Rowan and Martin's News of the Future... were they prescient or Illuminati insiders?

"Remember Marshall McLuhan?"

Remember him, Pericles? Yep, studied Understanding Media at uni in the 70s though I didn't agree with classmates who thought the book was cool.

Speaking of divergent series, television that is, not mathematical...

Found this short [1:34] Stephen Fry introduced Open University blooper which could be substituted for some of this thread's discussion:

http://www.youtube.com/watch?v=2un9rO2ZF4g

Dear UOG,

I think the mistake you are making is not continuing past zero and sticking with whole numbers.

This is what I get when I plug in n1=n(n+1)/2

-0.9 -0.045
-0.8 -0.08
-0.7 -0.105
-0.6 -0.12
-0.5 -0.125
-0.4 -0.12
-0.3 -0.105
-0.2 -0.08
-0.1 -0.045
0 0
0.1 0.055
0.2 0.12
0.3 0.195
0.4 0.28

Graph those little babies up and I think you will be sweet.

Dear SteeleRedux,

If you are intersted in Ramanujan’s approach to “summation”, see e.g. http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF, where you will find sentences like

“The series 1 + 2 + 3 + 4 + · · · can be 'summed' by zeta function regularization.”

or

“Whatever the "sum" of the series might be, call it c = 1 + 2 + 3 + 4 + ...“.

Note the quotation marks in both sentence. This is more or less what I had in mind when I wrote

>> unless he REDEFINES the concept of convergence in which case he is not speaking ordinary mathematics and then also his 1+2+3+4+5+ ... must be seen as meaning something different from what it normally means <<.

That redefinition is called zeta function regularization but I do not think this is the place to discuss zeta functions, which, anyhow, do not fall within my (past) specialisation. In particular, I know nothing about the application of zeta functions (and Ramanujan summation) to string theory but I am sure they do not use the relation infinity = -1/2 in this form.

Very roughly speaking, Ramanujan did to convergence of series what Lobachevsky did to Euclidean geometry: he did not disprove Pythagoras Theorem, only showed that in a some other (non-Euclidean) geometry it does not hold.

Dear George and warmair,

I had been happily conceding in the various discussions I've been engaged in that 1+2+3+4+5... does not = -1/12th based on warmair's link to physicscentral.

http://physicsbuzz.physicscentral.com/2014/01/redux-does-1234-112-absolutely-not.html?showComment=1391212975656#c9134991847062538477

Not that George hasn't provided some convincing rebuttals its just that I am a visual guy and needed the graph to kick me over the line.

But there is one issue that was troubling me and I'm hoping he might be good enough to sort it out, but I thought I might throw it to you guys as well. Looking at the below graph;

http://2.bp.blogspot.com/-F8iY78u3QWU/UuqOSIkcQyI/AAAAAAAAD9s/7Ici_NkPcmQ/s1600/graph+ABC.png

I might be further exposing my illiteracy here but why can't you subtract area A from area B and get left with area C which equals -1/12th?

Both A and B are the same size and surely it doesn't matter where they start on the axis as long as one is entirely positive and the other entirely negative, shouldn't they both cancel each other out? I concede the sum would then need to be written something like ...1+2+3+4+5...=-1/12th or whatever the correct mathematical equivalent would be.

Where are I going wrong?

steelredux/QUOTE..<<..why can't you subtract area A from area B and get left with area C..>>

TO BEGIN WITH..AREA..a and b..
are outside..THE AREA DEFINED..AS BEING OF C..

the vertical..liNE PASSES THROUGH..c
[IN THE FIRST DIAGRAM..it passes through..the Empty/unnamed..area..named a]

C IF IT RELATED TO ANYTHING..should relate to the unnamed AREAS
between b and a..BUT SUCH IS THE WORK OF DECEIT....IF YOU DID IT PROPER WAY[LIKE THE OTHER GRAPHS..it would b e more clear[see the first GRAPH]..THE VErticle line bisects c..yet not in your examp-le

think why.

LOOK IN A PROPER GRAPH..zERO..WOULD BE AT
THE central..FOCUS POINT

a proper graph WOULD HAVE ALL 'REAL NUMBERS...on one wing
then the negative numbers on the other...THEN at the intersewcting poiunt..thE VALUES..of each addition..[plus eACH NEGATIVE 'ADDITION']

THUS..ON ONE AXIS..would BE THE RESULT OF 1..plus 2..[IE 3...6..10..etc]

ON ITS opposite would lie
minus 3..minus 6 minus 10 etc

its all smoke and mirrors..[poiSENING THE WELL]
ITS DESIGNED TOI MAKE ALL OF YOU Feel dumb

look if george cant explain..it think WHY

ITS DESIGNED TO MAKE us feel dumb
but it in reality reveals even the clever are faking it

get bit?

if infinite = everYTHING
IT CANT BE JUST A FRACTION..OF ANYTHING

think of it like if god = the universe..or the sun
then jesus cant..be god..yetHE CAN REMAIN AS A SON..of the sun.

[you give me lemons
i make lemon aide.]