Incredible cretinism combined with some scientific proof. Or maybe a mind capable of outstandingly visionary ideas? ;) Welcome to the mind(s) of (a) physicist(s)! Because the following can probably really only happen to physicists:
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| I could think of nothing more convenient for a story like this ... ((c) Christopher Torres, LOL-comics) |
One is in a philosophical mood and posts "There is only one everything." What follows is a deliberate mixing of scientific results in the most queer-headed way possible. All in all it results in the following proof of the contrary which I cannot help but have to break down a little - not sure if out of suspicion towards mathematicians or out of a self-mesmerising-with-possibilities mind ... So the summary of the discussion following the highly philosophical statement was
The universe is infinite and there is an infinite number of infinities.
"Everything" really includes everything so it is the sum of all infinities.
Even an infinite number of infinities can be continuously numbered and
the sum of all integers is -1/12.
Thus, everything is less than nothing.
This might be a little crazy but all of it can be "proven". And here starts the really crazy part. The first statement that the universe is infinite is not yet proven right or wrong. Einstein once brought this down to "I know of two things that are infinite: The universe and human stupidity. Concerning the universe, however, I am not yet sure ..." So it might be infinite as well as finite. So far you can at least imagine that it could be infinite as even beyond matter there could maybe be somthing ... So with this we have to go with the assumption that what is not proven wrong may still be right. ;)
Then about the infinities. Once upon a time four months ago a friend of mine posted a video in his blog about infinities that summarises nice and easy (it is really possible to understand it!) how there are infinitely many infinities, how they are related and that you go crazy if you think about it. (Not kidding, the guy (Gregor Cantor) who made the considerations spent half of his life in mental hospitals because his colleagues were jealous of his genius and mobbed him into insanity.) You can find his post here. (Although the text is in German, the video is in English.)
Last but not least the thing with 1+2+3+4+5+... being -1/12. This is obiously the most crazy thing. But believe it or not this is used in string theory and e.g. the quantum field theory Casimir effect. According to a friend's friend a rigorous treatment of divergent series which the proof of the above sum relies on can be found here. This now is the "suspicion towards mathematicians" part because it is obviously as counterintuitive as it can be that the sum of all integers is -1/12. I tried to understand the principles of the linked proof and it seems that there really is a proof making use of cutoff functions and the like. (There are many more proofs to which you have to add quotation marks (-> "proofs") that are quite easy to understand but usually there are obvious faults in them.) However, for this more rigorous proof my application-oriented mind is definitely not twisted enough so there will have to be at least the discovery of the world formula involved before I will give it a second glance ... Until then I will stay with my physics and kepp on juggling math in ways that makes sense. ;)
