Timbre is a property associated with the shape of a sound wave, that is, the coefficients of the discrete Fourier transform of the corresponding signal. This is why a violin and a piano can each play the same note at the same frequency yet sound completely different. Now for light: if you mix red and blue light, the resulting wave has on average the same frequency as green, but a different shape. Is this why we observe it as magenta instead of green? So can we say light has timbre?  But other colours mixtures don't work! Red+green is yellow, but yellow is a pure colour, so apparently red+green has no unique timbre in this case; the shape of the red+green wave is identical to a pure yellow wave.
In music, when two or more pitches are played together at the same time, they form a chord. If each pitch has a corresponding wave frequency (a pure, or fundamental, tone), the pitches played together make a , which is obtained by simple addition. This wave is no longer a pure sinusoidal wave.  For example, when you play a low note and a high note on a piano, the resulting sound has a wave that is the mathematical sum of the waves of each note. The same is true for light: when you shine a 500nm wavelength (green light) and a 700nm wavelength (red light) at the same spot on a white surface, the reflection will be a superposition waveform that is the sum of green and red.  My question is about our perception of these combinations. When we hear a chord on a piano, we’re able to discern the pitches that comprise that chord. We’re able to “pick out” that there are two (or three, etc) notes in the chord, and some of us who are musically inclined are even able to sing back each note, and even name it. It could be said that we’re able to decompose a Fourier Series of sound.  But it seems we cannot do this with light. When you shine green and red light together, the reflection appears to be yellow, a “pure hue” of 600nm, rather than an overlay of red and green. We can’t “pick out” the individual colors that were combined. Why is this?  Why can’t we see two hues of light in the same way we’re able to hear two pitches of sound? Is this a characteristic of human psychology? Animal physiology? Or is this due to a fundamental characteristic of electromagnetism?
Fibonacci sequence and Euclidean algorithm's connection. Let $f_1, f_2,\dots,f_i,\dots$ be the Fibonacci sequence with $f_1=f_2=1$. For any $a,b\in\mathbb{N}$ with $a&lt;b$, suppose the Euclidean algorithm takes $n$ long divisions to compute $\gcd(a,b)$. If $a\le f_j$, then $n\le j-1$, for $j\ge2$.   I want to prove this problem. But I can't see any connection between Fibonacci and Euclidean algorithm. If anyone can give a hint about first step, it will be very thankful.  My guess is to use induction. What word (or how do you phrase things) do you use when the ostensible word for the class is the same as the word for a subset of the class?  For example, in the United States, there are many brands of sugared, carbonated soft drink that one can buy: Coca-Cola (or Coke), Pepsi, RC Cola, Sprite, 7-Up, A&amp;W or Mug Root Beer, etc). The first two are kinds of 'coke' or 'cola' (but no one says 'cola').  , one asks for any type of such drink as 'coke'. How does one then ask for the particular kind of 'coke' that is 'Coke' (pronounced the same)? Does one reduplicate and say a 'Coke coke', does one repeat with emphasis (or without), does one use a different word like 'coca-cola' (co-cola), or what?  The (perceived) difficulty (surely those in the South are able to get the drink they want somehow) isn't limited to there. Where the drink is called 'soda', if you ask for a 'coke', you'll still sometimes have the choice among Coca-Cola, Pepsi, etc. "Can I have a Coke?" the response might be "Is Pepsi OK?". "Sure, Pepsi, Coke, whatever." You don't use 'cola', you just ask for the particular kind and hope the listener will help differentiate.   Given these multiple strategies for disambiguating, what do you do say to get a 'Coke' in the southern US? are there any other examples of a hypernym being the same as the hyponym, and so creating a disambiguation problem? How do I scan for viruses with ClamAV? How to play MP3 files using Rhythmbox? Yesterday I just installed the Ubuntu 12.04 for the first time, the problem is that I can't play and of the MP3 files that I have.    I get this error:       Required plugin could not be found Python (v2.7) requires to install plugins to play media files of the following type: MPEG-1 Layer 3 (MP3) decoder   Please help me so I can play the files. Thanks "Baggage" versus "luggage" Value of Vandermonde type determinant Let $x_1,...,x_n $ are distinct real numbers.  Is it a formula for the Vandermonde type determinant $V(x_1, \cdots,x_n)$  whose last column is $x_1^k,\ \cdots,\ x_n^k$, where $k \geq n$, instead of $x_1^{n-1},\ \cdots,\ x_n^{n-1}$?  Thanks Infectious chicken pox My 21 year old son has chicken pox and has been home for a few days now. The spots are just starting to crust over.  I work with elderly people but have had chicken pox as a child - should I carry on working while he is here (hes usually away at Uni) and infectious? I'm using a  freely downloadable latex class file and the style is set to \bibliographystyle{ieeetr}. But when I cite something with \cite{} I get it inside ().   For example I get it as abc et al. (1) but what I want to get is abc et al. [1].   Please tell me how to get my citations inside [ ] ? I am writing a small KOMA-Script scrartcl document with multiple sections. In the table of contents, LaTeX fills the current line with dots between the end of the section name and the page number. Is there any way to customize this behavior? I would like to reduce the space between the single dots (i.e. use more dots in the same space). "Protect Questions" privilege page has confusing wording The wording on the  privilege page is confusing and would benefit from being clarified. See these questions on  and . Suggested wording from  is to replace this:  Which questions can be protected? Any question, even a deleted question, can be protected and unprotected, subject to the following restrictions:  The question must be at least a day old A user can unprotect any protected question   with the following:  Which questions can be protected? Any question at least a day old, even a deleted question, can be protected and unprotected. A user with the privilege can unprotect any protected question. Mail App keeps popping up in the background in Mac OS Mojave Is there a free program to (batch) change photo file's date to match EXIF? I want to specify a directory and have the software find all the photos in the directory and its sub-directories, and if they contain EXIF date/time, it sets their filesystem timestamp to match the EXIF. How can I attack an enemy's weapon? I want to hit enemy's axe to break it. How this is properly played in D&amp;D 5e? And what about shield or armor? Can I attack these items to break it? SQL IN Clause 1000 item limit Proof of an elementary property of Projection Operators I'm asked to show the following:  Let $X$ be a linear space, and let $P : X \rightarrow X$ be a projection operator. Restricted to the linear space $range(P)$, the projection $P$ is the identity operator, that is, $Px = x$ for all $x \in range(P)$.  If anyone could offer a hint for how to show this. I'm rusty with linear algebra so don't really know what I'm supposed to bring in outside of what's specified in the lemma/definition of projection. What is so special about the range of P that would make this so? Let's make the hot network questions icons clickable I would like to see the icons in the 'Hot Network Questions' right panel clickable, leading to the homepage of the site where the question comes from.  It would make it more comfortable to switch to the site when you want rather to visit it than to see that specific "hot" question. There is an experimental timeline view for questions now available on meta ONLY! (Now working on SO, SF, and SU as well)  This is partially motivated by comments about how difficult it is to follow very active questions which have a lot of activity, and also the feedback on the API which was heavily dominated by "we need to know what happened in this time range" type responses.  It can only be accessed through URL hackery at the moment. To get to it, enter question URLs like so:  https://meta.stackexchange.com/posts/{id}/timeline  This is a chronological timeline of everything that happened on a question, including   initial question ask answers  revisions comments closure, deletion, reopen, undelete, etc votes   all based on when they happened in chronological order.  We are thinking about making this a fourth tab on the question, like so:  Timeline | Oldest | Newest | Votes  Please try it out and provide feedback. It is still a little rough, so we are not looking for highly detailed bug reports, just more general feedback.  Timeline view for this question: A company is any form of business whether it is small or large. Generally the term &quot;company&quot; indicates a particular kind of business dealing in a specific product. An organisation is the larger form and generally comprises of a number of companies.  Simply, a company is an organization, but an organization is not just a company. An industry is the combination of companies in same line of business. Firm, corporation and business  are synonyms of &quot;company&quot;. An Agency is a particular kind of company, which serves as an intermediary between clients (other companies or individuals).  Is this correct? Is "coachee" even a word? If I am Rita's coach, is Rita my *coachee? (yikes) Is that even a word? Would it be correct instead to say she is my ward? What about terms for people at the other end of a mentor, sponsor relationship? Problems after upgrading to 14.04 (only background and pointer after login)