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Tuesday, August 23, 2011



Steve Allen is remembered mostly as a comedian and a musician. So it may come as a surprise to you (as it did to me) that he also did some very serious thinking.

“Dumbth”, published by Steve Allen in 1991, is about the dumbing down of America which has been gradually getting worse for the last 50+ years. His introduction describes the phenomenon very well. 

 He blames poor television programming for much of it. Much of what he says are things that we, who are over the age of 50, are familiar with and agree with, but he verbalizes, and lists for the record…

 He decries the educational system for teaching facts without teaching students how to think and reason, but he also blames the parents for not taking an active part in their children’s education. Oddly enough, he does not blame the president for the entire mess, even though he does take a few choice pot shots at president Reagan.

 He then lists 81 rules to improve.  These are suggestions that individuals can use to improve their own situation by sharpening their ability to reason, and do not require an act of congress.

recommended reading:

and along these same lines you may find interesting:

And yet another: Refering to Rule 81

 and one more:

Saturday, August 20, 2011

From Zero to Inifinity in a Flash

Infinity is a very difficult concept to wrap the brain around. When I was taking Integral Calculus (which I nearly failed) we would often have to integrate from zero to infinity without so much as batting an eyelash. We take zero for granted yet it is different from any other finite number. For example any number multiplied by zero is zero, and any number divided by zero is infinity.

Infinity, on the other hand has its own special qualities. It is not a number at all, but is unbounded. It has no limit. Pick any large number such as the national debt and divide it by infinity and the result is zero. Infinity reduces anything to zero by comparison.

A baby compared to me is very small, but compared to the earth I am reduced to an invisible dot. And compared to the solar system the earth is a very small dot. The solar system compared to our galaxy is a tiny spec and our galaxy is infinitesimal compared to our universe. And as difficult as it may seem to imagine, our universe becomes nothing when compared to infinity. Infinity is such a difficult concept to grasp that it drove more than one mathematican out of his mind.

George Cantor, a Jewish mathematician, thought that he would be able to comprehend God  (the Aleph), the infinite creator of the universe, if he could only understand infinity. He lost his mind, but he developed a whole new branch of mathematics that we now study as Set Theory.

Recommended reading:
“The Mystery of the Aleph”, by Amir D. Aczel
Mathematics, the Kabbalah, and the Search for Infinity.

Monday, August 1, 2011



The Nature of Gravity

 Have you ever been to carnival where there is a ride that is a revolving cylinder? It holds about 20 people, who walk in to it and arrange themselves around the perimeter.

 Then when the carnie throws the switch the cylinder begins to rotate and as it picks up speed the riders  feel themselves being pressed against the wall of the cylinder. Then the carnie lowers the platform they were standing on, and there they are suspended with nothing to hold them but the centrifugal force of the turning cylinder. Demonstrating Newton’s 1st law of motion, objects at rest tend to stay at rest and objects in motion tend to stay in motion until an outside force acts to change its speed or direction. In this case it is the friction of the rider’s feet with the floor that starts them moving, and it is the wall of the cylinder that forces them to change direction.

It is the same force at work in the centrifuge in chemistry class.

 Often times, in science we make models to help understand and explain difficult ideas. We make models of DNA, Atoms, Crystals, etc. we also make models of large things like the solar system, globes of the earth and so on.

 Understanding gravity involves understanding our 4 dimensional universe. Since we live in a 3 dimensional world, a concept of the 4th dimension is difficult because we have no perception of it. So it helps to make a model that is scaled down by one dimension, and our model becomes a 2dimensional world in a 3 dimensional universe.

 The 2 dimensional world might be the surface of a trampoline with 2D people that look like coins. And the massive object representing the world might be a large lead sphere. When we place the sphere on the trampoline, it caused the surface of the trampoline to bend down into the 3rd dimension. The people (coins) being 2dimensional, have no perception of the 3rd dimension, but they feel themselves being drawn to the sphere. They conclude that the sphere has a mysterious force called gravity that draws them to it.

 But we, being 3dimensional, can see that the sphere has no mysterious force, but rather, the coins are sliding down the slope of their 2 dimensional space ( the curved surface of the trampoline). Of course the problem with this model is that it requires the earth’s gravity to make it work. If we take our model up to the International Space Station (ISS), setup the trampoline, put the coins on it, and put the massive sphere on it, nothing happens, because there is no gravity.

Remembering the carnival ride, we can cause the ISS to rotate by attaching a couple of small jet engines. The resulting centripetal force causes the objects inside to be drawn to the sides of the ISS. And now we find that our model is working just like it did down on earth.    

So now we scale everything back up by one dimension, and we have a rotating 4 dimensional universe causing massive objects to warp the 3 dimensional space into the 4th dimension, which in turn causes smaller massive objects, like people and rocks, to be drawn towards the large massive objects.

The link below shows a rotating 4D cube.