(ctd)
>>The great Professor Feynman … discusses the difference between the mathematicians and physicists far more lucidly than I could put here. http://www.youtube.com/watch?v=obCjODeoLVw <<

I am not sure when the talk originated. Feynmann died in 1988 but the technical quality of the video (B&W, poor sound) seems to indicate that it was recorded much earlier. In my times, which are not as old as Feymanns’, pure mathematics and mathematical physics developed so to say parallelly for a couple of decades: We used to say jokingly that pure mathematicians knew many questions but did not know the answers, wereas applied mathematicians knew many answers but did not know what (mathematical) questions they were answering.

That has chages considerably in the recent decades: contemporary cosmologists, mathematical and theoretical physicists (the difference is rather subtle) need to use - and they do - very abstract mathematics, that would have been seen as purely self-serving and not very applicable, in my times.

>> So in a way it is you who is asking me to eschew reality for the abstract wouldn't you agree?<<

I did not ask you to eshew anyting, only respect mathematics when speaking of mathematics, and respect physics when speaking of physics. You introduced religion, so read it also as a an analogue of "Render to Caesar (Physics) the things that are Caesar's, and to God (mathematics) the things that are God's.

Mathematics without physical applications can, and does, exist, but is pretty useless. Physics, without proper mathematics does not exists, except in its most naive, degenerate forms. Explorers in physics originally use mathematics ad hoc (which does not mean using nonsense like 1+2+3+4+5... = -1/12) but they gradually need to make it more or less rigorous to make their physical theories more adequately reflect some features of reality.

>>It is this aspect I have found to be so intriguing, and the tension between the two disciplines is something I would not have believed existed before now.<<

I do not think this is a place to further elaborate on this "tension" from the perspective of mathematics or physics (or both).

Dear warmair,

Thank you for the sterling link. The correction is quite robust, persuasive and convincing to my unlearned eye. I see it was only posted yesterday and I will look forward, and read with interest, the responses it generates.

Dear George,

Thank you for your expansive post. We probably differ on the extent of the distinction between axioms and belief (as would Feynman I think) but so be it, the rest I am happy to take on face value.

Could I trouble you for a clarification though? By describing 1+2+3+4+5... = -1/12 as nonsense am I correct in concluding you see Ramanujan as having been completely wrong and if the equation appears to be a central tenet (even axiom) of String Theory (damn that is a lot of 'c' words) then the implication is that you perhaps see that entire field as nonsense also?

Ultimately I think the video and the debate it has generated has been great stuff, it has driven an interest in the topic from us plebs, seen some very high horses mounted along with potentially some spectacular dismounts, and for me at least given some inkling of just how romantic exploitative physics must be. These guys just seem like they are having so much fun.

Very instructive, Wm Trevor.

>>...ever since, infinity has been getting even bigger because of space expanding at some 74.3 plus or minus 2.1 kilometers per second per megaparsec (Mpc =approx 3 million light-years<<

But can you make that into a YouTube video? Remember Marshall McLuhan?

Talking of which, you might be interested in this. I was looking for the "Marshall McLuhan. What are you doing?" sequence on the Rowan and Martin Laugh-in. As you do. Instead, I found this...

"Berlin in twenty years from now, 1989. There was dancing in the streets today as East Germany finally tore down the Berlin Wall"

http://www.youtube.com/watch?v=oMPR9DalSPg

The short segment is at 4.13

For a comedy show, not a bad prediction, eh?

Lol. That should read exploratory physics not 'exploitative'. Darn spell checker.

BAFFLE Em with pictures..comes next

LOOK AT THE PICTures in-between..the quotes

<<..there will be pictures, and those are the most important parts.

Here we go . . .

I find it easier to understand things visually, so it occurred to me to plot out the series 1+2+3+4+ . . . at various points as you add the numbers. These points are called partial sums. This is what you get if you stop the sum after each step

for n=1 the partial sum is 1
for n=2 the partial sum is 1+2 = 3
for n=3 the partial sum is 1+2+3=6
for n=4 the partial sum is 1+2+3+4=10
for n=5 the partial sum is 1+2+3+4+5=15
etc.

If you draw the first five terms on a piece of paper, it looks like this

But you don't have to add all those numbers to calculate value at each point. The numbers, it so happens, are a sequence (1,3,6,10,15, . . .) that you can calculate with a simple formula called a generating function. In this case the generating function is

G(n)=n(n+1)/2

To get a number at any point in the sequence, like say the 5th spot, just plug in 5 for n, and you get the answer

for n=5, G(5)=5(5+1)/2=15

As it turns out, you can also use the generating function to figure out what the values would be between whole numbers. Essentially, you replace the number n with an x, which can have any numerical value you like. If you plot the result, you get this, for positive x.

The curve you see here goes up to infinity as x goes to infinity. So far, so good. But if we're going to plot the graph between the various values of n, we might as well look at negative values of x too.

When you do that, you get a graph like this>>..

THE BIG lie seems to be..on the vertiCLE AXIS
WHERE minus ONE TIMES Itself..EQUALS POSITIVE one..in both series
[THERE CANT BE A BELL CURVE]

it seems the phobia..is linked to nuthinness[ZERO/..oR RATHER FEAR..OF ZERO]

plot out the series -1+-2+-3+-4+ . . .
at various points..as you added the positive numbers. ..[These points are called partial sums.] This is what you get if you stop the sum after each step

for n=-1 the partial sum is -1
for n=-2 the partial sum is -1+-2 = -3
for n=-3 the partial sum is -1+-2+-3=-6
for n=-4 the partial sum is -1+-2+-3+-4=-10
for n=-5 the partial sum is -1+-2+-3+-4+-5=-15
etc.

If you draw the first five negative..terms on a piece of paper,
it looks like this..[..%..]..[OR THIS..[/]..not like this..[u]..