I am reading the textbook "The Cosmic Perspective 8th ed.", in the chapter describing the earliest moments of the Big Bang, one of the sentences is      [...] a sudden and dramatic expansion of the universe the size of that we call inflation. In a mere $10^{-36}$ second, pieces of the universe the size of atomic nucleus may have grown the size of our solar system.   It seems to me that such an expansion is much faster than the speed of light. Is the expansion of the universe not restrained by the speed of light?
just after the Big Bang and before inflation the currently observable universe was the size of a coin. One millionth of a second later the universe was the size of the Solar System, which is an expansion much much faster than speed of light. Can space expand with unlimited speed?
Do black holes have a moment of inertia? My question is in the title: Do black holes have a moment of inertia?  I would say that it is: $$I ~\propto~ M R_S^2,$$ where $R_S$ is the Schwarzschild radius, but I cannot find anything in the literature. Number of $(0,1)$ $m\times n$ matrices with no empty rows or columns How to determine the encoding of text? I received some text that is encoded, but I don't know what charset was used. Is there a way to determine the encoding of a text file using Python?  deals with C#. Hair Paricle System not rendering properly on plane One can show that $\mathbb{P}^n\times \mathbb{P}^m$ is birational to $\mathbb{P}^{n+m}$ by making note of the Zariski topologies and the canonical isomorphism between affine spaces $\mathbb{A}^n\times \mathbb{A}^m\to \mathbb{A}^{n+m}$.   Question: Does it follow that there is isomorphism $\mathbb{P}^n\times \mathbb{P}^m\to \mathbb{P}^{n+m}$? If so, what is an example of such an isomorphism?   Unfortunately I am having a hard time coming up with one, and haven't seen too many examples thus far. What information does the trace of a matrix give? Given this (very) tricky determinant, how can we calculate it easily?  $$\begin{pmatrix} \alpha + \beta &amp; \alpha \beta &amp; 0 &amp; ... &amp; ... &amp; 0 \\ 1 &amp; \alpha + \beta &amp;  \alpha \beta &amp; 0 &amp; ... &amp; 0 \\ 0 &amp; 1 &amp; \alpha + \beta &amp; \alpha \beta &amp; ... &amp; ... \\ ... &amp; ... &amp; ... &amp; ... &amp; ... &amp; 0 \\ ... &amp; ... &amp; .... &amp; ... &amp; ... &amp; \alpha \beta \\ 0 &amp; 0 &amp; 0 &amp; ... &amp; 1 &amp; \alpha + \beta   \\ \end{pmatrix} \in M_{n\times n}$$  EDIT:     I have to prove it is equal to $\frac{{\alpha}^{n+1} - {\beta}^{n+1}}{\alpha - \beta}$   Any help is appreciated, I just could not find a trick to ease it up! If we have a complex scalar $\phi$ we know that the gauge-invariant interaction with $A$ is given by $A^\mu J_\mu$, where $J$ is the Noether current of the $U(1)$ symmetry of the Lagrangian $$ J_\mu\sim \phi^\dagger\partial_\mu\phi-\phi\partial_\mu \phi^\dagger \tag{1} $$  If we have a real scalar instead, $J=0$ and the field doesn't couple to $A$: real particles aren't charged.  My question is: what if we took $$ J_\mu\sim \phi\partial_\mu\phi \tag{2} $$ to couple $\phi$ to $A$? The interaction is Lorentz invariant and renormalisable, but it is not gauge-invariant, which is probably a bad thing. At what point would this theory break down?  This is probably very naïve, but I think that the Feynman rules for this theory are straightforward. So I guess the theory makes sense at least perturbatively. The theory is probably flawed at a more fundamental level, but I cant't seem to find where (some kind of gauge anomaly perhaps?) Stretch and scale CSS background Is there a way to get a background in CSS to stretch or scale to fill its container? I'm cooking two different dishes in the oven at the same time that each require different temperatures. One is a roasted vegetable dish that says to cook at 475 for 35-40 minutes and the other is parmesan crusted pork chops at 350 for 40-45 minutes. What do you suggest I do? Variable-name \newcommand with parameters within another \newcommand How can I find posts related to lost reputation due to a "user was removed" message? Today I noticed that my reputation got truncated by 64 points, and when I looked at my reputation history, I saw  notifying me of points removal along to a "user was removed" message. Each has a slightly different timestamp, ranging from 12:39:04 to 12:39:43.    I can't find the questions/answers concerned by this (and I don't remember having won as much as 65 points once, making this even stranger). I would like to find out how I could have lost 65 points while I never won as much in a single question/answer.  Is there a way I can check which of my posts were impacted? Cleaning Contaminated Disc Rotors I've had an eternal struggle with my current bike over brake contamination. The levers and calipers are shimano ultegra r8000, so the latest and (almost) greatest.  I first noticed it when I took it to a repair shop (i no longer use) for a bleed, it came back and the front brake would squeal like crazy and at low speeds had little to no braking force. You can stop from speed but then struggle to come to a halt without using your foot.  At around 2000 miles I tried to replace the brake pads, when I took them out they were black with grime on both sets (front &amp; back), not to mention worn down to the metal. I replaced them with the L04C sintered pads, gave the callipers a good cleaning with a towel (no chemicals) and fitted the new set.  Annoyingly all of my braking issues are back, now I probably should have cleaned the rotors, I simply used some muc off disc brake cleaner on them. I would like to know the best way to clean the rotors, I've inspected the pads and they are looking fairly black now, with plenty of tread left. I'm going to abandon these pads and fit a new set. For the rotors I plan to completely remove them from the wheels (they are center lock fitted) and try and treat them off the bike, what is the best way to fully clean them? They have plenty of wear left in them but you can see these black grooves in them, and plenty of muck on the back that I struggle to get off.  Below are images of the rotors after soaking them in disc brake cleaners, waiting and then wiping them down with a clean, microfiber towel.   Front Wheel Outside Rotor   Front Wheel Inside Rotor - note the increased dirt on this side  Looking at ways people clean their disc rotors, I've seen plenty of suggestions that I would need to burn the contaminants off the discs. Would the best approach be to remove them and use a blowtorch, should I soak them in some nasty chemicals overnight before I try to heat them? Do I try baking them in the oven?  And finally, what is the best way to prevent the brakes from becoming contaminated in the future? it's really off putting when they squeal and don't perform how I'd expect because it means I'm more reserved whilst out riding on the bike, leading to reduced time riding around outside. I commute on this bike (50 miles a week) and then ride about 50 on the weekends also, so it see's it's fair share of road use. I tend to wash it once after my big ride on saturdays and will rinse it off if it's been raining, any day that occurs (since I live in north east england, the acid rain..). I've owned disc brake bikes before and never had half the issues I've had with this, I had a cheap trek with tektro brakes and the brakes were sharper and never had any issues with contamination whatsoever (i did around 500 miles on that bike before a motorist happened).  Thanks for any and all advice :) Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$ How do you find all subclasses of a given class in Java? How does one go about and try to find all subclasses of a given class (or all implementors of a given interface) in Java? As of now, I have a method to do this, but I find it quite inefficient (to say the least). The method is:    Get a list of all class names that exist on the class path Load each class and test to see if it is a subclass or implementor of the desired class or interface   In Eclipse, there is a nice feature called the Type Hierarchy that manages to show this quite efficiently. How does one go about and do it programmatically? Buffering in meters/km using WGS84 layers using QGIS I am using QGIS 1.7.4-Wroclaw and working with an SHP layer in WGS84. I want to buffer out to a certain number of kilometers from this layer using the ftools buffer tool.  I understand that the buffer tool always uses the layer units, which for WGS84 are decimal degrees. We all know that degrees don't convert consistently to meters, so how should I go about making my buffers?   Is it necessary for me to convert the shapefiles to a different CRS that natively uses meters?   If so, how do I choose one? For some reason I can't boot my system. I get an error akin to Operating System Not Found.   I tried bootrepair, and that didn't work. So then I decided I would just save my personal files, wipe everything, and reinstall.   But in the live session, when I go to the /home directory, my username folder isn't there, instead it goes to the Live CD's desktop and other directories. Is there some other error occurring? Is there a way to recover the files? In PostgreSQL, what is the difference between a "Stored Procedure" and other types of functions? I understand the distinction between:   Scalar functions Set-Returning-Functions (SRF)s Internal functions Window functions Aggregate functions of all sorts User-Implemented functions (which in PostgreSQL can be implement in any language) Etc.   In SQL Server "Stored Procedures" are permitted through EXEC. What does that provide over any other function executed with SELECT that returns NULL?  When PostgreSQL gets Stored Procedures what will they bring me, and what is the formal distinction if any between a function and a stored procedure in the spec?  I read Where do I place my own .sty or .cls files, to make them available to all my .tex files? What are the key principles that effective designs share? You have arrived on this page because you are clearly curious about underlying fundamentals that you can incorporate into your thought process when designing.  According to many that came before us, there are key principles that can be considered when creating an effective design. In the following answers, you will find useful theories from a variety of respected sources.  Use this question as a reference for navigating the variety of topics:  Gestalt Principles  &nbsp;&nbsp;  &nbsp;&nbsp;  &nbsp;&nbsp;  &nbsp;&nbsp;  Other Fundamentals and Useful Information  &nbsp;&nbsp;  &nbsp;&nbsp;  &nbsp;&nbsp;  &nbsp;&nbsp;  If you know of a topic that hasn't been covered here, please add an answer with references to respected resources and it will be added to the list.  Of course direct quotes and paraphrasing from respected resources are a must, but should be limited to a small paragraph per topic at most and referenced back to their source as thoroughly as possible.  A  has been posted before, but not to create a collection of snippets that are enlightening for graphic designers of any and all skill levels.