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Why Randomness May Not Mean What You Think It Means

Are you convinced that the shuffle mode on your iPod is messing with your mind? Or that certain numbers are bound to come up in the next lottery? If yes, you may be holding on to some serious misconceptions about randomness. Here’s what it means for something to truly happen by chance.

Randomness is an often misunderstood concept. Unlike a lot of precise math, randomness deals with ineffable concepts like odds and probabilities — concepts that our brains simply haven’t evolved to fully process and grasp; indeed, our brains are actually wired to find patterns and meaning in things that aren’t really there.

Another problem is that randomness tends to mean different things to different people. For some, randomness suggests a total lack of order in a sequence of symbols or steps such that there’s no intelligible combination or patterns. Others, namely scientists and mathematicians, describe it as a simple lack of predictability. Randomness in this context implies a certain measure of uncertainty.

But regardless of definition, people still make a lot of mistakes when thinking about it. Here are some of the most common misconceptions about randomness.

Picking Out Patterns

I’m having a never-ending debate with my father that’s nowhere close to being resolved. When he sets his MP3 player to shuffle mode, he’s convinced that it plays songs in accordance to some kind of system. For example, he complains that it alternates genres on an eerily consistent basis, and that it favors particular songs and artists.

Our brains can’t help but pick out patterns or tendencies in what are otherwise completely random events. We often find ourselves anthropomorphizing my iPod when it selects an apparent sequence of songs that go very well together.

What’s more, people tend to apply a different definition of randomness than what’s conventionally accepted. When we set our MP3 players to random, what we’re essentially asking the device to do is distribute the songs in the playlist in an evenly distributed manner. By playing songs by the same artist back-to-back, for example, our MP3 players violate this expectation.

But playing songs in a perfectly distributed manner is not random. In fact, it can been as something that’s highly structured. Hearing a song by the same artist back-to-back, or even back-to-back-to-back, is a random occurrence. It’s improbable, sure, but it’s random.

Relatedly, when listening to a playlist, it’s also important to keep a sense of probability in mind. For example, if a playlist contains 50 heavy metal songs, but only 25 dance tracks, the shuffled playback will be representative of this proportion; you’re simply going to hear more heavy metal songs given their predominance in the overall sample.

Items Are “Due” To Come Up

It’s also important to note that the preferences of your shuffle mode could be affecting the apparent randomness of your playback. Some MP3 players allow you to tweak the strength of the randomness (e.g. favoring starred songs, or certain artists), and some modes remove songs from the playlist as they go (i.e. non-repeat). Both of these will have a profound impact on the “randomness” of the playback.

But if the playlist is set such that every song is thrown back into the pool, there’s absolutely no guarantee that an unplayed song is somehow “due” to come up before the ones that have played before it.

Another example is taking a jack-of-hearts out a 52 card deck, putting it back in, shuffling the deck, and pulling it out again. While surprising, it was just as likely as pulling out any other card. The deck — or your MP3 player — doesn’t “remember” what came before.

Similarly, some numbers or items are said to be “cursed” or “blessed” because they’ve been previously observed to either come up rarely or frequently. Again, in a truly random system, no such claim can be made.

All Possibilities Are Equally Likely

Randomness happens, but it often happens within an overarching system. It’s often assumed, however, that randomness implies open-ended outcomes — that virtually anything can happen. Critics of Darwinian natural selection complain, for example, that there’s too much apparent design in evolution for randomness to be a guiding principle, and that there needs to be a divine overseer to help direct the process.

What the ID crowd fails to realize, however, is that evolution does function according to some very specific rules and constraints. Mutation, while giving the appearance of randomness, is indeed chaotic or stochastic in the sense that copying errors are constantly being made during sexual reproduction. But what is absolutely not random is the selection that follows; just because a mutation happens doesn’t mean it will be favored by the environment. And in fact, most mutations are detrimental to organisms.

Computational cell biologist Kathryn Applegate looks at it from another perspective:

Sometimes, the word random is used to mean unbiased. If you want to know who will win a political election, you make sure to poll a random sample of people, not just those hanging around a Tea Party rally. But the word random doesn’t have to mean that all possibilities are equally likely. When maternal and paternal chromosomes get together during conception, they exchange long sequences of DNA in a process called recombination. We now know that recombination happens more often in some places of the genome than others, but the specific sites where it will occur in a given embryo are impossible to predict. So recombination is random in the sense that it is unpredictable, but not in the sense that all outcomes are equally likely.

All Of Nature Is Potentially Predictable

There’s also a misconception that much of the randomness we observe in nature, like our failure to chronicle a truly Newtonian clockwork universe, is simply on account of our inability to properly measure all the variables at play. Eventually, the thinking goes, we’ll be able to make accurate predictions in previously — or seemingly — random systems.

But two 20th century discoveries have largely overturned this notion, namely quantum physics and chaos theory.

As Heisenberg’s principle of uncertainty has shown, we cannot be certain of a particle’s locationand its momentum; we live in a universe of fuzzy probabilities. Similarly, the chaotic and dynamic inner workings of a hurricane will forever be impossible to predict with perfect precision.

So between the two, we are fundamentally — and irrevocably — limited in our predictive power.

Quantum Math Could Explain Irrational Reasoning

by Gabriel Popkin, Inside Science

Quantum theory, developed about a century ago to explain the puzzling behavior of elementary particles, could also help explain seemingly irrational aspects of human reasoning.

The mathematics behind this highly successful physics theory has now provided a way to explain why people respond differently to survey questions depending on the questions’ ordering, scientists report June 16 in the Proceedings of the National Academy of Sciences.

Human reasoning is notoriously fickle, inconsistent and full of seemingly obvious fallacies. A prime example of such apparently irrational decision-making is the “order effect”: Researchers routinely find that the sequence in which they ask survey questions affects how people respond to them. In a 1997 Gallup poll, for instance, when surveyors asked people if they thought Bill Clinton was honest and trustworthy, roughly seven percent more respondents answered “yes” if they were first asked whether Al Gore was honest and trustworthy.

• Professor:ok let's do a little experiment. What do you think the probability is, in this 52 person class, that two people have the same birthday?
• Student:100 percent
• Professor:no...
• Student:yes
• Professor:there are 365 days and only 52 students, how is that 100%?
• Student:because there are two twins in front of me
• Professor:shit... Every time
È più probabile che venga a rapirmi un pandacorno e non che lui mi ami.
—  occhidamore
You have to learn to respect the uselessness of intuition.
—  Probability professor

Probability in Genetics

So far we’ve been talking about simple ratios, but how can we mathematically figure out the probability or the percentage that an organism will inherit a trait?

Consider a cross between YyRr and YyRr. Using a Punnett square, we can deduce that for colour, ½ the offspring will be Yy, ¼ yy, and ¼ YY. The same probabilites apply for shape: ½ Rr, ¼ rr, and ¼ RR. (Remember Y=yellow, y=green, R=round, r=wrinkled.) But how do we then figure out how many will be round and yellow, or green and wrinkled?

The rules of probability, of course.

We can determine the probabilities of the genotypes by just multiplying the traits we want to know about together. For example, what’s the probability of the pea ending up yellow and wrinkled? Well, we know that ¾ of our offspring will be yellow, and ¼ will be wrinkled. ¾ x ¼ = 0.1875. So about 18.75% of our offspring will be both yellow and wrinkled. (If you don’t like fractions, just use 0.75x0.25.)

What about green and wrinkled? ¼ x ¼ = 0.0625. So 6.25% will be green and wrinkled. We can do the same for the others:

Yellow and round: ¾ x ¾ = 0.5625 = 56.25%

Green and round: ¼ x ¾ = 0.1275 = 18.75%

Adding all of these up gets you 100%, of course. It also gives us our ratio that we’ve talked about—9:3:3:1.

Further resources: Probability in Genetics: Multiplication and Addition Rules video

My friend’s mom thought D&D was about studying witchcraft, but really we were studying math, probability, medians and means, in order to learn the right way to read a d4 and a d8 to simulate a d32 with a linear curve.  (From Gary Gygax’s AD&D Dungeon Masters Guide, TSR, 1979.)

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This is a fantastic chart showing the connections between several dozen probability distributions. I had actually found it several months ago, but I didn’t realize there was a click through link to this website that lets you highlight the connections and get a clearer picture on the relations. Even better, each distribution is linked to a PDF that contains common knowledge on that distribution.

You learn about some of these relations as you study probability theory, but it’s awesome to see them mapped out all in one place

…the most important questions in life are, for the most part, only problems in probability.
—  Pierre-Simon Laplace, 1814. Get to grips with the fundamentals of probability with the free chapter from Probability: A Very Short Introduction, on Very Short Introductions Online.