I never understood what the f really stands for in the f-stop values, like f/1.8. Wikipedia explains it in various articles, but I still find it very confusing. What I understand, though, is that it has something to do with focal length.  Should I assume, therefore, that bigger focal lengths capture more light? For example, should 85 mm f/1.8 lens capture a lot more light than for example 24 mm f/1.8?  References to back up my confusion:  The article about  goes on to claim:     The amount of light captured by a lens is proportional to the area of   the aperture, equal to:            Where f is focal length and N is the f-number.   The "f-number" is mentioned here. But the article about  claims:     In optics, the f-number of an optical system expresses the diameter of the entrance pupil in terms of the focal length of the lens; in simpler terms, the f-number is the focal length divided by the "effective" aperture diameter.   This seems very recursive. Why does the aperture article refers to both the focal length and the f-number, when the latter article claims that f-number already carries the property of focal length?  What's going on here?
With a Canon 550D camera and a Tamron 18-270 mm zoom lens, I tried to fix shutter time, aperture (f/8.0 to cover all zoom range), and ISO, so the exposure meter read 0.0 with 18 mm focal length and while focusing on a uniform white wall.  Then I changed to 270 mm focal length, but the exposure reading did not change significantly (only to -0.7).  However, I had expected exposure to change, since only (18 mm / 270 mm) ** 2 = 1/225 of the wall is now covered in compare the coverage when focal length is 18 mm, thus only 1/225 of the light gets to the sensor after the change of focal length.  Why does exposure not change when narrowing the field of view with change of focal length?
People seem to believe that one's consciousness is a "different" consciousness than that of others, but the "same" consciousness as the one that has been in one's body in the past and the one that will be in one's body in the future. How likely is this to be true and why?   Also, I have almost no knowledge about neuroscience, so please refrain from using neuroscience jargon if feasible. Can I install the 64 bit version? Are these adjectives interchangeable?  I always hear: 'An Arab man.' but never 'An Arabic man.' and I always hear 'Arabic coffee' but never hear 'Arab coffee.' I've been trying to develop an intuition based understanding of Bayes' theorem in terms of the prior, posterior, likelihood and marginal probability. For that I use the following equation: $$P(B|A) = \frac{P(A|B)P(B)}{P(A)}$$ where $A$ represents a hypothesis or belief and $B$ represents data or evidence. I've understood the concept of the posterior - it's a unifying entity that combines the prior belief and the likelihood of an event. What I don't understand is what does the likelihood signify? And why is the marginal probability in the denominator? After reviewing a couple of resources I came across this quote:     The likelihood is the weight of event $B$ given by the occurrence of $A$ ... $P(B|A)$ is the posterior probability of event $B$ , given that event $A$ has occurred.   The above 2 statements seem identical to me, just written in different ways. Can anyone please explain the difference between the two? Why can't variable names start with numbers? I was working with a new C++ developer a while back when he asked the question: "Why can't variable names start with numbers?"  I couldn't come up with an answer except that some numbers can have text in them (123456L, 123456U) and that wouldn't be possible if the compilers were thinking everything with some amount of alpha characters was a variable name.  Was that the right answer?  Are there any more reasons?  string 2BeOrNot2Be = "that is the question"; // Why won't this compile? Suppose that a box contains 10 red balls, 20 green balls, and 30 blue balls.   Suppose also that balls are drawn from the box one at a time at random.  What is the probability that all the red balls are drawn before the blue or green balls are themselves exhausted. What is the probability that as the last red ball is drawn, there remains at least one blue and one green left in the box.  The answer I was given is $\dfrac{7}{12}$ and a general equation is: $$ \dfrac{b g}{1-b}+\dfrac{b g}{1-g} $$ where $$ g=\dfrac{20}{60},b=\dfrac{30}{60} $$ but why? Theorem numbering In the season 8 episode finale of Game of Thrones the highest important lords met with Grey Worm to free      Tyrion and Jon. While it was pretty clear why they wanted to free Jon it was unclear to me why they also asked for Tyrion.   To make things even more strange, they asked about his opinion of a potential solution which becomes the actual final one in the end      (choose king and nominate someone).   I thought they (besides Sansa and Bran) don't like him and wanted to judge him? Or am I missing something? no match for ‘operator<<’ in ‘std::operator How do I do a SELECT * INTO [temp table] FROM [stored procedure]? Not FROM [Table] and without defining [temp table]?  Select all data from BusinessLine into tmpBusLine works fine.  select * into tmpBusLine from BusinessLine   I am trying the same, but using a stored procedure that returns data, is not quite the same.  select * into tmpBusLine from exec getBusinessLineHistory '16 Mar 2009'   Output message:     Msg 156, Level 15, State 1, Line 2   Incorrect syntax near the keyword   'exec'.   I have read several examples of creating a temporary table with the same structure as the output stored procedure, which works fine, but it would be nice to not supply any columns. How can reincarnated souls be summoned using Edo Tensei? Quoting ,     Reincarnation is the philosophical or religious concept that an aspect of a living being starts a new life in a different physical body or form after each biological death. It is also called rebirth or transmigration, and is a part of the Saṃsāra doctrine of cyclic existence.   Then, since Ashura has reincarnated into Naruto, and Indra into Sasuke, how can Uchiha Madara and Senju Hashirama (their previous reincarnation) be summoned using Edo Tensei? Suppose $G$ is a group and $K\lhd H\lhd G$ are normal subgroups of $G$. Is $K$ a normal subgroup of $G$, i.e. $K\lhd G$? If not, what extra conditions on $G$ or $H$ make this possible?  Applying the definitions, we know $\{ghg^{-1}\mid h\in H\}=H$ and $\{hkh^{-1}\mid k\in K\}=K$, and want $\{gkg^{-1}\mid k\in K\}=K$. Clearly, the best avenue for a counterexample is if $gkg^{-1}\not\in K$ for some $k\in K$ and $g\in G-H$.  If no such element exists, $\{gkg^{-1}\mid k\in K\}\subseteq K$ implies $\{gkg^{-1}\mid k\in K\}=K$ because if $k'\in K$, $gk'g^{-1}=k\in K\Rightarrow k'=g^{-1}kg\in\{gkg^{-1}\mid k\in K\}$. Possible to perform cross-database queries with PostgreSQL? I have a laptop with a full keyboard (it has numpad), but the laptop is not that big, and because of that the keys are relatively small, which means I am constantly finding myself pressing keys accidentally on the numpad part.  Is there a way to disable specific keys that I simply don't want? Error to calculate date diff with DateTime class How to generate all permutations of a list? I've heard Google's algorithm is based on PageRank, and that it has something to do with the links to your site. Can someone explain it, and more importantly, how I can increase my site's PageRank? Simple Proof by induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$ I'm trying to prove using induction that $9$ divides $n^3 + (n+1)^3 + (n+2)^3$ whenever $n$ is a non-negative integer. So far, I have:   Base case: $P(1) = (1) + (8) + (27) = 36, 36$ can be divided by $9$ so the base case is valid Inductive step: let $P(n)$ be the statement $9$ divides $n^3 + (n+1)^3 + (n+2)^3$. Assume $P(k)$ is true, so $9$ divides $k^3 + (k+1)^3 + (k+2)^3$.   And this is where I'm stuck. I'm not sure how to demonstrate that $9$ divides $P(n)$ when $n = k+1$. If someone could step me in the right direction that would be awesome. Thanks! How bad is it to use display: none in CSS? I've heard many times that it's bad to use display: none for SEO reasons, as it could be an attempt to push in irrelevant popular keywords. A few questions:   Is that still received wisdom? Does it make a difference if you're only hiding a single word, or perhaps a single character? If you should avoid any use of it, what are the preferred techniques for hiding (in situations where you need it to become visible again on certain conditions)?   Some references I've found so far:       If you're straight-out using CSS to hide text, don't be surprised if that is called spam. I'm not saying that mouseovers or DHTML text or have-a-logo-but-also-have-text is spam; I answered that last one at a conference when I said "imagine how it would look to a visitor, a competitor, or someone checking out a spam report. If you show your company's name and it's Expo Markers instead of an Expo Markers logo, you should be fine. If the text you decide to show is 'Expo Markers cheap online discount buy online Expo Markers sale ...' then I would be more cautious, because that can look bad."   And  on the same article     We can flag text that appears to be hidden using CSS at Google. To date we have not algorithmically removed sites for doing that. We try hard to avoid throwing babies out with bathwater.   Eric Enge      The legitimate use of this technique is so prevalent that I would rarely expect search engines to penalize a site for using the display: none attribute. It’s just very difficult to implement an algorithm that could truly ferret out whether the particular use of display: none is meant to deceive the search engines or not. Is there a word that describes a person who dies on his/her birthdate?