A little paradox I am having trouble with...

Ok, here goes. I am having some trouble understanding a certain concept. Please point out where I am wrong. I hope everyone can visualize this.

Between one second and the next is obviously one second of time. Now take that second and divide it in half. We have two halves of half a second. Now take one of those halves and divide it in two. We now have a quarter of a second. What I am getting at here is that I can divide one second into 'n' pieces; for that matter an infinite amount of segments. So if we assume that one second, and maybe this is where i am wrong, can be divided into an infinite amount of segments, how can "time" go through these infinite amount of segments in one second?

Any one follow me?

There's a name for this 'paradox' but I don't remember right off my head. The same scenario exists for anything that is measured: time, distance, weight, etc...

Something you may be interested in researching is Planck Units.


Enjoy. Physics is fun.

[edit on 17-9-2007 by WeaponsOfMassDistraction]

Believe it or not, I don't have an exact answer for you, but I have some interesting facts about how they categorize time in orders of magnitude.

I can't for the life of me think of the name of this paradox, but I know what you're talking about, or something similar, though the version I'm familiar with has to do with walking distances, steps and half steps and so on.

I wish I could remember what this paradox is called. If I could I'd google you up some answers.

But all I have are some hopefully helpful links.

wiki on the second

It's called Zeno's Paradox, basically stating that one second can be divided into infinite pieces. It's something like these pieces can be divided into infinite amounts, so everything works out.

Something like that.

Thank you Morphene! that was driving me insane.

Links to explanations of Zeno's Paradox:

en.wikipedia.org...'s_paradoxes

mathforum.org...

plato.stanford.edu...

Multiple thank you's!

I was racking my brain on that name for a while.

That is like quantum physics but based on time. The smallest of the small in terms of time itself. That is a strange concept. Maybe time just stops at some point.

Great question, i guess it may happen to such a point that one day it will just stop dead in its tracks. I think an important fact to remember is that time is not realy real. I need to say that better. Time is a measrement that Mankind created on Earth. We caled it time, we broke it down to its funementals and said this is how long a minute is, this is how long a day is and this is how long an hour is. So i guess its a great question, ill look some stuff up.

Take Care, Vix

I think some things are a paradox because we're looking at them in the wrong light. Your example with time was good, and i found it easy to visualize, but it applies to all units of measurement, not just time.

I mean, i guess i don't really believe in time. I guess i don't really believe in distance either. So, yeah, time and space don't really exist as we see it. You know, maybe that big bang never really happened, that it was awareness that expanded, not physical reality. There's no space or time in your mind, which is why it seems to break down, revealing your paradox.

Of course, those realizations don't imply that we are able to reject time and space, because they are products of the way our senses depict the reality in which we live. So that's why i have to keep setting my alarm.

Its because when you visualize the second being broken into segments you see lines or spaces in between these segments which makes the second seem to stretch. Therefore making the second infinitely long.

Its your own mind doing the stretching of this second.

So, therefor, If you can imagine the second being broken into pieces without putting anything in between these pieces then paradox solved.

wow that's an interesting paradox that I never knew of. So one finite second has an infinite number of pieces.

Originally posted by curiousbeliever
wow that's an interesting paradox that I never knew of. So one finite second has an infinite number of pieces.

Yes indeed, but they are all infinitely small so the paradox is resolved with an infinite quantity of infinitely brief periods.

I dont see the paradox, really.

Time travels at a speed of exactly 1 second per second.

i can convert that speed to minutes, hours, days, anything you like really

I would guess the infinites cancel out.

you must go threw an infinate amount of time sections, but each is infinatly small, so the equasion cancels out the infinates and it takes 1 second, but I am just guessing.

If I solved this paradox for the first time give me my 20 ats points I lost for bad quoting back

[edit on 19-9-2007 by Redge777]

This is similar to the "Richardson Effect", named for mathmatician Lewis Fry Richardson.

He created a thought experiment that involved the measurement of the coastline of an island (in his case, it was the island of Britain). He said that if you used progressively smaller rulers to measure the length of a coastline, that length will increase inversely with the size of the ruler being used. So is there a point that a infinitely small ruler will measure an islands' coastal perimeter as being of infinite length? Thus the paradox -- how can the measurment of an islands' perimeter be infinite?

This paradox is solved by quantum physics, which says that it is impossible to have an infinitely small measuring device.

Here's the wikipedia link to an article about Lewis Fry Richardson. Scroll about halfway down to find the part about coastline measurement and the "Richardson Effect". This is cool mathmatical stuff

en.wikipedia.org...

EDIT:
Here's another article about "Richardson Effect" and a scientific paper called 'How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension' by mathematician Benoît Mandelbrot of 'Fractal' fame. It seems that the coastline question is connected to the study of fractals and fractal equations.

en.wikipedia.org...


EDIT: Spelling

[edit on 9/19/2007 by Soylent Green Is People]

infinate segments X size each segment = 1 inch
infinate segments X 1 / infinity = 1 inch


infinate segments
------------------- X 1 = 1 inch
infinity

1 X 1 = 1 inch
1 = 1

I just proved it without fractals, the infinites cancel.

reply to post by Soylent Green Is People


your answer is completly different.

In his example the actual distance goes up as you get a more accurate measurement because you are making approximations as you cut corners. So 50 points is shorter then 100 points. So as you aproach infinity you aproach the real answer to coastal length without ever reaching it.

In the time example if you split a second once a hundred times or infinate times the total time is always 1 second. These may look similiar but they are different problems.

Is it because they're infinitely shorter than that single second?

reply to post by Redge777


You're right -- they are different, but seemingly similar. Here's one way of looking at it:

It matter was made up of infinitely small particles (i.e. every particle is made up of some smaller particle -- and that goes on forever), then the coastline would be infinitely long...if you had an infinitely powerful microscope, then the coastline would always have "nooks and crannies" (or tiny fjords), no matter how small you get.

Of course, most physicists don't think that the "smallness" of subatomic particles is infinite -- they say there is a basic particle that makes up all matter. Therefore, coastlines are NOT infinite.

Time, I think, is different... Matter has an inherent "grainyness" -- that grainyness being the smallest particle of matter. I don't think Time has a grainyness to it...there is no "smallest measurement of time".

We can measure matter. I don't think we can actually measure "Time" itself -- we can only measure the affects of time on our environment. Those are two different things. It seems to me that we can't really measure time because it has no grainyness -- there is no smallest measure of time.

This begs the question: Does time actually exist, or is it just an illusion -- a "phantom byproduct" -- of the unviverse? Can we measure an illusion?

This is all getting very complicated. Is this a good analogy? It takes me hours to cook a great meal and only a couple of minutes to eat it.