Tetration

As mentioned in the last post, 2↑↑2=4, but what does the ↑↑ symbol mean? ↑↑ is a symbol (there are many notation systems, like ^^) for the operation known as tetration. Anyone with a basic knowledge of mathematics will know that multiplication is just repeated addition, and that a*b is the same as adding a to itself b times. Exponentiation is similar, a^b is just a multiplied by itself b times. Tetration, now, is an extension of these. a↑↑b is a to the power of itself b times, so 3↑↑3=3^3^3. As you can probably tell, tetration makes big numbers quickly, and isn’t supported by many calculating devises, or at least not for very long. Here’s some tetration involving 2:

2^^1=2

2^^2=4

2^^3=16

2^^4=65536

2^^5=2^65536≈2*10^19728

And some involving 3:

3^^1=3

3^^2=27

3^^3=7625597484987

3^^4=3^7625597484987≈10^10^10^1.01

Countable and Uncountable Infinity

Hold on to your pants, this might get interesting here. What if I told you that some types of infinity are bigger than other types of infinity? It’s true. Just think about it for a second. The number of positive whole numbers, or natural numbers, is really big, infinite actually, because for the largest number you can think of I can just add one and there’s a bigger number. The set of natural numbers is what’s called “countably infinite” and any set of numbers that can be paired with the set of natural numbers is also considered “countably infinite”. Theoretically, any countable set can have its entire contents listed if the counter were given enough time. However, the set of all real numbers is not countably infinite because for every two values in the set there are infinitely many values between them. In fact, the set of all numbers between 0 and 1 is greater than the set of all natural numbers, that’s what uncountability does.

Double Post: Subsidies and the Prisoner’s Dilemma

Again, I’m sorry for missing a day, but I’ll do some related topics in today’s double post: Subsidies and the Prisoner’s Dilemma.

Subsidies are support income provided by the government to certain companies, namely agriculture and energy providers. In the past, these sectors were weak and needed support from their companies otherwise life in general would collapse (no food, no electricity, no fuel, etc.). I’m not going to argue that subsidies are not needed, I’m no expert in economics and it’s not my place to do so, but some subsidies, such as those that pay farmers not to farm (which I’ll get to in a bit because it has a little to do with the next topic) are counter-intuitive.

So what does paying farmers not to farm have to do with the Prisoner’s Dilemma? First we have to know what the Prisoner’s Dilemma is. Say we take two prisoners, Alvin and Bruce, who have together committed a crime (the details aren’t exactly important). If either one sells out the other, and the other confesses, the one who confessed gets one year in prison while the one who betrayed gets off free, if both betray each other, both will get three months in prison, and if both confess, both get only one month in prison. It’s, individually, in both Alvin’s and Bruce’s to betray, but it’s in their collective interest if they both confess. We see something similar in raw food prices. If a farmer produce large amounts of food, that food will be worth less due to inflation, than it would be if they produced less, but if farmer produce less food they are at the whim of the markets and could get in trouble due to other farmers potentially producing more food and driving prices down. That’s the farmer’s dilemma, and that’s where subsidies come in.

Double Post: Exponential growth and “free energy”

Okay, since I missed yesterday, here’s two fun facts. Exponential growth and “free energy”

First, exponential growth. Say you have a piece of paper a millimeter thick (yes, I realize paper isn’t normally that thick, but the point is the same). If you fold the paper in half (assuming there’s no air in the fold) you will have a piece of paper two millimeters thick. Folding the paper again will give 4 millimeters, then 8, then 16, and so on. This process, the increase by a certain ratio over each fixed period of time, is exponential growth, but only if the ratio is greater than 1 (in this case, the ratio is 2). Now let’s take the area of the same paper starting with, say, 10 square centimeters. After one fold the area of the paper is now 5 square centimeters, after another it’s 2.5, then 1.25, and so on again. This process, which is the same as with thickness, but with a ratio between 0 and 1 (in this case 1/2) is exponential decay.

Finally, free energy. That’s be great right? But that’s where we get to free energy suppression. The governments, oil and gas companies, and scientific communities of the world don’t want you to know that there are machines that can harvest energy from perpetual motion and zero-point energy. But those of you versed in physics will know that there is no such thing as a “perpetual motion machine” and that zero-point energy cannot be “harvested”. But that’s where suppression comes in. If you say those things then either you have been manipulated by the scientific establishment into believing them, or you are actively participating in the cover-up. One popular free energy concept is the “motionless electromagnetic generator” which harnesses vacuum energy to provide power without any input into the generator itself. Its inventor, Dr. Thomas E. Bearden, stated in 2001 that it would be in production in a year. I haven’t seen any motionless electromagnetic generator, likely because, even in 2012, ten years behind schedule, no working MEG has been built. It also doesn’t help that “Dr.” Bearden holds a Ph.D., which he bought, from one Trinity College and University, which has “no building, campus, faculty, or president, and run from a post office box in Sioux Falls, South Dakota”
PS: I’d like to note, although it may be obvious, that I in no way endorse the “free energy suppression” conspiracy theory because that’s exactly what it is, a pseudo-scientific conspiracy theory.