Limits and application of limits in GW predictions

[tar]

I had some arguments with my calculus teachers about limits and integrals, that I obviously lost, but never did I understand the principle.

 

If the whole idea of an integral is to determine the tendency of a tiny slice with which you can then describe the whole by multiplying the slice by the number of slices, then "tending toward zero" is a characteristic of your slice size to begin with. If you need to look at the thing and as you consider your formulae, you make the determination that this or that term is tending to zero...how can you, or at what point is it proper to "call it zero"?

 

Regards, TAR

Where this comes into LIGO is the fact that in order to sense a GW, space has to contract or expand a thousandth the width of a proton. This is pretty darn close to zero distance. Much tinier than any slice we are able to make.

[fiveworlds]

how can you, or at what point is it proper to "call it zero"?​

 

 

I remember people here saying before that we only need something like 40 digits of pi to calculate everything to 100% accuracy so I would assume that if something goes beyond a 40 digit decimal then it is fairly safe to call it zero.

[tar]

fiveworlds

 

in my 12 segments of the sphere thread I was able to determine using an Euler calculator that the areas of my divisions at 15 degree sections were equal, and you could set the digits to which you wanted to figure to 14 or 20 digits or something, but when attempting to figure the areas of my divisions when the sphere is sliced up into minutes and seconds the numbers, even to the highest precision they provided, were way to rough to multiply out by the total number of sections and check that they added back to the total area.

 

Whatever digit pi was taken to in the calculator, was not enough for my purposes. That is I was having a hard time figuring the area of a minute by minute diamond like section much less a second by second section, to the precision required to then translate these measurement to the globe and come up with a square footage number.

 

That is the digits to the right of whatever the calculator's precision was, were the ones that made the difference.

 

regards, TAR

for instance suppose I wanted to figure to 100% accuracy how many yds of thread I would need to weave a tarp that would cover exactly 1/155,520,000th of the globe

how many digits of pi would I need?

Edited July 3, 2017 by tar

[beecee]

 

Where this comes into LIGO is the fact that in order to sense a GW, space has to contract or expand a thousandth the width of a proton. This is pretty darn close to zero distance. Much tinier than any slice we are able to make.

Pretty damn close but not quite zero, which attests to the incredible precision of our instrument/s.

Same sort of accuracy and precision was necessary with the GP-B experiment.

The way I see it is that if spacetime can warp, twist and curve in the presence of mass, then why not wave?