Imaginary Numbers: What the heck is it really?? How can a number be imaginary?? Well friends, let me tell you, on this Halloween Night, they are real. There are INDEED numbers which are considered imaginary. They have very special properties which do not exactly line up with what one might consider the "conventional" theory of mathematics, but is now so embedded in it, that it matches theory to a T. Quantum Mechanics cannot be described without imaginary numbers. So what are they?? Well, imagine this. What is a square root? A square root is a number which, when multiplied by itself, equals another number, it's square. So, the square root of 4 is 2. 2 multiplied by 2 is 4. The square root of 16 is 4. 4x4 = 16. Numbers whose square roots are a whole number are referred to as perfect squares. Now, let's consider this. Consider negative four. -4 times -4 = 16. So, the square root of 16 can be either positive or negative four. For the most part we forget the negative, since it's usually most practical to use the positive number. However, it does lead to a complex situation, there are no square roots for negative numbers??
That's kind of a pain for lots of calculations, and actually limits the boundaries of physics and mathematics. So, they came up with a solution. It's an imaginary number, called i. i stands for imaginary. Now, if you square i, you get negative 1, the square root of -1 is i. This allows us to have the square root of a negative number, which happens from time to time in calculations. What does that mean in reality? Well, there are what are known as real numbers, any number, positive or negative with any number of decimal points, finite or infinite. Then we have imagiary numbers, which gives us literally infinitely more numbers. It's also possible to have a 2-D plot of numbers, real on the so-called x-axis, and imaginary numbers on the y-axis, which means you can now plot a combination of these numbers. So there you go for Halloween, some spooky imaginary numbers.
Next up: multiple infinities. Infinity is the biggest thing ever right? Wrong. Turns out, there are different infinities, each bigger than the next. This was in the mix for hundreds of years, but was finally set in place by Georg Cantor, in the late 1800's. So can it be? Well, all of these talks of multiple infinities starts in a field of mathematics called Set Theory. I actually took a Set Theory course in college, just to understand how this whole multiple infinities thing works. Let me tell you, while being very, very exciting, at the same time, it is very very complicated, and tedious. So tedious and literally insane that its father, the aforementioned Georg Cantor, went insane several times, spending much of his later life in insane asylums. He also had many detractors, including the incredible Henri Poincare, who said that his contributions were a disease infecting the discipline of mathematics. Unfortunately, Cantor turned out to be right. I think Cantor and Kurt Godel, with his incompleteness theorem, were like the two most famous hackers of mathematics. They just take this wonderfully, painstakingly logical structure, hack inside, and just bring it to the ground, with the implications of what they discovered using the rules of mathematics.
So let's first simply consider integers, i.e. whole numbers, no decimals, negative and positive, so in the positive direction we have 1,2,3,4.... on and on, and in the negative direction we have -1, -2, -3, -4...and on it goes. So there are an infinite number of integers, right? However, we have developed a system where theoretically, given enough time and resources, you could count them all right? We know how to order them, and how to count them. This is what is referred to countably infinite. You know that after 100,000, the next number is 100,001. And on and on. Now next, we need to consider all the numbers which have decimals. Even just 1.1, 1.2, 1.11, 1.12, numbers which are referred to as rational numbers, as in having a repeatability to their decimals, feels a whole lot bigger a whole lot faster. Now let's consider irrational numbers, like pi, and e, and any other weird number which repeats on and on in no pattern whatsoever. These are referred to uncountably infinite, meaning that there is literally no way to count them all. And, if you took each number like this, and put them inside of a bracket, like [1.2123124124124, 223.2342938414234....,43.1234124,....] this is referred to as a SET of numbers. Now, the SET of irrational numbers simply between 0 and 1, is more vast than all the countable integers, and this is how we arrive at different levels of infinity. So, every time you think you have a bead on the universe, it will throw you a curveball and send you flying out in some other direction believe me.
There is an AMAZING book which covers this in great detail, and is unbelievably readable. It's called Everything and More, A Compact History of Infinity by David Foster Wallace, my favorite author. Do yourself a favor and grab this book. You'll be better off for it. Go to the library, or click this paragraph to head over to amazon to get it. Don't worry, I'm not making anything off it, just a great recommendation.
Back in 2004, CERN received a statue of Shiva, doing his Cosmic Dance, which was given to parallel the cosmic dance of the universe, being studied at CERN. It also has a long standing history with India and its scientists, so the Indian government gave the statue as a gift. Here's a link to the article where they received the statue.
There have always been occultish rumors going on at CERN. Everyone is of course afraid of them creating black holes "accidentally", or searching for the Higgs Boson, aka. the "God Particle". So, some of the people there performed some sort of "Satanic Ritual" which involved the alleged human sacrifice of a woman, all caught on tape for your viewing pleasure. It was actually a big scandal for CERN, but, un(?)fortunately, most likely fake. Up to you to decide. Scientists can sometimes have a morbid sense of humor, and probably don't mind feeding into the spooky rumors surrounding CERN in general. However, as of right now, noone knows who did it, or why, or if it was a hoax or what. It's probably fake though guys...or is it?? Here's the full video of the "ritualistic sacrifice" at CERN.
So another asteroid came uncomfortably close to Earth, didn't hit, and was known to be passing by, by SCOUT, our current method of detecting as many near earth objects as possible. One day guys...really, shouldn't this be the priority for our species? No? This and electric cars? Getting off gas and MAKING SURE SOMETHING DOESN'T CRASH INTO THE EARTH!?
Speaking of which, I had the opportunity to fly to Mexico this October, and had the opportunity to fly over an ENORMOUS crater from an asteroid impact with Earth, well before human civilzation. This was not the Chicxulub crater, you know the one which was the size of Staten Island which was allegedly responsible for the extinction event which killed the Dinosaurs 66 million years ago. It was an incredible thing to see, and also that it looks like it might have slid after it hit, and how the people in this region just built right up to the crater and then no more, leaving it untouched.
I also ventured out to the Vanderbilt Museum out here in Centerport on marvelous Long Island, NY, to check out a Halloween Planetarium laser show, and was able to touch and check out an asteroid chunk which was allegedly 4.6 billion years old. Wait I thought the earth was only 5000 years old.......Happy Halloween friends.