Six times nine equals forty two. This is a cultural and mathematical certainty.
But it doesn’t … does it? Yes it does!
Understanding how this apparent aberration of mathematics works can unlock the secrets of life, work, relationships, business, and, you know, everything.
So don’t panic! Grab a cup of tea, find your towel, and prepare to disrupt your universe.
Why forty two?
Forty two is a very important number.
In fact, it’s not just a number. It is the answer. The ultimate answer. The answer to life the universe and everything.
There are many people who know this. If you ask forty two people what the meaning of life is, one of them is certain to say “forty two”. I suggest you actually try this and let me know the results via clinkedin.
That forty two is the meaning of life, the universe, and everything, is established in Douglas Adams epic five book trilogy ‘The Hitchhikers Guide to the Galaxy’.
In this fantastically funny story, a super-computer named Deep Thought is constructed to “Answer the Ultimate Question of Life, the Universe, and Everything”.
After several million years of analysis, Deep Thought reveals, to a very disappointed audience, that the answer is “forty two”.
“I checked it very thoroughly,” said the computer, “and that quite definitely is the answer. I think the problem, to be quite honest with you, is that you’ve never actually known what the question is.”
Clearly there is great importance in understanding, and asking, the right questions.
And so the question is sought.
Following a set of bizarre circumstances involving; the story’s protagonist, Arthur Dent; the end of the world; some cavemen and a bag of scrabble letters … a candidate for the missing question is identified as;
“What do you get if you multiply six by nine?”.
How six times nine equals forty two is never addressed by Douglas Adams in any of his books, but this is where things get interesting, so stay with me.
What do you get if you multiply six by nine?
Six times nine is fifty four isn’t it? So how can six times nine be forty two?
It didn’t take long for the mathematically astute Douglas Adams fans to calculate, and point out (with great pride), that 6 * 9 does in fact equal 42 when using a base 13 counting system.
A what now?
Grab your towel. I’ll explain.
Humans in most of the world count in blocks of 10. We count to 10, increment a unit of tens, count to 10 nine more times, add an increment of hundreds and so on. This is called the ‘base 10 counting system’, or more commonly, ‘decimal’.
Anthropologists believe the base 10 counting system evolved from humans having 10 fingers and using them to count with. If we had 12 fingers, we’d probably count in base 12.
The base 10 counting system is however not the only counting system. There are many more, and they are being used all around us. Some of the more common of these are;
Decimal (Base 10) – the counting system we commonly use today.
Counted as: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 … 99, 100, 101, 102, etc
Mathematically in base ten: 6 * 9 = 54
Duodecimal (Base 12) – prior to decimalization this system was used in the United Kingdom and its empire for counting money, measures of length, and measures of weight. It is argued by some mathematicians as functionally superior to decimal.
There is even a society in the United Kingdom called the ‘Dozenal Society’ who advocate changing from a decimal to duodecimal counting system. Though I don’t think they have a plan to give us additional fingers.
Counted as: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 20, 21, etc
Mathematically in base twelve: 6 * 9 = 46
Octal (Base 8) – Used in some native American languages. Has been proposed as a counting system several times in Europe over the last few hundred years. Is the counting system of the Na’vi from the movie Avatar.
Counted as: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, etc.
Mathematically in base eight: 6 * 9 = ERROR as there is no 9 in octal.
Binary (Base 2) – the fundamental counting system of contemporary computers.
Counted as: 0, 1, 10, 11, 100, 101, 111, 1000, 1001 … etc
Mathematically in base two: 6 * 9 = ERROR as there is no 6 or 9 in binary. However, Decimal 42 is represented as 101,010 in binary.
Hexadecimal (Base 16) – a popular counting system used in computing. Also the traditional Chinese counting system for weight.
Counted as: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21, etc
Mathematically in base sixteen: 6 * 9 = 36
Tridecimal (Base 13) – probably most famous for being the counting system in which six times nine actually does equal forty two.
Counted as: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 1A, 1B, 1C, 20, 21, etc
Mathematically in base thirteen: 6 * 9 = 42
Assumption, perception, reality!
If we assume that the expression 6×9=42 is in base 10, either through choice, or unawareness of existence of other counting systems, then it will look wrong and confusing. We might dismiss it as an error.
Knowing even that there are other counting systems, enables us to see how this expression can in fact be correct.
Sometimes when things look wrong, or complex, they actually aren’t. We just don’t know that we don’t have all the information.
Solving the Mysteries of The Universe
Astronomers once believed the earth to be the center of the universe. Based on this assumption, albeit arguably an evidenced observation at the time, an intricate geocentric model of the solar system was developed by Claudius Ptolemy circa AD 150.
In the Ptolemaic model, the Sun orbits the Earth, and the planets travel in circular epicycles which themselves follow a deferent orbit around the earth.
The result is a somewhat intricate set of gravity defying interplanetary spirals.
Ptolemaic (Geocentric) Model
Despite being completely wrong about the actual motion of the planets, the Ptolemaic model was pretty neat at predicting the planets observable positions. So neat in fact that it remained the favored model of planetary motion for over thirteen hundred years.
That is until Nicolas Copernicus seriously challenged it with the heliocentric idea that things were actually much simpler. And perhaps the Earth and other planets actually revolved around the Sun!
Copernican (Heliocentric) Model
Awesome Video
This video shows a cool animation of how both models work.
Although the geocentric (Ptolemaic) model is fascinating, and the video above shows exactly how fascinating, I think we all know which is the preferred model among today’s scientific community.
Forty Two?
So why is 6 * 9 = 42 the most powerful formula in the universe?
Because it serves to reminds us that our perception of reality is shaped by the filters and limitations of our experience and knowledge.
Remembering this helps open our minds to more possibilities and solutions.
Answers, explanations, opportunities, love, happiness, fortunes … whatever it is that we seek … might easily be found in realms we aren’t currently even aware exist.
I propose this to be true for everything; from simple mathematics, to celestial motion, to the meaning of life, the universe, and everything.
And … 42 is just a very, very ordinary funny number.
———
Addendum
What does Douglas Adams say about all this?
Did he have some deep hidden meaning behind the whole thing?
Apparently not. Forty two was just an ordinary, arbitrary, funny number.
When asked about six times nine actually equaling forty two in base thirteen, he is reported to have responded;
“I may be a sorry case, but I don’t write jokes in base thirteen.”
“Binary representations, base thirteen, Tibetan monks are all complete nonsense. I sat at my desk, stared into the garden and thought ’42 will do’. I typed it out. End of story.”
References
1-∞: Why are there no references or notes in this article?
Did I just make it all up? Do I have no respect for my sources? What sort of academic blasphemy is this?
Well, I read an awesome book recently by John Taylor Gatto. It is called Weapons of Mass Instruction: A Schoolteacher’s Journey Through the Dark World of Compulsory Schooling.
It is an excellent book and I seriously recommend it. After Hitchhikers Guide to the Galaxy of course.
It would be an understatement to say Gatto is a strong advocate of critical thinking.
Having had it bashed into me at uni, one thing that stands out in Gato’s book is a complete lack of source referencing . At first I found this perturbing. Had the book been presented academically as a paper, I would probably have given it a big fat F for failing to reference the sources of stated facts.
However it got me thinking. Which was probably the point.
In today’s information age, it is incredibly easy and mind expanding to fact check ideas yourself. So I’m going to follow Gatto’s lead and let you enjoy critically researching any of the facts and ideas presented in this article.
If you would like to comment or discuss any of the material here, you can find me on clinkedin.
More information from the interwebs
Pretty nice video about numbers and counting systems – TranslatorsCafe.com
Another awesome video of the geocentric model – Youtube.com
Weapons of Mass Instruction: (Downloadable PDF Book) – wordpress.com