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    Unusually warm winter for 2015

    Europe has long had warm winters starting say several years ago. Back in 1944 during the Ardennes offensive there was like a foot of snow. You can see for yourself the weather of Berlin, Stockholm, Warsaw, Helsinski. Not a single snow flake in Europe...
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    NASA's greenhouse effect not correct?

    NASA says Earth's greenhouse effect makes Earth 33 C hotter than the Moon. All of that warming can be explained by Earth having 1 bar of pressure compared to the Moon having no pressure. Going from the Moon to Earth is like going from the top of the troposphere to sea level, roughly speaking...
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    Some insights about the Riemann hypothesis needed

    Wow! Totally didn't know that. Many thanks! :smile:
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    Is it really true that, for any n > 0 , there is a prime between 2 ^ n

    So far, tested my strong conjecture, which is a strengthening of Bertrand's postulate, to 655 million less 1, where the smallest difference has increased from 1 to 527. As for n being powers of 2, so far, tested using Mathematica to the exponent being 700 where the difference has increased from...
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    Mass of the universe?

    Methinks the universe is infinite.
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    Autistic Einstein?

    Speaking of Jacob Barnett, he now lives in the same small city where I live. Woohoo! :biggrin:
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    Is it really true that, for any n > 0 , there is a prime between 2 ^ n

    If it's so easy to prove, I wouldn't have considered it worthy of being a conjecture. :wink: When n is prime, my conjecture reduces to Bertrand's postulate when n is prime. It's what happens when n is composite that makes my conjecture interesting. :cool: I won't publish anything unless I'm...
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    Some insights about the Riemann hypothesis needed

    Some sources refer to values of functions as height. I suppose it's easier for some people to comprehend. :tongue: Any possible way to depict graphically what the Riemann zeta function looks like? Or would this be too complex to do, no pun intended :tongue:?
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    Some insights about the Riemann hypothesis needed

    Starting at 22:50 of the given link, there's a pretty cool computer depiction of Riemann's zeta function. :cool: Can anyone make a comment as to how realistic this particular depiction might be?
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    Some insights about the Riemann hypothesis needed

    In other words, most of the points on the line where the real part is 0.5 do not have height 0? Also, could the Reimann zeta function evaluate to negative values?
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    Some insights about the Riemann hypothesis needed

    The Riemann hypothesis states, whenever the Riemann zeta function hits 0, the real part of the input must be 0.5. Does any input with real part being 0.5 make the function hit 0? Also, assuming the hypothesis is true, would it suffice to prove that if the input's real part is not 0.5, then the...
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    Is it really true that, for any n > 0 , there is a prime between 2 ^ n

    Interestingly, it appears that, for any k > 0, the number of primes in the range (2k , 2k + 2 \times k2) \geq k. The difference between 2k + 2 \times k2 and the kth prime above 2k appears to be a non monotonically increasing function of k and that only when k = 1 do these two values equal each...
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    Universe finite or infinite during the first instance of inflation?

    We are on the same page that numbers are infinite even though we can count numbers? :tongue:
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    Universe finite or infinite during the first instance of inflation?

    Therein lies a twist. How can people ever know if the universe is flat? People once thought Earth is flat, yet Earth is round. Scientists now think the universe is flat, but how can they be sure they are right? No instrument in the world, no matter how accurate, can ever determine if something...
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    Universe finite or infinite during the first instance of inflation?

    An infinite series can either converge or diverge. By the same token, in my opinion, the universe could be considered either finite or infinite depending on how it expands. Just my 2 cents. :tongue: http://en.wikipedia.org/wiki/Series_%28mathematics%29
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    Is it really true that, for any n > 0 , there is a prime between 2 ^ n

    I formulated my original first conjecture into a weak conjecture and a strong conjecture. The weak one is the same as my original first conjecture. The strong one is that, for any n > 1, the number of primes in the range (n , n + how many prime factors n has × the sum of n's prime factors) \geq...
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    How to become a genius ?

    I stand corrected. It appears to be 10% usage. http://www.scientificamerican.com/article.cfm?id=people-only-use-10-percent-of-brain
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    How to become a genius ?

    By using your brain more. The average human only uses some 4% of brain power.
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    Confused about i

    i squared is -1.
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    Logarithm question

    Since u = log8x, you have -1 = log8x.
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    Is it really true that, for any n > 0 , there is a prime between 2 ^ n

    There is also a Firoozbakht's conjecture, which is of the same nature as Cramér's conjecture. :cool: http://en.wikipedia.org/wiki/Firoozbakht%E2%80%99s_conjecture Legendre's conjecture and Oppermann's conjecture are of the same nature. http://en.wikipedia.org/wiki/Legendre%27s_conjecture...
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    Numbers are infinite, so why would the universe not be infinite?

    If numbers are not real and part of the universe, then why are there rules in them? For example, http://en.wikipedia.org/wiki/Pythagorean_theorem Numbers therefore are discovered, not invented. :biggrin:
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    Numbers are infinite, so why would the universe not be infinite?

    After all, numbers are part of the universe. :biggrin:
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    That galaxy at the end of 'Empire Strikes Back'

    The center part looks too big and too uniform to be real.
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    Has technology made humans weaker?

    Well, one thing's for sure. Technology has certainly greatly increased the ranges of variation in people's physical attributes. :tongue:
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    Logarithm question

    To me, this is the same as log8 (x^log8(x)), because you can only have a single input with the function log8.
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    Logarithm question

    Yes, this is clear.
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    Logarithm question

    Of course. :tongue:
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    Logarithm question

    I don't see why not. What's in brackets is considered a single entity.
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    Logarithm question

    You can try it out on a calculator and see if there is any difference between (log8(x))^2 and log8(x)^2. :biggrin: http://web2.0calc.com/
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