fom
Posts:
1,968
Registered:
12/4/12


Re: Matheology §252
Posted:
Apr 21, 2013 12:54 PM


On 4/21/2013 9:03 AM, WM wrote: > On 21 Apr., 12:22, netzweltler <reinhard_fisc...@arcor.de> wrote: >> On 21 Apr., 11:07, WM <mueck...@rz.fhaugsburg.de> wrote: >> >> >> >> >> >>> On 21 Apr., 10:02, netzweltler <reinhard_fisc...@arcor.de> wrote: >> >>>> On 20 Apr., 19:03, WM <mueck...@rz.fhaugsburg.de> wrote: >> >>>>> All atoms of the accessible universe and all positions they can take >>>>> belong to a finite set. >> >>>> How do we prove, that the number of possible positions an atom can >>>> take along a line of 1 cm is finite? >> >>> By accepting quantum mechanics and excluding theology (these >>> assumptions taken as axioms for those who believe (as an axiom) to >>> need axioms) a proof is given here:http://arxiv.org/ftp/arxiv/papers/0709/0709.4102.pdf >>> pages 23. >> >>> Regards, WM >> >> What about a position between two quanta? Should there be no decimal >> fraction for a position between two adjacent quanta along this line of >> 1 cm? > > Quantum theory tells us, contrary to Einsteins's false beliefs,
Once again, claims without proof. When have the significant theories of Einstein been falsified? And, why are quantum theorists so anxious to obtain a quantum gravity that does not contradict Einstein?
> that > unmeasurable events do not exist.
No. Just imaginary worlds.
http://en.wikipedia.org/wiki/Manyworlds_interpretation
> The electron or photon does not > simultaneously have fixed position and momentum (that would contradict > some results of interference experiments).
Of course, that would be explained by the fact that the mathematics describing continuous motion requires differentiable neighborhoods around each point.
One cannot have physics that contradicts the mathematics just because the WM's of the world turn simple mathematics into quantum voodoo.
And, the recognition of this fact may have come from the study of general relativity rather than quantum mechanics.
http://en.wikipedia.org/wiki/Scale_relativity
Scale relativity addresses the possibility that differentiability necessarily breaks down in small domains.
> > Mathematics, contrary to Einstein's false beliefs, is nothing but a > condensation of reality. This should answer your question. >
Perhaps. But that condensation involves the principle that statements are either true or false. The problem did not come out of the mathematics of the latenineteenth century. Rather, it lay with the mathematics as it came into the nineteenth century. The foundational debates arise from the fact that the philosophy of physicists such as WM is often inadequate to their beliefs.
> Nobody can hinder you to believe in things that nobody can say, think, > identify, measure. But that is not science.
It would be more correct to say that that is "science".
When do scientists make the effort to actually justify their positions to the general public? They do not. They use their influence with respect to the economics of technology corporations and universities to establish their positions through the fundamental totalitarian power of government authority.
The same mathematics that WM complains about is used for economic analysis. The economics of paying for governments is bound to the profits of corporations. There is a great deal of competition between governments over these matters that is fundamentally disrespectful of the general citizenry.
The heroic view of "science" is a lie. WM's statement would suggest that anyone can walk into CERN and conduct an experiment for themselves. No. That is not how it works. So, for most people, "science" is being told what to believe without being able to verify it for themselves. That they accept what they are told stems for the fact that it is mostly irrelevant to their daytoday lives.
==============================================
WM is an unabashed ultrafinitist who refuses to fix a largest finite number. Each "n" in his description depends on the subsequence of triangular numbers.
> F(n)=Sum_i(1..n)(i) > > 1 :=> 1 > 2 :=> 3 > 3 :=> 6 > 4 :=> 10 > > and so on
According to Brouwerian intuitionistic reasoning, when WM's construction reaches the point where the sequence of triangular numbers exceeds the ultrafinitist limit, the contradiction nullifies the construction.
This is WM's model of mathematics:
http://en.wikipedia.org/wiki/Finite_model_property
until he reaches his contradiction and it vanishes.
=====================================
The triangular numbers correspond with the number of 'marks' representing numerals or significant denotations occurring in any of WM' representations of the form:
1 2, 1 3, 2, 1 ... n, ..., 3, 2, 1 ...

This number of 'marks' satisfies a structural feature of the natural numbers called a directed set:
Defintion
A binary relation >= in a set D is said to direct D if and only if D is nonempty and the following three conditions are satisfied:
DS1)
If a is an element of D, then a>=a
DS2)
If a, b, c are elements of D such that a>=b and b>=c, then a>=c
DS3)
If a and b are elements of D, then there exists an element c of D such that c>=a and c>=b
So, WM's geometric reasoning for any given n obtains a finite model domain with its cardinality given by the associated triangular number. The triangular number is the "element c" of condition DS3 from the definition.

Finally, Brouwer's explanation for finitary reasoning is used because WM refuses to commit to any mathematical statement with coherent consistent usage.
Brouwer distinguishes between results with regard to 'endless', 'halted' and 'contradictory' in his explanations
"A set is a law on the basis of which, if repeated choices of arbitrary natural numbers are made, each of these choices either generates a definite sign series, with or without termination of the process, or brings about the inhibition of the process together with the definitive annihilation of its result."
WM cannot be an ultrafinitist and expect others to not hold him to task for it. In constrast to Brouwer, he repeatedly states that there is absolutely no completed infinity. Therefore, there must be a maximal natural number for his model of mathematics. Beyond that number, there is no mathematics.
That is WM's belief as surmised from his statements and reasonings as opposed to what he says with rhetoric.

