The number 7 octillion is only for comparison … in the argument [about infinite knowledge].
Hi Miles. Okay, I'd misinterpreted the statement "to reach" the quantity of human atoms.
The point of the argument is the unlikelihood that man can understand or even comprehend "all knowing".
Ah, that makes more sense! Thanks.
Well, 7 octillion is 7 thousand trillion trillion. That quantity itself is incomprehensible, ha.
So, topsquark pointed out: rate is a ratio of total bits per elapsed time.
\(\displaystyle \text{rate} = \frac{\text{bits}}{\text{time}}\)
To solve that equation for time (i.e., to obtain a formula for time), we multiply each side of that equation by the fraction (time/rate).
\(\displaystyle \frac{\text{time}}{\text{rate}}×\frac{\text{rate}}{1} = \frac{\text{bits}}{\text{time}}×\frac{\text{time}}{\text{rate}}\)
Do you see on the left-hand side that quantities
[imath]\text{rate}[/imath] on top and bottom cancel, leaving just time?
Likewise, on the right-hand side, quantities
[imath]\text{time}[/imath] cancel on top and bottom. That yields the formula for time:
\(\displaystyle \text{time} = \frac{\text{bits}}{\text{rate}}\)
Using Scientific Notation, your bits are 7×10^27 (seven octillion is 7 followed by 27 zeros).
Your rate is 11×10^6 (eleven million is 11 followed by 6 zeros).
\(\displaystyle \text{time} = \frac{7×10^{27}}{11×10^{6}}\)
We may factorize that fraction:
\(\displaystyle \text{time} = \frac{7}{11} × \frac{10^{27}}{10^{6}}\)
There's a property of exponents for simplifying a ratio of powers having the same base: Subtract the exponent in the denominator from the exponent in the numerator and raise the base to that.
\(\displaystyle \text{time} = \frac{7}{11} × 10^{27-6}\)
7/11ths of 10^21 seconds is still hard to comprehend, as an interval of time. We could divide it into trillion-year sub-intervals. How many would that be? Let's see.
60sec/min × 60min/hr × 24hr/day × 365.25day/yr × 1000000000yr/unit
That equals 3.15576×10^16 seconds per trillion years.
Dividing the time (for the brain to reach 7 octillion bits) by our trillion-year unit yields roughly 20165.1468 units.
In other words, the brain would need a trillion years to pass more than 20,165 times to approach 7 octillion bits. (Humans will be extinct long before that.)
But here's a thought experiment, for your infinite-knowledge argument. You'll agree that the brain has a finite storage capacity. Each new "piece" of knowledge creates additional pieces of knowledge because each new piece has relationships with existing pieces, and those relationships themselves become new pieces of knowledge (with each of those creating yet more "pieces" of new knowledge). At some point, the brain will be "full" and all remaining knowledge beyond that point will be effectively shut out from comprehension. (One reason our brains are not full now is the breakdown of unused circuits by neural processes while we sleep, increasing resources.)
Another thought. Human senses have evolved specific structures for interacting with reality. As such, they are extremely constrained. That is to say, there is a LOT of stuff (knowledge) taking place within reality that humans cannot perceive (and never will). From my point of view, it's almost arrogant to think that a person could ever attain absolute knowledge. But, that's human nature. (Some people still think we're the pinnacle of the universe.) I'm glad you're on the right side of the question!
[imath]\;[/imath]
