User:Archgimp

About Me
I'm a doting father with three beautiful children, a new wikipedian, and obsessinve problem-solver, which probably explains why I ended up managing a business' IT system. I have recently become obsessed with maths, having found that it offers a sandbox where problems always have solutions, even if you can decide what that solution will be (thanks, godel).

I was drawn to wikipedia whilst arguing about whether $$0.\overline9 = 1$$ and found that it does. Since then I've been drawn into the study of prime numbers. A study which is taking up all my spare time, and most of the time I don't have to spare too. The twist is that I will endeavor only to use wikipedia to learn. So any misconceptions I pick up on the way will be as a result of how something is explained. This means I will be attempting to elucidate articles which can be misleading wherever possible.

Below I will keep a record of my current ideas based upon what wikipedia has taught me and a record of edits I've made to articles which gave me the wrong idea in their current forms. Also I will keep a list of my current intuitive understanding of some issues, and as I resolve them using wikipedia, I will score them through and reference the articles which pointed me in the right directions. Hopefully that will provide a useful resource for any of you with the same ideas as me and would otherwise be doing many hours of tedious trawling to find the correct way to express your idea or proposed solution.

My Intuitive Preconceptions

 * $$0.\overline9 \neq 1$$ => I was wrong! See: Talk:0.999.../Arguments
 * Prime numbers are inherant in any number system, furthermore they are independant of any base and any symbology we choose to use to represent them.
 * The answer to the distribution of primes will be found in studies of waveform functions.
 * Primes are not special in the traditional sense, and are used to fill in the gaps in composite numbers. As such they are more neccesary than 'blessed'.
 * The best way to study primes is to begin without a number system and imagine the process you go through to create one. So begin with 'nothing' and 'something' and work from there.
 * Numerical magnitude is directly equivalent to numerical discretion.
 * Cardinality of infinite sets is an undecidable problem. You can choose the answer you like, and it will be logically correct.
 * Mathematics and quantum phenomenon share a direct link.

What I'm thinking about right now
Ok so lets see if when we take actual size out of the equation, the distribution of primes becomes more obvious. For that I need to work out a function that:

$$n \in \mathbb{P} \Rightarrow 0 < f(n) < 10$$

Here's what I got:

$$f(n)=\frac{n}$$

So now we can take all the primes between 1-10 and 11-100 etc and see how they relate to each other as their magnitude increases.

An interesting observation
29-11-2006 Probably quite obvious, but I'm looking for articles on wikipedia that explains it (any hints please add to my discussion page).

Using my function above - running the $$\big\{ n \in \mathbb{P} : \mathbb{P} > 10^n, \mathbb{P} < 10^{n+1} \big\} $$ through a sin function and plotting the results on a graph looks like a random bunch of peaks and troughs. However using our function above, $$ f( \big\{ n \in \mathbb{P} : \mathbb{P} > 10^n, \mathbb{P} < 10^{n+1} \big\} ) $$ produces a pretty steady sine wave...

Interesting.. I will keep checking wikipedia's pages to find out where this may be discovered. If you already know, let me know on my discussion page.