Later on he revealed that he had been filming himself flip the coin for hours, only stopping once the 10 in a row sequence came up.

“We live in a world of symbols and abstractions, and many a man dies by his own cliches.”

I cannot recall who said that but I do recall how that teacher, among others, showed me a method to reduce the need for symbols and to clarify abstractions; literacy, numeracy and the scientific method.

It is satisfying to see those teachers’ lessons confirmed whenever I or someone else finds a pattern that is actually there, not merely perceived. That’s how we learn, how we progress.

Though I guess a repulsion/attraction solution would have worked too.

Intelligence?

Finding differences is easy. Ask any computer to compare two photographs of the same subject and you get tons of differences. Ask one to tell you how they are the same and you likely won’t get a meaningful answer. Many intelligence test provide images that are superficially different then ask which one doesn’t fit with the rest. The key to solving them is finding the underlying pattern of the group.

Science unravelling the universe is pattern recognition on steroids. All hypothesis models are statements of pattern.

By the way, is there a word for human tendency to find patterns? At least it’s somehow realted to pareidolia

The BA said:

The answer is they are both exactly as likely. You have a 50/50 shot at a heads or tails on each throw, so any 10-throw sequence is just as likely as any other! But we look at the second sequence and see no information in it. We assume it’s just random, and therefore more likely than a sequence where we perceive there is information, like five heads in a row followed by five tails. But each is just as likely.

In fact, there is more information in the second sequence than in the first. According to information theory (or at least my interested layman’s understanding of it), the more easily compressed a sequence of bits is, the less information it contains.

Yeah, but there’s probably a bunch of other people who play those numbers, so if by some miracle you did win, your pot would be much smaller than if you played some obscure number set.

Now, with the dot patterns… Is it not also true that the picture on the right is as equally likely as the one on the left (assuming a simple pixel-on/pixel-off array) but the “type” of pattern on the left is more likely than the “type” of pattern on the right? (Yes, I realise this wasn’t really the question)

I’m now sitting here having fun with Photoshop noise patterns and looking for faces. I’ll get the kids to help tonight.

Sadly even there conception of how low of a chance that number has to come in is probably still to high. Powerball is about a 1 in billion chance if I remember.

Not really. “Random” is used as a magical incantation by frequentists but to Bayesians and other regular folk it simply means “unknown”. It is further presumed that the output of “true” random number generators are uncorrelated and unbiased, hence “random” means “unpredictable”. Note that any correlation or bias would make them “predictable” — at least potentially.

You know coin flipping is not really random. I can flip a coin and make it come up heads everytime or any other pattern I can imagine.

Yes, so can a lot of stage magicians but it takes a skill most people haven’t bothered to acquire.

I must have studied too much probability

Really? Where? Most stat courses only briefly touch on the subject. To the frequentist it’s simply counting although what probability really means is at times hotly debated. No need to go over the entire history here but statistics is coming full cycle back to its roots — in large part because of the efforts of E. T. Jaynes. One of his books “Probability Theory: The Logic of Science (Vol 1)” has been released posthumously and is available through Amazon and elsewhere. A good, fairly easy read.

Though math is my weak point (let’s not even use the term Calculus… shiver!), I find the show interesting for it’s introducing me to various ideas and concepts in the science of Mathematics.

J/P=?

Doesn’t make me smarter than any who picked the wrong one, just a different flavour of geek.

The coin-flipping example always does people’s heads in, due to random probability being subject to so much fuzzy magical thinking. People imagine the universe seeks balance in all things, I think, and pushes to make things neat and tidy.

Sorry, but the universe is a big, glorious mess, and the maid exists only in your mind.

This reminds me of many articles on “how to catch a student faking data”. I usually fall over laughing as I look at the analyses which reveal a decidedly “intelligent design”. Well – not too intelligent obviously if the student believes they know oh so much that they’ll get away with it. On the down side, in many (most?) cases it’s difficult to set up to check on all students’ experimental results. Sometimes the result is not so bad – it is obvious that the student has real(istic) data and that it is incorrect assumptions about the measurement errors which are revealed in the analysis (honest students often assign too large an error).