RE: The Dichotomy that never was…nor should ever be

Personally I believe in nothing and need nothing. A belief which will never change. I would simply paraphrase Descartes as 'sum, ergo sum' being unsure about the 'thinking/cogito' aspect. Allow me to go back to my current Kenken problem and 'think' about it!

I thought I should remind the pillars of democracy

@teddy wee? I thought that was just Scottish and NZ!
I use it occasionally but consciously thinking 'too many years in NZ'

RE: Racial bias vs racial blindness

I recall dating a Mauritian woman, very dark skinned, but never thinking of her or seeing her in that way. The only thought of colour was when I wondered how to manage our children through school, given the certainty of teasing and bullying. French was a problem too, because my French was on a par with her English. As it happened we never got quite close enough to proceed and she returned to Mauritius. What I do remember most of all is her cooking Gateaux Piments on a Sunday morning, and her winning 'A night in Travelodge' which we spent together, and which her large family celebrated in style! A Mauritian New Years Eve in Sydney!

I thought I should remind the pillars of democracy

@lj well no it is not about Australia - instead it is a direct potshot at the American system, as the blog explicitly states. Perhaps you read shallowly too - leave it to you to work out the grammar of this 'too'
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I thought I should remind the pillars of democracy

@lj well no of course not, it is not about Australia but about the staggering distance American polarisation has achieved from other Western nations. Yet at the same time the Australian elections demonstrate how a two-party system of democracy is disintegrating under the weight of public rejection. If you don't comprehend I am not surprised, since you are mired down in the two-party system.
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RE: How an atheist cured himself

@ab well as you know I never read what you write, but i rather wonder at your incoherent insistence.

The religious zealots ... apostate atheists - shrug, no big deal! I am not and never will be, I don't grasp absurd ideas. You do, the more absurd the better it would seem.

I thought I should remind the pillars of democracy

@ab well that was a spectactularly incoherent rant, wasn't it? no idea what you were trying to say. The thread is comparing the handover of government in USA 2020-2021 with that in Australia 2022. Stick to the point if you understand it, otherwise refrain.
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I thought I should remind the pillars of democracy

It's curious that I have never or perhaps seldom seen the word megalomaniac used here - but surely that is the right word. Grace? Totally absent. In our minor version of democracy the defeated bows out and the victor assumes control. In US version the corrupt defeated before the event raves about corruption and cheating, then attempts a coup d'etat. 18 months later it is still so, and a large number of Americans swallow the crazy bait. Something is amiss in that society, methinks!
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Playing the magic square puzzle...

Rotations about the diagonal, as expected

Playing the magic square puzzle...

@merlot @ted used matrix algebra, and that allows programming - but there are 20 equations and 18 variables, 2 equations need elimination. I haven't solved it - very time consuming by logic.

RE: Have a history teacher explain this if they can

Random stuff - coincidence exist wherever you look for it; one born every minute if that gives you a frisson!

Playing the magic square puzzle...

@ted by diagonal symmetry there are (at least) two solutions

Playing the magic square puzzle...

Eliminating redundant constraints
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The four corners and the central quadrant are derivable, so that reduces the equations to 4+4+8+2=18
Still 2 too many, and the diagonal constraints are used in the proof, yet they are the only candidates.
So perhaps we need to show the other constraints imply the diagonals.

RE: So many "LIKES"....So little "HI's". What gives?

@OP I get more than enough of the 'hi!' mail, but the number who exceed half my age, are not strikingly good looking, and do not live in America is in single digit territory. Usually I am about grandpa age. The number who respond with appropriate interests and age I can count on my thumbs.

Playing the magic square puzzle...

I am not teaching him matrix inversion - you'd accuse me of being Charles Dodgson! I'm doing it by pure logic and elimination. Notice how the 23-11 diagonal pattern propagates as a result of the initial clues. The 2x2 square constraint in fact makes it considerably easier, not harder.

Playing the magic square puzzle...

@merlot think of the 2x2 square as defined by its top left corner. Then every square except column 4 and row 4 has a corresponding 2x2. This is the 3x3 square R1C1 - R3C3 - 9 squares.
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Haha I see 7 is too easy. Here's a level 9, which is getting pretty fiendish!
I left a shot in of the browser tab so you can see the url if you care to visit the website.

Playing the magic square puzzle...

@ted for the 4x4 there are 4+4+2+9 = 19 equations for 16 variables so there is clear redundancy, non-independency. But yes I missed the requirement for all 9 2x2 squares! Back to the drawingboard, but it still makes bot the boy and myself think intensely.

Playing the magic square puzzle...

there are 9 2x2 squares - I knew that the 4 quadrants and the centre can be proven to do that, but the other 4 I never considered!

Playing the magic square puzzle...

Oh I am wrong - it does indeed say 'and each 2x2 square - that is not normal!

Playing the magic square puzzle...

There is no requirement for the R1C2xR2C3 square to add to 34, nor for R2C1xR3C3; the Four corners and the central square yes. The requirement is clearly stated in the image.

When n is a multiple of 4 there are additional properties. Not sure how Ramanujan comes into this however, but it is amusing.

Playing the magic square puzzle...

Merlot the quadrants in 4x4 and 8x8 magic squares are also equal to the sum - the corner 2x2 squares also sum to 34 in the 4x4 case. Hence you notice the 17 but it is in two rows. It is not a requirement of the puzzle.

Playing the magic square puzzle...

no there are frequently two solutions where you may have a rectangle
a or b | b or a
--------|---------
c or d | d or c
Where you can swap a/c b/d
if a+c = b+d then row and column sums are unaffected if located appropriately
The second solution I provided is a valid second solution. Yours was valid too.
The linear equations do not express the full problem. You have n^2 variables with 2n+4+c equations. Morever they are not linearly independent. I've forgotten the terminology for problems involving one-one pigeon-holing.

Playing the magic square puzzle...

yes - look at 1 and 3 - they cannot go in rows 2 or 4, and they cannot go in the same column. Since column givens add to 18 and we need 16, so (1,15), (3,13) occupy 4 squares in two columns. The first trial of 1 at R1C1 turns up trumps. Sometimes there are dual solutions involving exchanging ab/ba pairs and symmetry. Using linear algebra doesn't seem to work since the equations are not independent.
9,8,3,14
12,5,2,15
6,11,16,1
7,10,13,4 seems to be such a dual

Playing the magic square puzzle...

Since the four corners add to 34, that tells us that R1C1+R4C1 = 16, so R2C1 = 34 - 16 - 6 and that is the last even number. All the others remaining are odd, two each per column and each column pair adds to 16...

Playing the magic square puzzle...

but you will note that the centre four and the corner 4 do add to 34 as expected - just not the 4 rows, and one of the diagonals.

Playing the magic square puzzle...

Rows Columns and Diagonals all have to be 34 - not just columns

RE: FRIENDSHIP

Someone here says you grow out of friendships? I have very few - one hand is enough. But in fact I find you grow into them and they are life-long, they are truly cherished.

RE: First date red flags

A memorable failure - blind 'date' 40 years ago. Attractive athletic blonde professional Canadian woman but after 5 minutes knowing we had zilch in common, cappuccino unfinished, I stood up, excused myself having a migraine - paid the bill and left. Abject failure.

Hundertwasser - Wellington NZ 1970s

If you look at the google map for Kawakawa, the Hundertwasser toilet figures prominently

Hundertwasser - Wellington NZ 1970s

Oh Hundertwasser didn't make things the way you expect them! Just look at the windows and lines in his buildings
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