How Probability Misleads Us About The Universe

In our quest to understand the Universe, theoretical physics is perhaps the most powerful tool we have as far as making predictions goes. On the one hand, we can measure how the Universe behaves on cosmic scales, gaining information about the laws and rules that it follows as well as its composition. We can then go back to the rules that govern it, throw in the raw ingredients, rewind the clock back as far as we’re willing to go, and simulate what type of Universe we’ll get out.

We can run the simulation as many times as we like, of course, and determine what the odds are of getting a Universe with certain structures or phenomena within them. When we go out to make our measurements, however, we only have the one Universe to observe. Most of the time, our observations align very well with what our simulated predictions indicated we ought to expect. But sometimes, we find phenomena that had extremely low probabilities of occurring. Critics of modern cosmology often point to these examples as proof that we’ve gotten something fundamentally wrong, but that’s generally a bad scientific practice. Probabilities can, and often do, easily mislead us about the Universe. Here’s how.

Let’s start with a very simple example that’s purely mathematical in nature: flipping a coin. Assuming the coin is perfectly fair, there are only two possible outcomes, heads and tails, each having 50% probability. You run all the simulations, flipping as many imagined coins as many times as you like — let’s say it’s one billion — recording all the possible results you can imagine. You can choose how you divide the different flips up: a billion flips all in a row, 1000 different series of a million flips apiece, or 100 million flips of 10 in a row.

You could, of course, simply calculate the probabilities exactly, since this is a simple enough problem that the math is straightforward enough. In general, however, most physical processes that we’d simulate are too complicated, and you can always reduce your errors further by making a more accurate or comprehensive simulation.

Then, with all that out of the way, you perform the real coin flips, and compare them to your simulations. What you get out could, quite possibly, be extraordinary.

Let’s say we choose to flip 10 coins. What results do you expect?

Most of us, instinctively, would anticipate that we’d get 5 heads and 5 tails. Indeed, that is the most common outcome if you flip 10 fair coins, but it’s not overwhelmingly likely. In fact, the odds that you’ll get exactly 5 heads and exactly 5 tails in 10 flips is only 24.6%: about 1 in 4 odds.

If you flipped ten coins and got the same result ten times in a row, you might think that something was rigged. How, after all, could you get saddled with such an unlikely outcome? The odds of getting ten flips that are either all heads or all tails is pretty low, at just 0.2%: 1 in 512.

And if you flipped ten coins and saw that, amidst your results, there were 5 heads in a row in there, you might be a little bit surprised. Should you be? As it turns out, each time you flip 10 coins, your chances of getting 5 heads in a row is 10.9%: approximately 1 in 11 odds.

You might look at these results with more (or less) suspicion, depending on what your expectations were. If you flip a coin 10…

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