What I do want?

 

Sometime in the early times I realize the importance of the Three-Body Problem. It’s impossible for an experimental physicist an upgrade to theoretical physicist. But I have found my slice. If the majority of researchers are working around, for Me sophistic theories, I have tried to return to the beginnings, rethink the basics, complete, change if necessary, conducted only by the sense of beauty. For this was necessary to forget a lot of habits (with my ignorance was easy). In other words I have tried to think as the big old brains, which have invented the “devices“ and who has a “robot portrait” of how must look a solution. The solution probably needs an entirely new codifying”, symbolism etc. to manipulate the information’s concerning this problem in a compact way. This is the mean reason of any mathematical construction. “First the horse, then the wagon”. The almost 300 years delay in solving the problem can have the origin from a strategic mistake. I don’t believe that the big olds forbid us to change all, if necessary. The problem is the central object and the way can be a “Retour à la nature”.

            The knowledge has some traps.

When the big old-timers have created the differential calculus, they create this for solving some problems. Probably the creation was beginning with a “robot portrait” of the needed tool. This is mainly a system of problems; divided in sub problems, sub-sub problems etc. and the known requirements of the needed solutions. At this level they have solved a part of problems, has ideas for an other part, remaining a lot of unsolved problems. The solutions of the solved part was developed, constructing in the same time a symbolism, as natural, as suggestive, as it seems to they, at that level of knowledge, historical background etc. Later the solved part was developed by others; the symbolism was changed caused by the historical evolution, the different cultural background and by the “optimization” for this solved part. This later means that the symbols has become more suggestive for the solved part, moving away from the starting problem stack. The process was repeated recursively at higher levels of knowledge. The resulting image is a town with a mixture unfinished buildings of varied height, with a part of them with the construction stopped. The policy of the continuation of the construction of the town highly depending on the distribution of the big buildings.

The resulting traps are:

-         Drunk from the successful part we have lost the starting problem stack, that “robot portrait” probably in the cleanest form in the mind of the “big old-timers”

-         The symbolism reflect rather this zone, than that of the original problem stack

-         Much more the graphical elements of symbols was constructed by different persons, with different cultural backgrounds, at different historical stages, exhausting long time ago the Greek letters, abandoning the Gothic ones

-         The process of learning, forming our habituations, delimited learning honestly even a part of the construction, the modality of viewing the things, the preferred ways of thinking, attacking the new problems.

Consequently is necessary:

-         A “Retour à la nature”, to the original notices of the “big old-timers” rediscovering the original “robot portrait”, a job for the historians of science

-         To construct an as much natural symbolism as possible for the knowledge reflecting primary the domain of problems, not that of the solved part. Of course this is very difficult, different symbols are naturally connected to the same things in the head of different peoples. We can only hope in a best compromise, taking in mind even the prize of forgetting the old system and learning the new. Much more, the new system must be permanently servicing.

-         To rethink everything, beginning with the basics, and carrying with as, by the symbolism, the “dark” zones. In other words, reopening the old, abandoned gold mines, continuing the opening and reprocessing even the sterile. Completing the whole image, inventing the missing elements at that level, where the construction was abandoned, partially forgetting the higher levels.

Of course this a very good ideology for an ignorant ex-experimenter physicist, who never could be an authentic theoretician, remaining to practice some kind of  “naïve painting”.

 

 

Now some ideas, in completely random order:

1. The eyesight is a complicated process, I don’t know too much about it.
• What I know:
1. At the early days the baby see a reversed image, as this appear on the retina, the motion to left appears as motion to right. Later the brain learns to invert this.
2. From the to plane images of the two eyes the brain construct the spatial one.
3. The brain is holographic. “Anything in anywhere in a small form”
4. The brain is as a “virgin” set of simple electrical circuits, in which the learning process burns-in the connections.
• At the other we use mainly two methods to represent the space on a plane:
1. The projective geometry convention – the 3 orthogonal projections of the space figure
2. The perspective representation.
• On the display of a computer the perspective image can be changed rotating internally the behind space object.
• These suggest a way to see 4-dimensionally.
1. A figure with the structure of the projective geometry, but with 4 projections. Seen with color filter eyeglasses, or intermittent colored lighting, we can learn the brain to construct a model of the 4 dimensional space.
2. Replacing 4 projections by 4 connected perspective figures again rotatable. Much more display a 3-dimensional perspective figure on a holographic display, of course again rotatable in the 4-dimensional space.
2. With the help of the computers we can use “spatial” mathematical formalism, for example 3-dimensional matrices [See my site, article a.)] Much more we can invent three-dimensional formulas for partial derivatives, multidimensional integrals, etc.
3. The color is used in mathematical formulas, but now we can use the sound, the animation for background information, properties of a complex mathematical object, useful especially in the case of “heavy” encapsulated objects or objects containing in the definition place holders of un-understood things.
4. Parallel use of alternate notations underlining one or other aspect of a mathematical object, demonstration.
5. “Experimental” mathematics, developing the method to understood, learn, and develop mathematics starting from simple problems. Later the use of the minimal but covering example as “veterinary horse”.
6. In mathematical texts many symbols recur, this fact suggests”compression”, on this “macro” level. The frequency of the symbols and groups of symbols are characteristic for that text, mathematical construction, and proof.
7. Many times I have meet situations suggesting the following commonplaces:
• „Go [forward] or die!”
• „The devil conceal oneself in the details.”
• „Ordnung wird sein“
• „Licht, mehr Licht!”
• „Don’t see the forest, because the tree.”
• Can’t solve a problem? Solve 2 [solve a twin of problems]!
8. When in our way is a break, not the nature is wrong, the way is badly traced.
9. For fast orientation:
• “The main idea is …”
• Input-output
• Is like the …, but with the difference [An alternate form of the inheritance from OOP. Much more the experience gained in programming in making ergonomically good programs can be return to the mathematical formalism. Any analogy is a full-duplex connection!]
• Investment-gain.
10. Achieving knowledge is like solving a puzzle.
•  The pieces are information units, the knowledge about a part, coded in our way (focused on the inspected part, generally ad-hoc, at the level at least – namely to be sufficient for manipulate the “local” information’s of the part. Generally this subjective, context dependent coding, but which one was constructed in a coherent way from one “big brain”, who has a “robot portrait” of the part, thing to understand, is used “as is” from the followers, developers. Its come the time when the added knowledge “call for” the rethinking, recoding.
• The pieces of the puzzle are objects, with a few properties, selective connecting anchors to other pieces, input-output properties (for example a theorem), state properties (different auxiliary conditions, in which the theorem works in a similar, but different way) an object as in OOP programming. The objects can be many simple or a fewest, but complex. At the end we have an optimal, intermediate set of pieces, the optimal tree of the system, decomposed in subsystems, sub-subsystems, etc. But how must be the pieces at the early, intermediate stages, of the incomplete knowledge? If they are to simple we have to see simultaneously, to many, with just one property, the color. Or with the minimum set of the properties for identifying a member of the set. At the other side, fewest, but most complexes pieces, with sophisticated comportment, not contradictory defined at least at that level of knowledge. But must be a very brain, which can manipulate these objects, a chess champion, previewing 15 steps or something like this. A signal that something is wrong are the surprise theorems, discovered by the above high performance brains, but pointing that the construction is not the proper for the studied part. (Again geocentric, with high performer people, who has capable to calculate trajectories in this system) I think that in a good construction every step, every theorem, must be simple, almost straightforward. Is not the best way to carry in our mind heavy “encapsulated objects”, even if we can do. Inherently at this stage we have a lot of un-understood, dark zones, properties, pieces marked by some “place holders”, the frontiers of the un-understanding. In time the number of unsolved sub problems growth and made the thinking very difficult, the construction foggy. At this moment is better to return to the basics. [The simple hint in the mathematics: If a mistake, clear the entire table!]
11. If the construction starts inclined arriving at a height it collapse.
12. From geocentric to heliocentric.
13. Look farther!
14. They are applicable:
• The laws of the war
• The laws of the economy

Almost the same thing, the keyword is “efficiency”

15. Investing in the “meta-level”, but how much?
16. Toward an Esperanto of mathematics we must take in account:
• The archetypes
• The limited number of characters in the phonetic alphabets.
• The power of pictographic “alphabets”
17. To return to the basics is something like reopening the old gold mine and exploit it with the improved, new technologies.
18. Sometime the situation looks like this: We know the stone hatchet; the school produces better and better stone hatchet manufacturers, but can produce the inventor of the iron hatchet. The situation is similar in the informatics; the fast development of the hard and the soft force us, the users, to learn new programs, based on new principles in a new way.
19. Dynamical programming of the scientific development, driving in an unknown zone.
20. Finally some kind of heuristic principles from my own experience:
•   I. Without unbound umbilical cords!
•  II. Economy of letters, temporary notations.
• III. If 3, then all 3!   [3 variables, 3 dimensional space, 3^rd degree homogeneous polynomials, derivatives.]
• IV. Say “NEY” or “What if not?” [Break the barriers of proper mind, appeared from the experience, from learning, up to the formatted reflexes, old associations]
•  V. The basics must be as ill considered as possible, and needs to be periodically revised and if necessary reconstructed [Retour à la nature!]. First, good axioms, good machine level instructions, good point of view, coordinate system (geocentric Þ heliocentric). The house must growth vertically, must have a sufficiently large/deep base.
• VI. How much to invest in the methodology? Forgetting some things, reflexes, etc., learning some others
• VII.  Anything must be appear in one completely symmetric form and in another completely asymmetric form. The completely symmetric form activates our aesthetical sense guiding us in the jungle. The completely asymmetric is the form, which reduce the problem to a solved sub problem.
• VIII. Can’t solve a problem? Solve two! [Dubleaza potul si  continua!]
• IX. The 3-dimensional space is basically non-orthogonal!
• X. If trying to solve a problem on different ways we are stopped by corresponding set of difficulties [sub-problems looking unsolvable], then most of these sub-problems have a common origin. Sure, all these sub-problems are connected via the original problem. The difficulty is to find the basic sub-problem at the unknown origin [Geocentric or Heliocentric?]
•  

 

 

http://www.geocities.com/cornel1001

 

http://ck2002.freeservers.com/

 

 

 

mailto:cornel1001@yahoo.com

 

mailto:cornel1001@hotmail.com