13 more posts in this thread. [Missing image file: cosx.png]
In high school I was often bored and thus I played around with my calculator a lot. I noticed some interesting occurrences, but I'm just now trying to figure out the nature behind them.
For example, if you take the natural log of any number except 0 numerous times, the answer will eventually even out to the solution of " x = e^x ", or the "fixed point" of f(x)=e^x.
This number is approx. 0.3181315 + 1.3372357i
By this I mean, if you do ln(ln(ln(ln(ln(ln(ln(...ln(x) you will eventually get that number.
My first question: Is there's a standard notation to write "take the natural log of a number x or infinite amount of times".
Also, I am curious on how to solve for such equations that can't be solved algebraically or with any calculus I have learned so far.
For example, the solution to x = cos(x) can't be solved algebraically as far as I can tell, so how would something like that be solved (The answer, which would be the "fixed point" of f(x)=cos(x) is about 0.739085)?
Lastly, can the solutions I have mentioned be written in any non-decimal form? By this I mean, say you have this seemingly-random number "4.810477381...". At first it seems like it isn't related to anything, but it's actually sqrt(e^pi). Could it turn out that the solution to x = cos(x) is actually *exactly* the cos(of number probably involving pi or e)?
Thanks for reading, pic shows approximations for the fixed point of cos(x), one of the examples I was talking about.
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I just read an interesting scientific paper on what seems to be a practical design for a gravity-wave generator of useful efficiency. Admittedly, it was on the arXiv, so it's not the most credible source, so I'd like to ask you- can you look over this and tell me if it's legit? It's way outside my field of study.
Also, is it true that in some analyses, gravity waves colliding will create a static gravitational field?
I realize that, pending an actual detection of gravitational waves, that this is largely a question of theory and speculation.
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I really need help and I think this is the best place to ask. I'm an alcoholic, during all the university years and my last working years I have done nothing but drink, usually until blacking out. For obvious reasons I don't have many friends, that's why I need your help /sci/
I live in a 'third' world country so I could go to work drunk, with a hangover or drink there. For different reasons I decided to stop drinking, mainly because I want to study a master's degree. I have 6 weeks without drinking and I have noticed my short term memory is deteriorated, I tried doing some calculus and it took me a lot of time...
so I want to know, what can I do to 'recover' my brain? someone told me that probably I just needed some nutrients and another that possibly doing some algebra could help. What can I do?