Watching “Sum of Natural Numbers (second proof and extra footage)” video on YouTube, and I’m amused how the proof got to an answer of -1/12 for the summation of 1+2+3+4+n… (i.e., n to the infinity). Part of the proof, the professor uses the geometric series (if I’m not wrong about this to be geometric series) of — 1+x+x^2+x^3+x^n… (as n to the infinity) equal to 1/1-x — to manipulate more numbers in more ways to come up with -1/12 as the answer to the sum of the infinite basic numbers such as 1+2+3+4+n… (as n to the infinity). So, I guess if the proof in which the professor explains in the video is correct, adding basic items in a series to the infinity would equate to -1/12. Nonetheless, what mind-blowing about this is that adding all the positive things yet it turns out to be a negative thing as in -1/12 (negative for sure). Check out this video right after the break.
What is even more nifty is that I found another video on YouTube which relies on the video above to refute the -1/12 answer to the sum of positive things, and the video would argue that -1/8 is the real answer to this scenario. Well, by now I’m totally confused by both videos for sure. So, is it -1/12 is the answer to 1+2+3+4+n… (to the infinity) or the answer would be -1/8? Check out the next video right after the break.
Anyway, it’s quite amusing, and I’m not sure if I’m ever going to be able to understand this proof. Anyhow, maybe someday my mind will be a little brighter than now and I’ll definitely see how -1/12 would be the answer of the sum of infinite positive numbers. Or is it that only the sum of all positive number series would equate to -1/12 or -1/8, but adding non-series numbers in total to the infinity would not equate to such answer? But, all numbers like natural numbers can always be counted to the positive, thus does it really matter that non-series numbers in total to the infinity would turn out to be any differently than -1/12 or -1/8?
To be honest, I was wondering about how time and space can be infinite or not, and a similar question on Quora (Can time be infinite and space be finite?) got an answer which directs me to the first YouTube video which I had posted near the very top of this blog post. Yep, that’s how I found out about these videos.
Right now, I imagine time as in a single tide travels to an imaginative beach in which this beach got no sand barrier to block the tide, and this tide would ride on into the infinity and would never be able to hit against the sand barrier of the beach. I imagine that each tide is a time. Thus with this imagination I can conclude that each tide is an origin which represents a time medium. Nonetheless, this time tide medium isn’t a regular tide, and so it would have history of time, like bookmarks of time. Anything which rides upon the time tide medium would move forward with time, but leave history in bookmarks of time tide medium. This imagination would allow me to go further by concluding that I can travel in time by revisiting the bookmarks of time tide medium, or perhaps I can jump to another time tide medium to visit the bookmarks of time of not my own altogether. If this is possible, does it mean jumping to another time tide medium would mean escaping the current universe? After all, I assume that different universe should allow a different behavior of time tide medium, because each time tide medium could behave differently altogether. Anyway, this whole crazy mess I just ranted on is my imagination, and it has no proof of anything — meaning it’s nothing in reality and just an imagination (i.e., a fairy tale).