Mathematical Beauty

[aeolium]

One of those processes need not involve the "external" senses at all but result from internal "thinking" about concepts that idealise from those external sensations and actually build on them - resonate - to make "beautiful" ideas that have no real world connections.

Yes, as you were suggesting in an earlier post, and also reacting to the elegant concision that can contain enormously powerful ideas within a few symbols. On the other hand the BBC article suggested that those "emotional" areas of the brain were stimulated by actually viewing the equations so not wholly separate from the external senses.

As Blake said, "A tear is an intellectual [=imaginative] thing".

[clive heath]

I remember working through a trigonometrical theorem about Euler's Line at school which has a degree of beauty about it. Is it not the case that the lovely book "Bach, Escher Gödel" spends some time proving possibly a priori that 1+1=2? Hey! My o In Gödel just came up with an umlaut automatically!! Magic!

[Gordon]

I remember working through a trigonometrical theorem about Euler's Line at school which has a degree of beauty about it. Is it not the case that the lovely book "Bach, Escher Gödel" spends some time proving possibly a priori that 1+1=2? Hey! My o In Gödel just came up with an umlaut automatically!! Magic!

Yes, that book is thought provoking but I found it a bit long winded - he could have made his points in a lot less space. In looking for fundamentals of knowledge we are entering the realm of philosophy and of Descarte's search for something solid [ie dependable, reliable] in the experience of being. Deep stuff for a dismal Friday afternoon!

[aka Calum Da Jazbo]

no wonder Descartes is disappointing [solid v being?] is there any matter that is solid? solid is an experience of being ....

it may not prove possible to define this universe as everything and for all time and everywhere in which case all our truth is local ... does that mean other truth may still be universal and would we know how to know it

apologies [Friday; Rain; Coat On]

[french frank]

I did once take some tutorials on Descartes and have just disinterred my copy of Discours de la méthode - one of those 10/18 'perfect bindings' which shed all their pages individually. I shall read the pages that remain tonight, and assume that, if it doesn't make sense, some vital pages have been lost :-/

[Gordon]

Is this beautiful? Looks like that Ferneyhough score! Note what it says at the bottom.

[LeMartinPecheur]

1 + 2 = 3 in decimal but 1 + 2 = 0 in ternary; it looks different but it is still "true", the notation does not change the "truth".

I thought in ternary 1 + 2 = 10, cf binary 1 + 1 = 10 and come to that in decimal 1 + 9 = 10 (something of a pattern here methinks) Have I missed something?

[ferneyhoughgeliebte]

http://www.youtube.com/watch?v=TtruYROTXY4

... one drop of water added to another drop of water = one (bigger) drop of water.

(Or, as Morecambe & Wise put it: "How many full-stops in a bottle of ink?" "48,967 or one very big one.")

[Gordon]

I thought in ternary 1 + 2 = 10, cf binary 1 + 1 = 10 and come to that in decimal 1 + 9 = 10 (something of a pattern here methinks) Have I missed something?

Yes, there is a TEN-dency there!! Well spotted LMP, you didn't miss anything, I did, I dropped the carry Glad to see you are on your toes out there!

And in Hexadecimal of course 1 + 9 = A which is 1010 Binary and just 101 ternary but 12 Octal!! But in Roman 1 + 1 = 11 and 1 + 2 = 111, 1 + 3 = IV and 1 + 4 = V. Try doing sums with that notation without an abacus. If you think that is hard try doing sums in India or Sri Lanka!!

[Gordon]

http://www.youtube.com/watch?v=TtruYROTXY4

... one drop of water added to another drop of water = one (bigger) drop of water.

(Or, as Morecambe & Wise put it: "How many full-stops in a bottle of ink?" "48,967 or one very big one.")

I can see that Bertrand Russsell would have trouble with you fhg!! Anyway in "a bottle of ink" there are NO full stops!!

[ferneyhoughgeliebte]

I can see that Bertrand Russsell would have trouble with you fhg!! Anyway in "a bottle of ink" there are NO full stops!!

Apart from the one on its holidays hovering over the "i"

("That Bertrand Russell once refused to get into my cab!" )

[Gordon]

Apart from the one on its holidays hovering over the "i"

("That Bertrand Russell once refused to get into my cab!" )

OOOH!! you are sharp today! I thought I could sneak that past but no flies on you eh!