Mercury

[FraterUFA]

Ben Franklin was a genius at constructing them ... straight out of his head on to paper, just writing the numbers down in columns like a printer

 

Heh, there is nothing genius about this. It's just an old parlor trick. I learned how to do it when I was eight and amazed my friends and teachers with my incredible skill.

 

Here's a 5x5 I just whipped up in Excel. Had to make sure I still knew how to do it :-)

 

UFA

[Brian]

yes, that is a most interesting aspect.   The model I use is like the basic imprint , the hardware,  the planets are always in the same positions in relation to each other on the map  ( so we all have an Ego, Id, Super consciousness 'inner and outer gate' , etc. on the map ) but the natal arrangements create variant pathways and energies - that is how 'the psyche' manifests and how 'one's psyche' manifests within the map.  Then one can go about balancing it. 

 

 

 

 

I made dhal out of black moong once ....   I can understand the need to make a demonic face after tasting it . 

 

 

 

A type of 'yantra' can be constructed from planetary magic squares by simply consecutively joining the numbers in the square with a line, coloring the figure with the planetary colours in question ... and in some cases, the related jewels and metals were stitched on as well ... the end result is like a big ' yantra - thangka ' . 

 

The Sun;

 

 

 

 

Part of a robe / cape  ;

 

 

 

Ben Franklin was a genius at constructing them ... straight out of his head on to paper, just writing the numbers down in columns like a printer .............

 

....................

 

..............  

 

Here is his 'Square for Mercury'  ....  join the dots ( draw a line from 1 to 2 to 3 to ....  64 then back to 1 )  to see the ' mandala '  .

 

 

 

 

 

Its still pervasive in a way here ... even straight jewelers will talk about ones birth stone or jewel. 

Now isn't that interesting! Not the mathematical nature of the square itself but the pattern it reveals.

[Nungali]

Heh, there is nothing genius about this. It's just an old parlor trick. I learned how to do it when I was eight and amazed my friends and teachers with my incredible skill.

 

Here's a 5x5 I just whipped up in Excel. Had to make sure I still knew how to do it :-)

 

UFA

 

Mhe ... thats  kids stuff !      If you know the formula .     Ben's were slightly  more complex  . 

 

But yes ... you are amazing  anyway  !  

 

The simplest is probably Venus ; just write out the numbers r to l up and down in a 7 x 7 grid  ...  then reverse the diagonal lines .

 

(PS .... dont use the ones in the GD book   .... error ....   { one can tell when one is just copying them with out understanding as  the error has been repeated ... for some time } ). 

[Nungali]

Now isn't that interesting! Not the mathematical nature of the square itself but the pattern it reveals.

 

 

6 

 

 

[Brian]

Oooooo...

 

[FraterUFA]

Mhe ... thats  kids stuff !      If you know the formula .     Ben's were slightly  more complex  . 

 

True, but they are made in the same way. Just swap the columns and rows until you get the pattern you want. 

 

 

But yes ... you are amazing  anyway  !   

 

No... you're amazing 

 

UFA

[Nungali]

True, but they are made in the same way. Just swap the columns and rows until you get the pattern you want. 

 

 

H   u  h  !    What about the number order within the rows ?  Maybe what you say could apply to a couple of low number simple squares ,  but usually its a lot more of a process than that . 

 

As far as I know, some squares require a lot more construction than that . 

 

maybe I misunderstand you ?     Swap the columns and rows to the magical order ... from what order ? 

 

I am assuming a natural square to begin with ;

 

1    2   3  4   5 

6    7   8  9  10

11 12 13 14 15

16 17 18 19 20

21 22 23 24 25  

 

how did you get your square of 5 above by just swapping rows and columns to get  

 

 

 

 

 

No... you're amazing 

 

UFA

 

No, I'm confused  

 

 

https://nrich.maths.org/1337

Edited January 13, 2016 by Nungali

[RigdzinTrinley]

I made dhal out of black moong once .... I can understand the need to make a demonic face after tasting it .

 

 

Wahaahaahaa that made me so happy

[FraterUFA]

H   u  h  !    What about the number order within the rows ?  Maybe what you say could apply to a couple of low number simple squares ,  but usually its a lot more of a process than that . 

 

As far as I know, some squares require a lot more construction than that . 

 

maybe I misunderstand you ?     Swap the columns and rows to the magical order ... from what order ? 

 

I am assuming a natural square to begin with ;

 

1    2   3  4   5 

6    7   8  9  10

11 12 13 14 15

16 17 18 19 20

21 22 23 24 25  

 

how did you get your square of 5 above by just swapping rows and columns to get  

 

 

 

 

 

 

 

No, I'm confused  

 

 

https://nrich.maths.org/1337

 

The square you started with isn't a magic square... all of the rows, columns and diagonals must add up to the same number. Start with that. Then it can be transposed to any other magic square by swapping rows and columns.

 

UFA

[Nungali]

 What ?  

 

 

The square you started with isn't a magic square...

 

 ha har , very funny.    

 

Okay I will play along .

 

The first one is a natural square. There are two main processes to change the 'natural square' into a magic one, depending on if it is an even or uneven number ,  for the low numbers 

 

Its a very common concept and is  clearly shown (along with 'natural squares' ) in the link I provided .

 

Did you look at that ? 

 

 

 

all of the rows, columns and diagonals must add up to the same number.

 

So, after all the info and pics I provided .... you thought I had not realised that  ....         thanks for that info  !

 

Actually, it can be a lot more than that, in some of the really smart squares. like the Ben Franklin large number ones; all the columns up and down, the diagonals, boxes of 4 by 4 at each corner, groups of 2 in cross patterns and many other symmetrical shapes create the same  number totals or patterns within them . 

 

But you may not realise that from a quick glance and a comment  like ' Simple ! I could do that in primary schoo! !  '   

 

 

 

 

 

http://www.oocities.org/~harveyh/franklin.htm

 

 

 

Start with that. Then it can be transposed to any other magic square by swapping rows and columns.

 

UFA

 

 

 

So ... I 'start with that' .  I assume you mean  : start with a magic square "  ?  

 

Ummmm   .....    yeah .  What I mean is , how do you make a magic square in the first place ? 

 

(Jeeze ! )  

 

Not  just take one already made and swap the columns around and say "Look ! I made a magic square ." 

 

[ Hint ; a square that is 'magic' will still have those properties if it is upside down or a mirror image           ]

 

Anyway .... my answer  to what you said is  'No it cant ." 

 

It cant be transposed to  any other magic square !   It might be able to be transposed to another square of the same number. 

 

Again , check the link I posted in my quote box in your above post.

 

Here is a very simplified explanation  - he is right for the very basic simple square numbers , but wrong in his claims as well, for being for all squares - but he is just a little kid

 

 

 

 

Now ,   Frater ,  were you pulling my leg, 

 

 or I am still confused by what you mean 

 

or you were confused ? 

[FraterUFA]

Its a very common concept and is  clearly shown (along with 'natural squares' ) in the link I provided .

 

Did you look at that ? 

 

What you've posted are not "very common" concepts at all and no, I didn't look at your link. Is this really what you spend your time on?

 

Ok, I'll bite:

 

Benjamin Franklin (1706-1790), the early American scientist, statesman and author, is known as the creator of bent-diagonal magic squares. (Actually these squares are not magic in the accepted definition because the two main diagonals do not sum correctly.)

In his lifetime he published an order-8, an order-16 and a magic circle. The order-16 and the magic circle were first published in Ferguson’s Tables and Tracts Relative to Several Arts and Sciences (London,1767). In the next few years, all three were published in various works and personal letters.

 

Aaaaand I'm out. And I wasn't pulling your leg. I don't have any clue what an order-8, order-16 or magic circle are. A magic square is the same as it always was though: rows, columns and diagonals add up to the same sum. I learned how to do this as a kid. Looks like Ben spent a lot more time on this, easy to do when there's no Internet (trust me).

 

I guess this is vaguely interesting and I learned something new but there aren't enough minutes in the day as it is. Tell me why this matters.

 

UFA

[Nungali]

Tell you  why it matters ?   How would I know ?

 

You were the one that entered with a 'I can do what Ben Franklin did and amazed kids at school ' comment.  

 

You also seem you say you know what a magic square is but are unaware of the various types and styles and dimensions of them , 

 

I dont know why that matters either . ... cause I am not doing that stuff. 

Edited January 16, 2016 by Nungali

[Apech]

 

Mercury is very low on this thread now.

[rex]

Diagram showing Mercury's intermediary function:

 

Edited January 16, 2016 by rex

[FraterUFA]

Tell you  why it matters ?   How would I know ?

 

You were the one that entered with a 'I can do what Ben Franklin did and amazed kids at school ' comment.  

 

You also seem you say you know what a magic square is but are unaware of the various types and styles and dimensions of them , 

 

I dont know why that matters either . ... cause I am not doing that stuff. 

 

Well, what I said was accurate. I told you it's trivial to make a magic square, then I told you that if you swap the rows and columns you can transform it into any other magic square while retaining its core properties. That includes the variants you shared. My point in doing that was to demonstrate that there isn't anything particularly interesting about what Ben Franklin was doing. 

 

So I'm still left wondering why you brought up those variants in the first place? They seem arbitrary to me. I assumed there was a point that I wasn't seeing but I guess not.

 

UFA 

[FraterUFA]

Diagram showing Mercury's intermediary function:

 

 

This was a favorite diagram of mine for many years.

 

However, I'm going to point out something which is not obvious from a theoretical perspective but is proven immediately by practical work. The above diagram is inaccurate from a laboratory standpoint: Fire is not volatile, it is fixed. If you follow the implications of this, you will see that it means that Mercury cannot be the intermediary.

 

Best,

UFA

[Nungali]

Well, what I said was accurate. I told you it's trivial to make a magic square, then I told you that if you swap the rows and columns you can transform it into any other magic square while retaining its core properties. That includes the variants you shared. My point in doing that was to demonstrate that there isn't anything particularly interesting about what Ben Franklin was doing. 

 

So I'm still left wondering why you brought up those variants in the first place? They seem arbitrary to me. I assumed there was a point that I wasn't seeing but I guess not.

 

UFA 

 

Its  trivial to make a magic square  ......       

 

whatever . 

 

The point was a response to the poster where I first mentioned it in relation to yantra  and the other  reasons ....   well,  they lie in the other responses I got .   

 

If its trivial to make ( or use ) a magic square ... tell it to the G.D.  and Israel Regardie . 

 

Since you would have no idea what is trivial to me, I must assume you mean it's trivial to you  ..... so why waste your time here with this ? 

[FraterUFA]

Its  trivial to make a magic square  ......       

 

whatever . 

 

We're getting way off the topic at this point, but your reply comes off to me as pretty defensive about something which is so easily verified.

 

Perhaps you are referring to something else. I am using the classic definition of a magic square:

 

A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ...,  arranged such that the sum of the numbers in any horizontal, vertical, or main diagonal line is always the same number (Kraitchik 1942, p. 142; Andrews 1960, p. 1; Gardner 1961, p. 130; Madachy 1979, p. 84; Benson and Jacoby 1981, p. 3; Ball and Coxeter 1987, p. 193)

 

 

If its trivial to make ( or use ) a magic square ... tell it to the G.D.  and Israel Regardie . 

 

Israel Regardie was a therapist, maybe math wasn't his strength. So I decided to make a 7x7 in Excel for you. I timed myself and it took just a bit over four minutes. Here you go:

 

 

I made another, this one took less than a minute. I could make a bunch more, but surely you still don't think it's that difficult, do you?

 

 

There are a lot of magic squares of any order and the fact that I produced two of them in a trivial amount of time from my head proves that they aren't difficult to create. I don't dispute that you could place some arbitrary restrictions on them and make it much more difficult. But again I ask, "why?" This seems as pertinent to the topic as Sudoku.

 

Best,

UFA

[FraterUFA]

Here, I whipped up one more for you. It's a 5x5 in which all the diagonals sum to the same number, even if you wrap them around the square. 

 

 

It took three minutes for this one. I had time to spare while waiting for my ride.

 

UFA

[Zhongyongdaoist]

It's mathematical magic my friends, magic squares that is, and neither Israel Regardie, nor the Golden Dawn knew much about either, though the originators of the Golden Dawn were perhaps more savvy in their own thinking and practice than their successors and 'tis a magic most Mercurial, dealing as it does in the formal properties of Systems and most appropriate to this thread.
 
Magic squares are a well formed set of mathematical objects called matrices and matrix mathematics is one of the most important mathematical studies because of its importance to Linear Algebra.  One of its most significant uses in the Twentieth Century was it application to Quantum Mechanics, where a some clever matrix mathematics turned out to be the equivalent of Schrodinger's Wave Equation and these two together tiled the floor of the Temple.
 
Now, just as a point of continuity here, I will note that the swapping of rows and columns is an important aspect of using matrices in mathematics, and in their application to solving systems of, for example, linear equations, aiding greatly in simplifying the problem.  Their application to magic is another matter, and rather complex and I cannot enter into any detail great detail, but such magic squares are used in Chinese, Indian, Arabic and Western magic.  I made a considerable study of them in the 1980s as part of a project of applying modern mathematics to magical practice which I first started pursuing in my teens in 1967 to 68.  Among other things that I discovered pursuing that larger project is that information theory can be constructively applied to maximizing the results of Divination and has suggestions for improving the technique of various types of divination.
 
My application of these ideas to Geomancy was very fruitful and demonstrate that criticisms made by Aleister Crowley are more a lack of his imagination then of Geomancy's potential.  I will note that the extensions which I made did not require information theory, and I started them before I started to use information theory, but it did require some insight into the logical structure of Geomany and how it called out for such extensions.
 
I wish I had more time talk about this, but it really could fill a couple of books, and even a cursory outline might be more a source of confusion than edification.
 
As a note astrological magic is one of the major applications of Mathematical Magic.  Astrological magic was largely neglected in the magical revival, but was considered essential in traditional magic.  Interestingly, I was first drawn to Astrological Magic because of my study of the "Church of Light", teachings again largely in the late Sixties.  Anyone interested in whatever happened to the "Hermetic Brotherhood of Light" (hint, hint Nungali, if you haven't realized this before.) could do worse than scratching around there and seeing what turns up.  Though from the perspective of post Golden Dawn English speaking magic it is widely off the mark, it is much more compatible with the Continental systems of Papus et. al., though unique in its outlook.

 

 

 

Edit: Added ". . . and most appropriate to this thread" to the first paragraph, a change which I had made, but there was a passing squall (get it? squall = sql error) that blew it off course.  The squall lasted only for a few minutes.

Edited January 19, 2016 by Zhongyongdaoist

[RigdzinTrinley]

 

"The spirit of mercury"

 

Ernst Fuchs

[FraterUFA]

Thank you, Donald. I appreciate that you take the time to pack so much information in your posts.

 

It's mathematical magic my friends, magic squares that is, and neither Israel Regardie, nor the Golden Dawn knew much about either, though the originators of the Golden Dawn were perhaps more savvy in their own thinking and practice than their successors and 'tis a magic most Mercurial,

 

I have been practically begging for someone to step in with some informed thought on this and seeing as someone finally has dared to offer some (you), I will do the same: I see the concept of Mercury - in the classic alchemical sense - demonstrated by analogy in the magic square.

 

Mercury is the animating force of nature, within which can be found all possibility, all that ever was, is or will be. Within it is contained every possible human experience. For instance, every word, sentence or paragraph that I type, or will ever type, can be shown to be found in potentia within the "Mercury of English letters" (and this is something that can be readily demonstrated). That this Mercury contains not only truth, but also every possible lie, is a fact that is overlooked by most occultists and this oversight leads to countless errors, illusions and fantasies... but I digress.

 

An analogous type of potentia is found in numbers. There is an indeterminate numerological Mercury which can be thought of as the principle of counting. Then there is the somewhat determined Mercury which consists in the numbers themselves. Finally, that Mercury congeals into the fully determined form of a particular magic square.

 

So in classic alchemical thought, Mercury is not an intermediary or uniting principle, it is the principle of life (eg: potentia). Without sulphur and salt (energy and form), it cannot manifest in physical space-time. Without mercury, the chemical structures and physical forms of life remain inanimate shells, incapable of manifesting the recognizable signs of life and subject only to decay. The alchemist begins with the form and works his way up the rungs of the ladder of life, slowly developing an understanding of the universal Mercury (along with concrete demonstrations of that understanding, though that is incidental IMO) and as his understanding unfolds, he comes closer and closer to the apprehension of "God".

 

I wonder if something similar is possible in this mathematical realm.

 

dealing as it does in the formal properties of Systems and most appropriate to this thread.

 

We are all familiar with the numerological uses of magic squares which appear throughout texts going back to at least Agrippa and for me at least, that lends them a greater degree of credibility than the inventions which appeared from the 19th century (tainted as they were by fantastical pseudo-occultism). However I am left with some questions: What is the intended use of these squares? What is the basis for their alleged power?

 

Magic squares are a well formed set of mathematical objects called matrices and matrix mathematics is one of the most important mathematical studies because of its importance to Linear Algebra.  One of its most significant uses in the Twentieth Century was it application to Quantum Mechanics, where a some clever matrix mathematics turned out to be the equivalent of Schrodinger's Wave Equation and these two together tiled the floor of the Temple.

 

I'm impressed (though not surprised) that you recognized where this came from. I learned the basics of magic squares when I was kid, but it wasn't until I studied higher math that I learned the trick of swapping columns and rows. 

 

Now, just as a point of continuity here, I will note that the swapping of rows and columns is an important aspect of using matrices in mathematics, and in their application to solving systems of, for example, linear equations, aiding greatly in simplifying the problem.  Their application to magic is another matter, and rather complex and I cannot enter into any detail great detail, but such magic squares are used in Chinese, Indian, Arabic and Western magic. 

 

I am not asking you to enter into any great detail, but can you share why you cannot?

 

As a note astrological magic is one of the major applications of Mathematical Magic.  Astrological magic was largely neglected in the magical revival, but was considered essential in traditional magic.  Interestingly, I was first drawn to Astrological Magic because of my study of the "Church of Light", teachings again largely in the late Sixties.  Anyone interested in whatever happened to the "Hermetic Brotherhood of Light" (hint, hint Nungali, if you haven't realized this before.) could do worse than scratching around there and seeing what turns up.  

 

Interesting... I quoted from their materials in an old thread somewhere. There are some interesting ideas contained in CC Zain's writings.

 

Best,

UFA

[Apech]

fuchs1.jpg

 

"The spirit of mercury"

 

Ernst Fuchs

 

 

'Ernst fuchs' - is an incomplete sentence.

[Brian]

 

'Ernst fuchs' - is an incomplete sentence.

Perhaps Ernst is indiscriminate.

[Apech]

Perhaps Ernst is indiscriminate.

 

 

You are right of course it could be a statement about what Ernst habitually gets up to rather than a specific action requiring an object.  I was wondering if perhaps he is related to Ernst Suchs who is not very good at anything?

Edited January 20, 2016 by Apech