Mental Arithmetic 000

I have been studying mental arithmetic for a good long while, now, and I thought I'd jot down some of the things I have picked up along the way.

I'm starting with the simple stuff to begin with, but I'll gradually make my way to the more involved maths later on.

I've looked at Vedic Mathematics and the Trachtenberg System, and I can tell you that they have taught me some beautiful things. I can also tell you not to fear numbers. Unlike people, they will not let you down.

So let's begin with something really basic: multiplying by 11.

A lot of people probably never got past the times tables at school. Times tables are probably something to fear for so many. And yet with systems such as Trachtenberg, you don't have to memorise any tables to master multiplication.

Here's a great example, and I might as well throw you in at the deep end with a big one.

Try multiplying 3,467,189 by 11.

Before you get out your calculators, let me show you how to do it quickly and efficiently, without having to do long multiplication.

First, add a zero to the start of the number:- 0 3 4 6 7 1 8 9

Now write it down, if you cannot do it in your head to start with:-

0 3 4 6 7 1 8 9

The first digit (the right hand digit) is always written down unchanged:

0 3 4 6 7 1 8 9
              9

Now take the next number of the left - 8 - and add the 9 to it:-

0 3 4 6 7 1 8 9
           ¹7 9

The result, 17, should be written down as above, with the 1 written in the top corner. Make a note of it.

The next operation with the 1 in the next column is performed in exactly the same way: add the 1 and the 8, only this time add the carried 1. This yields 1+8+1 = 10:-

0 3 4 6 7 1 8 9
          ¹0¹7 9

This carries on, adding the 7 to the 1 and the carried 1:-

0 3 4 6 7 1 8 9
        9¹0¹7 9

Then the 6 to the 7:-

0 3 4 6 7 1 8 9
     ¹3 9¹0¹7 9

Next, the 4 to the 6 and the carried 1, then continue all the way to the leftmost number, the zero:-

0 3 4 6 7 1 8 9
   ¹1¹3 9¹0¹7 9

0 3 4 6 7 1 8 9
  8¹1¹3 9¹0¹7 9

When you get to the zero, treat it as any other number. Zero, plus anything carried, plus the neighbour on the right, in this case the 3:-

0 3 4 6 7 1 8 9
3 8¹1¹3 9¹0¹7 9

The product is 38,139,079.

The basic rule, therefore, for multiplying by 11 is Add each number to its neighbour and any carries from the previous column.

Try it with some smaller numbers, like the ones below.

23447	13324	8368	14679	2149	22314	88217	88125
9947	23189	27592	193057	46837	35962	245827	36937
4102	1038	6295	19376	9385	20587	8628	59276

Answers in the next post.

Ida Craddock

Ida Craddock

The Weiser Books blog has an entry titled Sexual Outlaw, Erotic Mystic & the Wickedest Woman in the Victorian World. Its topic is Ida Craddock, a woman who lived and died before everyone I know who is alive today was even born.

"Ida Craddock was an occultist and mystic who claimed sexual congress with angelic beings. Educated, ambitious, and widely read on all esoteric subjects, she wrote about her divine relations in a pamphlet entitled Heavenly Bridegrooms."

And that isn't all. She "advocated women’s rights and made it a personal mission to educate her Victorian peers on the particularities of the marriage bed – explicit in detail and a little shocking even now. Her work, carried out largely by correspondence and subscription, garnered praise from the socially enlightened (and the women who benefited from the information), and damnation – even prosecution- from an outraged patriarchy."

The patriarchy lied, connived, perjured themselves and moved fencepost after fencepost, revelling in perverse and perverted sexual sadism as they maltreated and hounded this woman to suicide. It was the turn of the old century. They knew no better.

Nowadays, of course, we do know better - well enough to be able to see the wool being pulled over the public's eyes. Well enough to be able to find people to advocate our rebellions and to back us up against persecution and sadism disguised as Puritanism.

Well enough to think about how Ida Craddock died, and to be able to stand up when somebody else is persecuting someone else and "making an example of them." Well enough, in fact, to be able to call shenanigans, and to point the fingers at the accusers and expose them as sexual sadists and demagogues on a power kick, rather than "upholders of justice and morality."

So here's to Ida Craddock. When Samuel Weiser does release the book on her life, I shall be very interested in acquiring a copy. I will let you know if and when I do.

Reading Cat

Edit: I ought to add that August 20th '10 happens to be the 120th anniversary of H P Lovecraft's birth.