The Probability of Nothing

Riddle: How is language like Willie Mays? Answer: It rules center field! Of course, I am referring to ontological ‘center field’: the tiny, daily transactions (like photon exchange) that bind society (or the world) together. 

But language can play tricks on us…especially when it deals with stuff at the ends of the ontological spectrum. Take the word itself, ‘nothing’, for example. ‘Nothing’ is a noun and, as we know from primary school, a noun represents a ‘person, place, or thing’.

Which of these does ‘nothing’ represent? None, obviously. The word itself tells you all you need to know about its meaning: ‘nothing’ = ‘no thing’. Now we have a word that fails to meet the definition of a noun playing the role of a noun in ordinary speech. What could possibly go wrong? 

Well, because we use the word, ‘nothing’, as a noun, we could begin to think of Nothing per se as something (some ‘thing’). This is an instance of what Alfred North Whitehead called “the fallacy of misplaced concreteness” - the fundamental fallacy of Western metaphysics.

Then what is ‘nothing’? Today, we have a number for it: zero. But we didn’t have that number until the 13th century (Fibonacci) and it wasn’t universally accepted into arithmetic until the 18th century (Leibniz). If zero is a real number like other real numbers, then is nothing something?

We also have another mathematical symbol for Nothing, ø, the null set. This notation insulates Nothing from the domain of real numbers. We are used to the idea of ‘Ineffable God’: God so far transcends our world that nothing we say about God can be true or even meaningful. Divinity is a language unto itself, or as a five-year-old grandchild once explained to me, “God is outside the numbers.”

We’re not used to the idea of ‘Ineffable Nothing’. And yet, ‘nothing’ transcends all things just as God does. God, aka Being, Value, Love, is the ontological opposite of Nothing, which is the absence of ‘I am’ (Exodus), ‘it is’ (Genesis), ‘you are’ (Gospel of John). 

We begin, as all serious philosophical essays must, with Robert Frost, the ‘Quantum Poet’. In his best known poem, The Road Not Taken, he sets out the quintessential existential dilemma: “Two roads diverged in a yellow wood…”

Happens a million times a day, every day! Frost, subject to the human condition, must pick a path, ‘sorry I could not travel both and be one traveler’. Frost makes his choice, ‘I kept the first for another day’; but hero that he is, Frost realizes that this is a forever decision, that the universe bifurcates at this point: ‘Yet knowing how way leads on to way I doubted I should ever come back’. 

Nor does our hero hide behind the rationalization of ‘objectivity’; he knows that the road chosen is in no way superior to the other, for ‘both that morning equally lay’. Standing at the point of divergence, at the moment of choice, both roads are equally real, equally attractive, equally effective, and therefore ontologically identical. 

Frost’s choice is apparently unconditioned. He is as likely to choose A as he is B. Initially, each option has a probability of P ≈ 50%. Since each P > 0, both exist! But whenever Frost’s choice of one path becomes irrevocable (P = 100%), then the alternate route (P = 0) ceases to exist…for Frost. It is no longer part of his Actual World. Proposition: ‘X exists, iff P(x) > 0’.

Once P = 0, the alternate path no longer meets Gregory Bateson’s existential criterion: it’s no longer ‘a difference that makes a difference’. When there was no longer an option for Frost to pursue ‘the road not taken’, it ceased to exist…chez Frost. 

Much of Western philosophy is based on a false conception of Nothing. When we say ‘nothing’ we often have in mind something: a void or a vacuum, ‘nothing’ relatively speaking, but not absolutely nothing. 

Our ‘nothing’ tends to be ‘something…dimly lit’, a bit like Hades in Homer’s Odyssey. It’s even been called ‘a receptacle’, ‘a womb’, an ‘ether’, ‘pure potentiality’. Today, the cognoscente call it ‘negative vacuum pressure’. Nothing can’t be any of those things, not even metaphorically. Nothing can only be nothing. Nothing has no hair. It’s not a depression left in the fabric by ‘something’ when it departs. It’s not negative space, negative energy or negative vacuum pressure; it’s not positive or negative, it’s nothing. 

It’s good to know that we are not alone in our thinking. Perhaps we’re not mainstream (yet) but we’re definitely not flying solo. In fact, we share our perspective with Parmenides of Elea, the father of Western philosophy: “It is not to be said or thought that ‘it is not’…It is or it is not…let go the one (it is not) as unthinkable, unnamable, for it is not a real route.” 

‘The road not taken’ cannot be ‘said or thought’ or even named because ‘it is not a real route’. When Frost reaches his destination, he is surrounded by reporters all with a single question: “Why did you choose that path?”  

To which Frost answered, “There was more than one path?”

Parmenides viewed the World as both the ‘Realm of Things as they Appear’ (Doxa) and the ‘Realm of things as they Are’ (Aletheia). In the realm of Doxa, Frost confronts an apparent existential choice. In the realm of Aletheia, the apparent ‘choice’ is without consequence and so does not ‘exist’; it’s not a ‘difference that makes a difference’ because ‘both that morning equally lay’ and both led to the same destination. There was no objective reason to prefer one over the other.

So there never was an existential dilemma because there was really only ever one path (a path and its mirror image). This perspective pops up all across ‘the fruited plain’ of Western philosophy, but for now, let’s stick with Quantum Mechanics (QM)! 

Hugh Everett’s ‘Many Worlds Interpretation of Quantum Mechanics’ states (roughly) that everything that can happen does happen…in its own universe. Corollary: Whatever did not happen could not have happened, because if it even might have happened, it would have happened. Try saying that 10 times!

An entity’s worldline is its ‘route’ but apparent routes that pass through ‘counterfactual space’ are not real routes; their probabilities are all equal to 0. If it isn’t now, it never was, it could not have been, and it cannot come to be in the future. Only real routes are ‘real’. 

Everett channels Parmenides…2400 years later. There is ‘is’ and that’s all there is…no might, no should, no would, no could, just is. Let’s apply this way of reasoning to questions involving probabilities, beginning with a traditional Hasidic folk tale:

Once upon a time, a certain Rabbi was on his way home from Schule when he encountered  an elderly widow crawling on her hands and knees under a streetlamp. Not wanting to play the part of passer-by in a future production of The Good Samaritan and eager to perform one last mitzvah before going to bed for the night, the Rabbi offered to assist.  

"I've lost my shiny penny, the only thing I have left in the world," the widow wailed.

"And is this where you lost it?" the Rabbi inquired innocently.

"No," she replied. "I lost it over there."

The quizzical Rabbi, still hoping to be helpful, asked, "Then why are you looking for it here?" 

"Because the light is better!" 

This story is often presented as a commentary on the widow's folly, but in fact, the widow is the hero of the story. She defies conventional wisdom. Why look for a lost penny in pitch darkness where there's no hope of finding anything? Unlit space is not part of the widow’s world; from her perspective it is Nothing. So the only ‘rational’ thing for her to do is to search under the lamplight where P > 0. 

Let’s rephrase: the probability of the penny being under the light is actually 100% (P = 1) because the penny has to be somewhere (P=1), and every other possibility has zero probability (P = 0): 1 – 0 = 1. But the probability of her finding the penny under the light is much, much less (P < 1)…but not zero (P > 0). 

Ok, this sounds officially crazy. How can the probability of the penny being under the lamp be 100% when we said earlier that the penny is probably not there? Once again, we find our answer in Quantum Mechanics.

According to QM, everything is everywhere all the time and anywhere you look there is a finite possibility (however low) that you will find your quantum there…as long as you’ve confined your search to places that exist for you. 

Now that we’re comfortable applying Parmenides’ ontology to situations involving probabilities, we’re ready to apply it to the greatest floating craps game of all: ‘Pascal's Wager’ (1670 CE). 

Confronted with the God Question, French mathematician, Blaise Pascal, employed a forerunner of what is today called ‘Game Theory’. Pascal divided a sheet of paper into four quadrants. Across the top of the page, he wrote, “I believe that God exists;” down the left-hand margin, he wrote, “God does exist;” and then he filled in the appropriate truth values: (0,0), (0,1), (1,0), (1,1).  

Pascal reasoned that one of four things must be true: (1) I do not believe that God exists, and he doesn’t; (2) I do not believe that God exists, but he does; (3) I believe that God exists, but he doesn’t; (4) I believe that God exists, and he does. 

So God is ‘free’ to exist or not and you are free to believe or not. Yet, scenarios 1, 2, and 3 are effectively identical. They amount to the same thing. Believe whichever one you choose; it makes no difference. They are interchangeable because they each produce the same incremental value: (0*0) or (0*1) or (1*0), i.e. Zero.  Only #4 (1*1) is different; only #4 generates incremental value. 

Quadrants 1, 2, and 3 do not meet Gregory Bateson’s criterion (for ‘being’, above). They produce zero incremental value so there is no ultimate value difference among them and their contribution of value to the world is null (ø). Since all other options generate 0 incremental value, P(4) must be 100% (P=1): 1 –  (0 + 0 + 0) = 1.

To quote a medieval Irish poet, “Naught (0) is all else to me save than Thou art!” Centuries later, Pascal proved that this is not just a statement of subjective faith…it’s a statement of objective reality.

David Cowles is the founder and editor-in-chief of Aletheia Today Magazine. He lives with his family in Massachusetts where he studies and writes about philosophy, science, theology, and scripture. He can be reached at dtc@gc3incorporated.com

ress, Literary Journal Spring 2023.

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