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Mathematics

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Zziggy
1148491.  Thu Sep 10, 2015 3:53 am Reply with quote

Because mathematicians are awesome and beautiful and wonderful people.

 
PDR
1148494.  Thu Sep 10, 2015 6:35 am Reply with quote

...at the 50% confidence interval...

:0)

PDR

 
bobwilson
1148558.  Thu Sep 10, 2015 7:42 pm Reply with quote

I thought it was to explain mathematically why he spelt "caesar" in that particular way?

 
gruff5
1148639.  Fri Sep 11, 2015 10:06 am Reply with quote

were they "proper" mathematicians or accountants, surveyors, engineers etc?

 
gruff5
1148644.  Fri Sep 11, 2015 10:40 am Reply with quote

This is a great video explaining the deepest unanswered question in mathematics:

https://www.youtube.com/watch?v=d6c6uIyieoo

If we solve the Riemann hypothesis, I reckon we can then, as a civilisation, collectively put our feet up.

 
Zziggy
1148645.  Fri Sep 11, 2015 10:45 am Reply with quote

gruff5 wrote:
were they "proper" mathematicians or accountants, surveyors, engineers etc?

That's not proper mathematics!

 
gruff5
1148652.  Fri Sep 11, 2015 11:16 am Reply with quote

hence the word "or" in my sentence.

From the Riemann vid, a sidebar prompted me to once again watch the vid on 1 + 2 + 3 + ... = -1/12

hmm, very interesting, but does rather provoke once again my prejudices against completed infinity!

 
Zziggy
1148655.  Fri Sep 11, 2015 11:24 am Reply with quote

Ahh my bad, I totally skipped over the 'or'. Carry on :)

 
gruff5
1149078.  Mon Sep 14, 2015 12:04 pm Reply with quote

thanks, Zziggy

Right, just in case anyone is out there watching this Carry On Mathematics lark, here's a very nice contextual vid on this -1/12 and infinity conundrum:

https://www.youtube.com/watch?v=0Oazb7IWzbA

The original vid about 1 + 2 + 3 + 4 + ... should be visible in the sidebar.

And a nice graph giving an idea of what's going on:

https://upload.wikimedia.org/wikipedia/commons/thumb/2/23/Sum1234Summary.svg/600px-Sum1234Summary.svg.png

 
bobwilson
1149135.  Mon Sep 14, 2015 6:43 pm Reply with quote

Quote:
Right, just in case anyone is out there watching this Carry On Mathematics lark, here's a very nice contextual vid on this -1/12 and infinity conundrum


Right at the beginning it states that it depends on determining a value for the sum 1-1+1-1+1-1+1-1+1-1+......

Everything else is dependent on that.

They assign the value of the sum as 0.5 (for reasons explained). But that's a purely arbitrary number for the sum - there are good mathematical reasons for assigning other values to that sum (anywhere between 0 and 1).

But it's an impressive parlour trick for an upmarket boudoir

 
gruff5
1149211.  Tue Sep 15, 2015 6:55 am Reply with quote

Yes, I have to agree with you that those manipulations of divergent and otherwise non-converging series look like parlour tricks and there's a lot of upset commenters below. Even if such figures as Euler and Ramanujan used these kind of tricks, I don't find them alone convincing.

But apparently there are other more rigorous maths methods (which I don't understand) which lead to the same result of -1/12

It was telling that Prof Frenkel in the contextual vid said that mathematicians themselves don't really understand what's going on here. And he called this a regularised sum, rather than a literal sum.

Similar to what Einstein said about quantum mechanics (paraphrasing): there is a truth here, but the theory we currently have underlying it is incomplete.

 
gruff5
1154884.  Fri Oct 23, 2015 1:42 am Reply with quote

Currently reading "The Infinity Delusion" by James Meyer. Interesting in parts, though also often long-winded, error-prone & repetitious in others.

One of the interesting contradictions he brings up is the "Alternating Harmonic Series" :-

1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + ...

For this series, it does matter in which order the terms of the series are added. So, for example, the series :-

1 - 1/2 - 1/4 + 1/3 - 1/6 - 1/8 + 1/5 - 1/10 - 1/12 + 1/7 - 1/14 - 1/16 +...

which contains precisely the same terms, but in a different order, has a limiting value of exactly half of the limiting value of the original series (proven by Bernhard Riemann 160 years ago). Riemann proved that you can change the order of the terms of the series to give practically any value you want for the limiting sum of the series.

This surely contradicts the notion of 'completed infinity' of modern mathematics. With the notion of completed infinity, the order of the terms is immaterial and the sum of the series will always be the same.

I'd choose Riemann over Cantor ...

 
WordLover
1154915.  Fri Oct 23, 2015 5:37 am Reply with quote

.....


Last edited by WordLover on Fri Sep 16, 2016 11:25 am; edited 1 time in total

 
gruff5
1155052.  Fri Oct 23, 2015 9:54 pm Reply with quote

I'm not introducing the labels for infinity - they are there already in the history of mathematics. Before Cantor, problems around infinity were averted by focussing on limits. Since that time, completed infinity has been thought of as a valid concept and limits to be unnecessary.

In the same way that in modern mathematics 0.999... absolutely equals 1.0 with no need for a limit concept, then the sum of the alternating harmonic sequence would absolutely always sum to the same value - no matter the order of the terms.

 
WordLover
1155208.  Sun Oct 25, 2015 1:49 am Reply with quote

.....


Last edited by WordLover on Fri Sep 16, 2016 11:24 am; edited 1 time in total

 

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