Shadow

Yes.

Nope. There's a nice identity I found when learning log's, [math]\sqrt[\log_y{x}]{x} = y[/math], although it's pretty much useless as far as I know. The only thing you can do with multiplication and/or division of logarithms is use the rules you already know; [math]\log{a} \cdot \log{b} = \log{a^{\log{b}}} = \log{b^{\log{a}}}[/math] and [math]\frac{\log{a}}{\log{b}} = \log{\sqrt[\log{b}]{a}} = \frac{1}{\log{\sqrt[\log{a}]{b}}} = \log_{\sqrt[\log{a}]{b}}{10}[/math].

I've recently discovered an absolutely beautiful visualization plugin for certain media players, and since it seems not many people know about it I decided to start recording songs with the visualization and uploading them on YT. The media players in question are AIMP and Sonique and each one renders the visualizations a little differently, so some songs look better on one while others look better on the other. I've already spent an insane amount of time trying to find screen recorder software that would enable me to capture the entire screen with a smooth framerate and at least reasonable quality, and so far I've only found one that works, namely BB Flashback recorder. The quality isn't even near spectacular, but at least the resulting video is smooth. The problem is that it only works with AIMP, and crashes when I try to record fullscreen with Sonique. Does anyone know of a good piece of screen recorder software that would enable me to capture the entire screen and get a smooth video? A lot of the ones I've tried have options for framerate, but I guess the computer just can't handle generating the images for the visualization and recording the screen at the same time, so in best case scenarios I get a jump here and there, worst case scenarios I get 2 frames/sec. I'm using Windows 7 64bit. Apropos, is there a way to set something like this up to capture every frame that gets sent to the screen? Ie. a "do not render next frame until the current one is captured" setting. It wouldn't make any sense for games and such, but it would solve all my problems; I'd just run the program, wait for it to go through the song even if it took an hour, et voila. For those of you interested, here is a link to the channel I'm uploading to.

I got 4.14159 using the following Mathematica code: Abs[NIntegrate[E^ArcSin[x] - Sqrt[1 - x^2 - Floor[x]], {x, -1, 0}]] + NIntegrate[E^ArcSin[x] + Sqrt[1 - x^2 - Floor[x]], {x, -1, 1}] - NIntegrate[E^ArcSin[x] - Sqrt[1 - x^2 - Floor[x]], {x, 0, 1}] Although I've no idea if it's correct.

My bad, I just skimmed the post and missed that part.

Incorrect; have a look at Shor's algorithm, although it should be said that it's very technical.

Try PMing a moderator to move this to Computer Science, I think you'll get more replies there.

The plot was generated by plotting the points [n, T[n]], with n from 3 to 50. The first few point would then be: n: 3 -> [3, [math]\frac{1}{2}^{\frac{1}{3}}[/math]] = [3, 0.7937...] n: 4 -> [4, [math]\frac{1}{2}^{\frac{1}{3}^{\frac{1}{4}}}[/math]] = [4, 0.590563...] n: 5 -> [5, [math]\frac{1}{2}^{\frac{1}{3}^{\frac{1}{4}^{\frac{1}{5}}}}[/math]] = [5, 0.73973...] n: 6 -> [6, [math]\frac{1}{2}^{\frac{1}{3}^{\frac{1}{4}^{\frac{1}{5}^{\frac{1}{6}}}}}[/math] = [6, 0.62266...] . . . It is clear that for even n, the values increase with increasing n, while for odd n, the values decrease with increasing n. I did make one assumption which I hadn't realized at the time, and that is that they both converge to the same number (such as [math]a_n = (-\frac{1}{2})^x[/math] and that might not be true. I actually wouldn't be surprised if this were the case, because it does seem to converge awfully slowly. I'll have a look later and see if I can figure it out. Yes, since that would be the approximate value of the limit if both the "even branch" and the "odd branch" converged to the same number. As I said, I unknowingly made an incorrect assumption.

I know, I was answering imatfaal's post Also, with a little more time on my hands I was able to look at you're code, and your algorithm is wrong. What you are calculating is [math](((x^y)^z)^w)^q=x^{y \cdot z \cdot w \cdot w \cdot q} \neq x^{y^{z^{w^q}}} [/math], which is what the OP is trying to find. I used Mathematica, specifically the function Fold, which is defined as Fold[f, x, {a, b, c, d}] = f[f[f[f[x, a], b], c], d] (The length of the list can be arbitrary) I then defined f: f[x, y] = y^x made x = 1/n and generated the list containing the second function arguments (In the function definition above they are a, b, c, d) using the function Table as follows: Table[1/n, {n-1, 2, -1}] which generated the list {1/(n-1), 1/(n-2), 1/(n-3)...1/4, 1/3, 1/2}. The final code for the function which gave the numeric value of the tetration operation was: T[n] = Fold[f, 1/n, Table[1/n, {n-1, 2, -1}]] I then plotted the following two sequences: Table[T[n], {n, 3, 50}] (blue) Table[(T[n]+T[n+1])/2, {n, 3, 50}] (red) Et voilà. In essence, I was building the power tower backwards, ie. starting from the top and building down. The number I posted is equal to (T[101]+T[102])/2.

You're going in the wrong direction; when evaluating the power tower, one must first evaluate [math]{\frac{1}{3}}^{\frac{1}{4}} = 0.7598...[/math] and then [math]\frac{1}{2}^{0.7598...} = 0.5905...[/math] etc. I'm short on time right now, I'll post more details on how I calculated the result later.

You're confusing tetration with repeated exponentiation.

Here is a plot of the sequence as n goes from 0 to fifty (blue) as well as the average of consecutive values (red). My computational resources are limited, but to the best of my knowledge the sequence converges (super, super slowly) to 0.6743563626906477538..., which is just some random number according to WolframAlpha. Hope this helps.

Special, yes. But calling them "life" is, IMHO, an overstatement. Another thing worth noting, sine waves are defined using the exponential function, so if anything that should be "life".

You're confusing number system with numeral system. The number systems are the different sets of numbers, ie. the naturals, the integers, reals etc. Binary, ternary, hexadecimal etc. are called numeral systems (similar in name, but completely different in meaning). But to answer you're question, if you're asking if 1/3 can be represented in binary, it can, but you get the same problem you would in decimal; the representation would again be infinitely long. Alternatively, you could the same fraction notation we use with decimal numbers to represent one third as [math]\frac{1_2}{11_2}[/math] but I've never seen that done before. Or, you could use the ternary numeral system to represent one third finitely as [math]0.1_3[/math]. Another example of how the finiteness of a representation depends entirely on the rules of representation we choose (ie. different number/numeral systems). I hope that last sentence makes sense.

You misread; I'm not referring to the finiteness of the numbers themselves, but of their representations; and while [math]\frac{1}{3}[/math] is a finite way of expressing one third, [math]0.333\bar{3}[/math] most certainly is not.

As far as I can see, it's a perfectly accurate metaphor; I'm not sure why you disagree. You can never exactly express a third using decimal numbers; you can with fractions. Also, what's pretentious about calling the universe "the universe"? I'm well aware of the different number systems. However, since introducing all that extra information wouldn't do anything to help the attempted simplicity of the explanation, I refrained from giving it. Also, since it might not have been obvious from my previous post, I was responding to the following: However, I might have misinterpreted the meaning; the way I understand it, and for me the post is not clear enough to be completely sure, the author was saying that numbers with infinite decimal places are "unreal". I was attempting to point out that there is a way to represent them finitely and thus helping the author accept their "realness", evidently not doing a great job of conveying that either. A piece of trivia, which you might already know, not even the complex numbers occupy the highest level; see quaternions, octonions and sedenions. keelanz: What numbering system would that be? The naturals?

Precisely; the problem is not with the Universe, but with our methods of describing it. People realized long ago that .3333...just wasn't going to cut it, and thus fractions were born (probably not true historically, but you get my point). Today, we use fractions to avoid (some) infinite decimal expressions. Think of decimal numbers as being a less perfect "language" than fractions with which one expresses amount.

It's 1234567 9 x 999,999,999, not 123456789 x 999,999,999 Fuzzwood.

Actually, that's not entirely true; you can represent infinity "with two ends". Just draw any line, as short or as long as you wish, and "count" the number of points it's made of. Or, I can say this a little differently; count the real numbers between a number and that same number enlarged by any positive amount, mathematically [math]| \langle x;\hspace{1 pt} x+y \rangle |, \hspace{1 pt} x \in \mathbb{R}, \hspace{1 pt} y \in \mathbb{R}^+[/math].

jamiestem, your accusations are not fair, you may just as well accuse hal, since he was the first person to post an answer that had no direct connection to your questions. But that would be as unfair as accusing swansont; this is a discussion, and discussions tend to develop beyond the original topic. The moderators are not going to do anything about a discussion that's civil and constructive. If it really ticks you off that much, PM any moderator with a request to split this discussion from your topic, and I'm sure they'll oblige. Answers to some of your questions can be found in the Wikipedia article, one of them being: "NISA estimates that the amount of radioactive material released to the atmosphere is approximately 10% of the 1986 Chernobyl accident, which is the only other nuclear accident to have been rated a Level 7 event.". This gives you a general answer to your questions; it's not another Chenobyl, at least not yet. Have a look at the following for more detail: http://en.wikipedia.org/wiki/International_Nuclear_Event_Scale#Level_7:_Major_accident http://en.wikipedia.org/wiki/Radiation_effects_from_Fukushima_I_nuclear_accidents#Discharge_to_seawater_and_contaminated_sealife As stated previously, Fukushima is not another Chenobyl. I confess I can only draw conclusions based on common sense, since I have next to no knowledge about these matters, but I wouldn't expect it to have as big an impact. But that's just my guess, I'd rather defer to experts in this matter. http://en.wikipedia.org/wiki/Fukushima_I_nuclear_accidents#Radiation_in_other_countries Hawaii: http://www.khon2.com/news/local/story/Fukushima-nuclear-plant-crisis-not-a-current/siBFlOZ-pEuxjzesWIVt8g.cspx Alaska: http://tobefree.wordpress.com/2011/03/14/radiation-from-fukushima-would-take-7-days-to-reach-alaska/ West coast: http://www.dailykos.com/story/2011/03/14/956447/-Fukushima-is-bad,-but-the-West-Coast-is-Safe East coast: http://www.dailykos.com/story/2011/03/22/958882/-Radiation-from-Fukushima-detected-on-US-East-Coast All of the above were found either using Wikipedia or with a simple Google search consisting of "Fukushima [city/area name]" Some other links that might help you: http://www.guardian.co.uk/world/2011/apr/12/japan-fukushima-chernobyl-crisis-comparison http://www.theworld.org/2011/04/fukushima-chernobyl-comparison/ http://rt.com/news/fukushima-impact-global-chernobyl/ http://communities.canada.com/vannet/blogs/editorsnotes/archive/2011/03/23/editorial-fukushima-s-global-impact.aspx Also found using simple Google searches. Maybe you should try that first next time, especially if you're so sensitive about discussions going off topic and/or are not interested in discussions, but in facts. Do note however that I have no way of verifying the credibility of the above links; I couldn't tell a blatant lie from truth in this matter even if the former slapped me in the face. Hope this helps you out.

Hey all, I'm aware that this is not a drug forum and that drug related questions get frowned upon at times, but this is a question to which I want an honest answer from experts in the field, based upon empirical evidence, previous research and existing literature and not some pothead answer who's knowledge is based on street myths. I got sick a month ago, and two weeks later was diagnosed with infectious mononucleosis. I'm not sure if it's done the same way here as it is in other countries, but with me they tested for the amount of white blood cells in my body, which was found to be thrice the normal amount (I remember the number being 29000, I believe the unit was [number of cells]/mm^3, but I'm not sure) and then the level of some kind of enzyme that (if I remember the answer to my questions correctly) is secreted by cells in the liver. I don't know the name, but going through Wikipedia, it seems like transaminase is the one. Anyway, my levels were 14x the normal amount, which is supposed to be 0.5 (again, don't remember the units, I only remember that their name sounded complicated, ie. it was some kind of medical unit), I had 7. I was in the hospital for 2 weeks, and in that time my white cell count went back to normal, and the last test I had showed my liver tests at 1.30, they've been dropping as fast as 1.0 in 2-3 days. My doctor said she's never seen anyone get better so quick. I also had enlarged lymph nodes, which are gone to the best of my knowledge. Both my spleen and my liver are enlarged, majorly (and will be for a while), but by how much I wasn't told. So, in a nutshell, my diagnosis was pretty severe, but my recovery very quick. I am now at a point where pretty much all of the external symptoms of mono are gone (ie. the tonsillitis, fatigue etc.), only thing I'm supposed to do is stay on a strict diet for at least two months and refrain from engaging in any physical activity, which is (after asking a couple of friends who have had mono before) standard procedure with mono, regardless of it's severity. Will smoking marijuana affect me negatively in any way? If so, how and why? I've done quite a bit of searching on the internet, coming up with mixed results. Some say it's fine, usually people talking from personal experience (although I also found this). Then you get people saying it'll slow down your recovery or rupture your spleen and stuff like that, but those same people also say you should "finish taking your antibiotics [for viral mononucleosis]" and "find something more constructive [than destroying your life] to do" etc., so I'm not entirely convinced about their credibility, it may as well just be stupidity or prejudice respectively talking. I've looked at Wikipedia and determined that THC is metabolized mainly in the liver, from which I deduce a possibility of it straining the liver and slowing down the regeneration process, but then again so is most of the stuff I ingest, and that doesn't do any harm as far as I can tell. I'm aware that it's better to be safe and refrain, but I'm past the acute phase, and I want to know if it'll actually do me any harm; is there some way marijuana negatively affects the liver/spleen, or slows their regeneration, or could it react with the virus in some way (I know that's not possible but just throwing out examples)...? Thanks for any and all answers.

What [math]E = m \cdot c^2[/math] tells you is that energy and mass are the same thing, in the same way that a cup with 50% of its volume filled up with water is both half full and half empty, at the same time. So yes, photons are matter. And they are also energy. It's the same thing.

I'm well aware that it's not exactly eight; a single look at the parity of the dividend proves the impossibility of the quotient ever being an even number. But that fact that it's an almost integer is in itself lolworthy; the fact that it's almost eight is roflworthy, in this context.

Just out of curiosity, I tried out 987654321/123456789. I lol'd.

Well, just got part of my blood test (a lot faster than I had expected) and it seems my liver is completely screwed up, which points to mono after all. So it's the hospital for me folks...wish me luck