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Thursday, November 4, 2010

x/0 and similar paradoxes

I have read the Wikipedia articles (http://en.wikipedia.org/wiki/NaN and http://en.wikipedia.org/wiki/Division_by_zero) and I have come to a few indefinite conclusions.

1) 0/0 is not equal to 1
2) Infinity/Infinity is not equal to one
YET
3) x/x = 1

So I have decided to redefine zero and infinity, and x.

Zero: The absence of any number, real or imaginary.
Infinity: The limitless expanse of numbers in all dimensions.
x: Any fathomable number, excepting when x does not equal 0.

If we take 0 x 1 = 0 x 2, it seems to make sense. However, when 0/0 x 1 = 0/0 x 2 is equated, it would seem that the equation would simplify to 1 = 2, obviously not correct. This may prove that 0/0, unlike x/x, does not equal 1.

If we had zero objects and wished to divide them amongst zero people, we would be handing out nothing to no one for eternity. (Obviously we would not bother in real life, but let us assume this just for the purpose of this example.) So I draw the conclusion that 0/0 = infinity.

I could now ambitiously define 0 as being the opposite of infinity (referring back to my definitions 1) and 2).

So if 0/0 = the opposite of zero = infinity, does this solve the paradox infinity/infinity? For if infinity is the opposite of zero, then surely infinity/infinity = the opposite of infinity = 0.

But then I am totally bamboozled by this:

If x/0 = infinity, then logically, x must be equal to 0 x infinity, right?
Does that mean that 0 x infinity can be expressed as any fathomable number?

Who knows.

Sunday, July 25, 2010

The Speed Of Light

I am currently reading E=mc^2 by David Bodanis, and a paragraph on the speed of light sparked my interest. It is not particularly relevant to my following idea, but just made me wonder.

If the universe is infinite, then would we not be traveling faster than (or equal to?) the speed of light?
Let me explain.
We live on lowly Planet Earth. Earth orbits the sun in our solar system in the galaxy of the Milky Way. It is my understanding that as other smaller galaxies orbit ours, we in turn orbit other, larger galaxies. And then that mass of galaxies orbits another larger mass of galaxies and so on and so forth. As the universe is supposedly infinite, this would mean that these orbiting masses would be infinitesimally large. Now, if we add up these speeds (the speed of the rotation of the earth + the speed that the earth orbits the sun + the speed that the Milky Way orbits anther larger mass and so on) the total speed would continue increasing to the point of infinity, much surpassing the speed of light. Therefore I would conclude (almost obviously incorrectly) that each person on earth is traveling infinitely fast.

How could this be? Would we not be invisible, as our image would be behind our own being? And so I could perhaps draw the possibility that if the total speed was fractionally smaller than the speed of light, we could calculate the size of the universe.

Thursday, June 17, 2010

The universe.

Yes it is a very large thing, and a very difficult thing to imagine. But perhaps an even harder idea to imagine than infinity is the idea of nothing. What is nothing and what does it look like? What did this space we live in now look like before the universe began? The Big Bang is a popular explanation for the beginning of the universe, and it is thought that the universe started off as a tiny bit of something (I don't know if you could call it "matter") trillions of times smaller than a proton and exploded due to some sort of fluctuation to do with matter and antimatter. Or so I have read. And I am rightfully skeptical even though scientists claim it is possible to look back to a few fractions of a second before the universe began. So anyway, we have this little bit of something, that is to be an infinite universe one day, and it is surrounded by nothing. And here it gets tricky. How can nothing "surround" something? It can't, because there is nothing there to do the surrounding. So we imagine this potential universe simply floating.
Now, if it were floating in nothing, which indeed it was, the scale of this potential universe would be infinite.
Let my explain my theory. If you were a tiny particle living in this potential universe, and at the edge of your universe was nothing, you could never, ever get out of the universe into the nothing, because you can't be in nothing. And so you would keep going forever, going all around the universe and bouncing off the edges without realising and simply carrying on with your mission. It would be like being a fly in a jar, and bouncing off the glass without realising, and still continuously heading for the world outside the glass. This is what I link to idea of the universe "bending", but in a more complex sense.
This could also mean that there could have been life in this potential universe, just on an extremely small scale, sextillionths of the size of us. And consider this, maybe our universe now is another potential universe, and it is about to explode larger still into the nothingness at its current edges, and on it will live beings sextillions of times bigger than us...
A never ending cycle.

Tuesday, May 25, 2010

I just watched the most amazing video on TED.com: http://www.ted.com/talks/william_kamkwamba_how_i_harnessed_the_wind.html
Some people are amazing, they can create the most incredible things from next to nothing. This guy is a true genius, and an inspiration to everyone. At the moment, I am working with a leadership forum, and we meet every few weeks. It is such a great experience working with young leaders, like me, and finding ways to work together to help our community and those in need. TEDx has an event in Wellington soon: https://www.facebook.com/pages/TEDx-YouthWellington/320037732382?ref=ts

Tuesday, May 18, 2010

Are we the same person that we were 10 years ago?

I have been doing a bit of research on this topic lately: I have written off a few myths, and pondered on others (for excessive lengths of time).
From a physical approach, I once heard that the cells in the average human were all different to the cells that had been there approximately seven years ago. I soon discovered that this was not true about all cells, such as brain cells. (I suppose this is quite clear, because if we lost all of those over a period of seven years, surely we wouldn't remember anything.)
From a mental and emotional approach, we are always changing our minds et cetera, but fundamentally we think in the same way as we did seven years ago.
I eventually came to the conclusion that for this question to be answered thoroughly, one needed to define "the same person".
I thought about this carefully. Could "the same" mean that even if we lost a few skin cells or a bump on the head made us forget a few things we would still be effectively the same person? Well, I actually don't think so. Even if we are 99.999...% the same, we are only partially the same. We are partially the same as every other human on the planet, and we don't call ourselves the same person. I like to think that "the same" should mean "exactly the same", and therefore with every instant (or frame, like in a film) we are somehow different than before. Whether it be that we are thinking different things, or that we have lost a couple of dead cells, or that our temperature has changed... anything.
And there you have it. At least, that's my view.

Saturday, May 15, 2010

I never finish anything

No matter how great my dreams or how genuine my intentions are, I never seem to finish anything I start. I have several unfinished paintings sitting in my art folder, one canvas sports only a mere sketch. Songs I have started to write live on wrinkled bits of paper, and spring up from unlikely places whenever I am looking for something else. Books I have started lie dormant on my hard drive. Empty diaries line my bottom drawer, covered in other bits and pieces that seem to have gathered there somehow. Sometimes I ask myself why I even bother. Why do I start these things in the first place? I write books because I have an idea, but never get any further than a couple of thousand words. Somehow the idea maps itself out so beautifully in my head, but it just never sounds right in words. I paint with every intention to sell my works at the local cafe, but even if I finish a few in a series, I never get round to making frames that fit. And for the songs... well I shouldn't even bother. I have minimal musical talent, and couldn't sing if my life depended on it. All in all, I might as well flush my next dream down into the realm of failure where my past dreams now reside. It's all quite depressing, isn't it? I really need to concentrate on extending the span of my attention... I'll keep you updated... whoever you are...

No one will ever find my blog HERE

It seems strange to think that the internet can make or break. It appears to me that publicity generally has an adverse affect (but I may be being rash). Take Justin Bieber. A couple of videos on YouTube, and he goes from someone who could easily have been someone like my younger brother to a teenage pop sensation with thousands, nay, millions, of screaming, screeching, squirming fans. If my near-16-year-old brother is anything to go by, Justin is probably only about 10% of the way through the maturing process. It seems unusual that a brain surgeon can go for the large part relatively unnoticed by the general public, while a 16-year-old kid can belt out a few in-tune notes and never have to work another day in his life. (I know that is an unfair judgement, however it does seem like that's the way things work on Planet Earth).
On the other hand, Eminem is too right in saying "Everybody wants you... Who could really blame you...
We're the ones who made you". And I should feel quite ashamed of myself if I stooped low enough to take Justin's hat. The way we behave around celebrities is unreal. It reminds me of a sort of variant of Sir William Golding's perception of human behaviour in groups -- like a frenzied pack of savages hungry for fresh meat. It's as though the desire for self-fulfillment can only be quenched by pinching a pint-sized celebrity and thus claiming some sort of weird achievement.
I find myself suddenly realising the extent of my hypocrisy in creating this blog, as the whole point of these things is to gain readers/followers... And so, perhaps, I should concentrate less on criticising Justin Bieber and wish him good luck with the hope that karma will see that I shall have some of it too.