Decorating

I need some clear UV - luminescent ink or paint that dries invisible, a large bristly brush, a toothbrush for fine details and a UV lamp.

When you're using the brushes, scrape the ends of the bristles towards you, not away from you, because if you scrape the bristles away from you, the paint sprays right at you.

The aim of my efforts?



Some peeps are content with a little rag rolling, some decking. I want to decorate my place to look like the Apocalypse came a little early. :)

Thought of the Day

The following image comes from the BBC's website.



Reading between the lines, it looks like:-

1) Nick Clegg's accusing Brown of ignoring him. ("Oi! DON'T look away from - are you bloody looking away - OI! Don't bloody sit there and blank me again!")

2) Brown IS ignoring him.

3) The fight for Number 10 does not involve Clegg at all - it is between the very solid Brown, and a half-transparent Tory ghost.

4) The more people believe in the ghost, the more he can manifest through the barrier separating him from the real world. Look! He's already garnered enough belief from the cultists to manifest a hand, kind of.

5) Not even 24 hours, and I'm sick to the back teeth of the bloody lot of them already.

Doctor Who

Matt Smith's new Doctor Who finally arrived on our TV screens.

I guess I'll have some thoughts on it later. Right now, I'm waiting for it to appear on iPlayer.

The A 101 Series So Far

The third part of the A 101 series is now up.

A 101 - The Smoking Room

A 101 - Forced Perspective

A 101 - Field Test

A 101 - Forced Perspective Now Up

A 101 - Forced Perspective

The link above connects to the sequel to A 101 - The Smoking Room. A 101 - Forced Perspective continues the story of Julia Markham as she comes to terms with the events of the first story.

A 101 - The Smoking Room

This is a fiction piece on the Erotic Mind Control Stories website.

Please note, the content of the story is NSFW.

There'll be more such links to stories in the future.

Being Human

Being Human's back on TV.

This is the BBC Three series about three people: a ghost, a werewolf and a vampire: who live in a little pink house in Bristol.

It sounds like bloody Rentaghost, but it isn't. There's blood, and pain, and fear, and horror.

Annie, the ghost, learned that she'd been murdered by her wife-beater of a husband. George, the werewolf, got wounded by Tully, and becomes an abortion of Nature by the light of the fullmoon. And Mitchell got turned by Herrick in a woodland in WWI.

Season 1 showed the three of them settling in and slowly coming to terms with being themselves, hiding from scrutiny and trying to fit in amongst the humans. This is Season 2, and war is looming on the horizon.

In the last ep of Season 1, George deliberately changed and, in wolf form, shredded Herrick. Mitchell had accidentally created a childe at the beginning - she gives up her existence at the end of Season 1.

And Annie rejects The Door, the chance to Pass Over which may only happen once in a ghost's existence, and acquired powers and relative solidity - now people can see her, even if they don't believe her to be a ghost.

So there are new complications in Season 2. Mitchell finds a new woman, whom I suspect might turn out to belong to this faction of hunters that's arrived in town; Annie's finding a new job in a pub; and George's girlfriend has been scratched by George, and could turn into a werewolf herself at any time.

But otherwise, life goes on. So it does.

Lovely.

And Survivors is coming on soon, along with CSI: NY, NCIS, Numb3rs and CSI: Crime Scene Investigation on five. TV is getting interesting, for once.

Caganer at Christmas

Menja Bé! Caga Fort! I No Tinguis Por A La Mort!

Christmas Runup

The Christmas runup is upon us, whether we want it or not. I haven't made any sort of plans at all for anyone's gifts, but I have told my folks that I will volunteer to help Mum out with the Christmas cooking, doing all the heavy lifting so that she won't have to.

It's awful, having no money just shy of Christmas.

Quiet Week

Most of this week, my various email inboxes have been unbelievably silent. Not even much in the way of spam.

I hope this trend does not continue after Thanksgiving weekend, and that people begin coming back online. Otherwise the internet may have to close out of lack of interest.

Approaching Vedic Mathematics

Vedic Mathematics is a mathematical philosophy derived from study of the Vedas, the sacred Sanskrit Hindu texts. The philosophy has a number of highly practical techniques, known as Sutras, with hard mathematical applications: one Sutra called "All from 9 and the last from 10" is applied quickly in obtaining numerical complements in subtraction:-

10000
4457 -
5543

Sixteen Sutras exist, each finding uses in various parts of mathematics. A comment I made just now to a post on the Vedic Mathematics blog, however, has emphasised that you do not need to know all sixteen by name and all at once. You only need to know a couple at a time, to become familiar with them, and move on to others until you are familiar with the lot of them.

You can take your time learning VM, and as I commented:-

So it is okay to go slowly when approaching Vedic Mathematics, as a husband may approach his wife on their wedding night, knowing that Vedic Mathematics is a loving partner who will be with you, and faithful to you, forever.

Vedic Mathematics India Forum blog

RIP Edward Woodward

The actor Edward Woodward died today. He was 79.

It is a very sad day today.

That is all.

Doctor Who: The Waters Of Mars

I just watched the latest episode of Doctor Who on BBC1. "The Waters of Mars" just made its debut on British terrestrial TV, and my word it was terrifying.

Oh, but what an ending. I felt shocked. That must be the first time I have ever felt shocked by Doctor Who since "The Seeds of Doom" with Tom Baker.

Storms Battering the UK

The weather has been bad all week. But it has become windy as well these past few hours.

I noticed some minor damage in front of my folks' house when I paid them a visit. The winds have knocked over a plant and broken the pot it was resting in.

It's worse down South, so I hear.

I hope that this is not yet another early sign of global warming.

A Thought To Think Upon

"Where all think alike, no one thinks very much."
-- Walter Lippmann

Just Testing

If a = n₁x, then

b = n₂a is also a multiple of x.

Feeling Ill Today

I hope nobody minds if I take a brief break from all this blogging. Yesterday, I believe I have caught the same flu that has been going around all this time.

I will return soon. I promise.

Awesome Responsibility

I am now an official contributor to the Vedic Mathematics blog. I issued my first two posts here today, and the third post will be tomorrow morning where I shall continue my thread on divisibility.

I chose not to simply reproduce my thread on this blog for that other forum, but rather to write it all afresh, from scratch. The Vedic Mathematics blog also has something the thread on this blog does not have: examples.

The idea is that I can give answers to the examples in the morning, before moving on to the next blog entry - with examples of its own for the readers to solve. In the next thread, I will provide answers to those examples, and so on.

The philosophy with my threads is simple. I wish to engage the readers in the process of learning by offering them examples for them to do. Perhaps this will encourage others to write to the blog - certainly to study vedic mathematics with renewed vigour.

We shall see. :)

Divisibility By Four - A Close Look

Now, in one of my previous posts I described how to check that a number is divisible by 4 by examining the two rightmost digits. Let's take a closer look at this phenomenon.

100 is divisible by 4 exactly 25 times. Between 0 and 100, every other even number is divisible by 4; 4, 8, 12, 16 and so on.

However, if you look, there is a pattern to the way the numbers fall. Let's look at the first five multiples of 4: 4, 8, 12, 16, 20.

Notice how the last digits are 4, 8, 2, 6, 0. The first digits here would be 0, 1 and 2: 04, 08, 12, 16, 20. Two of the tens digit numbers are odd; the rest, even.

Now the next set of five multiples: 24, 28, 32, 36, 40. And again, it's even, even, odd, odd, even. And we see a pattern forming.

Does this pattern continue in the next set of five digits? Let's look at 44, 48, 52, 56, 60. Even, even, odd, odd, even.

That makes it three times. Definitely onto something.

So the rule for checking for divisibility by 4 should be: If the number is even, check the two rightmost digits (tens and units).

The number is divisible by 4 if:-

Tens digit	Units digit
Even	4, 8 or 0
Odd	2 or 6

This test works whether the number is 16, 76 or 3,465,234,772,236: if the last two digits fit the pattern in the table above, it is divisible by 4.

Try it for yourself with the following numbers:-

456
364
394
3,766
4,966
4,632
58,646
57,638
294,576
3,944,858
29,338,476
29,445,674

Checking for Divisibility by A Prime Number, Part 002

Here, I'll introduce a little terminology.

- The subject number is the number you are testing.

- The target number is the number for which you are testing for divisibility.

- The remnant is the number that remains.

First of all, check that your number is a prime number - that its only factors are 1 and itself. If the number is a non-prime, you'll have to check that the subject number is divisible by both or all factors.

Now work out the multiples of that number, from 1 to 5.

For example: the multiples of 7 from 1 to 5 are 7, 14, 21, 28, 35.

The multiples of 13 from 1 to 5 are 13, 26, 39, 52 and 65.

The multiples of 17 from 1 to 5 are 17, 34, 51, 68 and 85.

And so on.

Begin with your subject number.

Now either add to that subject number, or subtract from it, the multiple of your target number that leaves the last digit or digits as 0. Divide the remnant by 10 and repeat until you get a single digit. If that single digit is not 0, the number is not divisible.

Consider testing 15,579 by 19.

First, subtract 19 to leave 15,560. Getting rid of the 0 leaves 1,556. Subtracting (4x19=76) yields 1,480. Again, getting rid of the 0 yields 148. Subtracting (2x19=38) yields 110. Removing the 0 yields 11. Adding 19 yields 30; getting rid of the 0 yields a final digit of 3. This is clearly not zero, so 15,579 is not divisible by 19.

Another example: testing the divisibility of 345,246 by 13.

First, subtract (2x13=26) to yield 345,220. Dividing by 10 yields 34,522. Subtracting (4x13=52) yields 34,470; division by 10 produces 3,447. Adding 13 yields 3,460; discarding the 0 yields 346. Deducting another 26 yields 320. Dividing by 10 yields 32; adding (6x13=78) yields 110. Dividing by 10 yields 11; adding (3x13=39) yields 50, and a final division by 10 produces a single digit, 5. 345,246 is not divisible by 13.

This tool has just been added to my growing arsenal of mathematical techniques. I commend it to the house.

Checking for Divisibility by A Prime Number, Part 001

I have long wondered how to check a number for divisibility by an awkward number such as 7, 13, 23 or 31.

Checking for divisibility by other numbers could not be easier, once you know what to look for.

To check that a number is divisible by 2 (i.e. that it is an even number) check the last digit. Is the digit 2, 4, 6, 8 or 0? If so, the number is even.

To check if the number is divisible by 4, you have to check the last two digits. If the last two digits are one of the fifty multiples of 4 less than 100, from 00 to 96, the number will be divisible by 4.

To check if the number is divisible by 8, you have to check the last three digits. If the last three digits are a multiple of 8, from 000 to 992, the number will be divisible by 8.

A similar formula works to check for divisibility by 16, 32, 64, 128 and higher powers of two: for 16, check the last four digits for divisibility by 16; for 32, check the last 5 digits for divisibility by 32, and so on.

A number is divisible by 5 if the last digit is 0 or 5; it is divisible by 10 if the last digit is 0.

To check if a number is divisible by 100, 1000, 10,000 and so on, count the number of final zeroes in the number you are testing for divisibility. If the number has that many last digits all zeroes, the number is divisible by that number. (For example, to check if a number is divisible by 10,000 check if the last four digits are zero, e.g. 14,560,000).

A number is divisible by 3 if all of its digits add up to 3, 6 or 9: e.g. the digits of 165,289 added together yield 1+6+5+2+8+9 = 31; 3+1 = 4. Therefore 165289 is not divisible by 3.

If the number is divisible by 3 and it is also even, the number is divisible by 6. If the sum of all the digits adds up to 9 and only 9, the number is divisible by 9.

A number is divisible by 15 if it is divisible by 3 and its final digit is 0 or 5.

And lastly, to check for divisibility by 11 check the difference between the sum of all the even numbers and all of the odd numbers: if the difference is 0 or 11, the number is divisible by 11.

For example, to check the number 5,112,832,549 for divisibility by 11, add up all the odd numbers together and all the even numbers together, and deduct the larger number from the smaller:-

5+1+8+2+4 = 20; 1+2+3+5+9 = 20. 20 - 20 = 0.

The number 5,112,832,549 is divisible by 11. (Check it yourself).

To check for divisibility by a non-prime number like, say, 12, check for divisibility by its factors - in this case, divisibility by 3 and 4. Similarly for 25, check the last two digits to see if they are 00, 25, 50 or 75. To check for divisibility by 33, check for divisibility by both 3 and 11, and so on.

These are the basic mechanisms to check for the common numbers 2, 3, 4, 5, 6, 8, 9, 10 and 11, and of course the non-prime numbers.

So what, then, of prime numbers such as 7, 13, 17, 19 and so on? Well, I only came across a nifty technique that works for all such numbers. Once you know how to do this for, say, 7, you'll know how to do this for any and all such prime numbers.

And all you have to do is to remember the first five multiples of your target number. In the case of divisibility by 7, for instance, all you need to remember is 7, 14, 21, 28 and 35.

Vedic Mathematics

I am a big fan of Vedic Mathematics, ever since I let Shakuntala Devi's teachings into my life back in the 1970s. Her book, Figuring: The Joy of Numbers, has been bedside reading for more than 30 years, and this year I picked up the basic text, Vedic Mathematics, written by Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja - the core Vedic Maths text, something that ought to be considered the standard text for all maths students.

The Vedic Mathematics blog has an ever-growing following of devotees to this field of mathematics; and as I develop my own understanding of Vedic Mathematics, I will not only be posting here - I aim to contribute to this other blog, too.

Dream I Had

I'm awake now, but earlier on I had a disturbing dream.

I dreamt that I was outside. It was dark, and in the trees all around me were owls, hooting. There were a mated pair of them; one's call was complementing the other.

I rounded the corner of a very old building, and there on a low, mossy brick wall wall was a large brown owl. It looked right at me. I found myself looking into its dark, beady eyes for a moment before movement to my left distracted me.

A cat was approaching the owl, ready to pounce. No damned way was I going to let this cat take down this magnificent bird, so I jumped inot stop it, knocking it iff the wall. I did this with about two or three cats.

I didn't see the owl after that; presumably it took off. There was a raven, though, and it gently brushed my cheek. I felt warm inside, as though loved and chosen by Raven Himself.

And then I remembered that Raven in some cultures is Trickster.

Owls, cats, ravens.

A New Voice

To blogspot, this is my first blog entry. But it's not my first blog. I have a number of blogs, scattered throughout the internet.

I joined this blogging site because of my subscription to the Vedic Mathematics blog: a blog which I aim to promote on this site and others.

Further entries in this blog will explain what Vedic Mathematics is, of course, and why it is important today.

That is all for now.