I Love You , Dad

This one is for my father, who introduced me to Mike Oldfield when I was ten and Tubular Bells II came out. I know you read this.

He got me TB I after I enjoyed TB II, and when when TB III came out I was entranced, and took it across the world with me.

This video is a very small pastiche of TB III.

"And the Man in the Rain picked up his bag of secrets, and journeyed up the mountainside, Far Above the Clouds, and nothing was ever heard of him again, except for the sound of Tube - You - Lah - Bells "....





The sight of Big Ben at the end is no accident, of course. Mr Oldfield wanted the last clang to be exactly at the same time as Big Ben chimed Ten ( Big Ben is the name of the Bell in the tower, not the tower!)

Mike Oldfield has such a distinctive style of guitar playing that I can now tell if it is him or not just by listening. The reason is that he uses his fingers sideways, not parallel, to the guitar arm. It is quite unique and no-one else does it.

And all this thanks to my Father, Yoshi.

Thank You Dad!

Gedanken for the Memory

A thought experiment.

A black hole is a place where light cannot escape from, that is, the escape velocity exceeds the speed of light.

But from the equations, there is a distance from the center of the Black Hole where light can "orbit". Light can literally "flow" around the Black Hole just like any other object in orbit.

Consider this: What would happen if a circular space station around this black hole were constructed at about the same distance as this critical distance?

What would happen?

More elaboration is needed. Ignoring any engineering problems, or tidal effects (the former can be conquered over time, the latter by finding an extremely large black hole), you will have this: a hoop-shaped space station with a black hole at it's center. The radius of this "hoop" is the same radius as the critical radius for light. That is, light at this radius neither enters or leaves the black hole, it just circulates around it.

And the space station is built around this critical radius.

The question is.....if you were "on" this exact critical radius, which is now inside the space station, what would you see?

Two things are clear:

First, the space station will look straight, and not curved in any way.

Second, since the light goes around the black hole and will actually hit you on the back of your head, the REAL effect (not illusion) will be that at some distance away along the "straight" corridor, you really will be looking at the back of your own head. Or rather, an infinite many of them at regularly spaced intervals.

It is a weird, but real, effect, caused by the equations of General Relativity.

Here is the rub, and a question for which I have no answer:

Knowing that the space station is circular, yet seen as straight, what would happen if a broomstick was slowly pointed forward along the "straight" corridor? What would you see as you pushed the long stick further out from you?

And the Winner is.....

Having recently taken another trip to Europe to personally oversee how my SSA project is continuing to grow in popularity, it prompts me to list some other inventions, that maybe didn't quite make it thus far.

1. The polystyrene anchor

2. The inflatable dartboard

3. Battery powered battery charger

4. Helicopter ejector seat

5. Re-usuable bathroom tissue

6. Black Highlighter

7. Fire-proof matches

8. Waterproof sponges

9. Solar-powered torch

10. Glow in the dark combat uniform

Permission to laugh is granted.


One of these ten is a viable invention that actually has a use (and has been made).

Can you guess which one?

Inifinities.....

...come in all shapes and sizes.

We all know what infinity is, don't we? Or do we?

Sure we do! It's where something goes on forever, never stopping, like the number of numbers. There is no highest number because they go on forever, right? And the decimal portion of Pi goes on forever, does it not? It begins 3.1415926... and never stops and never repeats.

We are so used to this concept of "infinity" that we are almost blase about it.

Allow enlightenment to take place.....

Suppose there is a hotel with an inifinite number of rooms, all occupied by guests.

What does the owner do when a new guest arrives? Why, he puts guest 1 in room 2, guest 2 in room 3, guest 3 in room 4....and so on up to infinity, leaving room 1 empty.

What does the owner do when an infinite number of new guests arrive? This one requires a little more thought.....

Simple, really. He puts guest 1 in room 2, guest 2 in room 4, guest 3 in room 6 and so on up to infinity, leaving an infinite number of "holes" ie vacant odd-numbered rooms. All guests are now occupying rooms. Does that mean the owner somehow now has 2 times an inifinite number of rooms? NO! he still has an infinite number of rooms with a guest in each!

It gets even stranger. Georg Cantor proved that there is more than one "type" of infinity. This guy was involved in set theory, the theory of certain classes of objects, such as the set of cars, the set of brown cars, the set of brown cars with at least 2 wheels, etc.

Sometimes sets can be inside each other, sometimes not. For instance, the set of Green Cars is different from the set of Brown cars, but above the third set "the set of brown cars with at least 2 wheels" is contained inside set 2 "the set of brown cars" AND set 1 "the set of cars".

Cantor took this a little further and argued that sets sometimes can contain themselves. For instance, the set of cars is not a car itself, but the set of all sets IS a set, so it is contained within itself. These are called "self-swallowing" sets. Another example is the set of ALL things that are not brown cars.

So, You have ordinary sets eg "the set of brown cars" which are not members of themselves, and self-swallowing sets eg "the set of all sets".

The question arises: Is the set of all ordinary sets ordinary or self-swallowing?

Inspection shows it is neither. Try it! Assume it is an ordinary set.

So, the set of all ordinary sets belongs to neither group.

The argument put forward above is called the "diagonal" argument for reasons which are not at all clear. Here comes Cantor's same argument, but in the form he proposed.

To begin, suppose we wish to count all numbers. Not just integers such as 1, 2, 3 etc, but ALL numbers, including those with decimals. Well, one of them is pi = 3.1415926.... Another is e = 2.718281828....... and ALL the others in between and around , such 9.80665, and 5.5, 100.99999 and 2.9979. Suppose we list them all in order. For simplicity, let's just consider all those less than 1.

It would look something like

0.1111111111111111....>>>> to infinity
0.2222222222222222....>>>> to infinity
0.3333333333333333....>>>> to infinity....

and suppose our table lists them ALL, one after the other. Obviously there are an infinite number. There is a proof that there is at least one number NOT in our table of the infinitely many "numbers".

It goes like this:

Take the first number, 0.1111111111111.....and change the first column to a "2" creating 0.2111111111111....

Take the second number, 0.222222222222.... and change the SECOND column to a "3" creating 0.2322222222222....

Do the same with the third number. So we will have

0.2111111111111111....>>>> to infinity
0.2322222222222222....>>>> to infinity
0.3343333333333333....>>>> to infinity....

where I have changed the third column in the third number to a "4". Now look at the diagonal. It says 0.234.......to infinity.

It is clear that this number is NOT in our list, as the first column is different from number 1, the second is different for number 2, and so on up to infinity. For any "n", the digit in column n is different from the nth digit of the number "n", so our "made-up" number, derived from adding 1 to the diagonal is absolutely NOT in the list.

But didn't we say that our list was of ALL the numbers all the way to infinity?

The reasoning is that there MUST be another "kind" of inifinity somehow "bigger" than the one we had. In fact, there is not only "one" different kind of infinity, but an infinite many of them, each, in some abstract sense, "bigger" than the last.

This result is true and has had many implications for math, especially for that man Godel again, who said that not everything is proveable within the system. This is a paraphrase of that theorem.

Age-old Debate

WARNING! VERY SUBJECTIVE POST! Comments welcome!

Tonight members of the UK Parliament will vote on a new Law, or rather a change in an existing one.

At the time of writing, the maximum legal term allowed for an abortion is 24 weeks. If the embryo ("foetus" to abortionists, "unborn child" for anti-abortionists) is older than 24 weeks, it is illegal to perform an abortion. Tonight it will be decided whether to lower this to 20 weeks.

The reasoning behind this is cited as improvements in embryo survival rate in premature children. Although this data refers to embryos born after 24 weeks, it is decided tonight whether it may apply to embryos between 20 and 24 weeks.

The Catholic Church's stand on this is as it has always been: "Abortion is murder". Other bodies of people object on moral ground. The question remains: After how many weeks does it become wrong, if ever or never?

Facts aside, there is another viewpoint other than "Is it right or wrong, and if wrong, after how many weeks?".

It is this:

For nine months, the embryo resides in another person's body, feeding off that body as the "host" ingests food for it to grow and survive upon.

It may sound a callous way of putting it, but essentially these are the facts as to what is happening.

I can even think of a name for the embryo during those stages.

A parasite.

What do you do with parasites?

Squish them .

Just For Laughs Part One

This is the sort of thing that makes me laugh.......

A Sequence of Events

A sequence is a succession of numbers that follow on from one another.

The simplest is

1, 2, 3, 4, 5, 6.....

Where all you do to get the next is add 1 to the last.

2, 4, 6, 8, 10....

is similar, in that you add 2 to the last one.

1, 3, 5, 7, 9....

is also similar, adding 2, but starting at a different number.

So much for addition.

How about 1, 2, 2, 4, 8, 16, 32....

This one is where you multiply the previous two to get the next.

Or even,

1, 2, 3, 5, 8, 13, 21, ......

where you add the previous 2 to get the next.

And so it goes on.

So, a common puzzle is to guess what the next one is....

Try this..

1, 4, 9, 16, 25....?

The answer is of course 36, each being the square of the integers.

This one..

1, 8, 27, 64....

The answer is 125, since they are the cubes of integers.

What about this one?

3, 3, 5, 4, 4, 3, 5, ?

That's harder - the answer is 5, the numbers being the "number of letters" in the integers. ONE = 3, TWO = 3, THREE = 5 etc

NOW, try THIS one...

1, 1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 6, 8, 8, 8, 10, 9, 10, 11, ?

What is next? First prize is a can of worms

The Most Remarkable Formula in All Math.......

.....involves three of the most famous constants of all, all encompassed in five symbols.

The constants are:

"pi", the number equal to the circumference of a circle divided by it's diameter, numerically, 3.1415926.....

"e", perhaps less-known, but maybe equally widely used. It is the base of natural logarithms and is the limit of ((1 +1/n)**(n)) as "n" gets nearer to infinity:





"i", the square root of -1, the "imaginary number",

-1 itself,

and an equals "=".

In visual form it is:









In order to get to this amazing result, an understanding of calculus, complex numbers, and trigonometry is needed.

Now When I'm Smiling I Know Why.......

Perfect Day, Perfect Night,

Perfect Song, Mr. Right...?

Loose Elastic

One of the funniest events ever to happen to me occurred in one of my Korean classrooms. My job was to teach these kids (aged 8-15) English in English.

The problem with Korea is that almost the entire population wants to speak English but can't. But they are getting there (gradually). They employ native speakers of English to be present in their English Language, er "Schools", and although technically my mother tongue is NOT English, INHA University managed to get me clearance to teach as a special case.

It's very easy. However, because of the way the system works, I never knew what classes I was to teach next, nor the age range.

So I got into the habit of asking each student what their names were before I started to teach, writing them down in my notebook, along with their position in the classroom (with 300 students, it was sometimes very difficult to recall names. These Koreans ALL look alike!)

In one of the classes, I had a new student. A little girl, aged maybe eight, very small in stature and quite angelic looking. She sat on the front row, right beneath my lectern. She had very big eyes couched in innocence. So, I started asking names. "My name is Danny", My name is Emma", "My name is Sandra", all of them announced rather shyly, and I wrote the names down.

Then the new student. I bent my head down and said quietly, so as not to embarrass her. "What is YOUR name?" I barely whispered.

Looking straight ahead, taking a huge deep breath, and with a voice Mr Richter would have been proud of, she bellowed

"MY NAME IS L U C Y !!!!!"

to the astonishment of all present.

I almost dropped my marker pen.