There's useful, and there's interesting - the two are very different things! If these were used in engineering calculations, quantum mechanics (or anything along those lines really) I'd class them as useful. Something that just makes a fun puzzle comes under the category of "fun and interesting" in my book, but not really useful.
Math question (semi-simple)
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having read the press release that you linked.
I believe that Toshibas "Magic Square" algorithm actually is the name that they are calling it, (ie it's a square, and it's a bit magic).
and doesn't relate at all to the magic squares like you posted, (where all line horizontal/vertical/diagonal add up to the same number).
my opinion, is what Berry said...
Useful application would be something that had a practical purpose, engineering, electronics, if it related to biology, mechanics, anything where these held a clue or an answer, a problem solving ability...
Games, are fun, and do serve a purpose of occupying the mind or wasting up time. but that's not the kind of purpose that I was after.
and I know that they say that doing suduko puzzles help stave off senility, but that's more to do with exercising the mind, (any logic puzzle would have the same effect).
I believe that Toshibas "Magic Square" algorithm actually is the name that they are calling it, (ie it's a square, and it's a bit magic).
and doesn't relate at all to the magic squares like you posted, (where all line horizontal/vertical/diagonal add up to the same number).
my opinion, is what Berry said...
Useful application would be something that had a practical purpose, engineering, electronics, if it related to biology, mechanics, anything where these held a clue or an answer, a problem solving ability...
Games, are fun, and do serve a purpose of occupying the mind or wasting up time. but that's not the kind of purpose that I was after.
and I know that they say that doing suduko puzzles help stave off senility, but that's more to do with exercising the mind, (any logic puzzle would have the same effect).
Re: Differing opinions
1.0871e-12
I've not studied Eigenvalues/Eigenvectors yet (next year) - but it seems that one of the Eigenvalues every magic square is the number that you get when you add up each row/column. Interesting!
You could probably write a Brute-force n*n magic square maker with that fact... perhaps
1.0871e-12
I've not studied Eigenvalues/Eigenvectors yet (next year) - but it seems that one of the Eigenvalues every magic square is the number that you get when you add up each row/column. Interesting!
You could probably write a Brute-force n*n magic square maker with that fact... perhaps
wonderboy1953
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Because algorithm is part of the title, I believe just the opposite.
It would take further research to clarify. In the meantime I want to cover another aspect to the usefulness of concepts because something that seems to be a mere curiosity can lead to something of great importance.
For people who are really into mathematics, there is the story of the Konisberg bridges puzzle which for many years was a source of curiosity and recreation. Leonhard Euler (who I mentioned before) went over to investigate. From his study he developed the very important branch of topology (later extended by Poincare) which is taught at many colleges.
In this area, my own belief is that all areas of mathematics, no matter how trivial they seem, have potential importance and not just something to play around with.
Would you care to try to solve the puzzle I put up?
JogaBonito1502
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Linking Magic Squares to the cause of Euler's success as a mathematician is absurd. If Magic Squares can't stand on their own as useful tools then they aren't useful. Not that hard of a concept to understand.
I know that the first rule of life is never argue with an idiot as they just bring you down to their level and beat you with their experience... but.
look at the press release that you linked to.
toshibas news desk said:
so lets look at the facts here.
There is no known algorithm for generating magic squares.
the only algorithms that can be used are genetic algorithms (which are a successive approximation tool)
Toshiba didn't create an algorithm to generate magic squares.
they created an algorithm that uses lookup tables to enable a greater resolution to be displayed from a lesser signal and hence reduce the bandwidth needed for signal transmission.
(also enables still scenes in film to require almost zero bandwidth, which is very impressive, as at the moment, still scenes in video transmission would still be assumed to be changing.)
impressive yes, but using magic square number games no.
errr, no it wouldn't all the information needed is in the press release, just because you googled two words together and found a press release it doesn't mean it's a fact, had you read and understood that press release then you wouldn't think it needs more research.
I thought we were talking about Magic squares, not bridge puzzles...
should I just believe that you can't actually find a use for magic squares either?? hence this constant changing the subject? now to bridge puzzles... which again have no use past playing games.
you appear to have a fundamental misunderstanding of how peoples brains work...
as I said earlier, the more you use your brain the better it gets, the more you tax your brain, to harder you push it, the more you make it work, the better it gets, or in the case of old age, the less worse it gets.
in this respect the brain is much like any other muscle in your body.
IF you play with number games, then you will get better at them. your brain will be improved, to that extent, playing with any number game, magic squares, bridge puzzles, practising long multiplication in your head, large number addition or subtraction even anything that may tax your brain or cause you to think is useful to developing your brain.
at the end of the day though, something being useful as a mental exercise, and something being useful as a mathematical tool/formula/process/method/theory etc is very different.
but at the moment, magic squares don't have a practical purpose at all. and I can't see them getting a practical purpose, since the squares are not uniform enough to be able to be generated, then how are they going to find a use in the rather formulaic and strict world of mathematics?
no, I'm not denying that magic squares may be useful (meaning have a real practical purpose at some point in the future), but then can only ever be used as lookup tables, since there is no formula to create them, people have used lookup tables for years (though this was before calculators, when you couldn't just find the natural log of a number, you had to find it on your reference chart).
bridge puzzles are frankly ridiculous, and again have no practical purpose. (past mental exercise).
basically, magic squares only have purpose as a mental exercise, which makes them about as useful as a game of hangman.
You mean every curiosity of maths is important because it might make you think?
as I said above you missed the point, the people that you mention didn't go on to be great because they played magic square games, they went on to be great because they exercised their brains.
the simple fact is that had there never even been a magic square game then they would have still exercised their brains, just with a different game, and would have still been great people.
it's been solved! everything about it has been solved. right down to the eigenvalues/vectors... in fact we only moved onto eigenvalues and vectors because your math problem, had been solved.
if you've got a different puzzle you need solving, or the solutions that were given aren't good enough, or you missed them, then say what you're missing?
wonderboy1953
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More particulars to help you solve the puzzle
In post #22 you had this to say: "I believe that Toshibas "Magic Square" algorithm actually is the name that they are calling it, (ie it's a square, and it's a bit magic)...." So here you believe.
Now we have this: "Toshiba didn't create an algorithm to generate magic squares." Apparently you went from belief to certainty. Well this "idiot" still believes that Toshiba's technology relates to magic squares as what you've said doesn't convince me.
Then you really put your foot in your mouth when you had this to say "There is no known algorithm for generating magic squares." Wrong. First there's a website that generates 5 x 5 magic squares (where you enter certain numbers that will generate them). Even more than that I created a magic square maker about 25 years ago (using BASIC programming) that would theoretically let you make 144 4 x 4 magic squares (over 16% of all of them - the 5 x 5 website I seriously doubt can generate all of the 5 x 5 magic squares as there are over 275 million of them which would take over eight years to do if you make one magic square per second). This software I created was so good that when I let my friend try it, I couldn't tear him away from it (since then I acquired more knowledge plus the computer technology has substantially improved).
JogaBonito1502 also had this to say: "Linking Magic Squares to the cause of Euler's success as a mathematician is absurd." Not at all. Many parts of math relate to other parts of parts of math. So for example about 17 years ago it was proven that elliptic equations are equivalent to a large set of modular forms (which subsequently has changed to all of the modular forms). Now if you have an elliptic equation which you can't solve, then translate it into a modular form, solve it, then translate the solution back or vice-versa. The Euler analogy is just to point out the potential of expanding the magic square knowledge into something more useful (I gave the Karnaugh map example earlier).
Again quoting from root: "it's been solved! everything about it has been solved." Not on this website and it appears I'm the one who actually invented it, in fact I have to give you more particulars so at least you can understand the puzzle better.
Here's the actual puzzle. With respect to the rows and columns of the magic square (semimagic) I gave you in post #1, relate them to the numbers 1,2,3 and 4 to come up with the secondary magic number of 85 (right now I'm still teasing a bit, but I'm sure that someone with enough imagination can solve this puzzle so root don't strain the brain too much).
In post #22 you had this to say: "I believe that Toshibas "Magic Square" algorithm actually is the name that they are calling it, (ie it's a square, and it's a bit magic)...." So here you believe.
Now we have this: "Toshiba didn't create an algorithm to generate magic squares." Apparently you went from belief to certainty. Well this "idiot" still believes that Toshiba's technology relates to magic squares as what you've said doesn't convince me.
Then you really put your foot in your mouth when you had this to say "There is no known algorithm for generating magic squares." Wrong. First there's a website that generates 5 x 5 magic squares (where you enter certain numbers that will generate them). Even more than that I created a magic square maker about 25 years ago (using BASIC programming) that would theoretically let you make 144 4 x 4 magic squares (over 16% of all of them - the 5 x 5 website I seriously doubt can generate all of the 5 x 5 magic squares as there are over 275 million of them which would take over eight years to do if you make one magic square per second). This software I created was so good that when I let my friend try it, I couldn't tear him away from it (since then I acquired more knowledge plus the computer technology has substantially improved).
JogaBonito1502 also had this to say: "Linking Magic Squares to the cause of Euler's success as a mathematician is absurd." Not at all. Many parts of math relate to other parts of parts of math. So for example about 17 years ago it was proven that elliptic equations are equivalent to a large set of modular forms (which subsequently has changed to all of the modular forms). Now if you have an elliptic equation which you can't solve, then translate it into a modular form, solve it, then translate the solution back or vice-versa. The Euler analogy is just to point out the potential of expanding the magic square knowledge into something more useful (I gave the Karnaugh map example earlier).
Again quoting from root: "it's been solved! everything about it has been solved." Not on this website and it appears I'm the one who actually invented it, in fact I have to give you more particulars so at least you can understand the puzzle better.
Here's the actual puzzle. With respect to the rows and columns of the magic square (semimagic) I gave you in post #1, relate them to the numbers 1,2,3 and 4 to come up with the secondary magic number of 85 (right now I'm still teasing a bit, but I'm sure that someone with enough imagination can solve this puzzle so root don't strain the brain too much).
Re: More particulars to help you solve the puzzle
a look up table... (I didn't think I'd be having to explain the idea of a lookup table to someone who claims to be a programmer).
like this
00 1 2 3 4
1 1 1 4 5
2 6 8 4 3
3 2 6 5 1
4 5 6 2 4
see, look at co-ordinate 3,4 it's a four. -it's a table that you can lookup values from...
that's a square, and if you can use it in such a way that you can reduce the bandwidth needed for transmitting a signal, then that's really cool. perhaps I shouldn't have confused you by saying it was a bit magic. and the table is a square. but it's not a magic square number game.
in short the toshiba "Magic Square Algorithm" appears to be a catchy title, rather than an example of the use of magic squares.
What About Even Orders?
There is no known algorithm for generating even-order normal magic squares -- that is, normal magic squares where n is even.
really, just google for magic square generating algorithm, there is no algorithm for generating even squares that I could find.
so what I said is completely correct, there is no algorithm for generating all magic squares. how can you use magic squares in a predictable sense if they can't be predicted?
As I said earlier...
your Toshiba article was just a proof of your read comprehension failure. it's not a proof that they are useful. because it doesn't appear to use magic squares.
Right...
I agree with what you are saying, to a point.
there is a certain amount of usefulness in mental exercise.
and for example people study one area, and whilst they may not make any ground in that area, their interest leads them to develop methods in a completely different area...
So for example a rabid interest in Magic squares, might lead a person to develop the idea of karnuagh maps. that means that the person who developed karnaugh maps was clever, it means that they developed a new way of working.
it doesn't prove that magic squares are useful. it wasn't the magic square that lead to the theory or method being developed.
so that's not really providing a purpose or use for magic squares.
you claimed it was interesting. and asked what was interesting about it.
in that respect everything that you had asked had been answered...
What I would suggest is this.
in future, if you have a question, ask the question entirely, don't just quote a 4x4 grid of numbers and ask what's interesting.
then come back and tell us what you actually wanted to know was what makes the grid interesting in relation to number games, why this grid is particularly interesting in relation to the sub-squares in the grid, how the grid relates to numbers 1 - 4 to form an interesting secondary magic number....
you see how there's a difference there?
a look up table... (I didn't think I'd be having to explain the idea of a lookup table to someone who claims to be a programmer).
like this
00 1 2 3 4
1 1 1 4 5
2 6 8 4 3
3 2 6 5 1
4 5 6 2 4
see, look at co-ordinate 3,4 it's a four. -it's a table that you can lookup values from...
that's a square, and if you can use it in such a way that you can reduce the bandwidth needed for transmitting a signal, then that's really cool. perhaps I shouldn't have confused you by saying it was a bit magic. and the table is a square. but it's not a magic square number game.
in short the toshiba "Magic Square Algorithm" appears to be a catchy title, rather than an example of the use of magic squares.
What About Even Orders?
There is no known algorithm for generating even-order normal magic squares -- that is, normal magic squares where n is even.
really, just google for magic square generating algorithm, there is no algorithm for generating even squares that I could find.
so what I said is completely correct, there is no algorithm for generating all magic squares. how can you use magic squares in a predictable sense if they can't be predicted?
As I said earlier...
the answer is none.
your Toshiba article was just a proof of your read comprehension failure. it's not a proof that they are useful. because it doesn't appear to use magic squares.
Right...
I agree with what you are saying, to a point.
there is a certain amount of usefulness in mental exercise.
and for example people study one area, and whilst they may not make any ground in that area, their interest leads them to develop methods in a completely different area...
So for example a rabid interest in Magic squares, might lead a person to develop the idea of karnuagh maps. that means that the person who developed karnaugh maps was clever, it means that they developed a new way of working.
it doesn't prove that magic squares are useful. it wasn't the magic square that lead to the theory or method being developed.
so that's not really providing a purpose or use for magic squares.
that's not even remotely close to what you said.
you claimed it was interesting. and asked what was interesting about it.
in that respect everything that you had asked had been answered...
What I would suggest is this.
in future, if you have a question, ask the question entirely, don't just quote a 4x4 grid of numbers and ask what's interesting.
then come back and tell us what you actually wanted to know was what makes the grid interesting in relation to number games, why this grid is particularly interesting in relation to the sub-squares in the grid, how the grid relates to numbers 1 - 4 to form an interesting secondary magic number....
you see how there's a difference there?
11 05 08 10
02 16 13 03
14 04 01 15
07 09 12 06
ok, first, how do you think that your magic sqare (given in post 1) is semimagic? far from semi magic,
it's magic fully (rows columns and diagonals all add to 34)
plus the corner 2x2 squares and the centre 2x2 adds to 34
plus it's pan diagonal...
semi magic would be where the rows and columns add up to 34, but the diagonals don't.
also looking back earlier in the question you said
the intermediate squares don't all add up to 34
look at the intermediate square on the left hand side
2+16+14+4 = 36, not 34
and the intermediate square on the right
13 + 3 + 1 + 15 = 32 again not 34
the square at the top centre
5+8+16+13 = 42 (not 34)
and the middle centre square makes
4 + 1+9+12 = 26 (not 34)
I think that the square that you want is
12 06 15 01
13 03 10 08
02 16 05 11
07 09 04 14
it's slightly neater as every horizontal and diagonal are 34
also all broken diagonals are 34
plus every 2x2 square (not just the corners and centre) add to 34
Horizontal
(12 + 6 + 15 + 1 = 34) (13 + 3 + 10 +8 = 34) (2 + 16 + 5 + 11 = 34) (7 + 9 + 4 + 14 = 34)
vertical
(12 + 13 + 2 + 7 = 34) (6 + 3 + 16 + 9 = 34) (15 + 10 +5 + 4 = 34) (1 + 8 + 11 + 14 = 34)
diagonals
(12 +3 + 5 + 14 = 34) (1 + 10 + 16 + 7 = 34)
broken diagonals (2x2)
(6 + 13 + 11 + 4 = 34) (15 + 8 + 2 + 9 = 34)
broken diagonals (3x1)
(6 + 10 + 11 + 7 = 34) (15 + 3 + 2 + 14 = 34) (13 + 16 + 4 + 1 = 34) (8 + 5 + 9 + 12 = 34)
squares (2x2)
(12 + 6 + 13 +3 = 34) (6 + 15 + 3 + 10 = 34) (15 + 1 + 10 + 8 = 34) (13 + 3 + 2 + 16 = 34) (3 + 10 + 16 + 5 = 34) (10 + 8 + 5 + 11 = 34) (2 + 16 + 7 + 9 = 34) (16 + 5 + 9 + 4 = 34) (5 + 11 + 4 + 14 = 34)
wraped squares (1x2 + opposite 1x2)
(6 + 15 + 9 + 4 = 34) (13 + 2 + 8 + 11 = 34)
and corners
(12 + 1 + 7 + 14 = 34)
plus of course
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 16 = 136, and if you divide that by the amount of numbers you're adding at any one time (4) 136/4 = 34
anyway...
with your square
11 05 08 10
02 16 13 03
14 04 01 15
07 09 12 06
I believe that what you want is...
11 x 1 + 5 X 2 + 8 + 3 + 10 * 4
11 + 10 + 24 + 40 = 85
and if you do that to all the rows you get a new (not)magic square where everything adds to 85 in the horizontal only. vertical columns are not adding to 85 so the square isn't magic?
11 10 24 40
02 34 39 12
14 08 03 60
07 18 36 24
and if you do the same with the verticals, then strangely the new vertical lines add to 85, but the horizontals don't (so again a not magic square, not even semi magic)
11 05 08 10
04 32 26 06
42 12 03 45
28 36 48 24
if I do the multiplication going backwards and forwards (11x1+5x2+8x3+10X4 next row 2x4+16x3+13x2+3x1 and so on)
11 10 24 40 = 85
08 48 26 03 = 85
14 08 03 60 = 85
28 27 24 06 = 85
I still don't get a magic square... (verticals break)
same things happen with the diagonals
as a last ditch attempt I'm going to try multiplying in this grid pattern
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
(ie if I make a semi magic square of the number you're asking me to relate your fully magic square to)
11 10 24 40 = 85
04 48 52 03 = 107
42 32 03 30 = 107
28 09 24 18 = 79
= = = =
85 99 103 91
which still isn't a magic square...
you say that it shouldn't be too hard for someone with a little imagination.
I'm finding it quite difficult to make a semi magic square making products of the numbers in your square by 1 2 3 4. I can make the numbers add up to 85 multiplying either rows or columns by 1,2,3,4 in turn, but that doesn't make a semi magic square.
(of course if I just multiple all the numbers by 1, then 2 then 3 then 4 I can make a fully magic square, but this doesn't relate to the number 85...)
perhaps I'm just misunderstanding the question that you're asking.
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