however, since he does not understand such a being to exist.

3. Consider a painter’s thoughts of his or her next masterpiece, to the finished masterpiece itself. They have a rough sketch of the painting within their minds, but since it does not physically exist they cannot fully understand that painting.

4. It follows from 3. that it is greater for any object to exist that to not exist.

5. But if point 4. is true, then it would be impossible to think of the greatest possible being unless that being existed. Otherwise, there could exist a greater being, having all the attributes you gave to your greatest being plus the attribute of existence.

Chapter 3: That God Cannot be Thought Not to Exist

6. We can think of a being that must exist, and this being must be greater than one that we cannot think of as existing.

7. By that reasoning, if that being from 4. couldn’t exist, it would be lesser than another thing in our thoughts that could exist in reality.

8. Thus, we’ve reinforced point 5: that being must exist in reality.

9. By extension of points 6 through 8, we cannot even think of this being as not existing.[23]

10. We can’t think of anything greater than God.

11. This “being” we’ve been referring to must be God, otherwise we’d contradict point 10.

12. Praise God, isn’t He wonderful, etc. etc. etc.

Philosophers fell in love with this style of proof. The possibility of finding a proof for god using nothing but logic is like finding a long-forgotten civilization without leaving the house. A number of big-names have come up with their own versions, such as Gottfried Leibniz, Kurt Gödel, and René Descartes. The Stanford Encyclopaedia of Philosophy lists five more “distilled” variations on it:

1. God is a being which has every perfection. (This is true as a matter of definition.) Existence is a perfection. Hence God exists.

2. [24]

3. It is possible that God exists. God is not a contingent being, i.e., either it is not possible that God exists, or it is necessary that God exists. Hence, it is necessary that God exists. Hence, God exists.

4. [It is analytic, necessary and a priori that][25] Each instance of the schema “The F G is F” expresses a truth. Hence the sentence “The existent perfect being is existent” expresses a truth. Hence, the existent perfect being is existent. Hence, God is existent, i.e. God exists. (The last step is justified by the observation that, as a matter of definition, if there is exactly one existent perfect being, then that being is God.)

5. The word ‘God’ has a meaning that is revealed in religious experience. The word ‘God’ has a meaning only if God exists. Hence, God exists.

6. I exist. Therefore something exists. Whenever a bunch of things exist, their mereological sum also exists. Therefore the sum of all things exists. Therefore God—the sum of all things—exists.

(http://plato.stanford.edu/entries/ontological-arguments/ , retrieved April 30th 2011)

Missing from that list is Leibniz’s Monad theory, which borrows an ancient Greek idea. A “monad” is a super-atom of sorts; they make up every substance and contain consciousness, yet cannot be changed or destroyed, only divided into infinitely small pieces. No two are alike. They’re classified by the abstract properties they’ve been granted; “Entelechies” do little more than move, “Souls” have the added ability to remember things, and “Spirits” are permitted to reason. While all modads are tied to physical bodies, Leibniz claims there’s a special monad out there that is not attached to a body, and does nothing but continually create new monads. This god monad is stopped from just cranking out “Spirits” by the laws of nature. This system cannot be improved on, according to Leibniz.

None of Leibniz’s contemporaries agreed on that point.

The sixth on that list is a close match for Descartes’ “proof” for God. The scare-quotes are because Descartes would probably object to that argument being called a proof, let alone one of his own. In general, he thought God’s existence was obvious via intuition, instead of rational arguments. As a result he never bothered to write up a formal rationale, but instead randomly scattered bits of logical argument and informal reasons throughout his work. He took full advantage of this sloppiness, by throwing out many variations and forcing his critics to comb through his entire work to clean up his “proofs.” Fortunately for me, his arguments boil down to a mix of proofs that I have or will cover in this book, so I don’t need to elaborate further.

Gödel’s proof, by comparison, is both much better and much worse. Instead of dealing with “perfections” or simplistic “attributes,” his proof works on “positive, morally aesthetic properties;” examples of these include “perfectly just,” “all-powerful,” “merciful,” and “absolutely moral.”

Out of all the Ontologicals I’ve presented, Gödel’s is easily my favourite. It’s much better than Descartes’ “proof” because it is a well-structured logical argument, presented in a formal logical system with well-defined rules. It’s also much worse, for the same reason:

That chart-junk is called “modal logic,” and is a little tough to understand without study. Would another translation help?

Assumption 1: No property in collection P will be the inverse of another property also in P.
Assumption 2: If a property is in P, and if for all objects with that property that implies the existence of some other property in every possible situation, then the collection P also contains the other property.
Theorem 1: If a property is in P, an object might exist with that property.
Definition 1: An object has the “God-like” property if, and only if, that object has every property in P.
Assumption 3: The “God-like” property is in P.
Theorem 2: At least one object might have the “God-like” property.
Definition 2: A property is an “essential property” of an object if, and only if, every property that object has must be implied by the essential property, in every possible situation.
Assumption 4: Any property in P must be within P in every situation.
Theorem 3: If an object has the “God-like” property, that property must be an essential property.
Definition 3: An object has the “Anselmian God” property if, and only if, all its essential properties imply that, in every possible situation, an object exists with that essential property.
Assumption 5: The “Anselmian God” property is in P.
Theorem 4: There must exist an object with the “God-like” property in every situation.

I think this is enough examples to begin pulling out some common threads. To begin with, Ontological proofs ignore concepts grounded in reality and instead focus on using pure logic. The only potential exception is “existence,” depending on whether or not you think ideas have an existence outside or independent of the universe. From there, they start rattling off attributes and properties of god, and through some carefully-constructed logic come to the conclusion “god exists” by proving something god-like has the attribute of “existence.”

[22] This is the Latinized version of his name; in the Middle East, he was known as Abū ʿAlī al-Ḥusayn ibn ʿAbd Allāh ibn Sīnā, which was sensibly shortened down to Ibn Sīnā.

[23] Points 6 through 9 match up with the section of Proslogion that I quoted earlier, so you can decide how accurate my attempts at translation were for yourself.

[24] The second version is the rephrasing of Anselm’s argument I quoted earlier.

[25] My best translation from philosopher-ese is “it follows from and is proven from prior knowledge that…”

Proof of God: The Cosmological Proof (4)

Absolutely Nothing

But that isn’t the only nothing out there. I’ve described the best “nothing” we have evidence for. Some of the religious argue this is the wrong “nothing” to be thinking about. Take this review of Laurence Krauss’s book “A Universe from Nothing,” written by Robin Schumacher:

You would think that by the title of Krauss’ book he answers the question that Leibniz posed, but he doesn’t. Instead, he redefines what ‘nothing’ is. ‘Nothing’ to Dr. Krauss would be empty space or the quantum vacuum. Neil DeGrasse Tyson, who is an astrophysicist at the American Museum of Natural History, says in his brief review of the book: “Nothing is not nothing. Nothing is something. That’s how a cosmos can be spawned from the void — a profound idea conveyed in A Universe From Nothing that unsettles some yet enlightens others. Meanwhile, it’s just another day on the job for physicist Lawrence Krauss.” [21]

Fair enough, let’s consider a more basic nothing. First on the agenda is demonstrating that it exists. Here, we stumble badly; Schumacher’s review asserts all “the scientific evidence points to the universe exploding out of true nothingness,” yet as I’ve shown above there is no evidence for this, and we can never find any by definition.

Think about it: we define things by partitioning the universe into “parts of X” and “not parts of X.” A definition of “nothing” cannot throw anything into one of those partitions, because the instant it does our “nothing” consists of at least one thing. Everything we know of must go into the other partition, which means that we are perpetually finding evidence for things that are not nothing. Thus we will never have evidence for that definition of “nothing.”

Let’s ignore those trivial details, though. What would this “nothing” be like? Well, nothing, of course. The scientist’s version of nothing, as I outlined above, includes rules like “Heisenburg’s Uncertainty Principle” and the “Conservation of Energy;” these would have to go. You’d also have to toss out all the rules of logic, as they too are something.

Which means we also have to toss out “something cannot come from nothing” from this nothing. But if there is no rule that prevents something from forming from nothing, then why couldn’t something spontaniously arise? It’s not against the rules, as there are none.

So even if we accept Schumacher’s “nothing” as possibly existing, it’s still possible for something to arise from it!

So Bad It’s Not Even Wrong

Even if you can somehow find a way past all those problems and patch up Cosmological, you face a minor problem.

The conclusion of Kalam is that the universe was caused… and that’s it. At no part of the argument does it say what that cause was. Do we need a god to cause a universe to exist? As we have no clue how to cause a universe, we don’t know. This opens up the possibility of a non-god creator, which we cannot rule out unless we offer up evidence (which, as I’ve argued, will never arrive).

In other words, Cosmological doesn’t even prove the existence of a god! Its continued popularity in religious circles should be an embarrassment to believers the world over, for that reason alone.

[21] http://carm.org/lawrence-krauss-atheist-definition-of-nothing

Proof of God: The Cosmological Proof (3)

There Are No Stupid Questions

While Hume has me in a philosophical bent, let me ask a question of my own. Can you prove to me that the universe exists?

It sounds like a trivial question. Shouldn’t the keyboard under my fingers, the photons smacking into my eyeballs, or my ability to think about myself suggest an obvious answer?

But think about it a little more. That keyboard is not the universe, but something that exists within a universe. The same can be said for those photons and even my thoughts.[16] In fact, at no point in my life will I ever interact with the universe, I will only deal with the things contained in it.

We can’t say the same about my keyboard, those photons, or the thoughts bouncing around my skull. I can verify my keyboard exists by looking at it, test my eyes’ ability to detect light by comparing where it says my hands are to what my body has to say about the matter, and hook myself up to a brain scanner and watch the activation patterns of my neurons change over time. These aren’t absolute proofs of existence, true, but by combining multiple lines of evidence I can push my uncertainty down to an arbitrarily low level.

As this simple question demonstrates, the universe is qualitatively different than any physical thing. It is an abstract container, which can only be properly described by referring to the things within it. And yet Cosmological wants us to treat it the same as any other physical object. The sloppy nature of language hides this conflict from us, making the proof seem more rational than it actually is.

It’s a Mad, Mad, Mad, Mad World

All that would be bad enough, but so far all I’ve discussed is theory. Wouldn’t it be nice if there was also some hard physical evidence that the Cosmological proof fails?

There might be, but it’s going to take a little explaining.

Remember the phrase “you can’t get something from nothing?” Imagine we’re able to break that rule, exactly once. Something would pop out of nowhere, and set off a chain of causes, moves, and so on. This would form its own hierarchy that might intersect the primary one at some point, but would still lead back to separate single “mover.” Applying the Cosmological proof to this tree would result in two gods, one per tree. This is a bit of a problem if you only believe in one god.

Polytheists would be fine with it, but even they have limits. The highest number of gods I’ve heard of is in the 300 million range, for Hinduism, but this seems to be an estimate of historical and forgotten gods instead of the number actively worshipped. Nonetheless, once we get into the trillions of trillions of gods it becomes difficult to keep a straight face. If this exception can happen with no limit, those numbers are easy to reach.

So if we could find some way to get “something from nothing,” we’ve again broken Cosmological. I can think of two: the Casimir Effect has been well-demonstrated but only goes half-way, while Dark Energy is probably a clean break but needs further study to prove this.

Bring two metal flat metal plates really close together, to within a few thousand widths of an atom, then attach a force gauge to at least one. You’ll measure a force tugging the two together, even if there’s no electric or magnetic fields to draw them together, and everything is in a complete vacuum. What’s creating the Casimir Effect is likely virtual particles popping out of empty space unevenly.

Wait, empty space is creating particles? It’s strange, but true. To explain how, I have to tackle a much more fundamental problem: energy.

Philosophers had long thought there was some sort of force or fluid driving life. From the time of Gottfried Leibniz in the 1600’s to the work of Lord Kelvin in the late 1800’s, this definition became more and more abstract:

There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law—it is exact so far as we know. [17] The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.

(The Feynman Lectures on Physics, 1961)

The best metaphor I can think of is money. It used to be a physical thing, a solid coin or token you carried, but in my time it’s been reduced down to a few magnetic disturbances on a computer hard drive in some far-off land. You could exchange some “cash” for tea, chocolate, or a good massage. Likewise, by selling tea or giving a massage you can earn some of this abstract quantity back. Just like energy, money only becomes useful when it’s transformed into an action or something material.

Also like energy, it’s a positive quantity; you cannot have less than zero dollars,[18] and once you reach zero dollars you’re stuck until someone gives you a donation. Forces can front you some funds; if you hold up a ball above the surface of the Earth, it has some money/energy “stored” thanks to gravity, and once you let go it hurriedly starts converting that into motion. The two Relativity theories say that matter itself can also supply some currency, like in a nuclear reactor or radioactive decay.

In empty space, where forces like gravity and magnetism are absent and matter doesn’t exist, you’d expect the bank balance to be firmly at zero. This makes sense; otherwise, you could use empty space to do some useful work, by creating something out of nothing.

There’s another possibility, though. Canada used to have “Vagrancy Laws” which mandated that every citizen must carry a certain amount of change on their person.[19] On the surface, both lead to the same results since you can’t spend below your limit, whether it’s zero or a greater amount. There are some subtle differences, though. For instance, you could temporarily go below the legal amount when consolidating your change at the bank, or during a private card game. If you had no cash on you, however, both scenarios would be impossible. This doesn’t have to break the law, though, so long as you always end up above the limit while in public.

Werner Heisenberg added a key feature to Quantum Mechanics in 1926. His “Uncertainty Principle” states that there are limits to how defined some quantities could be. If you knew the momentum of a particle very well, for instance, you couldn’t be very precise about its location. This perpetual uncertainty is not the fault of the experimenter, but built right into the fabric of the cosmos.

The Uncertainty Principle applies to empty space, too. Thus a perfect vacuum cannot have an energy level of zero, because then you would know its value with certainty. In fact, not only must it contain some energy, but that energy must fluctuate too lest it be known with certainty. So while every other physical theory we know of views an empty void as, well, an empty void, Quantum Mechanics views it as a perpetually churning, frothing hotbed of action.

Just like in our metaphor, a non-zero minimum energy has some side-effects. The twin Relativity theories point out that energy and matter are interchangeable, so the fluctuations in a perfect vacuum wind up creating “virtual” particles that live for incredibly short periods of time before popping back out of existence. These don’t have to play by the rules of normal matter, leading to such oddities as negative energy and time travel. The kind and strength of these particles depends on the size of the void, and this leads to the Casimir Effect. The tiny distance between the two metal plates constrains what particles can pop out of the vacuum, yet the open space behind the two plates does not. The pressure of the interior particles can be less than or greater than those of the outside, depending on the exact distance, and thus the two plates are forced together or apart.

This sounds like a clear violation of the Conservation of Energy, but remember the money analogy. If everyone has the minimum amount of cash, then everyone’s equally poor and no work can be done. Likewise, all that virtual particle action averages out to a minimum value, which cannot be borrowed against.

Does it make sense to call this an “empty void,” then, if it isn’t empty?

This is where “something from nothing” begins to break down. If we call this void “nothing,” then it clearly is creating “something” in the form of matter and forces. It’s tempting to declare it to be “something” and dodge this bullet, but then what can we call “nothing?” If no such thing exists, then the “something from nothing” argument is meaningless since there must always be something!

There is a way around this counter-argument, though. If we redefine “something” as anything above this minimal vacuum energy, then the contraction goes away. Since these virtual particles are exactly at the minimum, we can dismiss them as averaging out to nothing in the long run. I’m not certain the Casimir Effect can be waved away so easily, but some physicists like Robert Jaffe think it can be explained without needing to invoke virtual particles. This would mean the void is not producing force, and thus not producing “something.” The Casimir Effect is very small and difficult to study, so it could take some time to sort out who’s right.

Or, we could look for the answer in the stars.

The calculations of Edwin Hubble[20] and others before him have been tested, re-tested, and verified via other means. Physicists and astronomers are convinced the universe is growing in size. On this grand a scale, the only force that can effect expansion should be gravity; the weak and strong forces have no effect here, and all charged particles average out to zero electromagnetic force. Gravity may be the weakest force on the block, but it only pulls; over long distances, this adds up and has the effect of pulling the universe back together. We should see the rate of expansion slowing down over time, as a result.

Instead, it is accelerating. Two competing teams first discovered this around 1998, and other observations have backed them up. Something within the universe is pumping out extra force and energy that is pushing everything away from everything else, and yet the source of this isn’t visible from our lonely planet. The prime suspect behind this “Dark Energy” is the energy of empty space, as I just described above. These virtual particles create a force or pressure that drives matter apart, and more virtual particles are created as the size of the universe increases. It’s a tidy explanation, which also vindicates the Casimir Effect as I described it.

It isn’t a perfect explanation, though. For one thing, the energy of empty space is at least 10⁵⁰ times greater than Dark Energy’s observed value, and could even be a staggering 10¹²⁰ times too strong. It also leads to problems in the early universe, where this energy suddenly turns into an attractive force, and there are some observations related to the density of our cosmic neighbourhood that further muddy things up.

Still, it’s the best explanation we have right now. And no matter what the true answer is, we know that we have something currently within our universe that’s creating energy out of nothing, in clear violation of the “something from nothing” assertion.

Yet again, we find the Cosmological Proof amounts to nothing.

[16] That last one depends on my counter-arguments for the proof from Mathematics, specifically the section on dualism. Feel free to skip ahead, if you’re feeling sceptical.

[17] Feynman may have gotten this wrong. I’ll get to the details shortly.

[18] Yes, some Canadian citizens owe more than they own due to credit and loans, but for this metaphor I’m ignoring those messy details.

[19] That portion was repealed in 1972. In theory, it was to ensure each citizen could call someone to get out of trouble. In practice, it was used to punish the poor and homeless.

[20] Hubble would make a good subject for a book. He was a handsome, charismatic athlete who hung out with Hollywood stars, yet still lied to fluff up his resume and seems remarkably ignorant of the theories his data was supporting or refuting.

Proof of God: The Cosmological Proof (2)

Hume’s Trip to the Pole

This line of thought brings up another objection, one that was first noted by David Hume.

Hume, who lived from 1711 to 1776, was one of the first philosophers to examine proofs of god with a sceptical eye. As my future self will mention, my thoughts on miracles will be little more than his thoughts with a light dusting of cheese and vinegar. He also examined the Design proof, and weighed in on Cosmological as well. While he gives several objections to the last one, I’d like to focus on this one:

… The WHOLE, you say, wants a cause. I answer, that the uniting of these parts into a whole, like the uniting of several distinct counties into one kingdom, or several distinct members into one body, is performed merely by an arbitrary act of mind, and has no influence on the nature of things. Did I show you the particular cause of each individual in a collection of twenty particles of matter, I should think it very unreasonable, should you afterwards ask me, what was the cause of the whole twenty. This is sufficiently explained in explaining the cause of the parts.

(Dialogues Concerning Natural Religion, Part 9)

As I’ve mentioned before, at the core of Cosmological’s argument is a hierarchy. I can turn this into a visual metaphor by drawing a series of ever-branching pipes:

[diagram of a tree of pipes]

As we follow the flow down these pipes, we jump from cause to effect, or from mover to moved, or from creator to created, or along whatever relation was used to construct this version of Cosmological.

[diagram of an arrow flowing down these pipes]

Since these pipes have a finite length, we can attach a rope to one point, then swim around the pipes until we run out of pipe but still have some rope in hand. We can just as easily picture the rope attached to the top of this pipe hierarchy, and then pull ourselves along it until we reach the very source of all the flow.

[diagram of a rope feeding through these pipes, acting like a measure of time]

Thanks to the rope trick, it’s easy to ignore the branches and just think of it as one pipe with a well-defined beginning. Note that we don’t care about an ending; so long as there’s a beginning, we can always pull ourselves towards it. In contrast, consider a long pipe with no beginning or ending at all.

[diagram of an infinite but straight pipe]

If we attach the rope and explore, we’ll run out of rope no matter how much swimming we do. Likewise, if we pull ourselves along an attached rope, we’ll still have plenty of places to explore once we’ve reached the end of it.

Cosmological compares these two layouts, and rejects the second one. It claims an infinite pipe or chain of relations is an absurd idea, and faced with no other alternative claims the hierarchical version is the only way to go.

But are those two the only possible choices? Consider instead a loop of pipe, like so:

[diagram of a pipe bent into a donut shape]

We have a finite length of pipe, which satisfies Cosmological’s rejection of the infinite, and yet at the same time there’s no beginning or end to this pipe! If we pull ourselves along a rope we find drifting in the current, we’ll again be faced with a void that we’re free to explore. We can use this rope as a measure of how far we are from the “beginning.” If we just float and let the rope spool out, we note that we get further and further away. If instead we pull ourselves up, our rope gets shorter and shorter until we run out of rope. From this point, everything is after the beginning, since we need to let out some rope to move away from this point. This will come in handy later.

[diagram of a donut pipe with a rope attached to one point]

But for now, we’ve found a third way, one that avoids infinite spaces while also avoiding the need to stop at a First Mover. This derails Cosmological, since it was counting on finite space implying a First Mover, and again renders the proof useless.

No doubt you’re sceptical of my metaphor. We know our universe had a definite beginning, because we’ve found the evidence in and between the stars. Real life is not a one-dimensional loop, but a four-dimensional expanse of space and time. How can the two be similar?

Very easily, in fact, so long as you think four-dimensionally.

Back in 1905, Albert Einstein published his theory of Special Relativity. In this landmark paper, he proposed that space and time are actually the same thing, differing only in what direction you look, and that both of these are warped by gravity. It sounds crazy, but one hundred years of observation have backed up Einstein’s claim, and Special Relativity 2.0 (better known as General Relativity) has become one of the most successful theories ever proposed. [A]

The standard metaphor for General Relativity, handed from generation to generation, is the rubber sheet. Plunk a heavy round object, like a bowling ball, on one that’s been suspended in air, and it’ll sink down and pull the sheet with it. Take a smaller round object, say a marble, and roll it across the sheet towards the big one. It’ll go in a straight line until it reaches a bent part of the sheet, where it’ll veer towards the heavy object. Do this well enough, and you can get the marble to orbit the big ball before friction ruins the fun.

If we’re allowed to warp the sheet, however, what’s stopping us from warping it around until it touches itself? We’ve just reached the other standard cosmology metaphor: the rubber balloon. This is usually used to explain the Big Bang, by showing how space stretches and makes everything look like it’s rushing away from you. But we could also think of it as a potential model for how the universe is shaped. It has a finite area, even if you continue to inflate it, but at the same time you could walk around this shape without ever reaching an edge. This is exactly like the ring of pipes I outlined above, only in two dimensions.

A three dimensional version is too big for me to visualize, unfortunately. That one-dimensional version is actually in three dimensions; I needed to twist the pipe around so that it would meet itself, and the only way to visualize that from the outside is to invoke another dimension, and I also implied the dimension of time indirectly by having our metaphorical swimmer swim. This diver within the pipe has no way of accessing the second spacial dimension, let along proving it exists, so I haven’t spoiled the metaphor. Likewise, to explain the two-dimensional version I really used four dimensions to get the point across. I need one more dimension to describe a three-dimensional extension, but my poor brain was only designed to work in four dimensions and fails miserably when dealing with five.

And yet that hasn’t stopped similar brains from thinking about higher dimensions. Einstein was able to cope with a four-dimensional space-time by using math as a crutch, and other scientists have used the same trick to think about our world in eleven or more dimensions. To name an example, Stephen Hawking has proposed a theory that would visualize time as a sphere like the Earth, with the “North Pole” label replaced with “Big Bang.”

I was never built to be comfortable with higher dimensions, but that doesn’t rule out their existence. We humans were convinced the world was flat for a very long time, until a few of us realized we actually lived on a very, very, very, very big sphere. It only looked flat from our limited perspective. Cosmological makes the mistake of assuming its narrow perspective is the only one, that there must only be two ways to organize the world.

All this talk of spheres brings up another good rebuttal, though. Let’s return to my pipe metaphor again, with the rope attached to the head of Cosmological’s hierarchy. The proof asks us to pull ourselves hand-over-hand up the rope, until we run out of space and rope. It then asks what would happen if you tried to take up one more length of rope. It points out this would take you outside the pipe, and that the only thing which could survive out there is a god. Ergo, god exists.

But does that make sense? In our metaphor, we are constrained to follow the pipes, and to always have a length of rope greater than or equal to zero. We have no way to get outside out of either limit, and yet Cosmological is asking us to think about what’s on the outside. That doesn’t fit into our metaphor at all! David Hume indirectly realized this; since you can’t reach outside of the pipe, once you’ve swam around and reached every point within the pipe, you don’t have any place left to go. If you understand everything within the pipe, you understand everything.

[diagram of person banging on pipe, from the inside]

Let’s now extend the metaphor back to the proof. Note that “cause” and “effect” are exclusive; one object cannot be the cause of, and the effect of, another object. The same applies to creation, movement, and any other system used by variations of Cosmological to organize the hierarchy. This not only creates Cosmological’s hierarchy, it also defines a direction; if we just let things play out naturally then creators create, movers move, and so on. Having established all this, the proof asks us to go against the natural flow and walk back up the hierarchy to the top, being careful never to backtrack. Once it runs out of universe and reaches the pinnacle, it tries to take one more step. The universe defines where we can and cannot go, however, so this is the same as asking us to step outside the universe. The result is nonsense, even though every step before then seems perfectly reasonable.

This assumes a hierarchy, of course, which has a definite start. If our universe is more like a circular pipe or spherical balloon, our choice of start is arbitrary. Fix our metaphorical rope to whatever place you wish to call the start, and then take a stroll. Sometimes the rope will lengthen, sometimes it’ll shorten, but in no direction will you be forced to go beyond the “start.” Even if you make a beeline straight for it, the rope will merely shrink down to nothing then immediately lengthen again, without forcing you to backtrack.

This fits perfectly with our modern view of the universe. Relativity makes time and space interchangeable, so any physical metaphor works equally well with time. While asking “what happened before the universe” seems to be a valid question at first, it’s actually the same as asking “what’s beyond the end of the rope,” “what happened before time existed,” or “what’s North of the North Pole,” all of which are absolute nonsense.

And yet the Cosmological proof requires us to ask those questions, and requires us to think of them as perfectly valid, otherwise it has no place to insert a god. We’ve found another flaw in the proof, only this time there’s no escape hatch.

[A] Whoops, past me screwed this one up. As Rob Grigjanis points out, the Special Relativity papers of 1905 ignored gravity. I also misunderstood spacetime a bit. While space and time are integrated, there’s a difference between purely spatial paths and purely temporal paths through this space. I think one of Brian Cox’s book covers this well for a lay audience.

Proof of God: The Cosmological Proof (1)

Proof from First Cause, or the Cosmological Proof

Have a quick look around you.

Are you sitting in a chair? Did you ever wonder how that chair got there?

I’m willing to bet you or someone else placed it there. I doubt you created it, though; more likely, a team of people fashioned it out of wood and metal, gave it to another group who transported it to a store or warehouse, where another bunch helped deliver it to you. Where did that first team get their materials, though? The wood was probably harvested from a forest, the metal dug up from a mine. The trees got their nutrients from the soil and the sun. No matter which path you take, both trace back to the Earth or the Sun.

So far, everything we’ve discussed has come from something else. The materials came from elsewhere, and somebody or some process helped shape it. The chair was “caused” by human effort and the proper materials, the tree was “caused” (in a loose sense) by sunshine and nutrients gathering in the right place and the right way. We can do this thought experiment for every object in the universe.

We should be able to do this for the universe itself. It’s a material thing, after all, though perhaps a little larger and more complicated than our chair.

At this point, the chain of causes breaks down. We can’t name anything within the universe as a cause, since by definition that’s a part of the universe itself. Any potential cause must come from outside. But what lies outside the universe, in a place we can never hope to explore?

There’s only one being we know of that could live outside the universe. God, after all, is the only possible being with enough power to create a universe, and in countless religions she does exactly that:

In the beginning God created the heaven and the earth.

(Genesis 1:1, Jewish Old Testament, King James translation)

They say it happened long ago when there were no people nor anything, and when earth and the black sky did not exist “Let us make the earth and the black sky,” he said. He began to study and talk about how both the earth and sky might be made.

(“Myths and tales from the San Carlos Apache”, collected by Pliny Earle Goddard)

Nights, days, weeks and seasons; wind, water, fire and the nether regions—in the midst of these, He established the earth as a home for Dharma. [11]

(from the Sikh religious text “Siri Guru Granth Sahib”, translated by Singh Sahib Sant Singh Khalsa)

Then, at last, slowly uprises Tane-mahuta, the god and father of forests, of birds, and of insects, and he struggles. With his parents; in vain he strives to rend them apart with his hands and arms. Lo, he pauses; his head is now firmly planted on his mother the earth, his feet he raises up and rests against his father the skies, he strains his back and limbs with mighty effort. Now are rent apart Rangi and Papa, and with cries and groans of woe they shriek aloud: ‘Wherefore slay you thus your parents? Why commit you so dreadful a crime as to slay us, as to rend your parents apart? But Tane-mahuta pauses not, he regards not their shrieks and cries; far, far beneath him he presses down the earth; far, far above him he thrusts up the sky.

(“Polynesian Mythology & Ancient Traditional History of the New Zealanders,” collected by Sir George Grey)

Therefore, there’s only one possible cause for the universe, and that’s god.

Golden Oldies

The Cosmological proof is, without a doubt, the most popular of its class. Surprisingly, it’s also one of the earliest formal arguments we know of, dating back to Plato’s last work, Laws. In the tenth chapter of this dialogue, the wise “Athenian[12] ” scoffs at those who deny the existence of the gods, who claim they were man-made inventions that bend to human whims. To show their folly, he builds a simple proof by cataloguing the types of motion that exist in the universe. After ticking off nine, the “Athenian” describes a tenth type, that is capable of moving itself and other objects. He then points out this tenth must be the greatest of all, and reaches the core of his argument:

ATHENIAN: I mean this: when one thing changes another, and that another, of such will there be any primary changing element? How can a thing which is moved by another ever be the beginning of change? Impossible. But when the self-moved changes other, and that again other, and thus thousands upon tens of thousands of bodies are set in motion, must not the beginning of all this motion be the change of the self-moving principle?

CLEINIAS: Very true, and I quite agree.

ATHENIAN: Or, to put the question in another way, making answer to ourselves: If, as most of these philosophers have the audacity to affirm, all things were at rest in one mass, which of the above-mentioned principles of motion would first spring up among them?

CLEINIAS: Clearly the self-moving; for there could be no change in them arising out of any external cause; the change must first take place in themselves.

ATHENIAN: Then we must say that self-motion being the origin of all motions, and the first which arises among things at rest as well as among things in motion, is the eldest and mightiest principle of change, and that which is changed by another and yet moves other is second.

(Laws, Book X, translated by Benjamin Jowett)

From there, the “Athenian” needs only a little bit of hand-waving to turn this primary mover into what he calls a “soul,” but modern readers would recognize as a god.

The argument next appeared roughly 1,300 years later, in Avicenna’s studies of ancient Greek thought, only this time it proved the existence of Allah instead of the Greek gods. Later scholars, most notably the influential Al-Ghazali, would condemn all of Plato and Avicenna’s work as a corrupting influence, but retained the handy Cosmological proof.

Thomas Aquinas independently claimed Cosmological for Christianity some 200 years after Avicenna, in his Summa Theologica. Aquinas’ version shows why this proof continues to be so popular. Not content to merely repeat Plato’s chain of movers, he created three more variations of the same proof and claimed each as a newcomer. One is the chain of causation I used in my introduction to Cosmological; another is a chain of creation, which traces back to singular creator; and the last is a chain of perfection, leading to the most perfect being possible.

Plato’s original argument has endured because it is so very plastic. To come up with your own variant, all you need is some way to organize every object in the world into a hierarchy.[13] You then claim that an infinitely deep hierarchy is absurd or impossible, then place atop this tower of induction the god of your choice. In the 2,500 years since it left Plato’s mind, Cosmological has been polished down to an invincible single sentence:[14]

You can’t create something from nothing, unless you’re a god.

Because I Said So

It would help if we had a more formal version of Cosmological to run through point-by-point. The Kalām[15] version of Cosmological, as promoted by William Lane Craig, seems like a good start:

Whatever begins to exist has a cause.
The universe began to exist.
Therefore, the universe has a cause.

We can easily modify this to cover all other versions of Cosmological:

Whatever begins to exist was created has a cause creator.
The universe began to exist. A finite number of movers must exist.
Therefore, the universe has a cause. a being more perfect than all must exist.

Returning to Plato, he rejected the idea of an infinite chain of movers or causes because he didn’t think infinite things existed in the real world. Most thinkers who invoke the Cosmological proof agree, and like Plato stop this infinitely long cascade by placing an infinitely-powerful being in its path. Thus in order to stop an infinite thing from existing in the world… they propose the existence of an infinite thing in the world. Hmm.

And looming over it all is a cherry of a contradiction that Cosmological tries to ignore. If everything has a creator or mover or what-have-you, and god is something, then what created/moved god? After all, this proof rests heavily on the idea that everything can be put into a hierarchy, with no exceptions, but then it turns around and grants one exception. Doesn’t this derail the entire train of thought? If we’re allowed to grant exceptions, what prevents me from saying the universe is an exception too? Philosophers have been fine labeling their god of choice the “First Mover” without any evidence to justify it, so I fail to see why I can’t slap the same label on the universe, given an equal amount of evidence.

[11] “Dharma” probably means “religious path” here, but in other contexts it could be closer to “religious law” or “social structure.”

[12] Scholars suspect this mysterious Stranger from Athens was supposed to be Socrates. Plato never named the character directly because he bore little resemblance to the Socrates from Plato’s earlier dialogs. The youthful version was perpetually questioning and dripping with excessive humility, while the later one knows the truth and kindly shares his lessons with lesser people.

[13] Why a hierarchy? Let’s take creation as an example: a lump of clay can be used to create many things, like pots or plates, while those pots or plates have only one creator, the clay. The same one-to-many branching applies to causes, movers, or whatever other mapping you use, and when laid out on paper naturally leads to a hierarchy.

[14] Sorry, that’s a lie. The ancient Greek Parmenides nailed it when he said “ex nihilo nihil fit,” and he pre-dated Plato!

[15] “Kalām” refers to an early school of Islam, that valued knowledge and thought theological arguments were best settled by debating it out. I approve, if only because it cuts down on the number of holy wars.

Proof of God: Introduction (3)

Whither Proofs?

Why must we bother with proofs at all? Most people don’t put much thought into religion, and are content to know the gods exist through feelings of connection and occasional revelation.

One problem: those are proofs!

We’ve picked up a warped idea of what a proof is via math class. Our teachers tried to wow us with long, subtle chains of reasoning that are impressive mental achievements, but on the elaborate side of proof’s definition. In reality, all proofs consist of two things: an assertion, and one or more bits of evidence that the assertion are true. Length and subtlety are optional:

Assertion: At least one number is even and prime.[10]

Evidence: 2.

There’s nothing in the definition that says proofs must be convincing beyond all doubt, either. Take this example:

Assertion: the length of the longest side of a right-angle triangle multiplied by itself is equal to the sum of the lengths of the two remaining sides multiplied by themselves.

Evidence: Draw such a triangle on a sheet of paper, with plenty of margin. Draw three cubes around it, with one side of each shared with the triangle. Cut out both of the two smaller squares, and place one of them over the untouched larger square. Fill in the remaining visible portion of the largest by cutting up the remaining square. Once done, no part of it will be visible, and no part of the last square will be left.

This is a pretty lousy proof. For one thing, it never really explains why the math works out. Since it operates in the physical world, it’s easy to make a measurement error and falsely conclude you’ve shown it to be wrong. Worst of all, it only proves a single triangle at a time. Repeating the procedure for a thousand triangles only shows that there are a thousand triangles that live up to the assertion; any or all of the infinite remainder might not.

A mathematician would reject that proof outright, and for good reason. In the universe of math, we know every law and every way those laws combine. We have no excuse for considering something “reasonably” true, because we have all the tools we need to verify that it’s absolutely true.

In the real world, we don’t know all the rules. We don’t even know if the rules are constant, or change on very long time-scales, and so we’ll never reach absolute certainty. Instead, every proposed proof is given a court trial of sorts; we gather up all the contrary proofs and evidence we know of, and ask if the sum total gives us a reason to reject the proof. If so, we toss it out and either look for something better or put a different proof on trial. If not, we stamp it as “reasonably likely to be true, until further evidence comes in.”

That lack of certainty doesn’t make the above proof useless. It’s unlikely that a misfit triangle would lurk between two tested ones. Even if this assertion is only approximately true, it would be less complicated and easier than the real answer, and gives valuable hints towards a better proof. Absolute certainty isn’t needed, at least in real life.

We can easily rearrange those earlier statements about the gods into proof form:

Assertion: God exists.

Evidence: Sometimes, I can feel his presence.

Assertion: God exists.

Evidence: The world fits together too nicely to be the product of chance, and must instead have been designed.

You won’t see either of those argued about directly in a philosophical journal, yet both make assertions based on evidence just like their more formal cousins. Both, in fact, are just informal versions of the Proof from Transcendence and the Proof from Design, which have been seriously debated in those same journals for longer than journals have existed. By examining the evidence for both, we can evaluate their assertions in the same way. As I hope to demonstrate in later chapters, perhaps that feeling you get from your god has very natural causes, or there are other explanations for design out there that don’t require the supernatural.

Every informal assertion about god can be formalized and turned into a proof. By looking at the simpler and cleaner logic of the second, we can examine both at the same time and see how effective they are at proving the existence of a god.

It’s no wonder believers are uneasy with formal proofs.

Gotta Catch Them All

I’m left with one final objection to overcome. Given the unending multitude of proofs for a god, how could I possibly cover them all?

Let’s turn back to Comfort and Behe’s proofs. While both seem very different on the surface, they share one common trait: they point to some order within the universe, and declare that the only possible source for that order comes from a god. Instead of spending a few paragraphs going into specific details on each, I could have instead demonstrated a way to produce order that does not require a god as a counter-example. I then throw the question back, and ask how either person knows this mechanism, or another like it, wasn’t responsible instead.

That is exactly what I do in the chapter on Proof by Design. By exploiting these common traits, I can cover a multitude of proofs with a single argument. Coming up with counter-examples is much easier than coming up with proofs, and by raising a number of them I can at least call into question the certainty behind such proofs. This saves me a lot of effort, and serves as partial insulation against proofs that are not in this book or that have yet to be invented. It helps that proofs only seem to come in a few categories:

Something exists, and only a god could have created that something. Examples include the universe (Proof from First Cause), consciousness (Proof from Intelligence), and holy texts (you can guess this one).
There is an order to things that could only be created by a god. Examples include life (Proof from Fine Tuning), and morality.
We are required to have a god, in some way. Examples include logical arguments (Proof from Logical Necessity), the universality of belief (Proof from Popularity), and the benefits of belief (The Pragmatic Argument).

As you read through this book, you might notice that even within these categories there’s a lot of overlap. I could have easily placed the Proof from Fine Tuning in any of them, to name but one. In answering the last objection, I’ve dredged up an intriguing question: is it possible to construct a universal counter-proof to any god?

I’ll leave that to the last chapter. In the meantime, I have a lot of intellectual ground to cover…

[10] Take a pile of X pennies, candies, or elephants. If you can divide them into two equal piles, X is an even number. Now take the above pile and try to rearrange it into a rectangle with no leftovers. If the only one you can manage is one item high and X long, or vice-versa, X is a prime number.

Proof of God: Introduction (2)

Definitions

My first task is the hardest: what is a god, anyway? A definition of something acts like the foundation of a building. Everything is built upon it, so if the definition is even slightly loose the entire thing could topple over at the slightest touch. The sheer variety of religions suggests a single definition of god is impossible.

Which is why I’m using two:

God: Something which can or could perform an action which is, or was once considered, impossible to duplicate by any entity that is not a god under any circumstance.

God: Something which can or could perform an action which is, or was once considered, contrary to the physical laws of the universe.

To save my poor typing fingers, I’ll nickname them “practical” and “theoretical,” in order of appearance.

Obviously, I must spend some time challenging and probing my definitions for weakness, otherwise you’d have little reason to take them seriously. I’ll have to get a little philosophical at times, but I’ll try to keep it to the bare minimum needed for this roast. The end goal is to ensure these definitions meet three criteria: they will not call a non-god a god, they will not call a god a non-god, and if there’s uncertainty in the definitions we’ll find disagreement in real life as well.

I’ll begin with a triviality: is an orange a god? Both definitions talk about actions, not objects, so they might seem ill-suited to the question. Oranges occupy a space and time, however, reflect a certain spectrum of light, and have an outer skin that protects soft, juicy innards. All of these are actions, even though an orange performs them passively. So we can apply both definitions by cataloguing all the attributes of an orange, transforming them into actions, and adding these new passive actions to the list of active things an orange can do.

“Theoretical” says oranges are not gods. For each that has been studied, all have followed the laws of the universe. You might get smug and point out this isn’t proof that every orange is so obedient, and you’d be right. Why, then, aren’t we hurriedly searching every orange for this potential violator?

The answer comes from, of all places. a monk. William of Ockham’s[4] original phrasing of this principle doesn’t quite roll off the tongue:

Numquam ponenda est pluralitas sine necessitate

[Plurality must never be posited without necessity]

Fortunately, in the intervening centuries other authors have developed variations that are much easier to understand:

If two or more theories explain something equally well, the theory that makes the least assumptions is the most likely to be correct.

The “simplest” or least assuming answer is usually the correct answer.

Extraordinary claims require extraordinary evidence.[5]

I lean on Ockham’s Razor pretty heavily, so I’ll spend some time defending it. Let’s consider two theories:

In the next hour, a meteor will crash down from above and smack your foot.
In the next hour, nothing special will happen.

As of now, you’ve got no way to tell between the two theories and no way to tell what will happen. Should you start piling pillows on your foot?

Let’s break both theories down. In order for the first one to be true, we need:

A meteor to be on a collision course with Earth.
Said meteor to be coming in on a trajectory aimed at where you’ll be in an hour.
Said meteor to be large enough for at least one part to survive re-entry.
Said meteor piece to have enough energy to break through whatever structure is currently above your head.
Said meteor piece to travel through the atmosphere and architecture in a path guaranteed to hit your foot.

For the second one to be true, we depend on:

So while both theories may look identical right now, one requires far more extraordinary events to fall into place. It makes sense say that the first theory is unlikely to happen, even though we can’t put a number on how unlikely it is to happen, and even though we have no proof that it won’t happen. This is Ockham’s Razor in a nut-shell; it’s a heuristic or guide to what’s worthy of consideration, which deals with theories that have equal amounts of evidence going for them, based on the assumption that the most likely thing to happen will most likely happen.

This is not Ockham’s Razor:

According to Occam’s Razor, the simplest explanation or the one with the fewest assumptions that explains the facts is to be preferred. Creation makes one assumption—that God is who He says He is in the Bible—because if this is so, then He must have done all that He said He did. This adequately answers all the problems of origins posed above.

Evolution has many assumptions and none of them provides an answer to anything.

According to Occam’s Razor creation wins!
( “Occam’s Razor and creation/evolution,” by Russell Grigg. http://creation.com/occams-razor-and-creation-evolution, retrieved July 31, 2012)

What’s wrong? While it’s true that biological evolution relies on several assumptions, all of those are fairly simple and easy to show in real life. Evolution does not require the existence of a god, at all. In contrast creationism, or the theory that a god created the universe, depends on the existence of a god merely to make sense. That would have far-reaching, profound effects on the entire universe, and thus counts as an extraordinary assumption.[6]

To properly use Ockham’s Razor you need to do more than just count assumptions, you also need to consider their relative likelihood and their net effect on the world too. A long string of probable events beats out a single improbable one. A vast number of small changes to the world are more likely to happen than one big change.

Back to the orange problem. We have two theories: an orange that violates the laws of the universe is lurking out there somewhere, or all oranges obey the law. If the first one is true, then we have to assume that at least one orange is special, in that it can bend laws that appear rigid according to every test we’ve thrown at its boring peers, while those peers, and indeed everything else we know of, is not special. If the second is true, we’ve made no further assumptions; the very term “law of nature” implies that there are no exceptions, so we’re already covered. Ockham’s razor tells us a frantic orange search is unnecessary, for now at least.

“Practical” is less clear. My interior is soft, but not juicy, and I don’t reflect the same kinds of light, so an orange can already do two things that I can’t. Note that “practical” uses the word “any,” however. An orange tree can bud out a fruit that will eventually become an orange, and so can duplicate one. You might retort that you consider orange trees to be gods, thus saving the orange from being robbed of god-status, but I can counter by replacing the genome of some other seed with an orange’s and letting it grow. We wind up in an arms race, declaring more and more things to be gods until we run out of things, and at this point I’m all too happy to give in. After all, everything is a god when compared to nothing.

Ah, but perhaps I misinterpreted the question. Instead of asking if “any” orange is a god, we should consider if “that” orange is a god. Now you’ve pinned me; quantum mechanics puts a hard limit on what we can measure, so even if I tried to recreate a specific orange atom-by-atom, I could never perfectly duplicate it.

Fortunately, I don’t have to. “That” orange is an abstraction. Bits of the orange are constantly flying off into the environment and vice-versa, so the atom-by-atom definition of “that” orange is different from moment to moment. You can only come up with a useful definition by ignoring those changes, so my reconstruction doesn’t need to include them either. The same logic applies to the quantum fluctuations I was worried about last paragraph. You might argue that I don’t have the technology to build an orange to the detail required to suit your definition, but “practical” placed no time limits or restrictions on what I could use. I’m permitted to take the age of the universe and use every atom within it in my efforts.

Both definitions have survived oranges, but what about the colour orange? “Theoretical” easily pins this as a non-god, since no definition of orange can be made without reference to light, which itself obeys the laws of the universe.

“Practical” is not far behind. I simply ask you what objects you consider orange, analyse the light coming off them, and duplicate it via some other object. If you instead want orange as defined by everyone, I simply repeat this procedure for everything that can detect a colour called orange and rig up something that matches every definition, on a thing-by-thing basis if need be.

Time for something trickier. In 1983, in front of a large crowd and a huge TV audience, the magician David Copperfield made the Statue of Liberty disappear. Removing a 225 tonne, 47 metre high sculpture is an impressive feat that puts many religious miracles to shame. Does this act make Copperfield a god?

Both definitions say no. Magicians do not honestly claim to bend space and time to their whims, or that they alone are capable of their feats. It’s all just a trick, even if that trick took years of training and no other magician alive now or ever could duplicate it. So long as it could be matched by another magician with sufficient time and space on their hands, “practical” argues that this conjurer should not be a god, and “theoretical” reached the same conclusion long ago.

Consider Thor next. He’s a Norse god that can control the weather. Tens of thousands of people believed in him a millennium ago; now, even those who’d like to revive the old Norse mythology don’t take that ability seriously. He’s still considered a god, despite this. Both definitions are careful to include forgotten gods, and controlling the weather seemed both unachievable and impossible to historic Vikings. Again, we reach the expected conclusion.

In Tripoli, Lybia on May 2010, a plane crash killed 103 people but spared one 10 year old boy. The Anglican Archbishop of Cape Town, South Africa, thanked God for saving this child. Surprisingly, he gave no reason why God did nothing for the other 103 people on the plane. Other theologians have thought more heavily and tried to explain why the Christian god can appear so lazy or fickle. Even if they are correct, it’s clear the Christian God can refuse to act. Both definitions permit this and pass the latest challenge.

Deism is a tricky case. There are only three central tenets to this religion:[7]

God exists.
God’s only action was to create the universe.
Only god can create a universe.

This god is a bit cold and sparse compared to the compassionate, active gods of other religions, but there’s still clearly a god there. It’s not clear whether this god is or was, though, since it must have existed before the universe, and may only exist before time began.[8] Both definitions are fuzzy about when and where actions happen, so they still work on this odd god. “Practical” is nearly the twin of the deist god; both divide everything in two, and claim one group can do something the other can’t.

Surprisingly, “theoretical” is less clear-cut. Deism says nothing about the conditions before the universe, so its god could have acted entirely by the book. The third clause provides an escape; since nothing within this universe can duplicate the deist god’s feat, “theoretical” can declare it to be a god relative to the universe you’re reading this in.

It does make you wonder what the simplest possible god could be, however. Deism whittles it down to a only three beliefs; could we cut one out?

Statements two and three are compliments of each other, placing a wall between god and everything else, so for now I’ll treat them as one. The first statement must stay, because if we don’t know whether god exists the second and third statements make no sense. If the second and third statements go, we lose the grounds for claiming the first. The property of existence is unique, since it is only assigned to something that already has other properties. We can say a kitten exists because it has soft fur, or it is an infant cat, but if all you knew about kittens was that they exist, you couldn’t use that information in any meaningful way. You’d never be able to verify I was telling the truth. You couldn’t find a kitten, even if you were feeling the soft fur of an infant cat while thinking over places to look.

Worshipping a thing that you could never interact with, or know if it had interacted with you, is nonsensical. Gods must do more than merely exist.

Dropping the second statement but keeping the third is also senseless. If only a god can create universes, and we live in a universe, then something like statement two must be assumed anyway.

Things get interesting if you drop claim three. A thought experiment will help show why.

Suppose you look up from this book to find a space alien sitting in front of you. It politely raises a tentacle and says “hi;” you politely faint and scream, though not necessarily in that order. With those pleasantries out of the way, Alien A explains how it got there. A million years ago, it was carefully frozen and placed on a giant ship hovering above its home planet, tens of light-years from Earth. That ship slowly plodded across the vast distance, gathering energy from the random junk in between stars, and once in a few aeons raising Alien A from stupor to let it repair the damage caused by a few cosmic rays that wiggled through the ship’s shields.

Just as Alien A finishes its tale, Alien B appears next to it, seemingly out of nowhere. After more pleasantries, B explains how it got here: in the far future, it learned how to manipulate space and time. Due to the laws of the universe, it guiltily adds, nothing else can or will do the same.

Is either alien a god?

A few would claim the first one is. If you were to explain the physical and engineering challenges faced by their race, however, most will change their minds. Why? On the face of it, Alien A is far more advanced than we are, and thus able to do things we can’t. However, the Voyager space probe is travelling faster than that alien’s ship. We know of animals that can suspend all activity for years, survive freezing temperatures, and repair their genome after having it blasted to bits by radiation. We have power sources that can last that long, and can build things in space to save us from lifting everything against Earth’s gravity. In short, while we can’t arrive on Alien A’s doorstep at the moment, it’s plausible that we could drop by later. Once they realize that we could duplicate the alien’s feat, most of those who called it a god would change their mind.

Here we find matching ambiguity in “practical” and “theoretical” as well. Alien A seems to be capable of something that nothing else can do, at first. As we examine the facts more closely, however, we realize that Alien A’s trick could be done by us “in practice,” and so change our minds.

On the other hand, we find that while Alien B’s skill is forever beyond our practical abilities, it could be done by anyone else “in theory.” The two definitions of god conflict, creating ambiguity.

This tale of two aliens has a real-life counterpart: pantheism. In that tradition, “god” is taken to mean the entire universe. “Practical” agrees with this declaration; the “non-god” portion of the universe is empty, and thus incapable of doing any action the “god” portion can get away with. “Theoretical” disagrees, since by definition this god obeys the laws of the universe. The ambiguity is mirrored in real life. Some atheists, most notably Richard Dawkins, regard pantheists as poetic atheists who can’t give up the word “god.” At the same time, both Taoism and Christianity were initially very pantheistic, while Buddhism, Hinduism and Islam all have sects that take pantheism to heart.

I can’t conclude without sharing the most troublesome case for my definitions: kings and queens. The first ruler to claim a “divine mandate” might have been an Egyptian some five millennia ago, but the documentation is too sparse to call it.[9]

Most of us are more familiar with the European rulers and Asian emperors of midæval times. The majority never claimed to be gods, content to “merely” act out the divine plan.

Even the Egyptian Pharaohs fall into this category: they claimed to be descended from the gods, and would become gods upon death, yet were only messengers while alive. Gilgamesh, one of the first and beet known god-kings, was only declared divine after his death.

True human gods are rarer. Naram-Suen of Akkad is the first we know of, but it’s not clear on what grounds he claimed divinity. Neither definition is much help, since the feat of being king or queen is easily duplicated by their successor. These human gods might solve this by claiming to be reincarnations of some deity, but this doesn’t explain how their successor can be alive at the same time without ruling as well. I’m content to dismiss this corner case by claiming these rulers are “gods” for purely political reasons, and don’t see them as much challenge to my definitions.

I hope I’ve convinced you those two definitions are reasonably robust and future-proof. Which one you choose as the ultimate definition is a matter of opinion, but at least all opinions fall somewhere between the two of them. In the process, I’ll have removed the objection that a god cannot be defined, and at least weakened the argument that I haven’t considered every possible god. Time for the next objection:

[4] His last name has a number of spellings. “Occam” seems to be the preferred choice of Merriam-Webster, but even “Hockham” is considered kosher. There’s also evidence that Aristotle and Thomas Aquinas

[5] This invokes the Razor from the opposite side, when too many assumptions have been thrown into the pile.

[6] Not buying it? I go into far greater detail in my chapter on the Teleological/Design proof, which hopefully will be enough to convince you.

[7] I’ll admit I’m abusing the term “deist” here. Most deists add additional claims, for instance that reason is a divine gift, and that a god does intervene in an entirely mechanistic way, with no personal element. Since those claims are quite similar to what most religions already propose, I’ve stripped my definition of deism down to a minimum to make it a greater threat to my arguments.

[8] I’m using “begin” in a very loose sense here. I have no idea if time exists “outside” the universe or space existed “before,” and my brain is unable to cope with a timeless space-less expanse (see?), so I need to abuse a word just to attempt to explain a concept. The worst part? I know it’s doomed to fail.

[9] For good reason: writing had just been invented, by the Egyptians!

Proof of God: Introduction (1)

Introduction

Here’s a homework assignment for you: Corner any adherent of any religion, and ask for proof that their God or gods exist.

They’ll refuse, with odds better than chance.

They don’t need proof, they say, because they feel his presence within them, or because nothing else can explain how well this world fits together.

I have moments when I realize things like this [Comfort’s argument, reproduced below] myself. Personal moments, when something very physical and small reminds me that the world can’t be an accident. Reminds me that the world fits together too nicely.

Good sex. Hard boiled eggs when you’re in a hurry. What salt water does to my hair. Peanut butter and milk. Giving birth. Aloe. Fingernails.

Now, I don’t get into debates with atheists, and I don’t think one can prove God to anyone else, but I feel it’s worth taking a second to admit to this… since I post a lot of sarcastic bits on this site, and this is a chance to cheese out.

The way a banana fits the hand is exactly the kind of thing that makes me believe… in something. As good an argument as anything, when one isn’t making an argument out of it.

Call it God, or call it lucky agriculture… either way it makes me think the universe has an order I can believe in.

(Laurel Snyder, May 14, 2007, http://www.jewcy.com/religion-and-beliefs/proof_of_god)

I understand that a lot of people do not believe in God because of the simple fact that there seems to be no evidence of Him. I believe the majority of atheists would believe if God showed Himself. So I’m just curious if you have ever asked the Lord into your heart? Because you can’t find God, if you are simply looking for proof. You can only find God when you truly seek after Him. Even just a small amount of faith will due.Even [sic] if you don’t sense His presence immediately. Simply by asking, “God I want to believe in you, so could you show up in my life?” Some people who don’t believe say, “Alright God, if you exist, then show yourself.” As in if they don’t see God show up, then they automatically rationalize that God isn’t real. But the truth is, you have to invite Christ into your life and then He will show up. You WILL feel His presence only when you invite Him into your life. God says draw nearer to me and I’ll draw nearer to you. You can’t see God face to face on earth, but you can feel Him.

(“Violet”, http://answers.yahoo.com/question/index?qid=20110209212839AA9uEI7 )

Only a select few will go farther, but those proofs are somewhat lacking. Ray Comfort, for instance, invokes what he calls the “Atheist’s Worst Nightmare”: the banana.

This fruit fits perfectly in your hand, and has a non-slip texture to help keep it there. You can judge when it’s ripe to eat by the colour of the outer skin. It’s easy to peel open, with the help of a well-placed fingernail. There’s a gentle curve for easy insertion into the mouth. The taste is pleasantly sweet, with no seeds to interrupt your enjoyment. Once finished, the skin is easily discarded and bio-degrades.

A pop can has many of the same attributes, and we know it was designed by humans for humans. Bananas are plants, though, so who could be the designer?

Humans, as it turns out.

Originally, the wild banana had large seeds, and was almost inedible to us. Over 7000 years ago, the residents of what is now Papua New Guinea began cultivating them for food anyway. By keeping only those plants that grew the best-tasting bananas, they gradually improved the taste and reduced the size of the seeds. The new-improved banana picked up fans throughout South-East Asia. Islam then spread the fruit across the Middle East, and may have introduced it to Africa[2] . Portuguese sailors discovered the banana in West Africa around 1500 AD, and began importing it to Europe. It slowly grew in popularity there, eventually requiring large tropical plantations to satisfy demand.

Bananas come in a wide variety of colours, from red to purple, and the majority of them have to be cooked before eating. The yellow “dessert” banana was discovered on a Jamaican plantation in 1836, and its unusually sweet taste and softness made it a hit in the United States of America. Modern agricultural techniques and refrigeration have turned this rare treat into a staple.

The banana is dependent on us for reproduction and protection. The lack of seeds means it can only spread by having a certain portion of the root deliberately cut off and replanted elsewhere. Selective breeding and our desire for a consistent product have robbed the banana plant of genetic diversity, making it easy prey for disease and parasites. In fact, the tastiest variant of dessert banana was killed off by a fungus in the 1960’s. Our current sub-standard replacement is being ravaged by the same disease.

This has been known for some time. If Comfort had only done a little research, he would have been spared the nickname “Banana-man.”

Or take Michael Behe’s argument about the bacterial flagellum. These look like little hairs but act like little propellers, whipping around in circles to drive the bacteria forward. The design of these flagellum is fragile, however; remove any one component, and it’s useless as a propeller. However, evolution works via small, incremental changes, not large leaps; having every piece simultaneously click into place by chance is so unlikely, it would be like tossing some metal into the air and having it land as a bicycle. If the flagellum was designed, not evolved, Behe proposes that the culprit was an “intelligent designer.” While he’s careful not to use the “g” word, the only potential being that could pull off such a design coup would have to be a god.

One problem: evolution doesn’t force a component to have only one use. Wings began as limbs with a flap of skin, which were useful for gliding, and slowly got better at flying and worse at supporting weight. Limbs are fins that stretched out via 500 million years of evolution, and so on. The flagellum bears a strong resemblance to a “secretion system,” generally a long needle-like structure used to stab other cells and inject them with poison, that has had one or two extra bits added on that allow rotation. Those extras are easy to mutate into place, so the flagellum could evolve after all.

Not only did Behe misunderstand evolution, an embarrassing gaff for a biologist, but he did it in a courtroom, so his mistake has been permanently etched into the public record.

Three Objections

This puts me in a bit of a bind. I could spend an entire book jumping from specific proof to specific proof, only to have my work dismissed as merely “cherry-picking” the worst of the bunch. Even worse, new proofs are easy to manufacture. Behe has move on to more subtle arguments surrounding the rate of evolutionary change, while Comfort can rapidly shift between dozens of well-practiced alternate proofs, deflating any rebuttal longer and deeper than a sound-bite.

And so far I’ve just considered Christian arguments. There are thousands or hundreds of thousands of other religions that have existed on this planet. Even within a single religion, there’s an incredible variety of beliefs. Returning to Christianity, depending on your sect God comes in a trinity or in singular form, God is Jesus, Jesus is the Son of God (and thus only partially god-like), or you yourself could become a God. He may actively alter the universe, passively sit by and provides comfort, or any mix in between. In the Old Testament, God is portrayed as a physical being:

And they heard the voice of the LORD God walking in the garden in the cool of the day: and Adam and his wife hid themselves from the presence of the LORD God amongst the trees of the garden.
(Genesis 3:8, King James translation)

And he said, Hear thou therefore the word of the LORD: I saw the LORD sitting on his throne, and all the host of heaven standing by him on his right hand and on his left.
(1 Kings 22:19, King James translation)

Modern Christians reject this, and agree more with the New Testament’s view of God as a purely spiritual being, outside the physical world. That fits well with Daoists, who put it more poetically:

The revealing of great virtue all comes from the guidance of the Dao.
The Dao is so fleeting, so alternating.
Alternating and fleeting, there are signs in between; fleeting and alternating, there are forms in between.
It is so deep and so very dark. In between, there lie feelings of life. And feelings of life are real, latent with trust.
From ancient times until today, the name of the Dao stays; it has been guiding us to the origin of the manifestations of all things.
How do I know the very origin of the manifestation of all things? It’s through the Dao.

Things rapidly get worse for me, though. The conflicting views on god imply that some of them must be incorrect. This in turn opens up the possibility that none of them are correct, and the true description of the divine order has yet to be discovered or was contained in an extinct religion.

So not only am I facing a Hydra[3] of proofs, I must also factor in multiple definitions of gods that don’t mesh well or have yet to be thought up! Looming over it all is the biggest problem of them all, the one I began with. Why is any sort of proof necessary in the first place?

This is a slightly daunting task. Obviously I can’t claim to be definitive, but as impossible as this sounds, I think I can make a reasonable go of it.

[2] There is some recent evidence that Africans may have domesticated the banana themselves, on or around 1000 BCE.

[3] An old Greek monster that grew two heads for every one you chopped off. It likely went extinct because of ever-increasing brainpower, which in turn led to ever-increasing boredom.

Proof of God: Acknowledgements

Acknowledgements

In absolutely no order, I must give thanks to:

[names]
Brandie and Zane, for helping debug some of my thoughts.
Daniel Dennett, who’s book “Darwin’s Dangerous Idea” tipped me off to Hume’s near-discovery of evolution.
Paul Buller, who accidentally helped me improve my section on the Cosmological proof.

How To Read This Book

Experienced readers may find themselves somewhat bored with this book. I’ve done my best to come up with novel arguments, but this territory is very well trafficked. If you find yourself nodding off or intimidated by the scope of this book, there’s no harm in skipping ahead. You can always come back later if need be.

If instead you find yourself short on time, or with no desire to wade through proofs you’ve heard multiple times before, here’s what I recommend:

Read at least the last chapter. It makes more sense if you read the Introduction first, but experienced readers should be able to puzzle out what they missed.
Hop around through the rest of the chapters as you fancy. Beyond the beginning and end, this book has a very non-linear structure and sometimes refers to previous or future chapters to support a point. Take advantage of that to graze along as you find the time and desire. I recommend skimming the chapters on Fine Tuning, Design, and Popularity, in particular.

Notes

Any writer that discusses science faces this dilemma: should I use scientific notation, or not?

As an example, I can write the speed of light as 299,792,458 metres per second, or as 3.00 • 10⁸metres per second. The little exponent piggybacking the 10 tells you how zeros to tack on to the right of the decimal place to get to the true value. If that exponent is negative you head left, unsurprisingly; our eyes are most sensitive to light that has a wave length of 0.000000555, or 555 • 10^-9, metres.

Scientific notation is much shorter than the conventional way, which seems like a clear advantage, but it also tends to obscure the true scale of large numbers. The difference between 2.0 • 10¹⁰ and 6.0 • 10¹⁴ seems bigger than the difference between 7.0 • 10¹⁸ and 9.0 • 10¹⁸, until you do the maths: the first is a difference of 599,980,000,000,000, while the second is 2,000,000,000,000,000,000. Human beings are lousy with large numbers, and the exponent in scientific notation makes that an order of magnitude worse.

The sheer bulk of conventional numbers creates its own problem, however: all those extra digits make them look more accurate than they really are. For instance, the size of the visible universe is 880,000,000,000,000,000,000,000,000 metres across. That looks extremely precise, but in reality we’re only confident of the first three digits. All but the first zero is mere padding to get those digits into the right place, and yet there’s no good way to remove the excess fluff.

The same number in scientific notation is 8.80 • 10²⁶. The precision is so easy to convey that it’s intuitive!

On the balance, I prefer to waste a little space to give you a better feel for how large some numbers are, so long as the zeros don’t get too crazy. Just be aware that the first two or three digits are usually the only accurate ones. [1]

My next problem is one of capitalization.

Christianity has decided that their god shall be called God, and can get rather snippy if you don’t fall into line. Yet God is but one of many gods that have existed through the ages, and in this book I’m aiming at a definition of god that encompasses them all. Given the choice of offending Christians by not capitalizing the word god, or offending other religions by implying their Gods are really just the Christian one, I’ve decided to go with the majority. Sorry, Christians, but I don’t mean offence by it, and if I do talk about your god in particular I’ll be sure to make liberal use of the Shift key.

There’s also the problem of pronouns. The Christian God is a “He,” which is both a generic pronoun and a male-specific one. Hindu gods have a definite gender, and some can also be considered a “she.” Deists roll their eyes at the suggestion of a physical shape to their god, let alone a gendered human-like one, so “it” is most appropriate. Satisfying everyone is impossible, so I’ve decided to satisfy no-one and freely interchange all of them.

While apologizing for my apologetics, I should also ask for forgiveness from polytheistic religions. To save my poor typing fingers, I’ll frequently refer to god in the singular. I’m fully aware of the possibility of multiple gods, and all my arguments should succeed or fail equally well in that framework, but it gets annoying to continually write “god or gods.” Again, no slight is intended.

Speaking of other religions, atheists are commonly criticized for focusing on one religion and ignoring all others. I’ve tried hard to avoid that.

[1] But not always. In 1983, the Comité International des Poids et Mesures decided to define the metre as exactly 1 / 299,792,458th of how far light travels through a vacuum in one second.

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