Pooling Resources

As a pool player myself, I usually have a fairly good game. I attribute this to knowing the angles the balls will go almost automatically from my knowledge of the 'billiard ball' equations of Newton's Laws of motion.

Professional players have to learn from experience only. I learn from both it would seem

Pool is played on a 2 meter table, and the pockets are large.

The game originated from another called 'Snooker' which was invented in India by the British in the days of the East India Company, circe 1770. This was played on a four meter table with smaller pockets and more balls. The rules were simple, pot a red, then another color, a red, then another color, and when all the reds are gone, pot the colors in sequence, viz yellow, green, brown, blue, pink and finally black. 90% of the time the game (called "frame") was won with still many balls on the table, each ball given a points value. red = 1, yellow = 2, green = 3, brown = 4, blue = 5, pink = 6, black = 7. Most times, a player had scored so many points it was not worth the opponenet carrying on.

Sometimes, a player would clear the table winning the frame, in one visit. One thing remained however. The MAXIMUM score from one visit to the table was 147 points (being 15 reds, 15 blacks, and then all the colors in sequence (27), total 147). This does not happen very often, as it is very difficult to use the white ball in such a way as to be able to pot the next ball afterwards (this is called 'positional' play).

The video below happened today at the Crucible theater in Sheffield, UK, at the World Championship.

Ronnie O'Sullivan not only scored 147, but did it in a very elegant way not seen before by anyone. The positional play is immaculate, especially on the shot where he pots a black and cannons into the red and pink in the middle of the table to set the red free.

It is notable that the British Commentary Team picked up that there was a chance of it as early as the 2nd ball.

Numbers don't ever End

Way back in the Anal(ls) of this blog I referred to the "persistence" of numbers

look up "Hailstone Numbers")

It goes something like this. A number's "persistence" is defined as how long it can keep going if you multiply its digits together...for example, take the number 213.

213...2 x 3 x 1 = 6 , persistence is 1, one step to 1 digit.

2132 = 2 x 1 x 3 x 2 = 12, then 12 = 1 x 2 = 2 , persistence is 2 ( two steps to get to 1 digit). Make it up as you go along.

Try it! Take that number, 4174.....4 x 7 x 1 x 4 = 112
1 x 1 x 2 = 2..persistence 2
Try 4173......4 x 1 x 7 x 3 = 84, 8 x 4 = 32, 3 x 2 = 6, so ...

4174 has persistence 2
4173 has persistence 3

Try and find a number with persistence 5. (clue - it's between 600 and 6000)

That is just "multiplicative" persistence.
Try "additive" persistence!

What is the smallest number of additive persistence of 6? Or multiplicative persistence of 6?

The conjecture is that no number EVER has persistence greater than 11, yet another example of Godel's Theorem - ie it is neither provable nor disprovable.

The Numbers Quiz - Solutions

1 -- 26 Letters of the Alphabet

2 -- 7 Days of the week

3 -- 7 Wonders of the World

4 -- 12 Signs of the Zodiac

5 -- 66 Books of the Bible

6 -- 52 Cards in a Pack (Without Jokers)

7 -- 13 Stripes in the United States Flag

8 -- 18 Holes on a Golf Course

9 -- 39 Books of the Old Testament

10 -- 5 Toes on a Foot

11 -- 90 Degrees in a Right Angle

12 -- 3 Blind Mice (See How They Run)

13 -- 32 is the Temperature in Degrees Fahrenheit at which Water Freezes

14 -- 15 Players in a Rugby Team

15 -- 3 Wheels on a Tricycle

16 -- 100 Cents in a Dollar

17 -- 11 Players in a Football (Soccer) Team

18 -- 12 Months in a Year

19 -- 13 is Unlucky for Some

20 -- 8 Tentacles on a Octopus

21 -- 29 Days in February in a Leap Year

22 -- 27 Books in the New Testament

23 -- 365 Days in a Year

24 -- 13 Loaves in a Bakers Dozen

25 -- 52 Weeks in a Year

26 -- 9 Lives of a Cat

27 -- 60 Minutes in a Hour

28 -- 4 Base Sequences in Genetics

29 -- 64 Squares on a Chess Board

30 -- 6 Balls to an Over in Cricket

32 -- 100 Years in a Century

33 -- 15 Men on a Dead Mans Chest

34 -- 1001 Arabian Nights

35 -- Death of a 1000 Cuts

36 -- 7107 Islands of the Philippines

37 -- 8 Legs on a Snooker Table

38 -- 3 Legs on a Milking Stool

39 -- 40 Days and Nights of the Great Flood

40 -- 4 Books in a Tetrology

41 -- 2.54 Centimeters in an Iinch

42 -- 99 Red Balloons by Nena

43 -- 4 Dimensions in General Relativity

44 -- 20 Beds on a Dart Board

45 -- 5 Main Terrestial Television channels In UK

46 -- 44 International Dialling Code for UK

47 -- 747 Jumbo Jet

48 -- The 3 Stooges

49 -- 3.1415926 = Pi to 7 Decimal Places

50 -- 20 Teams in the English Premier League

I feel so ALIVE - - - SO - - - Don't Stop Me Now!

I am having such a good time right now. Physics, travel, job, travel, Physics, travel, job, Ben, travel, Physics, Ben, friends, and of course Sex on the Beach!



Supersonic Man outta you! Miss FaranHEIGHT (FaranHITE) Travelling at the speed of Light!!! Yeah! (Lady Godiva???)


(Lots of lens flares at the end! Does my noticing physics things like this detract from my enjoyment? NO WAY! It merely ENHANCES it!) Thanks Freddie!

A Snapshot of Photography - 2

As promised, here is the second part of the Photography Bit.

So now the basics have been outlined, we can now go on to creativity. One of the problems of early cameras was that the lens the camera had was not really much good for landscapes. Many a time, the photographer wanted a shot of a beautiful Vista (TM) along with the trees in the foreground, just a few meters away.

He found that if he focussed on the hills, the trees would be out of focus, and vice-versa. His problem became known as "depth of field". That is, his focussing range was too small and not big enough to include both trees and hills.

Over the years, it was discovered there were two ways to make it bigger. The depth of field always became bigger if a shorter focal length was used, OR a larger aperture in the same lens.

There are drawbacks to each. In the first, if a shorter focal length is used, more of the landscape was included, and, sometimes, distorted. In the second, if a larger aperture was used, more light got in and a less sensitive film was needed.

In sports photography today, the problem becomes really acute, with closeups often desirable of a player dunking in basketball, for instance. For a close up to be done, a long focal length was needed, and subsequently, the depth of field became very small, so focussing on the subject was difficult. Here's an illustration:




For this shot I used depth of field to make your eye focus on the side of my face toward the camera. Notice how my left eye is out of focus.

Those of you who are smart will notice the candies on the table are ALL out of focus. This is because I used a frosted glass filter in front of the lens, that had a clear hole in the center. You can tell i used this because the candies on the far side of my face are much more out of focus than my left eye, because the two effects added together.

The lens I used was a 200mm lens with medium speed film.







Here's another example, a sports shot:

My team, Liverpool, had just won a soccer match 8-0. Peter Crouch is the tall guy, and the handsome guy on the left is the captain Steven Gerrard.

Notice how the crowd is out of focus. That's depth of field on a long lens. The lens looks like a 300mm, possibly 400mm.




So what are lens flares? Very often on TV, you see a car approaching in the dark with headlights switched on, but you see another exact copy of the headlights on the other side of the screen.

Other common lens flares come from sunlight and street lighting, the latter of which are often mistaken for UFOs

Here's a lens flare from the sunlight:

The diagonal array of lights you see from top left to bottom right are the lens flares.

But what are they?

Simply put, in this instance, they are miniature images of the sun pictured top left.

How do they get there?

It has to do with the way a camera lens is built up. The first lenses were made up of a single element, much like the magnifying glass schoolboys use to burn holes in paper. However, modern lenses look a lot more like this:



As you can see, there's more than one 'magnifying glass' there. There are eight.

Quite simply put, each glass bit produces at least one flare, and they are caused by unwanted reflections from the surfaces of the elements, when the light should be going straight through.

It's the same effect when you look into shop windows, when you have to shield the glass with your hands to see inside. The reason for this is that the glass does not want to let all the light through, and some gets reflected back into your eyes from the street. Lens flares happen for exactly the same reason.

So why does it happen? It's wave theory.

The best illustration I can think of is a washing line attached end-to-end to a piece of string. Grab the end of the string and move it up and down to make a wiggle. This travels to the place where it has been tied to the thicker washing line. The washing line wiggles a bit, but most of the initial wiggle is reflected back to you. It happens because the washing line is 'denser' than the string, just like glass is 'denser' then the air.

As you can imagine, if you have eight pieces of washing line connected to nine pieces of string, the potential for reflections is much larger.

In wave theory, they are called reflections, in photography, they are lens flares.

'Pushing' film and exposure compensation are related, and are just two different ways to allow more light into the camera. The first is an adjustment to make the camera 'think' it is exposing a less sensitive film, a useful technique in low light, but the downside is that photos are less clear (more grainy). Exposure compensation is used in situations where there is a lot of contrast. It happens a lot on TV when there is sunlight on only part of the playing field. The film cannot cope with bright light and darkness in the same image, so the cameraman adjusts the camera accordingly using Exposure Compensation, so that shadows look normal, and that daylight looks normal, but never the two in the same shot.

Take this shot:


In this shot, to use normal camera settings would have resulted in my image being very dark, as the trees in the (out of focus) distant background are normally lit. I had two choices: 1. use the light level from my shirt (thus bleaching out the background trees) or 2. use the light level from the background trees (thus darkening me into shadow).

I decided to do neither. I exposed for the background trees but used a small flash to light my image.

This technique is called 'fill-in flash'.

In some situations, especially like these, it is the only solution.

Finally, reciprocity failure. This only happens at extremes of light levels, and mostly in the dark.
Normally, light levels are linearly related, that is, you open the aperture to double, you have to double the shutter speed to let in the same amount of light, or halve the film speed.

At low light levels, this rule fails. Instead of opening the shutter for double the time, sometimes you have to open it four times longer than is usually needed, and even then there is no rule. It is almost always guesswork, because there is no known rule. The 'double one thing - halve another' rule fails, hence "Reciprocity Failure". A dramatic upshot of this is that if untreated, moonlit scenes which should be blue, actually appear green.

Once again, this is just textbook stuff off the top of my head. There is far more in the real world to deal with. Here I have given only a smattering of examples. This is why Photography is FUN!

Anger Management.....

WARNING!!! SUBJECTIVE POST!

......by Francois Frederyck Chopin.

This is one of my favorite pieces of all time, the etude (study), Opus 10 number 12 in C-Minor. It has been played by Igo Pogorelich (unique interpretation), Rudolph Kerer, Vladimir Ahskenazy, the Grandaddy of them all (RIP) Artur Rubinstein, and the closest I have ever heard to THIS interpretion, Tamas Vasary, but there's Good, Damn Good, and then there's Aya Nagatomi. She has a touch I have not heard since Vasary, even on this, one of the most difficult piano pieces of all to play.

It is not a long piece, but was reputedly written by Chopin (1810 - 1839), a Pole, after he learned that his Beloved Warsaw had fallen to the Russians in 1831. The anger is clear to hear, but this has never been more beautifully played here. Nagatomi uses the "piano-forte" feature of the grand piano (soft-loud) quite effectively, and has fine use of the pedal at the end. The accoustics of both piano and room are superb.

What fascinates me about the piano is that there is so much physics in it, for such a simply arranged instrument.

I post this in protest at a video posted to me on the Chess website, by someone who shall remain nameless, who obviously is not into this more "cultured" stuff.



Next post, my eclectic taste in music continues with an Iron Maiden classic.....

Numbers...?

So, just what is the point?

It began way back when one farmer wanted to know if he was richer than his neighbour. That's easy! Just count the sheep!.


Hang on a minute - what is counting? Ah, we just group the sheep and whoever has the largest group wins. Oh look! we both have the same number of fingers - let's compare the sheep by grouping them in groups of fingers and see who has the most! yeah!

So that's how it began. Soon, they found names for them all (Yes! All ten fingers!). As people got richer, they found larger and larger groups (All with names) were needed.
Then, the four basic operations were discovered - adding, subtracting, multiplying and dividing. With only these four, even today, people get along quite well. Nothing more seemed to be needed.

Then interesting things started to happen. Famer A had 9 sheep, but he owed Farmer B 11 sheep. These were called negative numbers, and today, they are usually written in red on bank statements. Farmer C had 15 sheep and 2 sons? How do the sons get equal shares on their birthdays? These were called fractions (rational numbers)and they are usually written as pennies on bank statements.

There was more to follow, as people started realising there is far more to this "counting" lark than meets the eye.

All sorts of things reared their ugly heads. Irrational numbers, percentages, squares, cubes, prime numbers, perfect numbers, imaginary numbers (each of which deserve their own posts) and even the fact that there is (at least) more than one type of infinity!

People found they needed to move sheep( money ) around without even knowing the exact amount, so equations were invented (see earlier post) to do this. If you wanted to find out how the number of sheep you had changed from day to day, you used calculus (see earlier post).

The point being, anything to do with numbers is all related as it all began with sheep (or cows, pigs, etc, or combinations of all three, plus the kids, etc, etc)

Comply Or Die

Three years ago I began this blog and I was also in the UK, and this event was happening. Now I have a choice to continue or to delete.

The photo above is of the winner of the 2008 Grand National, which I sadly missed by just a few minutes. The winning horse's name was "Comply or Die".

Well, I choose to Comply. After serious second thoughts, posting will continue here.

I am advertising in Private Tutor sections of the classifieds to see if my counter goes up. As of now, it is 6,021.

Numbers

Just what are they?

We use them everyday because we want to get to the next one.

We usually do it by adding, subtracting, or multiplying.

People with Bank accounts know about subtracting (it is called an "overdraft"). Sometimes they "add" as well.

People who are already rich know about multiplying ("profit").

How about "division"?

This happens when you have more than one bank account and you want to decide how much money to put in each.

And that is it.

For everyday life, this is just fine. But some people like to explore. Exploration is not limited to walking to new places with your feet. Some people like to walk with their minds. Numbers was one of the first areas to do this.

The first question was "Is there a highest number?"

The second was " What is it?"

Try it!

You quickly get into difficulties because cannot actually name the number you are thinking of. This is because most people have given up naming them. The reason? There IS no highest number.

The illustration is that no matter what number you care to name ( even if it is a ZigZillion master-scrutxillion ten billion billion smacktrillian)) you can always add 1 to it to get a bigger number.

So what is the point?

The Generation Generation Gap

No, not Grandparents.

I was on the local bus here in Oxford today on my way to a resaurant, in time for a meal booked at six. There is a place near here that catches it's own trout from the river the other side of the car park.

There were schoolkids on the bus, and one was striking. She was a beautiful blonde, no more than 15 years old, and was made up just as if she were about to go to a disco, but in a school uniform. She wore eyeshadow, eyeliner, lipstick, plucked eyebrows and wore purple nail varnish. She held herself, as most teens that age do, as if she knew everything, chatting to her mate every minute or so, flicking her exquistitely groomed hair every now and then.

Then came the Oxford students, and two girls got on and sat not far away. Over the aisle, they talked about their chosen subjects and lots of others. They wore neither makeup nor had any pretensions, and leaned toward each other eager to catch the other's opinion.

The juxtaposition was striking.

The first girl, a youngster who thought she knew everything.

The second two, only a few years older, knowing they DID NOT know everything.

I was fascinated.

It developed into a contrast when the younger one noticed the others. She made it clear by a mere expression that she despised them.

The observation is that people often give their opinion away by mere body language, and others, who simply want to learn, are not bothered by it what they convey to others.