Religion
Related: About this forumMath in a religion forum?
I've been reviewing Calculus, don't ask me why, and infinite series as well.
So this is about what we think, versus the truth. I was talking with a friend who does volcanology work, and on his drive through Oregon he suddenly broke out into sarcastic cutesy talk as he drove by a billboard that had a picture of a baby, and words to the effect that therefore god exists. Cute baby, therefore God. Shit, I look around and see diversity that makes me wonder about how it got to be that way.
If we add two and two, we expect to get positive four. And if we add every single positive natural number, we expect not only a positive number, but a big one. I'd have bet my life on it. I'll let anyone who might be interested enough to read my bullshit, and actually watch the video, the lack of a spoiler. But after watching the derivation, I began asking myself just what it is that I believe that isn't so. Could it even be everything I think? Did Kim Davis do god a favor, and deny marriage licenses, or is god really a hubcap on a 1961 Rambler American convertible in Whittier.
Actually, this is the math derivation video.
Jim__
(14,074 posts)Apparently a number of people complained about this video, so Padilla composed a response. Part of the response is justifying the manipulations he performed. But part of it refers out to other blogs that talk about why it makes sense when talking Physics. From his reply:
Nevertheless, having read the comments, tweets and blogs, if I were to ask again "what do we get if we sum the natural numbers?" I think my answer would now be "we upset people". From what I can tell, there have been two levels of objection: those that simply do not accept the result because of its apparent absurdity, and those that have taken issue with the "proof" presented in the video. To the former I assure them that while this result is utterly counterintuitive, there is a very clear mathematical sense in which this sum should be assigned this rather counterintuitive value. And most importantly to me, it makes sense when we start talking Physics. The corresponding Mathematics is deep and complicated and I won't go into it here. Instead, let me point you to a few resources online and you can take it from there:
I haven't read the references yet, but they sound interesting.
Gregorian
(23,867 posts)The fact that it's useful in quantum physics really shocked me.
I think my point in posting this was that when we think, we can't believe it. It's all so counter intuitive. But that's what makes life so interesting.
edhopper
(33,554 posts)They are not, in fact just adding every positive integer, they are subtracting, or if you prefer, adding negative integers.
And contrary to what some religious people believe, we do not live in an infinite world.
The games with S1 and S2, are just that , math games.
Gregorian
(23,867 posts)I like the mystery. But I'm more comfortable when I'm sure I know something. But the longer I live, the more I think we don't know any actual truth.
Infinity to an ant is different than infinity for an elephant. I don't know...
edhopper
(33,554 posts)No infinity is infinity, it is the same to any perspective, mathematically. Unlike things like the speed of light or relativistic distances.
But if you are trying to gleam some real world religious analogy from this, it doesn't fit well.
If this is more a philosophical exercise, it prompts some thought.
I still don't see why adding 1+2+3+4+5... should start with 1-1+1-1+1...?
And even then they say we can't have an answer so let's pick the average, 1/2, so they are starting with what isn't the real answer.
Why are they even using the first two sums for 1+2+3+4+5...
It's math games.
skepticscott
(13,029 posts)that 1-1+1-1+1...= 1/2, but you're right, the way it is presented in the video takes a leap.
As far as the sum of 1+2+3+4+5+6+...=-1/12, it actually can be derived, but only if you allow meanings of "+", "=" and "..." that are different than what are commonly understood and accepted.
edhopper
(33,554 posts)just mathematically interesting.
skepticscott
(13,029 posts)that the result generates among some people, once you've adjusted the rules to make it possible to derive a finite sum from that series, it is not an astounding result, any more than finding a number that you can square to give -1, once you've allowed the concept of complex numbers. Then it all makes sense.
Gregorian
(23,867 posts)I was comparing our intuition of what we expect from something (the math outcome) with what we think is the truth. I'm using it to question the insistence that there's a god. After all, we have taken events that happened on earth, and extrapolated them as a conclusion that there's a god. If people realized that what they think they know may be incorrect, we could maybe make some progress among people. I don't know, it seemed like being more open minded might help the human race. And on that note, it's dinner time!
edhopper
(33,554 posts)But too logical for most believers. And many accept faith over evidence.
But I applaud the effort.
muriel_volestrangler
(101,295 posts)Gregorian
(23,867 posts)Regardless, it's still an interesting phenomenon.
Yorktown
(2,884 posts)S1 = ∑ ( n : 1 to ∞ ) { - 1 ^ n } = 1/2 might be possible in quantum physics describing positions of subatomic particles, but does not apply to an euclidian sum.
btw, I'm sure one could prove even weirder things using quaternion 'numbers'
pokerfan
(27,677 posts)Not that Numberphile was wrong per se, just not as complete as they could have been.
http://blogs.scientificamerican.com/roots-of-unity/does-123-really-equal-112/
MisterP
(23,730 posts)the messiness of reality
and then that got messy, and now even messier
Gregorian
(23,867 posts)The whole racism, fear, religion, etc., concepts that people hold onto as if they were solid objects, may not be what we think.
All I'm saying is the world would be better if people just said "I don't know" more often.
Here's another infinite series, and how to make the outcome different by goofing with it. Or, does god exist, or am I just imagining things.