I really would like to discuss it with you but your ATTITUDE makes it very, very difficult.
Well,
I'm not the one threatening to put on ignore the people who disagree with me.
But the appalling ignorance of your mathematical theory makes it difficult to have any sort of a meaningful discussion. You're misrepresenting some of the fundamental aspects of mathematics
as they were known to Plato, let alone as they've been worked out in detail over the past hundred years.
Specifically, you're abusing the notion of the infinite, and in doing so, you're not actually doing anything useful with the mathematics.
You're correct that the number sequence
0 + 1 + -1 + 2 + -2 ....
does not have a unique solution in standard algebra. By rearranging the terms (which in standard algebra I am permitted to do -- addition commutes), I can show that the system sums to sero, diverges upwards, or diverges downwards. (N.b. I did not say "sums to positive infinity," because it doesn't, under any consistent definition of infinity.)
You're also correct that this is a major problem. Specificlally, most math hinges on the idea of a 'function,' a deterministic operation that always gives the same answer when you give it the same arguments. Addition is usually considered to be a function -- but this shows that an infinite series of additions is not.
However, this problem isn't confined to addition only -- I can get the same result with multiplication:
1 * 2 * (1/2) * 3 * (1/3) * 4 * (1/4) ...
can be shown to have a value of 1, to achieve a limit value of 0, or to diverge upwards. Ergo, multiplication is a function, but an infinite series of multiplications is not.
This is a genuine paradox, and one spurred the development of lots of mathematics; the general solution is that the properties of finite sequences
cannot, in general, be extended to the infinite. To properly address infinite sequences require the idea of limits and convergence, concepts that the sequences discussed above do not have, which in turn means that they
do not have solutions.
This preserves the internal consistency of mathematics.
Instead, what your page proposes is to develop a new
interpretation for the various mathematical symbols. Unfortunately, your new interpretation does not actually resolve any of the paradoxes, and instead introduces new ones. In particular, you suggest that the number zero actually represents the set of all numbers, and the number N, in general, represents "the set of all numbers except for N." This introduces an ambiguity in the interpretation of addition (does it represent the group-theoretic arithmetic transformation, or does it represent some bizarre variation on set intersection and union?) , but more problematically introduces a paradox in that under this framework, the number zero represents "all the numbers except the number zero," which in turn becomes "all the numbers except all the numbers except the number zero," and so on
ad infinitium.
You state in your page that "It is said that the sum of all real numbers is undefined but logicians and mathematicians made a mistake in formulating the rules concerning zero. We tested the hypothesis that all numbers might sum to zero, using a mathematical system where the value of zero is pre-set to be nothing. " This is
complete bollacks. Zero is no more pre-set to be nothing than one is pre-set to be the speed of light. In the standard algebraic framework, zero is a convenient notion for the identity element of the various fields (and we can prove that for any two related fields, their identity elements are isomorphic, so it makes sense). But in many applications -- temperature, for example, or sizes of sandpaper or crochet hoods, zero is specifically not nothing. Of course, the standard modelling of "temperature" (or crochet hook sizing) is also not group-structured, either -- but that doesn't typically matter.
But the
central point is that mathematics is an axiomatic systems, and defined in terms purely of internal consistency. Attempting to force an interpretation on it -- and in particular, attempting to force some sort of ontological system on it -- is an exercise in sympathetic magic. And even the conclusions that you attempt to draw
within the system -- for example, the existence of "Proto" and "Eleah" -- are rife with contradictions. Just as a simple example, you define the sum of Proto + Eleah as zero. I can, however, demonstrate by construction, just as you have, that the sum of Proto + Eleah is any number, or that it diverges either upwards or downwards.
Consider this sum, for example.
1 +
1 + (
1 +
-1) + (
1 +
-1) + ....
This sequence reduces to 1 + 1 + 0 + 0 + 0 ... or simply 2.
However, the italiziced subsequence is 1 + 1 + 1 .... or Proto, while the boldfaced one is Eleah. Ergo, Proto + Eleah is equal to 2 (and hence not zero), or else 2 = 0, or else addition doesn't commute, or else the concept of Proto + Eleah is not well founded. I argue, of course, that the latter is the case.
So from a mathematical point of view, your theory is internally consistent. But you want to use an inconsistent theory as an ontological model? I hope you're not proposing that the ontology of the real world is inconsistent, but I fear that you are.
But the key point -- and this was known to Plato -- is that mathematics
has no ontological implications.
I am willing to give you one more chance. If you can manage to interact with me without continually denigrating me, failing to listen to me, personally attacking me and generally treating me like something you scraped off your boots, then I will converse with you. If you cannot manage this, then you are going straight back on ignore.
Frankly, my dear, I really don't care. I
have listened to you, more than the quality of your ideas merits, and I find your "thought" purile, naive, ill-thought-out, badly expressed, clotted, and laced throughout with circular reasoning. When called upon any particular aspect, you resort to
ad hominem attacks and back-pedalling into a cloud of mysticism.. You have been unable to express any sort of consequences for your philosophical "theory," cannot even define your terms in other than a self-referential way, and will not respond to detailed criticism. And furthermore, these same issue were raised in discussions several years ago, and you have not even attempted to understand the criticism.
If you actually had a theory, it wouldn't matter whether or not I treated you badly. Arguments do not stand or fall based upon the bruised egos of their proponents. They do, however, stand or fall based upon reason, argumentation, and evidence.
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