Math for Dummies part 2

This maths lesson is a little bit harder than the first one, but it is more powerful. It is also the basis for all modern cryptography. A child of 12 or 13 who is good with multiplication and division can understand it. Let's begin.

Definitions: A prime number is a whole number that is divisible only by itself and the number 1. The number 1 is not defined as being prime. A number is divisible by another number if the resulting fraction is another whole number.

Theorem: There are an infinite number of prime numbers.

Proof: Proving that there are an infinite number of something is kind of hard. Let's assume the opposite and see if we can disprove it. So if we can disprove that there are a finite (or limited) amount of prime numbers, we have shown there must be an infinite supply of prime numbers.

Given that we have assumed there is a limited supply of prime numbers, we can easily list them. So we have a list of prime numbers for which we will use alphabetic symbols instead of the actual numbers:

a, b, c, d, e, f

There could easily be more, but for the time being we just list these. Now the math gets a little tricky, but just get your pen and paper and we'll be fine.

Assuming these list of prime numbers is complete, let's find out if there could be any more numbers that fit a prime definition that isn't in this list. Let's try a trick where we multiply all the prime numbers together and then add 1 to them:

(a * b * c * d * e * f) + 1

This resulting number cannot be divisible by any previous prime number. Any previous prime number in our list would always have a remainer of 1 (that's why we add 1 in there). It also cannot be divisibly by another other smaller number -- why is that?

Notice that any number that is not prime would be divisible by some other smaller numbers. The resulting divisors would either be prime themselves or not. If not, they could be divided again. Eventually, you will be left with a bunch of divisors that are all prime! Let's try this example with the number 20:

20 is divisible by 10 and 5. Clearly 5 is prime. But 10 is not.
10 is divisible by 5 and 2. Clearly 5 and 2 are prime.

So, any number that is prime is divisible by only itself and 1. Any non-prime whole number is divisible by (eventually) a series of primes.

So, backtracking a little bit to our number again:

(a * b * c * d * e * f) + 1

This made up number is not divisible by any of a, b, c, d, e, or f, and cannot be divided by any smaller number (because those smaller numbers would be in turn divisible by a, b, c, d, e, or f). So this number we invented is another prime number!

What we have shown is that if we believe we have a comprehensive list of prime numbers (no matter how long a list), then we can always generate a larger number that is also prime!

Clearly, there are an infinite number of primes.

Did you get it?

When the Levees Break

As Led Zeppelin said, "Cryin' won't help ya, prayin' won't do you no good. When the levees break, mama you got to move."

I watched Spike Lee's When the Levees Broke, a Tragedy in Four Acts

I thought it was quite good and certainly not as bad as anything that Michael Moore has produced. Unfortunately, people are quite stupid and idiotic. Put them in a position of stress and survival, and their eyes roll into the back of their heads and their brains (what little they have and use) shut down. I have some serious issues with the documentary:

1. If you did not leave New Orleans before Katrina hit, then I have no shred of sympathy for your plight
2. The levees were not bombed, you dumb fucking idiots
3. There are a lot of stupid, dumb, idiot politicians and bureaucrats who deserve a lashing. Nagin, Blanco, Brown, Chertoff, Bushes, and on and on. But if you live in Lousiana, you should be used to it. Louisiana politics are not just merely crooked or shadowy, they're downright corrupt. It's the political equivalent of Nigeria. If you don't like it, move or vote.
4. "I grew up here and my mommy grew up here and her grandmother grew up here..." As the New Orleans natives found out, everything is impermanent. Your life is transient, your house is not permanent -- as evidenced, the whole city of New Orleans was impermanent. It is better to remove attachments to things that are illusions (like cities, houses, family, people) and end your suffering. If you like suffering and attachment, then please, by all means, go ahead and suffer. It made some interesting TV at least.

Dirty, filthy, rotten blues

I've been exploring Pandora as noted in an earlier post. You will need to download a web plugin (you probably already have it), and sign up with your age and zip code (supposedly for music licensing issues), but it is totally free. They want you to buy the music that you like, but I ain't buying shit.

Well, now I have perfected most of my radio stations and I can share them. I have a generic "Classic Rock" station which is seeded with the usual suspects, Leddy, Jimi, Pearl, etc. If you need a translation, man, then, like, open your mind and go cosmic, man. Do some research -- smoke some dope, drop some acid, take some DMT, do some Kundalini yoga, go to Vietnam and get back to me, man.

This site is so good, I didn't even enter the group Cream, and it found Spoonful all by itself without asking. I of course added Cream, a grievous oversight.

I have a "Suicidal White Male" station, built mainly off the likes of Roger Waters, Coldplay and Peter Gabriel. I don't listen to it much, but it's there if I need to be down.

I've also got a "70's guitar solo" station, seeded with the best of Leddy, Jimi, Cream, etc.

Then there is the "Dirty Blues" station. And I must say, this is some of the best blues I have had the particular joy of listening to. In Los Angeles, there is a radio show called Nothin' but the blues. It is, unfortunately, pathetic because:

1. Oh, you want to listen during the week? Fuck you.
2. Oh, you want to hear some dirty, filthy blues? Sorry, it's not commercial. This is a jazz station. Nobody likes dirty blues, you disgusting mess.
3. Oh, you want to hear music? Sorry, we run 45 minutes of commercials per hour. We run money-grubbing begging sessions 50 weeks out of the year
4. Oh, you want to hear something new and unusual that you never heard of? Fuck you, this is a radio station with a 12 song playlist. We only play 25 minutes of music per show anyway, so fuck off.

With Pandora, I can listen to the world's greatest, filthiest, most bluesome blues there is.

I recently heard the one-two punch of Once I had a Woman followed by The Sky is Cryin' and I just about wet my pants, the seat, and the floor.

You want good blues? Turn off the radio. Put your vinyl down. Check out my Dirty Blues station here.

Math for dummies part 1

I was recently in the elevator, and there were two others besides myself in there. There were two floor buttons pressed. For the time being, assume that we are going up and there are only two floors remaining. I smiled as I quickly deduced that at least two of us would get off at the same floor.

I am starting this series because there are some extremely simple mathematical concepts that are actually quite profound. These are some of the fundamental theorems of math, but they can be understood by any 7 year old. It is a shame that 7 year olds don't get taught this stuff. It's simply bril.

Pigeon Hole theorem:

"If there are N pigeons and N-1 pigeonholes, then there must be at least one pigeonhole with more than one pigeon."

Proof:

Imagine, you have a certain amount of pigeons on your roof. You raise them for companionship, for transporting important missives via courier pigeon, and (of course), for food. Now, you have, let's say, 4 pigeons. Alas, you only have 3 pigeon holes. Not realising the impact of the this mathematical model and needing to house your pigeons in pigeonholes, you stuff one pigeon in hole 1.

You now have three pigeons and two empty pigeonholes. You cannot put another pigeon in pigeonhole 1 unless you want to end this proof prematurely. Besides, you have empty holes to use. So you stuff a pigeon in hole 2.

Now you have two pigeons and one emtpy pigeonhole. So you stuff a pigeon in hole 3.

Now you have one pigeon and no empty pigeonholes. This last pigeon must become a roommate to an existing pigeon filling an existing pigeonhole.

Easy.