Data is fascinating. And what’s even more fascinating is that the laws of nature produce predictable patterns in data. For example, if you toss a coin 100 times and measure how many times heads comes up, you’ll get a number between zero and 100. If you repeat that experiment again and again and again, you’ll get different values each time, but usually the number will be around 50, and 50 will come up more than any other value if you repeat the experiment enough times. If you plot this data, with the # of heads in 100 coin tosses on the x-axis, and the number of times the experiment yields a given result on the y-axis (a histogram), you end up with a Gaussian distribution.
This is what we call a probability density function. What it’s showing is that if you repeat the experiment, tossing 100 coins over and over and over again, 50 heads will come up most often, far more than 25 heads, or 2 heads. Essentially it means you have the greatest probability of ending up with 50 heads. Makes sense if the coin is fair. The peak, that is, the most probable result, is called the mean. The standard deviation shown above is what we call a confidence interval, and it’s related to the sample size and the probability of a coin coming up heads.
In our coin example, the mean is 50 (no surprise there) and the standard deviation is 5. So our confidence interval let’s us say “I am 68% sure that when tossing 100 coins, I will end up with between 45 (mean minus standard deviation) and 55 (mean plus standard deviation) heads. Within 2 standard deviations, the confidence goes to 95% (40-60 heads), and within 3 standard deviations it goes to 99% (35-65 heads).
At this point it’s abundantly clear that if you toss a coin 100 times, you’re very likely to see heads come up at least 35 times, and no more than 65 times. The fascinating thing about this is that, although unlikely, there is still a chance of heads coming up all 100 times. You may have to repeat the experiment a few million times to get there, but the probability exists.
Extend it!
We can actually use this for any random variable in nature, any measurement at all. It doesn’t have to be related to coin tosses, it just has to be random, meaning each measurement is independent of the one before it. If we measure this variable enough times, we will get a Gaussian distribution. It can be the number of times a bumblebee flaps its wings in a minute, or the age of a human being walking down the street. No matter what, if we measure enough times, BAM! Gaussian!
This IS an Astronomy post, right?
Yes. Yes it is…I’ll get to the point. When it comes to the universe, the same holds true for properties, quantities, and parameters. If I measure the amount of hydrogen in each star, I’ll build up a Gaussian distribution, along with a mean and standard deviation. The average is some expected amount of Hydrogen that a star is most likely to have, and most stars will be close to that amount. But just like with the coin toss, there is a tiny probability that a star will have some extreme amount. That it will be an outlier, a star with no Hydrogen at all, or perhaps a star made of an enormous amount of it. And with an exceptionally huge number of stars in the universe, these fringe stars are likely to exist.
What’s fascinating is that in probability, and in nature, the fringes provide the excitement. The outliers are puzzling, interesting, and help us define a comprehensive scientific theory. It’s great if you can explain the evolution of 95% of stars within two standard deviations of the mean, but if you have a theory that explains every star, even the extremely weird rare ones, then you have a solid theory. A strong theory will explain all of the observed stars, and you’ll be able to predict strange ones that you should be able to discover, which is actually another way of proving the theory. This works for any observation in the universe, all of science, not just stars.
This is why Einstein’s general relativity is such a beautiful theory. We keep finding ways to push the extremes of measurement to test the theory, and we predict new extremes like gravitational waves, and in every case, the theory still holds. Will it ever break down? A good theory can hold forever! A faulty theory will eventually break down.
Which is why it was perplexing to find a star made purely of Oxygen. No Hydrogen. A true outlier, a fringe star, unlike nothing we have seen before. 100 Billion Billion stars in the universe (roughly), and this is the only one we know of that is pure oxygen. This is an outlier, a star on the fringes of probability. And now we have a problem, because there’s no theory of star formation that explains it.
But that is the beauty of science, it’s the outliers that drive advancement, new theories, and the hunger for new explanations. Finding the same thing over and over and over doesn’t push us to come up with elegant new explanations, which is why science is continuously looking to the fringes, the extremes, for ways to probe current theories and develop new ones. It is the true essence of science.