All right,I will try my own attempt at an explanation,tell me if it makes any sense...
The concept of infinite divisibility would challenge any valuation of the world, because every event must be measured in spatial-temporal coordinates, and these imply quantities:if any finite number representing a magnitude contains an infinity then its mere enunciation would be a contradiction...
From the strictly abstract,if we consider,for example the number 2,111...we see that is an infinitely extense number altough we say that is less than 3;in this case we can solve the problem just by establishing conventionally the indivisibility in some point of the scale:we can see here that any number has no value else in itself more than which we give to it by convention:
If you go from 1 to 10 in the abstract realm of
mathematics,and you are in 9,but then you divide by ten the remaining distance(1/10); you would have to cover ten units to the goal,just as in the start point,and the difference between this units(0.1 of the initial unit each) and the initial ones only arises if you consider the initial ones as a comparative frame of reference,with no other "autonomous" value as being of different size as units than this comparison itself,and you only reach the "goal line" 10 when you stablish conventinally the indivisibility of the units in some point(let s say 0.1,from 9=0.1 x 10,and you reach the goal)...
Now,in the physical world,the role played by conventions in maths is accomplished by the concrete frame of reference that the perceptive limitations gives to our senses(frame of reference):
As Galileo pointed out,in a good example by physicist Mach(is the spelling right?):
Lets consider an apple on a table in apparent state of rest;an observer within the same room has the right to claim that the fruit is not moving,but as the Earth spins on its axis the apple is moving as well,what an observer in orbit can affirm;but the Earth revolutes around the sun(observer 3),the sun around the galactic core(observer 4 ),the galaxy with the local group of galaxies(observer 5),and so on:
Another example,if we show to a 2 mts man a room,and then to a 1 mt tall man the same room independently.
Which is the dinamic state of the apple?
Is the room big or small?
Well, all of the apple observers are right and both men can claim either that the room is big or is small because there is no absolute parameter to measure space(and therefore movement),and the value to it will be given by the frame of reference provided by the point of view of the observer,which in turn depends on his/hers senses of perception,natural or artificial;but as any number different from zero divided by other distinct as well from zero will be always different from zero,our point of view
will always deliver a finite quantity of units to measure the object(notwithstanding the fact that a physical limit as the size of photons may prevent us further sharpening of the observation,this limit has a value different from zero for each unit) ,and thus,in the case of covering a given distance we ll observe the object achieving the goal line after passing the amount of minimal units perceivable by us(which constitutes our frame of reference)AS LONG AS WE DON T CHANGE OUR RESOLUTION TO COUNTERMEASURE THE ADVANCE;for as we noticed in the abstract example,the numbers(or magnitudes)only depend of the value given by the basal units that constitute the frame of reference;this means that to change the resolution,or the extension of the minimal perceivable unit is to change the value of space itself:
Then if we imagine a distance to cover in the example of the ten feet of the initial post,independently of our capacity of resolution,this would mean to change arbitrarily our resolution(unit) beyond our minimal point(or frame of reference),or our valuation of space itself:
If we double it as we double the advanced space(1/2+1/2+...),we won t move:but if we aumengt the resolution by a factor of ten while doubling the advance:we ll be getting away from the goal¡¡¡¡
But as long as we remain stationary from the perceptive point of view,the object achieves the goal with no problem.
So we don t need an "absolute base" to contain magnitudes as we don t need it to claim the state of rest of the PC while the Earth is moving...
But if we have it,as Planck s lenght,then what happens with the faster/slower relation of the first post...?
Has this any sense?Help...
Javier
