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Re: Μαθηματικά

Δημοσίευσηby negentropist » Κυρ Ιούλ 27, 2014 12:46 pm

The extraordinary story of how in 1914 the self-taught maths genius SRINIVASA RAMANUJAN was brought from Madras to Trinity College, Cambridge, by the great English pure mathematician GH Hardy, who called their relationship 'the one truly romantic episode of my life'.





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Re: Μαθηματικά

Δημοσίευσηby negentropist » Πέμ Νοέμ 27, 2014 9:44 pm

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In the End, It All Adds Up to – 1/12 !!!




By Dr. Tony Padilla

What do we get if we sum all the natural numbers?

The answer we gave was, to the surprise of many I'm sure, −1/12.

It's by no means obvious, but this is the only sensible value one can attach to this divergent sum. Infinity is not a sensible value. In my opinion, as a physicist, infinity has no place in physical observables, and therefore no place in Nature. David Hilbert, one of the founding fathers of quantum mechanics, described infinity as "a mathematical abstraction that does not have a physical content". I think most physicists would firmly agree with this sentiment. The trouble is that divergent sums like the one we discuss in the video do appear in calculations of physical observables, such as the Casimir energy, or in the dimensionality of the Universe in bosonic string theory. Therefore, only a very brave individual would dream of attaching the value infinity to sums like this. Minus a twelfth is far less crazy a value when you start talking about Physics.


Why -1/12 is a gold nugget ?


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Re: Μαθηματικά

Δημοσίευσηby negentropist » Πέμ Απρ 09, 2015 1:15 am

0-D: Just a point. No width, no height, no depth, no duration. (i.e. A point) 1 static variable

1-D: A line. No height, no depth, no duration. (i.e. A line) 1 variable with change/adjustment

2-D: A plane. No depth, no duration. (i.e. A square) 2 variables

3-D: A space. No duration. (i.e. A cube) 3 variables

4-D: A timeline — Also imagine a Minkowski space and/or a tesseract/Hypercube. (ex. The timeline which we are on as things are unfolding every second, simple example would be picking up an apple)

5-D: 2 timelines. (ex. An alternate timeline in which some type of other outcome is possible in our given timeline, it could be like picking up two apples, or an orange, or something completely different)

6-D: What to jump through to get from one timeline to another. (ex. Think about a timeline where things can happen in our universe, but can not exist from our current position in time, so maybe a time when dinosaurs were still alive, and the outcomes leading up to the present day is completely changed by this event. Since we can't technically cross to this timeline because we know that dinosaurs are extinct in our timeline, this concept of "folding" of two timelines allows for a path to the impossible. Τhis creates a probability "plane", ie a phase space where we can freely move to any given timeline within our universe with its unique set of laws of physics. From an outsider's point of view afar, this phase space looks like a point containing every possibility in our universe. Therefore, many probability planes make a phase space representing all possible outcomes for a unique universe such as ours!)

7-D: All possibilities for a universe with one constant changed — many different phase spaces representing different unique universes make a "line" (ex. What if the laws of physics for our world was different in the sense that the speed of light constant or force of gravity was just slightly different? this would change everything and create universes with different make-up)

8-D: All possibilities with two constants changed

9-D: What to jump through to get from one universe to another. (Similar concept to 6-D where every possible probability is considered because we are now changing all kinds of constants to the point where these universes might look drastically more different than ours. Phase space allows us to move anywhere containing any of these possibilities. Phase space looks like a point from afar)

10-D: Infinity. (By now, all possible possibilities have been thought of)


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