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Subject:  Mathematics and physics of the decision and perception (recognition) process; conclusions
Some keywords:  Discrete mathematics, finite past, finite calculus, quantum physics, relativity, proper time, decision, binomial distribution, pascal triangle, graph theory, recombination, measurement, recognition, perception, information theory, combinatorics 

The Recombination Principle:
Mathematics of decision and perception

Abstract
Beyond all doubt there is an interaction between thoughts, will and matter. It's important, but  investigated only minimally in scientific, reliable way. Intention of this publication is to show concepts and also to suggest mathematical approaches to this topic.
 

Foundations

The information, which we perceive resp. measure from (past) physical reality, influences our decisions. But obviously also (our) decisions influence (future) physical reality. Every decision and every measurement implies the choice of one from several possibilities. This choice contains information which must be transferred. Therefore it isn't free of charge, it needs time and free energy. If this is completely ignored in mathematical physics, i.e. if the axiom of choice and (as consequence) analytic models with continuous number sets are used, there is a problem in the foundations - for these models cannot exist an equivalent in physical reality.

After mentioning the problem initial suggestions are made for alternative discrete mathematical approaches. The "probability to come back" of own information plays a central role. Proper time proves to be proportional to the sum of probabilities for return of own sent information. Among others the formulae indicate that all (in form of free energy) by us sent information is later perceived by us again in recombined form, and that the probability for this goes to 1 (in the course of proper time).

View main text

The texts also can be viewed off-line:

Download
After the download process unpack the file "wqed.zip" using common pack programs into an empty directory. You will get all (english and german) HTML files ot this site. Then start viewing by opening the file
index.htm
with your browser. Among others I tested it with internet explorer. If you wish you can additionally download external publications concerning the topic. The older texts are included in a separate download, because they are big and most often not necessary.


 
 
 
 
 

Older texts

If you can understand german language, you also might look at the older texts.  But only if  much time is available, it's worth to look at them.
Large parts are to be understood as collections of ideas
Most of the older texts I haven't written in the consciousness, that I publish them nearly unchanged in the internet later. They aren't written continuously[1]. They simply emerged: Often happened, that something has fallen into me, of which I thought that it would be a pity to forget it, I should write it down. If I could bring myself to do it, I then have it inserted in the texts at a hopefully suitable place. By the fact that I revised the structure now and then, a certain systematic arose progressively.

The older texts are rather extensive and available only in german language. They consist of three relatively big text blocks wq1, wq2 and wq3 which I in the essential successively have written. The first text block wq1 is attached only for better completeness. During short recapitulation I found in it many reasonable things, even if they may be sometimes naive. But my view perhaps has been more limited and I can't judge today, how far at the time, when I essentially wrote this first text block (before 1990, spelling and formatting later adjusted) still was influenced by the too literal interpretation of the concept "particle model" [2]. I started to write the second text block wq2 after 1990, after a turn in my thinking had happened. Since then more and more mathematical sections have been inserted into the texts. I considered this as necessary also for reasons of the objectivity - because we don't want to fool ourselves. Perhaps you will notice that the pure arithmetic is neutral [3]. Determining are our decisions. Just because of the importance and consequences of our decisions the text blocks wq2 and wq3 aren't free of ethical or philosophical contents (wq3 has been started after a new version of the formulary; after 2001 the updated version of the formulary is in the separate file wqm.pdf). The mathematical contents are not changed by this but the texts might become interesting also for those who find mathematical considerations difficult to understand.

Hint for reading
First look at the main text (english). Mathematical [4] and physical entry knowledge is necessary in parts. You then can decide, whether the older texts could be interesting for you at all. Particularly when reading the older texts you should concentrate on places which are interesting for you, because they need time for correct interpretation; it is doubtful, whether looking at the older texts is useful in case of lack of time. Some possibly interesting passages are marked by (***). You could for example first look at these passages by search order to "(***)". Or you choose immediately your own order, if you can judge, which passages are important and which are less important. Also the chronological order of writing contains information (see below). The compendium of formulas in wqm includes analogously[5] those of wq2 and wq3 so that I recommend the reference to the formulary in wqm for reasons of homogeneity. In HTML format there is a concise formulary, too.
Once again: Nix perfect
Greater sections of the older texts have been (still) in the outline stage and are often wonderfully imprecise[6]. It's an intermediate version[7]. Of course I couldn't check everything on complete contradiction liberty. However also an unvarnished version might be interesting. It additionally can give insight into the temporal order. Later parts are more likely relevant (in the average). Many not essential parts are meant as hypotheses and should be understood correspondingly, i.e. a hypothesis also can be false, but nevertheless can activate to think ahead. Also for that reason I did not remove all older chapters. In the normal case it should follow from the text what is more speculative and what is basal and obligatory. In the more obligatory parts I try to minimize the number of mistakes, I cannot do more faced with the topic. In addition, I have forgotten much. Writing down is also a memory help. Of course errors are to be expected, it is almost superfluous to mention this. Sense of the texts isn't primary faultlessness but information transfer (also stimulation to own ideas) so that we altogether proceed in the correct direction as well as possible.
Download of (german) older texts
After the download process unpack the file "wq.zip" and you will get the files
wq1.pdf,
wq2.pdf,
wq3.pdf,
wqm.pdf,
which you can view with the free Acrobat Reader

Contact

We want to come closer to truth (in as nice as possible way) which we can only do if we don't fool ourselves, i.e. if we correct recognized errors. To be able to write at all these texts and also while I wrote them I not only once had to upset well worn ways of thinking. It is not easy (for us). Perhaps your opinion is, that this or that passage should be omitted or corrected. Perhaps you have a helpful idea, especially to the main text. You can send me an email. We (joint with our information) complete ourselves (because of the recombination principle). Together we can make it better. 

Footnotes:

(1) They contain many very reasonable things, but also some out of date parts.
(2) I was too much influenced of the common concept that matter consists of an accumulation of smallest unchanging separated constituents being moved somehow by us. Of course it was clear to me that this is a simplification, but only since wq2 I began to understand the more detailed difficulties of this simplification.
(Particularly this mental outlook represents a dead end model and and leads to completely false conclusions. Problematic is among others that with this model the objectivization of the stupidity of (group-) egoistical behavior isn't possible.)
(3) Mathematics isn't orientated, if lonely, separately seen. A separation may be temporarily appropriate for reasons of comprehensibility, a too long, unnecessary separation holds the danger that the separated systems get set on their respective model ideas of and unnecessarily don't advance for a long time. A permanent separation is not to maintain, anyway.
(4) I hope that many mathematical contents are understandable also with high school degree. To the understanding of the further mathematical contents in most cases might suffice the basic training until the intermediate diploma of a nature scientific study or mathematics, computer science etc..
(5) wq2 contains old function definitions (P... instead of QP...) with old scaling of the horizontal coordinate k .
(6) Only gradually they became more precise. I didn't destroy all imprecise parts, for also from this better ideas can emerge.
(7) The completion of the subject obviously would last a little too long. I would already have clearly changed the reference system before. So this here will remain an intermediate result, however I am confident that it becomes better and better.



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