The Not-So Infinity Stones

My answer to an old, dumb question.

Dr.

William M Briggs

recently posted an interesting article about probabilistic theories of the Almighty. I recommend you read it all before continuing:

On The Probability Of God

As a thought experiment, I agree with most of it. It’s difficult to say “all” because thought experiments of this sort are so malformed. For example:

Take “omnipotence.” The man trotted out a hoary old argument: “‘Can [God] make a stone so heavy he can’t lift it?’ This suggests that omnipotence is impossible.” To him, “omnipotence” means “ability to do anything“. Given that definition, the probability “An omnipotent God exist” must be 0, because God cannot do everything.

But that is a screwy definition of “omnipotence.” Another, and the one I share, is “can do anything possible“. Creating stones too heavy to lift is an impossibility. It is like creating the number 2 equal to 3, or fashioning a married bachelor. It is like you saying “I cannot speak any words.” Even God cannot do the impossible. That means, with this definition, the man’s argument carries no weight. (Good pun!)

I suppose this is one way to square it from the rationalist’s perspective: God is not just logical, but the essence of logic. Therefore, He could not pull off the Stone Trick because to do so would violate the Logos.

But here we run into the problem that God has already done the impossible, by creating everything from nothing. So instead of attacking the problem from a logical or physical angle, let’s try the linguistic approach. The key substrings to the question seem to be as follows

1. [Can God make]

2. [a stone]

3. [so heavy]

4. [He can’t lift it]

Now let’s examine each of these parts individually before we try to reconnect them. In doing so, we’ll try to stay within the bounds of the mind which generates this ancient schoolboy fallacy. In other words, we won’t get into integrated information theory, quantum entanglement, morphic fields, or anything else that can’t be squeezed into the confines of a Hollywood action flick.

1. “Can God make…:

The answer is a simple “Yes”, no matter what clause follows this claim. God is the original and essential Maker of all things material and immaterial, including Himself. Due to our limitations, we humans cannot make more things than already exist. We can only dismantle and/or reconfigure existing things, bound by the Law of Conservation of Energy in a closed system.

The schoolboy doesn’t know this, which is indicated by his lazy use of the word “make”. In his mind’s eye, he might picture a gray-bearded wizard with a magic wand, zapping external material into existence. He most likely believes that consciousness itself, including his ability to draw the picture “in his head”, is an emergent property of biology, rather than the inverse of that. If he lacks meta-cognition, it never occurs to him that God’s consciousness makes things in the universal-domain the same way that his consciousness draws pictures in the head-domain.

2. “a stone…”

Here we run into our first spot of trouble. Despite how regularized it appears in our mind’s eye, a “stone” is actually a poetic structure, not a discrete entity. For instance, both mountains and pebbles are technically stones at different scales. But while we can somewhat measure regular properties of the latter (discounting quantum uncertainty), measurements of the former become strictly subjective and application-dependent.

We can point to a roughly pyramidal rocky entity on the horizon and say “mountain.” The word decrypts and decompresses in the mind to suggest all the potential transactions and modes. “Mountain” is a slope I might climb, an obstacle I might tunnel through, a shape I might paint on a canvas, a geologic region I might mine for useful minerals, etc.

But what a mountain isn’t is a coherent entity with indisputable properties. For instance, where does the “land” end and the “mountain” begin? We might say it has a definitive top, but its bottom and base edges are arguable and contingent. We could say a mountain’s definite properties theoretically exist, and that these properties are “stable” within some momentary snapshot of time. But our methods of measuring them are almost entirely subjective. Even our rulers are fundamentally unstable, unless we think that “sea level” is somehow a reliable constant.

Hills, valleys, beaches, and shorelines are also linguistic constructs, whose measurement depends entirely on models that can only yield abstract estimates. The words describing them are therefore examples of poetry, not science. And if mountains are “stones” that can’t be objectively measured, what about the Third Rock from the Sun?

Danita Delimont / Getty Images

Despite the image above, the vanquished Titan Atlas was famously sentenced to hold up the Heavens, not the Earth. He is the embodied poetry of mechanical forces like gravity and magnetism that keep celestial bodies from spinning off into the endless void of space. We will revisit this punishment when we investigate the “lift” clause. For now, we can stipulate that the “stones” he holds are unimaginably heavy, even by the rough estimates that our models provide.

So for this next part, let’s forget all about pebbles and mountains, and go cosmic in our scale.

3. “so heavy…”

For now, let’s forego all questions about mass and density, and stick with the schoolboy wording. Using Newton's Law of Universal Gravitation, the Earth is estimated to weigh approximately 13.17 septillion (1.3 x 10^25) pounds. There are many problems with using this method, however, even leaving aside black holes and “dark matter”. Like so many models, even its presumed accuracy might degrade exponentially with scale.

If we theorize a heavenly body of sufficient mass, then we can imagine a (stone) entity of this weight that exists on its surface. In the schoolboy’s imagination, this object would be the test for God, who perhaps manifests on the surface as a biological creature with a gravitational “weight” and mass of His own (and probably a bunch of bulging muscles and a cape, too).

Here we run afoul of a domain problem. While weight is not considered a practical consideration outside of the local system (i.e. so-called “zero”G is never zero), we don’t actually know what gravity is, or how distant bodies effect each other’s motion throughout the universe. To put it another way, if the finger of Atlas were to twitch in the vicinity of GN-z11, what kind of Butterfly Effect would it have on his shoulder?

Moreover, what does weight even mean outside the context of local observation, let alone from the perception of a non-local Observer who operates both inside and outside of the timespace domain, such that it is simultaneously both separate and integral? For instance, I could say that a blood cell weighs ~27 picograms. What does that weight mean within the local system of my body, as opposed to outside of it?

And if the cell is located within the dynamic system of my body, does that mean I am somehow “lifting” it?

4. “He can’t lift it?”

At last we come to the supposed “paradox” clause, in this classic game of Idiot Gotcha! First, let’s review our progress:

God makes a thing, which everyone agrees is in His (and only in His) power to do. The thing He makes has properties that are pseudo-measurable from our perspective within spacetime. One of these properties is selected for testing. In this case the property is weight, which purports to measure the force of gravity acting on an object's mass as measured in Newtons (N).

For our example, we will extend the normal force applications to the uncanny, supernatural or magical. In other words, while God may employ any of the primary biological or secondary mechanical methods, He is not limited to these lifting methods.

From our perspective as organic terrestrials, the direction of the gravitational force is “downward” (or, more accurately, inward towards the Earth’s core). To properly lift an object is to directly counteract and supersede the gravitational force, either via mechanical instrument (e.g. a crane, a forklift) by internally generated power (e.g. muscles, expelled breath), or some combination therein (e.g. use of a lever and fulcrum).

The result is an observable, continuous state change in 4-dimensional space, relative to some ground constant: the object was at altitude x before application, and then, excluding measurement, at something like altitude x + ϵ directly after application. It has moved some distance outwards from the ground.

With that in mind, say you’re walking across a flat, grassy plain with a date, and stumble across a big stone. You decide to impress the gal by deadlifting it from a standing position. When employing tools of measurement and plugging results into equations, we can draw somewhat more useful head-pictures of this feat of strength than “Thing go up, bro.”

First, we’d need to capture the following local data.

• Weight: Gravity pulls the stone down with a force based on its weight. The acceleration due to gravity is about 9.8 meters per second squared. Luckily, you’ve packed a scale in your bag of tricks, and determine the stone’s weight is 50 kilograms on the dot. So, the gravitational force on the stone is:

\(\text{Weight} = 50 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 490 \, \text{N}\)

• Net Lifting Force: Let’s say you’re pushing upward with a force of 600 Newtons. Since 600 Newtons (up) is greater than 490 Newtons (down), the stone will move upward.

\(\text{Net force} = 600 - 490 = 110 \, \text{N (upward)}\)

• Acceleration: This net force causes the stone to accelerate upward at a certain rate. To find the acceleration, we divide the net force by the stone’s mass:

\(\text{Acceleration} = \frac{110}{50} = 2.2 \, \text{m/s}^2 \)

Now, let’s say you start lifting the stone from your ground constant (height = 0 meters) with no initial speed (it’s not moving upward yet). The equation for the stone’s height h(t) h(t) h(t) after t seconds is:

\(h(t) = \text{initial height} + \text{initial speed} \times t + \frac{1}{2} \times \text{acceleration} \times t^2\)

Plugging in our values…

\(h(t) = \frac{1}{2} \times 2.2 \times t^2 = 1.1 t^2\)

So, as measurements are made at second intervals, the stone would be lifted 1.1m after the first second, 4.4m after the next, 9.9m after the third, and so forth. Of course, this low resolution model excludes huge number of important factors pertaining to the air resistance, balance, fatigue, body dimensions, lifting form, etc. It may even include factors that are unmeasurable and unknowable, such the lifter’s willpower and concentration. In other words, it contains all the flaws and misconceptions of classical physics, and a probably a multitude of others. It’s just a model, not reality. An incomplete map, not the terrain.

But this is the schoolboy version, so we can leave “eh, close enough” Newtonianism alone and apply the test to the Supreme Creator of Reality Itself. At first blush, we could say that God’s lifting force is somewhere between ϵ and <∞. We cannot apply zero or infinite force in this example, because both effort and measurement are implicitly called for. Similarly, the stone cannot weigh an infinite amount, because the experiment requires weight measurement (“so heavy”).

Altitude is measured from whichever constant is equal to the stone’s y-value at rest in a fixed position. The lifter’s position is presumed to be nearly identical to the stone’s (or, at the very least, the lifter’s point(s) of distal contact are). For the sake of argument, we will temporarily discount any sort of remote hi-tech gadgetry or psi ability, declaring that any such methods still ultimately require point-of-contact with the stone, either initially or over time.

So here is our stone, resting on an osmium plane on our superdense Krypton-like megaplanet. Presumably, the stone has been resting at this value since Wizard God zapped it into existence, and now awaits Comic Book God to don his spandex and crack his knuckles.

At this point, we might pause to note how childish this experiment really is.

The notion that God will fail to lift a stone of any size is absurd for too many reasons to count. For example, even if Comic Book God initially failed to lift it, he could still whip out his wand, reduce it to 1/100 of its mass, and then hurl it into the nearest star. Or push the entire planet away from the stone by altering gravitational fields. Or turn it into a loaf of bread and eat it.

But the stupidity of the “lifting” test goes much deeper.

During which interval of local time will we measure the force exerted upon the stone? If God exists outside of non-local time, how will we know when he has begun to lift, and when he has ceased his effort? If the universe is n-dimensional, could the lifting have occurred or not-occurred depending on which spatial and/or temporal dimensions can be observed? In other words, is the answer “Yes” for some observers and “No” for others, with both answers being equally true?

And from which ground constant does God begin to measure altitude, by the way? Sea level? Which sea, and on which planet? Which way is up?

Omnipresence means that “lifting”, while the concept serves as practical poetry for us, is an entirely meaningless concept in God’s non-local domain. Even if we say God is operating entirely within the observable boundaries of our 4-dimensional domain, the starting and ending positions of the stone would be fully interchangeable from His perspective. That’s because the quality of omnipresence means He simultaneously occupies both positions (as well as all other positions) in spacetime.

From his non-local perspective, God has therefore already lifted the stone, and never lifted the stone, and hurled it a quintillion light years away, and never touched it at all. His position is both inside and outside of the stone, in contact with it and on the other side of the galaxy from it.

Can He lift it?

What kind of stupid question is that?

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Let’s put it all back together now:

“Can God make a stone so heavy he can’t lift it?”

I can’t recall the first time I heard it asked, or what my response might have been. I also can’t recall what my conception of God was, if I even had one worth mentioning. But when I’ve heard it asked in recent decades, it’s typically by some smarmy atheist type, who thinks he’s just detonated a nuclear logic bomb in the form of a retarded Zen koan. “Riddle me this Batman!”

What I do wonder is whether such a person is putting his soul at risk. After all, when Satan follows Jesus around in the wilderness for forty days, he tests his powers by declaring he might not have them (oddly enough, two of these tests have to do with stones, and one of those with gravity as well).

Ultimately, I don’t think so. Or at least, not always. To toy around with a silly thought experiment and be blind to its flaws isn’t necessarily evil. It might not even be necessarily stupid; we just might not have the proper data or parameters, and will figure that out after bumping around in the dark for a while. God might laugh at such a person as a lovable dope, or a child whose early ignorance is endearing.

But for those who arrogantly persist in asking stupid questions, in the hopes of demoralizing the faithful?

Play stupid games, win stupid prizes.

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