Tuesday, 26 August 2014

The Secret Life of the Number Nine

I originally intended this to be a quick little post about some cool maths patterns and some fun facts about the number nine, but as I started to read more and more about this number, the post sort of took on a life of its own and, like John Lennon (I'll get to him later), I got a little bit obsessed with this number. You might be too in a few minutes ... enjoy!

"Do you have a favourite number?" I'd often ask the kids who came in for maths support at the tutoring centre where I worked last year.

The answer was often a shrug of the shoulders, a blank look or a look that said Are you insane? Aren't all numbers diabolical?

Usually, these kids struggled significantly in grasping the maths concepts they were being taught at school and as a result of having fallen behind their peers, were often disengaged in anything related to numeracy.

We often started the sessions off with work on their times tables because it's so difficult to progress in maths without a sound knowledge of them. My challenge was therefore to marry the times tables with something fun to achieve engagement. So after I'd asked them their favourite number, I'd tell them mine.

"Mine's nine', I say, "Do you want to know why?"

Luckily, no-one ever said no.

"Because nine is a magic number", I'd tell them. "You can find out the answers to your nine times table just by using your fingers. Lend me your hands for a moment and I'll show you".

For the purpose of this post, I borrowed my son's little hands to demonstrate.

Following this pattern, you can work out your nine times table all the way up to 10 x 9 , which looks like this:

But the magic of nine doesn't stop there. The number nine forms some fascinating patterns which I'd sometimes share with the kids too. Here are my six favourites ...

1. The inverse times table. Another cool thing about the nine times table is that whenever you multiply a number by nine, you can reverse the digits in the answer and every single time you will get another multiple of nine.

Let's put that to the test:

3 x 9 = 27        27 inversed = 72           72 = 9 x 8

7 x 9 = 63      63 inversed = 36        36 = 9 x 4

10 x 9 = 90     90 inversed is 09           09 = 9 x 1

2. Multiply any number by 9 and the sum of the digits in the answer will always equal nine.

For example:

2 x 9 = 18 (1 + 8 = 9)

6 x 9 = 54 (5 + 4 = 9)

12 x 9 = 108 (1 + 0 + 8 = 9)

3. And just when you thought the nine times table couldn't get any cooler, check this out:

123456789 x 9 =       1111111101

123456789 x 18 =  2222222202

123456789 x 27 =     3333333303

123456789 x 36 =  4444444404

123456789 x 45 =     5555555505

123456789 x 54 =  6666666606

123456789 x 63 =     7777777707

123456789 x 72 =  8888888808

123456789 x 81 =     9999999909

123456789 x 90 = 11111111010

4. There's an intriguing pattern involving the number nine in a subtraction exercise too:

Think of any number with two or more digits. Write it down.

Now write down the inverse of this number.

Subtract whichever number of the two is lower from the other.

The digits of the answer will always add up to a multiple of nine.

For example:

64 - 46 = 18 (1 + 8 = 9)

72 - 27 = 45 (4 + 5 = 9)

896 - 698 = 198 (1 + 9 + 8 = 18)

998877 - 778899 = 219978 (2 +1 + 9 + 9 + 7 + 8 = 36)

5. Here's another amazing pattern that occurs when adding with the number nine:

Think of any number containing two or more digits

The sum of the digits in the answer will always be equal to the sum of the digits in your original number

For example:

33 + 9 = 42 (3 + 3 = 6 and 4 + 2 also = 6)

111 + 9 = 120 (1 + 1 + 1 = 3 and 1 + 2 + 0 also = 3)

6982 + 9 = 6991 (6 + 9 + 8 + 2 = 25 and 6 + 9 + 9 + 1 also = 25)

6. I saved my very favourite one for last. This one's a   magic maths trick you can do to wow your kids or to just show off in general and make people think you have extrasensory perception :)

You will need:

1. A pen and paper

2. A person to trick

Steps:

1. Give the person you are going to trick the paper and pen and ask them to write down a number that is at least four digits long. They should keep this number a secret from you.

2. Now tell them to add the digits of that number together. For example, if the number they chose was 4903, the sum of the digits would be 16.

3. Now ask them to subtract the sum of those digits from their original number.

4903 - 16 = 4887

4. Next, ask them to cross out any number of their choice (except for a zero) from the answer they have just arrived at.

5. Finally, ask them to tell you what the number in front of them is now that they have removed one number.

For example, if they crossed out the seven, the number would be 488.

(4 + 8 + 8 = 20)

7. Calculate how many numbers there are between the number you have just arrived at and the next multiple of nine.

In this case, the next multiple of nine is 27. 27 - 20 = 7.

8. Wow the pants off the other person by telling them the number they crossed out was seven.

To test this trick out a little further, imagine that the number they chose to cross out was 4.

They would therefore tell you that the final number in front of them is 887.

Adding those digits together brings you to 23.

The next multiple of nine you come to starting at 23 is 27.

The difference between 23 and 27 is four (the number they crossed out)

This works for any combination of numbers as long at their original number has at least four digits and the number they chose out is not a zero.

How cool is that? Who could not be über in love with the number nine now?

But the mysteries surrounding this number are not just limited to the realms of mathematics; they permeate subjects such as religion, astrology, astronomy, the natural rhythms of life and the vernacular of our English language.

You would have heard, of course, that cats have nine lives and that a stitch in time saves nine. A human pregnancy lasts nine months and prior to Pluto being officially demoted to the status of dwarf planet, there were nine planets in our solar system. Astrologers still work with all nine original planets, however.

Nine is also significant in all five of the major world religions:

• For Muslims, Ramadan occurs during the ninth month of the Islamic calendar.

• In Hinduism, the number nine is featured in many of the concepts and practices of that faith. I am not familiar with the full extent of these, but have read that Hindus observe nine different forms of devotion and that the goddess Durga is worshipped each year for a total of nine days and nine nights. Hindus also consider the human body to be a city with nine gates which correspond with the nine points of entry/exit into the body (two eyes, two ears, two nostrils, the mouth, the anus and the urethra). I'm not quite sure why the vagina is not counted in this tally, but if you happen to know, please enlighten me!

Worship of the Sri Chakra (or Sri Yantra) is also central to the Hindu faith. The chakra consists of a total of nine intertwining triangles (five pointing downwards to represent the feminine and four pointing upwards to represent the masculine). Together they symbolise the union between masculinity and femininity and the communion of the cosmos.

source

• In Judaism, a period known as The Nine Days is observed every year during the first nine days of the Jewish month of Av (July/August). This time is set aside for communal and personal mourning for the tragedies that have inflicted the Jewish people throughout the ages.

Fascinatingly and disturbingly coincidental, the ninth day of the month of Av was the date of the destruction of both the first and second Holy Jewish Temples (656 years apart), the date when the Jews were expelled from England in 1290, the date Germany entered the war in 1914 and the day on which the implementation of The Final Solution was approved by the Nazi Party, in 1942.

• In Christianity, the Bible refers to the nine fruits and to the nine gifts of the Holy Spirit. The number nine also features in the Book of Acts, where praying at the "ninth hour" is referred to on two separate occassions.

The association of prayer and the number nine found in the bible led Roman Catholics to adopt the practice of observing nine day prayer rituals known as novenas (novem being Latin for 'nine').

• Buddhists believe that there are nine levels of consciousness and nine separate spiritual planes of existence that one must pass through prior to enlightenment.

In Buddhism, the number 108 (12 x 9) also features prominently: Buddhist temples contain 108 steps, they believe that there are 108 paths to reach Nirvana and it is said that if a person is calm enough to breathe just 108 times a day, that they will reach enlightenment.

• Both Buddhist and Hindu malas (prayer rosaries) consist of 108 beads. Mantras are recited 108 times on these malas as this number is said to be sacred and to be in rhythm with time and space.
• In other religions and cultures, 108 is also significant: in Islam, this number is used to refer to God. In Japan, the New Year is welcomed in with the beating of a gong 108 times in all the main temples. Traditional Indian dance comprises of 108 poses.
• Astronomers have discovered that the diameter of the sun is 108 times the diameter of the earth. They have also calculated that the distance between the earth and the sun is equal to 108 times the sun's diameter  and that the distance between the earth and the moon is equal to 108 times the moon's diamater.
• In the study of astrology, nine planets move through twelve houses, creating 108 possible combinations in total, which are collectively considered to represent the whole of existence.

The symbolism and significance of the number nine and its multiples have been a source of fascination to many throughout history, but possibly its most famous devotee of the modern era was John Lennon, who is quoted to have said that it was a number that "followed [him] around" his whole life.

Lennon was born on the ninth day of the month. His street number of his first home was nine and the names of the street, suburb and city in the address of that house all contained nine letters each.

He was the lead singer of the Beatles for nine years. During his time with the band and later as a solo artist, he released a total of three songs containing the number nine in the title:  One After 909, Revolution 9 (which appeared on the Beatles 9th UK album) and #9 Dream (which peaked at number 9 on the Billboard Hot 100).

The incidences in which the number nine surfaced in Lennon's life are too numerous to list here, but can be found over at The Beatles Bible.

When he was shot, Lennon was taken to Roosevelt Hospital on 9th Avenue, Manhattan. 'Roosevelt' and 'Manhattan' both contain nine letters respectively.  He passed away in the USA on the 8th December 1980, but the date in the UK at his time of death was already the 9th December.

He died at the age of 40, not even making it into middle age and yet significantly older than many other musicians who, as we know, have a tendency for living short lives. Much of this can be put down to drug and alcohol abuse, suicide and reckless living, but the fact remains that there an uncanny number of world famous musicians have lost their lives, via a variety of causes, at the age of 27.

These coincidences became so prolific that the group has been dubbed "The 27 Club". Its members include over 40 celebrated musicians including Jimi Hendrix, Janis Joplin, Jim Morrison, Jacob Miller, Brian Jones, Kurt Cobain and Amy Winehouse.

And so it begs the question: why 27?

According to Astrologers, this phenomenon is due to what is known as the Saturn Cycle. Apparently, Saturn returns to the position it was in at the time of our birth once approximately every 29 and a half years, but those changes begin to be felt when we reach 27 years of age and can remain into our early thirties. Saturn's return brings with it a sense of sobriety and an awakening to our own mortality. For some, Saturn's return is a positive time of re-focusing or finding new direction, but for others, it is a painfully intense period marked by the pressure of time creeping up on us and the realisation of the end of our youth. Whether positive or negative, it is a time of decision making and reality checks which can either lead to exciting new beginnings for some or, for others, a sense of feeling completely overwhelmed and ill-equipped to handle what lies ahead in the future.

In the study of numerology, the age of 27 is a highly-charged period of our lives because it is a multiple of nine and numerologists believe that this number signifies the end of one cycle of our lives and the beginning of the next. These nine-yearly cross-over periods are times of adjustment, of personal reflection and of letting go. The tragic death of Robin Williams occurred just three weeks after his sixty-third birthday, which saw the completion of his seventh nine-year cycle.

Can you see how the cycle of nine has played out in your own life?

For me, nine was definitely an age of change. It was the year my dad told me Father Christmas wasn't real and I cried inconsolably not just for the loss of the magic of Christmas, but for the realisation that everything that I had thought was magical was just make believe. It was also the year that I accepted that I was never going to be an Olympic gymnast like I had dreamed of becoming because if I were, I would already have been a lot more talented than I was. And it was during that year, around the time of the Barcelona Olympics, that my teacher gave us a piece of homework where we had to watch something to do with the Olympics on TV and write about it. I approached her desk and told her that I wouldn't be able to do the homework because we didn't have a TV at home. She looked at me as if I had just told her we didn't have a roof on our house. So I guess that was also the time when I started to realise that, in subtle ways, I was a little bit different from the other kids. There was a certain loneliness in that realisation. At nine, it's hard to appreciate your uniqueness. And although I have never really reflected on it until now, nine was also the age when I started to believe that I wasn't quite enough.

Eighteen was a time of firsts. Of rites of passage into adulthood. Of sometimes taking great leaps into that territory known as maturity and independence and other times wanting to hold back and cling to an ever-fading adolescence. I spent the year I turned 18 living in Sweden as an exchange student. I loved that my school life in Australia was finally over and I could now live abroad like I'd dreamed of for so long, but I hated having to live by the rules of Rotary International, the organisation I was signed up to. I often felt like an adult forced to live as a child. The organisation had four main rules which they called The Four Ds. They were: no drinking, no driving, no dating, no drugs. Of course I can see now the necessity of these rules, but what 18 year old living half the world away from home would actually get excited about them? There was, however, a fifth, unwritten, 'D', passed on in whispers from exchange student to exchange student throughout the years: Do it all but don't get caught.

Twenty-seven was an enormously pivotal year for me in terms of setting in motion a series of events which led to permanent change. A month before my twenty-seventh birthday, I moved to Sicily with my little boy, who was five years old at the time. I read in a guide book on the plane trip there that the population of Sicily was 5 million. We didn't know a single one of them. Twenty-seven was an age where I felt that if I didn't follow my dreams right then and there then I would miss the opportunity and never would. I still felt, at 27, that I could go anywhere I wanted and be anything I wanted to be (except a gymnast of course). I think I lost that feeling around the age of 29. Maybe that had something to do with good old Saturn.

My little boy is nine at the moment. He's always loved numbers; he uses them to help him understand the world around him. Nine has been an age of transition for him too. A time of breaking away and holding back. Of rebelling and resisting. Sometimes he gives me a little, then he takes it away. He knows that Father Christmas doesn't exist, he knows that nothing lasts forever, he knows what it feels like to never have the chance to say goodbye. He makes friends easily and he has lots of them, but he's learnt too, along the way, what it's like to dwell on the fringes. He's lost so much of his innocence and purity. His repertoire of profanities is more extensive than mine and he knows about things I'm sure I hadn't even heard of until I was at least 12 and yet, he's still afraid of the dark, still takes his teddy to bed, still tells me I'm the best mummy in the world when he's in a good mood, still wants a mummy cuddle when he hurts himself.

He still dreams of running at the Olympics one day too. In 2012, when he was seven, breathing down the neck of eight, that dream was so lucid, he talked of nothing else. He'd draw pictures of himself crossing the finish line in first place. He'd run up and down the backyard and beg me to time him to see if he'd improved his time from the day before. He'd fall asleep with a book on the Olympics he'd borrowed from the school library open on his lap.

That dream is still there, but it's fading. It's almost like, at nine years old, he's convinced himself already that even though he's good at athletics, he'll never be quite good enough.

He's breathing down the neck of ten now. My baby's going to be double-digits soon. I still haven't decided what I'm going to give him as a present, but I do know the two things I want to give him most of all.

I desperately want to be able to help him hold onto his dreams and never lose faith in himself. But there's something I want to give him even more than that: I want him to know that it doesn't matter how many medals and trophies he wins. It doesn't matter if he makes it to the Olympics or falls over at the athletics carnival at school this week.

I want him to know that it doesn't matter what he does or doesn't achieve in his life, because, no matter what, he'll always be enough for me.

Do you have a favourite number?

Do you remember anything significant about being 9, 18, 27, 36, 45, 54,63, 72, 81, 90 or 99?

Do you know any other fascinating facts about the number 9 or 108?

Friday, 8 August 2014

Bloody Mary Pasta

One of my favourite pastas to make this Winter has been Bloody Mary Pasta and yes, as you may have guessed by the name, it's pasta with tomato and vodka (minus the other ingredients that go into the cocktail version).

Now as far as I see it, the only down side of being in love with this dish is having to make frequent visits to the liquor store to stock up on vodka (I get approximately three meals out of one bottle). Being a solo parent, that means having at least one child with me each time I go which, I venture to say, is not a good look when making recurrent beelines for the vodka aisle! Sometimes, as I'm waiting in line to pay, I do feel the urge to shout out "It's for cooking, not drinking!" but I'm doubtful anyone would actually believe me.

On one of our recent family excursions to the grog shop, I gave my nine-year-old a little educational tour around the aisles, so he could see which parts of Australia and the world that wine is made in and other very important information they're not allowed to teach in schools. Our conversation turned to how expensive alcohol can be. He was gobsmacked at how pricey one single bottle of wine can cost. Then I showed him how expensive the spirits were. His eye suddenly caught on a bottle of 35-year-old Scotch Whisky and in amazement he shouted out "Mum! This one costs more money than you've got in the bank!" I'm not sure how he knows how much money I have in the bank but unfortunately he was right (and a rather large number of people in our neighbourhood know now too!)

But back to the vodka and the pasta. It's super easy to make and if you serve it for dinner guests you can have fun trying to make them guess the secret ingredient :)

Ingredients:

2 tablespoons of butter

1 onion, chopped

4 cloves of garlic, crushed

2 cups of crushed tomatoes

1 cup of vodka

1 cup of chicken stock

1/2 cup of cream

salt & pepper

500g of pasta of your choice (I used spaghetti in the photo above, but fettuccine and tagliatelle work better because this is a thick sauce. My kids' favourite is penne though because they can stick their forks easily through the hole in the centre :)

3/4 cup parmesan cheese, finely grated

2 tablespoons parley, chopped

Method:

1. Melt the butter in a medium-sized pot

2. Cook onion over low heat until tender

3. Add garlic and cook for 1-2 minutes more

4. Add the tomatoes, vodka and stock

5. Simmer until it becomes thick

6. Add the cream, salt and pepper

7. Cook the pasta. Drain and add to the saucepan

8. Mix through until pasta is covered with sauce

9. Serve with parmesan and parsley

My son was appalled the first time I cooked this and told him it had vodka in it. So we fitted in a little chemistry lesson there too about alcohol boiling off when it's cooked, which is about as far as my chemistry knowledge goes :)

And as you can see, it's well received by even the littlest member of our household ...

Have you ever cooked with vodka?  ... and by that I mean 'do you know any other recipes with vodka in them?' not 'do you cook with a vodka in your hand?' :)