Two interesting questions..

[Twitch]

Here's the first question, and probably the one that makes most sense!

Ok, imagine you have an isosceles , right-angled triangle. The length of the common sides is 1. Using pythagorus' theorum, the length of the hypothenuse is the root of 2.
Just found this picture on wikipedia; perfect.
http://upload.wikimedia.org/wikipedi...iangle.svg.png

This is a number that reaches on to infinity.. So why is the side a definite length? Or is the side infinite?
Obviously, if you were to draw it out as accurately as you can, you would be left with a definite length for the hypothenuse, and thus we think that no, the length is finite.
But, if the root of two is nonrecurring, then it does not end.. Therefore the length is infinte.
What are your thoughts?



The second one, is the concept of time! I got into thinking about this after reading Brian Greene's book "The fabric of the cosmos", and Terry Pratchets "Thief Of Time".. An odd mix, but it's lead to filling up very boring bus journeys so far..
So, anyway.. Bear in mind the concept of measuring time in seconds. Split a second in half, and so on, until you get to the smallest unit of time; if there is such a thing! What is your opinion? IS there a smallest unit of time? There are a few conclusions (or more questions) you can draw from either answer..
Yes, there is a smallest unit of time:
What is it? Would it be possible to measure? I'm guessing no, as we would need a way of measuring time at that level.. A caesium clock uses the fact that the frequency of the light emitted is 9,192,631,770Hz, but what can we use to get down to the smallest unit possible?
No, there is no unit of time:
Time is a concept of man, then! Other than that, we can ask, what allows us to move? Entropy laws state that there is a direction of time, but proving time was also a problem! The background behind entropy, is that anything will be have a higher entropy state (more disordered) as time goes on.. If there is no time, well then things shouldn't be able to move, perhaps? There would be no divide from the past, to now. So, we'd be stuck. And, probably, quite a few formulae would need to be rewritten... Perhaps the past now cannot be said to exist? But without a unit of time, there would be no distance from the past to the present, so we are, to a degree, in the past present and future?
However.. If there is no gap between now and a second ago (assuming that time is just a concept of man), how can we say that the reality presented to us now is any different to a moment ago? If there is no definition of a unit of time that is relative to a TRUE unit of time (ie, a tick of the universe), then the past cannot be said to exist?

What are your takes on this? If anything, it'll keep ya busy for a while!

[Douchermann]

Very good and intellectual questions, twitch. #1 is explainable, fortunately haha. Even if the decimal place is non terminating, the hypotenuse is still terminating. The idea is that each preceeding value in limits the proceeding value. So for example 1.254. The third decimal place is capped off at 1.25, meaning it can never reach that high, so it's stuck at anything less than 1.26 (nor can it ever go down into 1.24). If you add a fourth decimal place, then it would be capped off with the 1.254, meaning it could never go above 1.255. That way, if you say that a strip of paper is root7 inches wide, it will never be bigger than 2.645751311064590591 inches (my calculator displays 2.6457513110645905905016157536393). When the greeks/romans first figured out that the hypotenuse of a triangle with a leg of 1 was root 2, they tried to hide it from people because of the fear of being tortured or executed. Quite interesting

Question 2:
Oh boy. My theory is just that, a theory, so bear with me. Time doesn't have units, it is continuous and thus unmeasurable. It's like turning the faucet on. We use seconds a minutes to measure time, so perhaps using a cup of water. One cup full of water that the faucet puts out is a second. However, if you were to grab a drop, and subdivide it all the way to the atomic level, you could keep going. You can go into protons, neutrons, then quarks, and they're pretty sure there is a level past that. It's like an irrational number (similar to the first question). Time isn't just a fabrication of man, something has to explain why the toast took a second to fall from the plate to the floor (butter side down of course ).

First of all, I believe our species/civilization to be quite primitive. It wasn't more than 150 years ago that we would cut off limbs to save peoples lives. Thus, we shouldn't be expected to know that much. Second, I think some things don't even need to be explained. Somewhere, there are mathematicians and physicists being paid by enormous government grants, to prove that time exists. When they prove it, and release that to the public, 98% of the public is going to say "NO SHIT!".

Time travel; A couple months ago I was telling a friend of mine how it should be possible to travel, or distort time through massive sudden releases of energy. No more than 2-3 weeks later, I watched a video that claimed time travel should theoretically be possible by releasing large amounts of energy... I said it first! haha. That actually happens to me a lot. When I was a wee youngin, I told my father that they should put a switch or sensor in the passenger seat of a car, so if the passenger doesn't have his/her seatbelt on, it also makes an annoying noise. A year or so after that, I sat in someone elses car and a red light told me to put my seatbelt on. Then, a couple years ago, I was telling my friend that they should create a simple circuit in car radios that increases the volume as your speed increases (to combat road noise). I was sitting in the same friends 09 car a few weeks ago, and I could hear the radio no matter what speed we were going...
Enough of that rant though lol.

[Twitch]

Woo, a responce . Ok, that answers the first one! The responce to the second is interesting too!
Yeah, I agree that some things don't need to be known.. Why prove that time exists? Although that was the focus of my second question, it's for a hobby really! I don't need to be paid massive sums of money to start working on this sort of thing! And yes, it is kind of obvious that time can exist when we are measuring it..

Man, I think you need to stop telling people your ideas