Tuesday, September 22, 2015

Zen and the Art of Squirrel - the Dangers of Patterns

Earlier I discussed how you have to watch for patterns.  Patterns are a wonderful thing to understand.  Patterns can give you an idea of what you are going to be expecting and how best to deal with it.

Patterns are not always that great.

Another odd effect of some of these brain monkeys is that sometimes I find it very easy to perceive patterns.  Unfortunately not all of the perceived patterns are actually there.

Oh, I did mention that this is the part where we start to be acting crazy up in here?

Nope,  forgot to mention that, sorry, but yeah, this is where we start sounding like we are actually nuts.

I look at numbers.  I have always found them enjoyable.  I do not have the kind of skills that allow me to look at a Sudoku and solve it in one glance, but I am very quick at solving them.

I have always loved certain patterns of numbers.  Like the Fibonacci sequence.

1,1,2,3,5,8,13,21,34,55,89,144….

It is kind of cool when you see how many different places that one shows up in nature.

For a lot of my life I have been fascinated by prime numbers.

I would sit on a swing set thinking about prime numbers.

I would lie awake in bed thinking about prime numbers.

I would write programs to calculate prime numbers.

What is so fascinating about prime numbers anyway?  Well, there is no easily discernible pattern, although there looks like there should be one.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Two is an anomaly, it is the only one of the group that is even.  It also eliminates all other even numbers from consideration, which made writing a program to calculate primes much easier, I only had to consider odd numbers.

If you look at the spacing of the numbers it goes…

..1, 2, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 4….

Look at that, there is a…

1,
2,2
4,2,4
6,2,6
Gibberish…

Ok, never mind no pattern there….

Lets look at these numbers in binary

10
11
101
111
1011
1101
10001
10011
10111
11101
11111
100101
101001
101011
101111
110101
111011
111101
1000011
1000111
1001001
1001111
1010011
1011001
1100001

Well that is certainly interesting, and much easier to see than when you are lying in bed just imagining the numbers.  There are a few patterns that pop out, the wanderings of the zero and the fillings of the ones in a few sequences.  There is one pattern that looks like it will always work out.

And it is amazingly simple to see.

Any prime number of ones is the binary representation of a prime number.

11 = 3
111 = 7
1111, 4 ones, should not be prime, oh yeah, 15
11111 = 31
11111111111111111111111111111 (29 ones in a row)

536870911

Oh wait, what…

Not prime….

233*1103*2089

Another dead end for understanding that looks great until you get past where you can do the calculations in your head.

These are not the only things that show patterns that may or may not be there.  I often look at the positioning of earthquakes and where they are happening on a map and I have predicted several.  Although, predicting an earthquake in Chile gives you a 10% chance of success on any given day.

Patterns are interesting, but they are also dangerous.

Gambling machines run by patterns, to an extent, if you only sat and watched long enough you would start to see them.

I don’t have that much time, and I think that gambling is a waste of time.

Basically I consider it a tax on hope.

The cycles of depression and mania have patterns too, but they are not always the same.  You cannot assume that if you are up today you will be down tomorrow.  Or if you are down tomorrow, you will be up the next day. 

You will have a better guide, but that guide will not be 100%.

Patterns can be dangerous.

You have been warned.



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