Does moving really be a part of geometry?
Could you rephrase that question? 
Translation… Contradiction. If gravity effects all 3 fields than it is a fourth field.
Yes.
The figure in that picture moves, but geometric figures are actually immobile. So, it is a question of definition, of definional logic. If you want to describe a geometrical figure, then you actually do only consider that that figure is static, thus that that figure is immobile.
In this thread we are mainly talking about the philsophical meaning of physics and about physics itself; so moving bodies are one of the main physical premises; but moving bodies are not the main geometrical premises (this does not mean that it is impossible to have also moving bodies as a premise in geometry); so we have to be careful and should not combine physics and mathematics too much. Combining physics and mathematics too much has been being a problem of the physicists for so long - since the 20th century, especially since the second half of the 20th century. Another example is the problem of combining economics and mathematics too much, and this problem has been existing since the second half of the 20th century (we can talk about it in another thread). I do not say that we should not do it, but we should be careful with that. I argue not against the mathematics but against the domination of the megalomania in physicis, economics, and some other scientific disciplines.
I agree that geometry refers merely to fixed shapes. And mathematics refers merely to the logic between quantities. Thus neither can ever describe physical reality on their own. Physical reality is the changing of the changing wherein nothing is truly quantifiable nor fixed except on a macro/categorical mental scale (the crude map).
It’s interesting that you said “that there are more points in space than there are points in time”:
I thought that was interesting too. This came up in another between James and I.
And what was the result?
Space has infA^6 first order points (or more precisely: 4/3 Pi*((infA^2)/2)^3) whereas
time only has infA^2 first order points.
That is an extremely significant difference, especially concerning why the universe has substance, “exists”.
I don’t think there are orders of infinity. I don’t know how you came to this result, but I do know that if time and space are both infinite, there are not orders to them to that regard.
Are you saying that the completeness of a sequence is an order of infinity?
Say…
2,4,6,8,10,12,14,16,18,20,22,24,26,28…
vs…
1,2,3,4,5,6,7,8,9,10,11,12,13,14, 15…
Are you saying one set is twice as large as the other set?
In mathematics, infinity has both cardinalities and orders (exponential powers).
An infinite sequence can be greater or lesser than another and thus alter the cardinality (de Georg Cantor) of the “relative greatness of its infinity”.
But in addition to being merely greater or lesser, infinity can be raised to exponential powers, such as infA^2 (ref Edward Hewitt, Hyperreal Numbers)
A line in space can be ordered into the “real number” set, thus having infA^2 points. But that is only one of 3 dimensions. By including the other two dimensions, that line becomes a plane with infA^4 points and then a cube of infA^6 points.
Those are the “first order” points because merely the real number set was used to number the original points (even though there are infA^6 of them, requiring a higher order to individually number the first order points). But between any two infinitesimals (“1/infA”) can be an entirely new number set. Thus creating the range of “1/infA^2” up through infA^2 on a line. That constitutes a second order point referencing system. And that pattern can be continued indefinitely to any higher order. Thus there is no “absolute highest order of infinity”, no “absolute infinity”, and interestingly no “absolute zero”.
This is just exclusion in terms of orders of infinity… but you can also do overlap…
1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10… etc… is this a larger set than
1,2,3,4,5,6,7,8,9,10…
?
This is an excerpt from my introduction post to this site…
By definition of infinity, there is no highest order of infinity, and it is false that they cannot be counted… you can list any sequence with an algorithm… if the algorithm itself has infinite processing time, then there is no sequence. Cantor and Chaitin were wrong.
It’s considered a mathematical proof ala Cantor from over 140 years ago that all of the real numbers cannot be counted…
I use a techinique called 1 dimensional flooding to show that all of the reals cannot be counted in one list with one dimension, which is differnt than Cantors diagonalization argument.
use the lists…
012345678910…
123456789101…
234567891011…
345678910111…
456789101112…
567891011121…
678910111213…
etc…
To do one dimensional flooding, you simply add an infinite list to each place in the previous infinite list…
024681012151…
036912151821…
048121620242…
051015202530…
When the list converges at infinity, there is no way to begin counting…
12345678910…
13579111315…
14812162024…
Because you never pass the zero’s.
This is the proof that we cannot determine the limit of how much we can count.
Sorry forgot to add the disproof of Cantor’s diagonalization argument…
Once you do one dimensional flooding, you have to expand to another dimension to keep listing the sequences… diagonals can be subsumed by a third dimension, say list 1.1, or list 5.7 etc… or a 4th dimension 1…1, 5…7, etc…
It’s actually easy to absorb the diagonals by starting from the center and listing them from top to bottom in sequence using another dimension… what this means is that cantors proof that you cannot count all the reals is false. It also means that you cannot find the limit on what can be calculated!!! except that it cannot be everything!!!
Basically, James, what this means, is that there are no powers to infinity, each dimensional flooding is just as large as another dimensional flooding.
You first have to choose a standard length for your infinite series, else you can’t tell for certain what you are really saying. For example;
|N| = [1,2,3,4,5,6,…] can be chosen as a standard. And in that case, the series;
|X| = [2,3,4,5,6,…] is one number in the list shorter (the first) than |N| so
|X| = |N| - 1
You cannot legitimately say that;
[2+2+2+2+…] = [1+1 + 1+1 + 1+1 +…]
because the “length” of the infinite series is possibly different depending on the intention of the person who wrote the series. Did he mean to say that each 2 was merely being represented by two 1’s and thus the series are the same, or did he mean to say that the values in the second series are only half of the first series? If you do not specify a standard first, all kinds of non-nonsensical and ambiguous equations can form.
I noticed that Wiki makes that mistake in one of their articles.
…and if there are no powers of infinity, then the Cartesian coordinate system is fallacious.
Oh come on… you really think that 2+2+2+2 is twice as large as 1+1+1+1?
And the definition of completeness is somewhat ambiguous when it comes to infinities… so is it really minus 1 in your first argument?
Dimensional flooding holds that you can’t add a 1 to the list:
0.1…
but you can make a new list to accommodate this new 1.
Oh here we go with arithmetic 101.
If you have an infinite line with a total number of points on the line;
infA = [1+1+1+…]
and beside it, you place another identical line, do you have any more points?
is infA * 2 greater than infA?
2 * infA = [1+1+1+…] + [1+1+1+…] = [2+2+2+…]
By definition if you ADD anything positive to anything positive, you have more than you had.
Perhaps… there’s another way to look at it though. Let’s look at the 1’s a zeros… to demonstrate the point. [0+0+0+0…]+[0+0+0+0…] = [0+0+0+0…]
Which means that 1… +1… = 1…, or that you are superimposing the same infinity upon the same infinity.
If you “add zero” to anything, you ADDed nothing, thus you have the same as you started.
So no, it doesn’t mean that;
“1… +1… = 1…”
Let’s assume that’s true… why not two different lists for the two different one’s, just like there’d be two different lists for the two different zeroes, which means you can square zeroes.!!! =)
The 1’s and the zeros represent actual amounts. You can’t merely replace a 1 with a zero and have the same amount. We are talking about amounts, not arbitrary symbols. And the amounts are the sum of the series. Two series add up to more than one series, unless one of the series is merely null, zeros.