h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

When asking whether "zero" should be considered a natural number, one must first obtain an answer to the question of whether the number "zero" has been mechanically processed or otherwise tampered with through the use of as artificial coloring, flavor enhancers, or chemical preservatives.

In search of the answer to this question, I spoke with Mr. Zilch Bupkiss, the offical numerical spokesperson for the number "zero".
Mr. Bupkiss assured me that the number "zero" has remained unblemished in its pure natural form ever since it was first disovered under a cabbage leaf by a Babylonian mathematician who was trying to invent coleslaw. According to Mr. Bupkiss, the Babylonian mathematician became distracted by the discovery of the number zero and the invention of coleslaw was delayed by several thousand years.

Some may question the veracity of this story. Did the "zero" naturally occur under the cabbage leaf or was it a hoax planted there by a Sumerian practical joker attempting to pass it off as a natural phenomenon? Is cabbage indiginous to Babylonia? Was it really cabbage, or maybe it was Babbage?

And, if for the sake of argument we assume that "zero" is "natural", does it necessarily follow that "zero" is safe to use? Many naturally occuring herbs and other products have been known to have dangerous side effects. Shouldn't the number "zero" have a warning on its label cautioning consumers not to divide by it unless they have taken calculus first?

The number zero is not clubbed in with the other naturals, all of which are positively positive and integrally integers. I don't know if this is right or wrong - should zero be in that set? Is nothing naturally occurring? My landlord may argue that nothing often appears naturally (where he expects my rent to be).
Perhaps zero doesn't want to be seen with this common, countable set. Perhaps she is too arrogant. Perhaps she has heard too many times that mathematics would collapse with her. Perhaps giving her a pronoun adds to her arrogance. Mum! Mum! Help I'm anthropomorphising abstract concepts again! Pass the blue pills!

Did you ever associate numbers with colours and genders? I remember doing so when I was younger (about 10). This is is naturally occurring philosophy of youth I suppose.

Zero is white (obviously) and female.
All odds are female (except 1, and I think 9 is pretty butch) and evens are male (dull and divisible)
1 is black
2 is grey
3 is yellow
4 is green
5 is blue
6 is orange
7 is also green
8 is also orange
9 is purple

I don't know why.

I also manage to mix certain numbers up. I often hear two and write seven. Copying out numbers is a dangerous business. I've heard of numerical dyslexia, I wonder if this is similar.

Zero doesn't come into the natural numbers as it heralds the border between positve (natural) and negative numbers. Negative numbers are even stranger than zero. However the strangest of numbers I'm yet to come across (and studying double maths at A-level you come across a large number) are complex numbers. These assume that the non-existent, I should point out here, square root of one can be represented as i. Why i I don't know, but it i it is.

Complex numbers are far from the strangest numbers around. They are certainly some of the most difficult to represent as concrete examples, but they are exceedingly useful. Most often in my experience, they are used in intermediary steps where all your input numbers for the problem are real as are all your output numbers. However, in order to get an answer for your problem, you NEED to use imaginary and complex numbers.

One example is involved in deriving the equations for harmonic oscillators. Let's say you have a pendulum. Now you can calculate and measure without too much difficulty all the physical data (length of string, force exerted upon the pendulum by gravity, air resistance forces, etc...) needed to generate a function that maps out the path of the pendulum through time. However, to get to that function, you need to solve a set of differential equations, whose solution is only really findable through the use of imaginary numbers at several points in the proccess. When you're done, you end up with a function that can tell you the position of the pendulum at any given time. You'd never get there without complex numbers.

Maybe its because I havn't started uni, and am only just doing my A-levels, but calculus semms to be a much more straightforward method of dealing with harmonic oscillations. Just don't look at the graphical method, way complicated. Though most people think it works the other way round

Differential equations is a form of advanced calculus. The way they deal with harmonic oscillations at a high school level doesn't give you the whole picture. They teach you some formulae that apply in certain specific situations, but when you get to differential equations, you'll be able to figure out the formulae when you're given only the raw data.

You'll also be able to deal with other, somewhat similar situations that aren't covered by the formulae you have now. For instance, suppose that it's damped harmonic oscillation. Well, that all depends on the resisting force you're dealing with. If you've got a block on a spring that's lying on a table, you've got a velocity independent resistance. If it's just air resistance, then your resistance forces are proportional to the velocity with which your oscillating object is travelling. These can all be derived using differential equations and imaginary numbers.

I noticed that this thread wasn't getting the attention it deserved and thought I'd throw in my lot.

I think an Indian mathematician found the zero by the way... er... um...

"What the hell else do I know about maths?"

and a hangover of the arabic source of our numbers becomes obvious when you start to lay out numbers using a computer. Everything is left aligned until you come to numbers and then you need to use right align (or decimal align, I know, I know)if you aren't going to confuse your columns and you have to work from right to left when adding. Just as Arabs today would read from right to left.

Stunning revelation or what?

Complex numbers are very useful in engineering as a way to represent frequencies. If things (eg filters) are plotted on the complex plane it becomes much easier to visualise what will happen when parameters are changed.

The byte ordering of computer numbers is called the endian-ness. Most computers are either big-endian (lowest memory adress has the more significant part) or little-endian (the other way round).

An example of little-endian representation would be 03/04/2000 (3rd april 2000) as the date. 2000/04/03 would be writing the same date in big-endian notation.

This example was taken from the jargon file http://www.jargonfile.org/jargon/html/entry/middle-endian.html

Numerical dyslexia is called dyscalculia. Other symptoms would be poor geographical orientation; problems with small change when shopping; the mind going into 'free fall' when certain mathematical concepts are being considered.

On the plus side there would be excellent language skills and geometry is copable-with because of its pictorial elements.

If you search the internet for dyscalculia, there are interesting facts to be gleaned.