A Duke University researcher has a new
explanation for why those endless days of childhood seemed to last so much longer
than they do now – physics. According to Adrian Bejan, the J.A. Jones Professor
of Mechanical Engineering at Duke, this apparent temporal discrepancy can be
blamed on the ever-slowing speed at which images are obtained and processed by
the human brain as the body ages. As tangled webs of nerves and neurons mature,
they grow in size and complexity, leading to longer paths for signals to
traverse. As those paths then begin to age, they also degrade, giving more
resistance to the flow of electrical signals. These phenomena cause the rate at
which new mental images are acquired and processed to decrease with age —
infants process images faster than adults, their eyes move more often,
acquiring and integrating more information. The end result is that, because
older people are viewing fewer new images in the same amount of actual time, it
seems to them as though time is passing more quickly. [1]
Time passes by. No matter what we do.
In the beginning we processed
everything.
At the end, we will process nothing.
The result is not different, but all
the same.
Analyze everything and you reach a
point where analysis will be pointless.
Analyze nothing and you will realize
that you have analyzed everything.
It seems obvious and yet it is difficult to explain. Why do we lust for a good view? Why do we seek the openness of the sea instead seeing a nice… anything right in front of our eyes? What is so magic about a good view that makes us relax and our soul feel nice?
Humans are infinite creatures. Sons of God, we think and feel in His terms. We feel the infinite even though are finite senses will never experience it. And anything which reminds us of that makes us feel relaxed.
Hoping to tame the torrent of data churning out of biology labs, the National Institutes of Health (NIH) today announced $32 million in awards in 2014 to help researchers develop ways to analyze and use large biological data sets.
The awards come out of NIH’s Big Data to Knowledge (BD2K) initiative, announced last year after NIH concluded it needed to invest more in efforts to use the growing number of data sets—from genomics, proteins, and imaging to patient records—that biomedical researchers are amassing. For example, in one such “dry biology” project, researchers mixed public data on gene expression in cells and patients with diseases to predict new uses for existing drugs.
ENIGMA project on the other hand collects thousands of brain images to allow researchers to better understand nervous system wiring. (1)
Analyze too much data. And you will reach the same conclusion as you would have if you analyzed nothing at all.
How can everything behave differently from One? Parts exist just because something from which they derived existed in the first place. And how can the parts have different behaviour than that thing from which they were created?
Infinity. Nothing. Something.
So different.
And so similar at the same time…
From One to Many to Infinity and back again.
The only way out leads directly to where you started from…
Srinivasa Ramanujan presented two derivations of “1 + 2 + 3 + 4 + … = −1/12” in chapter 8 of his first notebook. The simpler, less rigorous derivation proceeds in two steps, as follows.
The first key insight is that the series of positive numbers 1 + 2 + 3 + 4 + · · ·can be transformed to the alternating series 1 − 2 + 3 − 4 + · · ·. The latter series is also divergent, but it is much easier to work with; there are several classical methods that assign it a value, which have been explored since the 18th century.
In order to transform the series 1 + 2 + 3 + 4 + · · · into 1 − 2 + 3 − 4 + · · ·, one can subtract 4 from the second term, 8 from the fourth term, 12 from the sixth term, and so on. The total amount to be subtracted is 4 + 8 + 12 + 16 + · · ·, which is 4 times the original series.
These relationships can be expressed with a bit of algebra.
Whatever the “sum” of the series might be, call it c = 1 + 2 + 3 + 4 + …
Then multiply this equation by 4 and subtract the second equation from the first:
The second key insight is that the alternating series 1 − 2 + 3 − 4 + · · · is the formal power series expansion of the function 1/(1 + x)2 with 1 substituted for x.
So it seems that -3c = 1 − 2 + 3 − 4 + · · · = 1/4. Now make another small calculation and voila!
But can this really be true?
Can the sum of POSITIVE numbers equal a negative one?
Can the sum of INTEGERS be a fractional number?
We tend to rely too much on assumptions. The whole science is based on assumptions. And when we rely too much on them, we tend to forget they even exist.
Watch closely. See the “proof” more carefully once more…
Srinivasa Ramanujan presented two derivations of “1 + 2 + 3 + 4 + ⋯ = −1/12” in chapter 8 of his first notebook. The simpler, less rigorous derivation proceeds in two steps, as follows.
The FIRST key insight is that “infinity” exists.
The SECOND key insight is that the series of positive numbers 1 + 2 + 3 + 4 + · · · (we CAN put these dots because of the first assumption) can be transformed to the alternating series 1 − 2 + 3 − 4 + · · ·. The latter series is also divergent, but it is much easier to work with; there are several classical methods that assign it a value, which have been explored since the 18th century.
In order to transform the series 1 + 2 + 3 + 4 + · · · into 1 − 2 + 3 − 4 + · · ·, one can subtract 4 from the second term, 8 from the fourth term, 12 from the sixth term, and so on. The total amount to be subtracted is 4 + 8 + 12 + 16 + · · ·, which is 4 times the original series.
These relationships can be expressed with a bit of algebra.
Whatever the “sum” of the series might be, call it c = 1 + 2 + 3 + 4 + …
Then multiply this equation by 4 and subtract the second equation from the first:
The second key insight is that the alternating series 1 − 2 + 3 − 4 + · · · is the formal power series expansion of the function 1/(1 + x)2 with 1 substituted for x.
So it seems that -3c = 1 − 2 + 3 − 4 + · · · = 1/4. Now make another small calculation and voila!
It seems as if c = 1+2+3+4+… = -1/12!
But this result is not logical!
So the same process could be actually proof that infinity does not exist!
Infinity…
What is that infinity which we all seek?
What is that infinity to which we all pray?
What made us think about it in a finite cosmos?
Are we humans thinking as Gods?
Or Gods thinking as humans?
Seek the finite.
And you will see the infinity staring back at you…
