Discussion in 'Physics & Math' started by god-of-course, Sep 20, 2003.
And what would the lengths of said sections be?
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"Not everything that can be counted counts, and not everything that counts can be counted."
- Albert Einstein (1879-1955)
Each orthogonal section will half the length of the total.
The total large enough at least to span across the universe.
Call the total 1 unit of length if you like, the point as always being volume is a finite commodity.
A fine quote, but not a meaningful answer to WhiteKnight's question. If something's finite, it can be counted. Whether or not it 'counts' (ie. matters) doesn't affect the fact that it has a length by way of being finite.
Well the question
cannot be answered by a specific number but it can well be answered by comparing one said section to the "length of the total" then there is an answer which "counts" namely the section is shorter then the "length of the total". Even if both parts of the comparition (a section and the total length) are (semi) endless one is shorter. How can that be? The only way I figure is that to be comparable they (both) have to have a size (otherwise they would be uncomparable). It implies finiteness (of unspecified length).
If something is finite with appropriate equipment it can be measured.
You are missing the point, though.
What volume is not an enclosure is the question you need to answer.
If the length is finite, it has a specific number.
Having a length or size does not imply finiteness. 'Infinite' is a valid length.
If the length is finite, it has a specific number. Malikiri
You still have the JR problem of confusing numbers and length.
Numbers are a concept of quantity derived from zero and units. Numbers are used to assess quantity.
Length is a property. (the property of being the extent of something from beginning to end)
One is not the other. Numbers have nothing to do with the existence of length.
If the length of a line is finite then such length can only be approximated (considering the unpreciseness of any meassuring equipment). What’s more really exact length would need an infinity of digits behind the decimal point (to be “exact”)).
The most far one can get in “meassuring/describing” a line is then an approximation of line's length. Such approximation of the length of a line sayes that eg. line l is longer then 10 cm and smaller then (eg.) 10.00000000001 cm. That’s a fair description of finite length.
Thus what I stated above holds its stand because the section Ls of an infinite line Li can be easily approximated namely
Ls > 1 cm
Ls < Li
That makes Ls pretty much described as finite and I do not really see what you are complaining about.
Re: re malkiri
I don't care how you measure it. Whether your equipment gives you 0.1% error or 100% error doesn't change the fact that the thing being measured still has a particular length that's independent of your measurement.
Your reasoning fails in assuming that because Ls < Li, Ls is necessarily finite. For example, the cardinality of the set of real numbers is greater than the cardinality of the set of integers, but both cardinalities are infinite.
I've just noticed how bloody long this thread is!!! 28 pages and only started on the 20th september 2003! Good going guys!
It was accepted in this thread to contemplate the (in)finity of lines on the scale of numbers. The set chosen was positive numbers and it is OK to compare sets as an example. But your comparition is not really to the point.
Please consider (again)
L line size L > 10 cm and L < 10.00000001 cm. The extact size of L cannot be expressed in numbers becase if we want to know <i>exact</i> size of the line we would need an infinite digit eg. 10.0000000000000055354457955...............infinity. <i>Exact</i> size of L (I egree that L has an exact size as you proposed) is not available in numbers (The extact distance from the first to the last point of L would require counting in infinitesimals (while attempting to get the required number with total precision) . (We can only specify that the line L is longer > 10 cm and L < 10.00000001 cm)
Ditto happens with line Ls which is a section of an infinite line Li.
The <i>exact</i> size of Ls is in macro-terms-uncertainty comparable to the micro-terms-uncertainty about the numerical representation of the size of L (from the previous alinea). Only the uncertainty of L’s size lies in infinitesimals while the uncertainty of Ls lies in the oposite of infinitesimal let's call this oposite "infinitegreatmals" (Very Biggy Big Numbers). But both lines (L and Ls) are finite, because L doestn’t reach 10.00000001 cm and Ls doesnt’ reach the size of Li. (L is not longer than 10.00000001 cm and Ls is not longer than Li – they both have unspecified length but they both are finite)
Re: re malkiri
It is to the point. The point it illustrates is that just because something is smaller than infinity does not make it finite, as you were claiming.
I'm not going to argue about measurements. We've been talking about a conceived, mathematical space, not physical reality.
Again, the same as I put forth above. Just because Ls is not as long as the infinite line Li (as you constructed at the beginning of the paragraph, I'm not sure why you made it finite at the end), does not make it finite. That is the reason for the comparison between cardinalities I presented last post - to show that not all infinities are the same size.
This has something to do with infinity... but maybe not what you guys discussing.
Ok, I just want to put this out there... It has no relevance to anything that has been discussed previously in this thread.. I think, because I've never read other parts of this thread, but it just seemed to me like the right place to post this, so here goes.
I was thinking about math one day, about geometry in particular, and to be even more particular, about line segments, and I thought "Whoa, if there are an infinite number of points between A and B, then does that mean that the line is therefore infinite, because it is made up of an infinite number of possible parts, and that, because of this, it actually has no measurement at all?"
And then, I was reading about fractals, and I was thinking about how, as you decrease the scale at which you measure, the measurement increases. You can decrease the scale infinitly, and therefore, the measurement is actually infinite, yet the object isn't infinite, is is confined to a certain space, but you can never acurately measure the object itself.
Now here to my question. What do we call this sort of "infinitely small"-ness? Does it have a specific name, or a specific mathematical symbol, like infinity, or is it simply the infinity sign?
I know this doesn't really have any relevance to the topic at hand, or maybe it has a little, but I just felt like throwing this out there.
(P.S.- I've just read this page of the thread and have realized that my statement is relevant to the topic at hand, although doesn't provide any true enrichment to the discussion. Oh, and just on the off chance that anyone was wondering, coincidentally, this very topic of infinite lines and the measurements thereof is exactly where I got my name [BetweenThePoints] from. I just thought I'd add that in there. It's pretty weird that someone starting talking about the very subject my name is based upon. Hehe...)
Hello between the Points.
Would infinitesimal be the word you are looking for.
It refers to numeracy more so than distance.
An interesting thought (arguement) I believe is this.
infintesimal : 1 - to small to be measured.
(math): a variable that approaches zero as a limit.
Since the above seems to indicate infintesimal is still a finite quantity but simply imeasurable (i.e. - Is NOT smaller than any finite number) and with zero being smaller than any finite number, zero becomes the inverse of infinity, not infintesimal.
But by the same persons favoring "infinity" that also claim "0" or nothingness cannot exist would to me be a contridiction.
If 1/Inf(zero or nothingness) cannot exist then it would appear the infinity cannot exist.
As perhaps previously stated on this thread, would see infinity as the infinitesimal approach to zero.
The series 1, ½, ¼, 1/8, 1/16, 1/32, 1/64 …… approaches zero in a never ending manner. That is within the realm of consistent with your reasoning is it not. Neither zero or infinity exist but are part of an numerical departure from 1 if you like.
Prefer not to confuse numbers and distance was the point.
When distance is considered analogous with 1,2,3,4……….a crime against logic is committed. i.e a proposed proof of the existence of infinite distance earlier on this thread.
A story of the universe.
There was no time. Everything was sizeless. (There was no size) Then came the Big Bang, which was an explosion of time within a sizeless point. Time was so quick that a distance of the universe (as big as it is now) would take a beam of light to pass through in a nanosecond. (read the universe came into being smaller than a tiny pea in an outburst of time). Time began slowing down and sizes got bigger (and bigger). The expansion we observe is the proces of slowing of time. Time wil be slowing on untill it finaly stops. Sizeless point will then disapear from the inside (at its last stages to travel a centimeter would take a beam of light an eternity.)
Distance is time.
As simple as that.
Think your saying there is an inverse relationship between time and magnitude of distance.
Time is something that does need units to exist. Its basic unit is an observation of a return to a previous situation.
Distance is not really related to that is it.
Why then the term "space time" ("spacetime"?) exists and what it measns. (I thougt that there was a dependance of one on the other in this concept)
Separate names with a comma.