Assumption Cost

We often speak of whether an hypothesis is likely or unlikely, but these words are misleading; for likelihood refers only to how often a specific case appears in a group of general cases, such as, for example, if it snows seven days out of ten in February in Scotland, but only two days in ten in March, the Scot may speak of snow being likely in February and less likely in March.

But when we speak of the assumptions of an hypothesis we are speaking of something quite different: the Big Bang theory is not, given the current state of astronomical observations, “more likely” than the Steady State theory, nor more probable nor anything like that. Probability has nothing to do with it. It is not as if, out of one hundred cases, the Steady State is found true in thirteen of them and the Big Bang is found true in thirty of them, and that therefore the Steady State model has 13% truth and the Big Bang 30%.

The reason why the Steady State model is not the current standard model is that the Big Bang model fits better with the evidence and makes fewer assumptions. It is easier to believe. It is easier to believe because the cost imposed on our credulity is low. The more assumptions we have to make, the more evidence that does not neatly fit the facts, the higher is the strain on our credulity.

We can call this strain the “assumption cost”.

Some assumptions are harder to believe than others. The assumption that requires more assumptions and more far fetched assumptions costs more credulity to believe.

One might think that whichever theory required the fewest assumptions and therefore had the lowest assumption cost would be preferred. Not so. Cost is only half the equation. Even as fantastic and absurd assumption, such as, for example, the assumption that light is always measured to travel the same velocity as seen by any observer, no matter what the position or motion of the observer, has a high cost. It is, on the face of it, an Alice-in-Wonderland assumption. But this assumption, the assumption of the theory of Relativity, has a huge payoff. The payoff is that the assumption, when its ramifications are explored, can explain and anticipate things that a less incredible assumption cannot explain.

The payoff is in the explanatory power. Newtonian mechanics cannot explain the procession of Mercury, nor the bending of lightwaves passing near a massive body. To a Newtonian, these things are coincidence, a mystery, a thing that is merely taken as given, and not explained by the theory. If light is found to bend near our Sun, and also to bend when passing near Arcturus, no explanation is given, and whether or not it will be observed to bend when passing near Betelgeuse or Eta Carina is left unexplored. The Newtonian model has no predictive power when it comes to these observations.

In the case at hand, the case of a religious experience, we have two theories: the Hallucination Theory and the Revelation Theory. The assumption cost of the Revelation Theory is high, because it requires we postulate supernatural events. But, having postulated a supernatural event, the explanatory power is also high. Under the Hallucination Theory, the content of the visions I saw was produced by an unhealthiness of my subconscious mind, a malfunction, and yet this malfunction somehow produced a coherent narrative event that fits nicely with the narrative of two thousands years or more of Western Christian tradition. Why did my subconscious mind decide to formulate characters and have them say lines and show me ideas and images which fit this narrative structure? Why not show me a hallucination about Santa Clause, Superman, or a Flying Saucer?

At this point, the Hallucination Theory is free to speculate without limits: I saw God rather than Wotan or the Wizard of Oz because that was what my subconscious mind showed me. Why did it show me that? It was not a conscious and not a planned decision, if we are talking about my subconscious. It was something my subconscious decided without consulting me. Now, to speak of the subconscious mind as making decisions is an oddity in and of itself: these decisions are not conscious decisions, not deliberate. And so we actually cannot know what factors went into the decision, or even if the mental event can properly be called a decision at all. It was merely an event that happened without rhyme or reason.

When I had a second religious experience a week later, once again, the narrative was coherent and fitted with the first, as well as with some two thousand years of Christian tradition. Now, this is an odd thing, to be sure. Under the Hallucination Hypothesis, this second event was just like a dream, no more meaningful than the first dream, merely a malfunction of my brain. Any yet, I have had dreams every night of my life, and I have never had recurring dreams, and I have never had a dream that was a direct sequel to another dream.

At this point, the Hallucination Hypothesis is asked to predict whether, should I have yet another religious experience, it will continue to fit the narrative, and be coherent with Christian mythology and teaching, or whether it will be about goats, or goblins, or the Ghost of Christmas Past, or the Grand National. Upon examination, we find the Hallucination Hypothesis is in the same sad state as Newtonian Mechanics: it simply lacks explanatory power. The Hallucination Hypothesis cannot explain why I should have a recurring hallucination, two in a row, and on the same topic, rather than, as dreams are, have one follow the other without rhyme or reason.

Under the Hallucination Hypothesis, any answers to prayer that follow after the prayers must be dismissed as “post hoc ergo propter hoc”, a coincidence.

Unfortunately, even if it should turn out that we live in a universe where prayers are answered, and supernatural events do take place, the Hallucination Hypothesis is structured by its assumptions never to be able to reach that conclusion, whether the conclusion is true or not.

The hypothesis does not have what Karl Popper identified as the defining characteristic of a scientific hypothesis: it is not disprovable. It is not a disprovable hypothesis: even if, after one hundred trials, one hundred prayers are answered, each one individually can be dismissed as “post hoc ergo propter hoc”, or coincidence. No number of trials can convince.
The Revelation Hypothesis has both explanatory power and predictive power.

If I am wedded to the notion that no supernatural events exist, then, of course, I must prefer the Hallucination Hypothesis: and yet I am no other than reasoning in a circle. By assuming that no supernatural explanations are true, I am left with the conclusion that no supernatural events occur, even if and when one occurs right before my eyes and to me.

The assumption cost of the Revelation hypothesis is clearly higher; but the payoff in terms of explanatory power is more than sufficient to defray that cost.