User talk:MacGyverMagic/WikiMagic/Gangleri

Note to admins: User:Gangleri is allowed to edit this subpage. [[User:MacGyverMagic|Mgm|^(talk)]] 19:36, Sep 30, 2004 (UTC)

Optical magic, Mathematical magic, Magic and / or cryptic words

- Note to People finding this talk because searching on words like cryptology, cryptic, encryption, decryption ...
- It is just noted here that historicaly magical squares have been used to encrypt messages since oldest times.

1

Dear MacGyverMagic I am not quite shure, if my work fits in with what you are doing at the WikiMagic. From [1] you may start at different pages. The first five show an "holusion" three dimensional effect. Hope you can see it. The page generates randomly the 384 possible Most-perfect magic squares of order 4. Some variants start from 1 to 16, some from 0 to 15, some use odd numbers only altenatively begining with +1 and -1 and so on.
"is:stórhundrað" is the Icelandic word for 120 (the sum of the numbers 0 to 15)and has somthing to about how I found the formula. "is:spá" means prediction and uses the 16 newer runes, "is:fleygletur" means cuneiforms and starts from nothing to 15, because the usage of 0 is another long story. "is:rómverskur" uses roman numbers. I stopped to look for other old numbering systems some days but have some more in mind.
These 4x4 squares are known from India. They have the property that you can make somthing like "fractal transformations". You may divide the square into four 2x2 squares and turn the upper-left and the buttom-rigth in one direction and the other in the other direction and still get a Most-perfect magic square. You can mirror the upper-left and the buttom-rigth on one diagonal and the remaining on its perpendicular diagonal. You also can only mirror the uper-left and buttom-right regarding the center of the whole 4x4 square. Or you do last mentioned transformation with the upper-right and bottom-left only. (Doing it with both is nothing new.)

2

The code is written in PHP and starts with a simple formula of the "straight neighbour values" (not placed diagonal) of a random number. At the 4x4 square these neigbours are always the same. This means all 16 numbers have 4 neigbours only (ond only the relative orther between these neighbours is changed) so it is easy to place them randomly if you know them or if you have a formula.
I can imagine that it could look good here or it could be placed at source.wikipedia if it is worth something. I have never used Java or Flash. Some properties of the squares could be shown moving the subsquares or the focus of attention and so on. I imagine that it would be interesting having the squares repeated both horizontaly and verticaly. Then it will be possible to show differen patterns by witch the original squares could be analysed and shaw that these patterns as you will see in step three of the "Sri Rama Chakra" example (if this does not show parallel lines) are all the same (only shifted in the endless field).
The higher order perfect magical squares (2^n)x(2^n) are generated on a generalisation of "straight neighbour values" to somthing you could call "associated key values" and their complements based on the original formula. You just have to choose in what direction you would like to expand the "original cell" from which you are starting and where to place the last key values.
- Note: The code will not generate "all known perfect magical squares of this order" as it would say today if you see what you cannot see (puzzled ?). It does not generate 4*n (as for n=3) eigther.
Meditating about the squares and reflecting the own toughts its worth and a point to thing about how cognition works and how patterns are involved. I explained you the fractal property and maybe you said "Wow!". I told about key values and complements and you probably sad "Oh no!". But is fractal a pattern of the square or somthing we need to be able to continue our taughts (the proces of thinking), to comunicate, and justify our opinion? As I saw on squares of higher order fractal it is not a class property.
The squares could be a part to start as a demonstration / exercise of the algebraic properties of their transformations in another part of Vikipedia. Here at some point the squares and their transformations are "identical". But remember the transformations can be aplied to itself. (See Note 2)

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Both kind of Java scripts moving and quite could be shown. The squares are such that they "remind" us about equilibrium and harmony. I was thinking that you could place them on a tablet and hold it with one finger only. Any change at one place involves a lot of other changes at other places. This means that growth is not possible in this system. By growth at some point there must be a decrease in another point. There is only transformation. We do not like to be reminded about this and say that this is philosolhy or "de:Weltanschauung" (?) and here is no place for thinks like this.
If numbers are starting from 0 to 15, 63 ... (see note 3) and are writen binary we see lots of interfearing patterns remind us about waves. Every plane of magic sqaures can be shown as interfearing / waving fields, but in this case the wave length is shorter then the square order. For each potence of 2 there are horizontal and / or vertical waves. To generate the squares the assignment of the potences of 2 to the amplitude of these waves does not mather (as long as it is unique) and I need to verify if the relative position of waves to each other cares.
- Note 3: The analysis can be done also with the odd number equivalent of the square.
It is a starting point to thig about lots of issues: horizont of interest, horizont of perception, horizont of cognition, inherent pattern, morphic field. Analysing the addition and / substraction of two squares is both a helpfull tool to understand vizualize the properties of the squares and a step to a higher algebraic object too. This is comming to a closed algebraic structure where all elements where inheriditing the most of the properties mentioned at the definition from [2]. To come the whole way back again from the puzzeleing things of this embarassing mathematical objects: The odd thing is that they do not fullfill the last 8 characters from that definition: "from 1 to n^2".

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I wanted to stop but ...

- Note 2: coming bak correcting the text I just want to point out what this means and what philosophical implications it has.
I realised some months before how complicated it is to focus at a particular property, to identify new properties, not to be influenced about others taughs, old taughts and so on. But the properties to be analysed are all there and they are there all the time. It is as known in quantum theory.
It is just like the iceberg picture in the logo of wikisource. We see / understand only a part of it at the same time and to see it all / to understand it we need to transform it. In the case of the iceberg we need to dive and you need to press CTRL-A at the first link I mentioned . We visualy can see only a surface not a space and if a computer tomograph is used we visuial still can see only a surface, maybe a more relevant surface for the focus of our attention.
But what is that thing which is only one thing and we need to transform it in order to see / understand what it is. I'm not puzzeling, I'm puzzeled myself. But magic squares where allways linked closed to some religius taugths too. So let write some issues I was puzzeled myself. Each magical square can be mirored and turned and doing so there are 8 different transformations. In addition the perfect magical squares allows also arbitrary shifting both horizontaly and verticaly. This means 8*4*4 and as there are only 384 squares (we know this, others have to find it out first) there are only three (see Note:) relevant squares which can not be transformed from one in to the others by standard technics. The technic of comparing two variants (in our case squares) by and referencing the relative row and column positions (or changes, deltas) in a matrix (transformation) will result in having the same amount of matrixes (transformations) and each matrix stands also for a variant (in our case a square). We may give some of the matrixes special names as "shift two colums horizontaly" and some not because we do not like to remember "shift one column left, rotate, shift one row up" unless this is a code for our safe, we remembered jumping like this as a kid on the street or whatever help we have to keep this in mind or would opone to remind it. But at the end we will see "there is nothing new", we just exhausted all the combinations and turned in a circle (to be more precised in different circles).
- Normaly esentially different magic squares are counted. This method is generaly used for all magic squares and does not relate to what was called "arbitrary shifting" before. Thuse this method of counting gives a n^2 (n = order of the square) higher number.
Generation of an additional (in our case a the third if we know two already) square (class) is possible referencing an already known variant of one class depending (?) on a variant from another classes. The matrix will differ from all the ones known before. This is an iterative method to and exhaustive work is necessary to found all possible new classes.
This sounds very, very embarasing and as more precise wording would be used, as easier it would be to follow, as soon as no possible ambiguity is left, no magic is left or supposed here.
Now listen to the words and note of the ethymology of them too: One (transformation) comes from the other and the third comes trough the seccond from the first and there are all one. --- A obviuosly wrong description of the simple and evident fact on the upper paragraph would be: The generation (of the new transformation) is the combination of (a transformation from) the first with (one of) the seccond.
I supose that to generate comes from genesis or is related to it. These wordings have been used culturaly and religiusly and the alegorical form allowed to interpret whatever to this words. Whatever? Realy? I was puzzeled another time. In order to understand the properties of the 384 (squares, I do not want to be cryptic) and maybe also before I found the 129th realising the fractal property I substracted and also added oftenly two arbitrary squares out of the 128. At some point I noticed that when the reference Indian square (I used that time) is turned clockwise with 90° and added to itselves it gives 4 subsquares all having the numbers 9, 16, 25, 18. Thats odd!? And I was long time thinking about. I even did not realized that 9, 16, 25 are the first Pythagorean numbers (and I studied some years mathematics) but this (the Pythagorean numbers) was not the point. What importance has 18? 18 in four subsquares? Some years ago I was reading a book about Kabbalah and I remebered the significance. At least it was good point to tranquilize and stop further researches at that time. I reverted to something I knew allready. That is a circle. And I remebered the book of Kohelet, Ecclesiastes about what is realy new.

To be appeded other time: relation to manipulation, intended omissions, confusion, ...
Noncryptic message: In moste cases you see somthing else as written. Sorry for all spelling errors. Regards Gangleri 06:32, 2004 Sep 27 (UTC)

PS: The text is not straight forward because first while rewritten, more and more ideas where involved, introduced and seccond it is not written in a native language. I applogize for this stile and you should know that thats me. I do not object criticism and hope that WikiMagic people are alowed to be a little diferent. Gangleri