Room with a View

Why put a telescope into space?

It is a simple question, but it also has a simple answer.

The atmosphere.

It is the reason why stars "twinkle". The best way to explain this is also simple. Dive into a swimming pool an look up. What you see is a distorted version of what you know to be "up there" because the water swirls and distorts the image.

Earth's atmosphere is just like that, the only differences being that it is a lot less dense, but far "deeper".

A similar effect can be seen in large cities, especially New York and San Francisco. The normal lights of the night can be seen to be twinkling just like the stars do. The only difference here is that the view is horizontal. The twinkling is due to pollution this time.

So, we sent the Hubble Space Telescope into orbit to capture color images (of the Crab Nebula) like THIS:

The Atom - Part Four

WARNING! THIS POST CAN BE BAD FOR YOUR HEALTH!

Now we had a real model of the atom to work with. All that was needed now was a mathematical formalism to describe it.

Independently Werner Heisenberg and Erwin Shrodinger worked it out, the former's was called Quantum Mechanics, the latter, Matrix Mechanics. They were exactly equivalent. Both worked the same way, one using differential operators, the other, matrices.

The guys "married" the two theories and came up with the single most important formula in physics, surpassing even Einstein's E = mc2.

The reason why the Shrodinger Equation is not widely well-known is because the pearl of wisdom in it is buried underneath the scary-looking math.

Here it is, plus the solution:




For those interested, it is an "EigenValue" equation. The left-hand side of the top line simply says, perform the calculation on Psi (the strange "Y" like letter), and you get a value for the energy of the particle of mass m on the right.

The V(x) is the potential energy, only applicable in electric fields (technically, gravitational fields also).

If we suppose the particle is clear of any such fields, V(x) is zero and the solution drops out on the bottom line.

That bottom expression is the simple equation of a travelling wave, ie the particle itself expressed mathematically.

The letter "i" is the square root of -1.

All of quantum mechanics can be described by this single equation.

Twigs

This little park and lake is 5 minutes away from my Liverpool place. I squeezed off about 15 shots, but this one turned out to be a stormer.

The composition was perfect, the sky exactly the right color (no polarizing filter) and water as calm as a millpond.

When we got up on Wednesday, I instinctively knew conditions were perfect, so I dragged Yuko out of bed at 10 am and we walked the short distance.

It was well worth it.

Primary

I have no idea where the name "prime" came from, but.... there are certain numbers that are "odd".

These numbers are whole numbers that cannot be devised.

For instance, 5. The only way you can successfully divide 5 by anything is by 1 and 5.

Same with 7. Same with 31.

These are called "Prime Numbers" and no-one knows where they came from.

We do know that there are infinitely many of them. It is easy to prove. Take any number, multiply it by all the numbers below it and then add 1. Instant prime number.

The problem was, is, always has been, and wioll haven be, however high the prime number, which one is next?

There have been many theorems to calculate the "distribution" of the primes. One of the greatest books ever to confront this problem was "The Lore of the Primes", a book long since out of print.

There are several formulae to predict the "average" distribution, but NO-ONE has ever been able to predict "the next one".

A subject of long fascination for mathematicians and non-mathematicians alike.

Interestingly, the subject has become under increasing scrutiny from the US government, as a means to ensure security. It's name has become "Public Key Cryptography" - a name which basically means "you can't decode this".

It's basis is simple: Take two really large prime numbers (at least 99 digits each)and multiply them.

The result is a number at least 200 digits long, but is only divisible by the two numbers you first thought of.

To find out those first two numbers, it would require 15 billion Cray XM-P computers working at twice the age of the Universe at triple speed with double entendres.

To say the least, if not less.