The Eighth Heresy: What are the Chances that Probability is Real?

‘Order’ is about how interesting a grouping is: all disorder is the same to us, just mess and only comparatively few groupings are interesting enough to stand out to us. Our perception of a pattern is not to do with the physics of the grouping itself, or any external physical fact, but to do with the way we see it.

To illustrate this, we can ask which is the more ordered and probable pattern of playing cards, Set 1 or Set 2?

Set 1

Set 2

Set 1 is clearly ordered and improbable, while Set 2 looks random and disordered, so many will think is much more probable. Shuffling Set 1 and getting to Set 2 would be seen as destroying order. Mathematically, each is equally unlikely. The odds against either exact shuffle coming up are 80658175170943878571660 636856403766975289505440883277824000000000000 to 1 against, the numerical presentation of 52!. This is much larger than any number relating to physical facts, such as the number of seconds since the start of the universe or the number of particles in it. Of course, some shuffles come up because there are the same number of possible patterns (52!) as there are chances against any specific one of them turning up. The reason why Set 1 seems so much more ordered than Set 2 and therefore more improbable is that it is interesting; it is one of a very small group of hyper-interesting patterns of cards. Set 2, seems more probable because we consider it just an example of the much larger group of disordered cards – this exact configuration is not more or less probable than any other exact configuration, but it is just an example of the sort of random mess that is very probable.

If you take every possible interesting order of 52 cards, say a billion or two patterns, the probability of any of them coming up by chance is still effectively nil. If you start with an interesting order of cards and shuffle them, it is seen as making a mess, as losing information. But this is strictly from our mental perspective and attitudes; it has nothing to do with the physical objects themselves. The random order of Set 2 above, which is so messy/low information, etc., can suddenly become so ordered and fantastically improbable that it must be faked, all by a change in our information. The pattern of cards in Set 2 is the first 52 digits of the mathematical constant pi 3.141592653589793238462643383279502884197169399375105 (with rules to make the Kings, Queens, Jacks and 10s into single digits[1]).

Magically, a shuffle that was random, and so probable, because it was just one of the set of trillions of shuffles we call random, becomes non-random and improbable, one of the few billion card orders that we call interesting. Order is a statement about our interest in a pattern, not about the physical world.

Probability is a measure of our knowledge, not a statement about things. What confuses the situation is that the math of probability solves the problem that the energy of waves has no specific location, that it exists as the difference between the peak and the trough of the wave, across the whole of that distance. Current math generally needs something defined in time and space to handle; it needs something to grab onto, so that it can explore precisely how the wave changes under various conditions. Therefore, math uses a trick[2]; it says that the energy of the wave is at one point (of no size in itself), but the location of the point can only be given by its probability across an area, across the wavelength. Like an old-school detective novel, you know the murderer is in the house (100% probability), but with four of the eight suspects with you in the dining room, there is only a 50% probability that the murderer is in the room – a probability that collapses to one or zero when the detective pins down whodunnit – that becomes zero with new information.

This use of probability should not be mapped onto the world, it has no physical existence, any more than the square root of minus one has a physical existence or even the number three, despite their mathematical usefulness. We can translate a probabilistic description into the real world, but it means we must lose the probability. Here, for example, is a description of sound waves in the style of quantum mechanics:

“In areas of high pressure, there is a higher probability of finding an air molecule than there is in low-pressure areas. In sound waves, areas of alternating high probability and low probability-of-finding-a-molecule move through the air. So, sound is a probability wave moving through air.”

Here is a translation of this into a physical description of a sound wave

“Areas of high and low pressure are created by an object vibrating in and out. The alternating areas of high and low pressure move through the air until they hit your ear, when they cause your eardrum to move in and out, which your brain interprets as a sound. So sound is alternating areas of high and low pressure, moving through the air.”

Both are completely correct descriptions. The first, QM style description, allows mathematical derivatives to be taken etc. but gets complex in explaining how the probability waves affect your ear. The second, physical description, explains how sound gets from emission to absorption but is mathematically unhelpful.

Changing the location of the energy of a wave from a vague smear to a set of specific, but only probable, locations, allows math to use calculus. In this way, math can deal with continuous change, such as the acceleration of a ball as it rolls downhill. Math, in effect, breaks the continuous change down into a series of single, but infinitely small changes. With the ball on the hill, this means each infinitely small step gets faster and faster, forming a smooth acceleration curve. Calculus enables you to perfectly model a wave in mathematics and predict its behaviour with as mucn accuracy as the undefined location of wave energy allows. But it should not be used as a description of the physical process. Four oranges minus two oranges is precisely two oranges, but ‘minus two oranges’ is not a physical description. Someone taking two oranges away is a physical description.

So it is incorrect to draw the conclusion that, because a mathematical picture give the right predictions for a process, that the picture is what actually happens physically. Not that many have stated this, but it was always something of an assumption – that, instead of electromagnetic waves, like light, being waves in a field, they were actually made up of ‘virtual’ particles, particles of zero size with only probable locations. There was, at the time, also a compelling reason for this: when fundamental waves are absorbed, they are absorbed at one point and at one time. But F-waves can be seriously long, kilometres long, and ‘nothing can move or communicate faster than the speed of light’, so there would have to be a period after one bit of the wave was absorbed before other bits could be absorbed. The idea of particles with only a probability of existence at any location meant that it was not a physical wave but the location probability that ‘collapsed’ into one, single location, all the virtual particles vanishing and turning into one real particle at the exact moment of its destruction at the point of absorption. The collapse of the probability function being mathematical, was not limited by the speed of light. Again, not that many people put it like this (none?), but it surreptitiously avoided the problem of absorption happening too fast; mathematical things can communicate faster than light, perhaps. Now that we know, from the experiments on entangled waves, that fundamental waves are not limited by the speed of light, they are ‘non-local’, the physical problem disappears.

If we want to be grandiose, mathematical concepts exist in the ‘Information World’, alongside truth, justice and beauty, not in the ‘Object World’, defined as those things that can be measured: protons, rocks and people. Information world attributes can and generally do apply to object world things, but they are not the same. The processes and concepts of math have extraordinary power, but dividing a cake in eight is not at all the same physical process as dividing an army in eight.

[1] 10s have value 0 or 9 or C10 = 5, court cards have values C J,Q,K = 3,2,3, D J,Q,K= 9,9,9, H J,Q,K= 3,8,9, S J,Q,K,=3,3,3. There is a ridiculous overweight of 3s and 9s in the first 52 digits of pi.

[2] It has been objected that, to describe one of the greatest mathematical breakthroughs as a ‘trick’ is insufficiently dignified. Fair comment, but we have yet to find a suitable alternative in common language.