Infants can only perceive in one dimension (closeness and farness). Young children can only perceive three dimensions (they can't plan or handle time). Teenagers and young adults can perceive 3+1 dimensions. However, this is all psychological and dependent on our personal growth, which means that someone could exist who perceives more dimensions than 3+1 and it wouldn't be a logical contradiction.  Is there any way to empirically test whether there are more dimensions? If there were 3+2 dimensions, then I could have a clock that is two-dimensional. Or I could have one clock that would tick in one dimension and another clock tick in another dimension.  How can we design an experiment to test this?
Is there any scientific experiment that can lead us to conclude we live in 3 spatial dimensions without the premise of the conception of limited dimensions?  Thank you all who helped in the improvement of this question (which was not clear at first).   EDIT:  I know that this can be a little philosophical, but it is also a scientific question.  Let's consider the scenario where the mankind was not ever able to see.  Let's also consider that this limitation could be surpassed thus not limiting us to reach a scientific and technological knowledge "similar" to what we have today.  Would this civilization of blind people reach the conclusion that they are living in a 3D spatial world?  Is the sense of touch enough to reach that conclusion? Is there any scientific experiment that can lead us to that conclusion without the premise of the conception of limited dimensions?  Would it be easier, harder, or just different to reach a conclusion predicted by the M-Theory? (please do not focus only on this last question)
So a company decides to raise money by selling shares of its stock. The stock is offered at an initial price of their determination. The stock is then traded in a market where forces of supply and demand, as well as speculation, affect its price.  When a company performs well (or makes decisions that will likely increase the company's earnings in the future), more people want to buy that stock than do people wanting to sell it. This creates demand for that stock which causes its sell/bid prices rise. When a company performs poorly, the opposite occurs; more people want to sell the stock than want to buy. This creates a surplus that causes sell/bid prices to fall.  Understanding this, people speculate over company performance to determine the future behavior of a stock, and attempt to "buy low, sell high" or "borrow high, return low" in order to make a profit.  But my question is regarding the first part of that process. What is it about company performance that causes the perceived value of its stock to rise? This is especially perplexing since I would guess that most people don't exercise their voting rights, and many stocks don't pay dividends.  It's not like a shareholder has any direct financial gains from increased company earnings (speculative stock pricing notwithstanding).  What is the intrinsic value of the stock?  It seems to me that all participants in a stock market tacitly agree that stock price will have a direct correlation with company performance. So another way of asking the question is, would an opposite agreement hold? What financially (this isn't a question about logistics, communication, or feasibility) stops all participants in a market from agreeing to value a particular company's stock inversely with respect to the company's performance?  Since I feel like I can't quite nail down my question, another form of it would be, why is stock market behavior driven by company performance? How to mount read-write an ext4 partition on Windows? I want to use ext4 on my external HDD, but it must be cross-platform. (At least Linux, Win7 &amp; WinXP).  Unfortunately, I haven't found any proper driver allowing Windows to WRITE to ext4. I've found , but it only reads ext4.     9. ext4 extent read-only, no  size truncating and expanding support   More:     Supported Ext3/4 features:         flexible inode size: > 128 bytes, up to block size   dir_index:    htree directory index   filetype:     extra file mode in dentry   large_file:   > 4G files supported   sparse_super: super block backup in group descriptor   uninit_bg:    fast fsck and group checksum   extent:       reading, writing with no extending.   journal:      only support replay for internal journal         Unsupported Ext3/4 features:         journal: log-based operations, external journal   extent: size truncating &amp; expanding, file deletion   flex_bg: first metadata group   EA (extended attributes), ACL support      Also, I have found a patch for Ext4Fsd v0.50 ():     New: Matt Wu has made a new release 0.50 at   ext2fsd.com.  Support for ext4 extents and fix   for BSOD on Windows 7.   I don't think it will be safe. Also I've read some words about writing ext4 in Windows could cause data loss on the disk...  What is the External HDD used for? - First, it will store backups, then family movies, pictures. Some music, and etc. It will be connected to a Raspberry Pi, if I finally receive it. It won't really move, just when it is used to migrate computer's data to a new one. The largest files it will store are Clonezilla disk images (I don't know, if they will be large files or not).  Can someone provide a solution for this problem? Or is there NO important enough difference between ext4 and ext3, and I should use ext3? - (If yes, then can I use Ext2Fsd for that ext3 mount?)  Thank you! Let $x&gt;0$, $y&gt;0$ and $z&gt;0$. Show that   $$x^3y+y^3z+z^3x\ge xyz(x+y+z).$$   I known we can't WLOG: $x\ge y\ge z$, if this, I can use rearrangement inequality, But other I can't it. Thanks? What's the typical microclimate in the aircraft passenger cabin? When preparing for a commercial jet flight it'd be nice to know how warm my clothes should be so that I don't freeze after sitting for several hours in say +16 degrees Celsius (61 degrees Fahrenheit).  What's the typical temperature in the passenger cabin? Are there air drafts? How cold and how warm can it reasonably get? I want to make my appexchange app available in multiple language like Spanish, dutch etc. so that depend on the language of the user they can access the app.  Is it possible in any way..  any help will be appreciated.. Thanks What's the main difference between int.Parse() and Convert.ToInt32 What is the main difference between int.Parse() and Convert.ToInt32()? Which one is to be preferred What happens when a creature enchanted with Soul Link would deal lethal damage to a player? Player A has 3 life left. Player B attacks with a  that has been enchanted by Player A's . Does player B win, or does nothing happen?  On the one hand, "whenever" makes it sound like the trigger (dealing damage) and the effect (healing damage) happen simultaneously.  On the other hand, combat damage doesn't go on the stack, while most other things do. So, possibly the combat damage is dealt, state-based actions are checked, and now it's too late for the Soul Link effect to heal player A.  If anyone knows which way is correct, my thanks! Is there the easiest way to toggle (show/hide) navigational grids in TikZ? In PSTricks, we can toggle the grids easily by showgrid=[false/true]. How to do it in TikZ? Doing as follows is tedious.    \documentclass{minimal} \usepackage{tikz}  \begin{document}   \tikzpicture  \draw[gray,very thin] (-4,-2) grid (4,2); \foreach \x in {-4,...,4}   \draw[red] (\x,-1.9) -- (\x,-2.1) node [below] {\x};   \foreach \y in {-2,...,2}   \draw[red] (-3.9,\y) -- (-4.1,\y) node [right] {\y};  \draw (0,0) circle (2);   \endtikzpicture    \end{document}   Is there the easiest way to toggle (show/hide) navigational grids in TikZ?  Edit  The navigation needs not only the grids but also the labeling numbers. My professor has stated the following lemma:  Let $U$ and $V$ be two vector spaces and $B$ a basis for $U$. If $f:B\rightarrow V$ is a map, then there exists a unique linear map $A: U \rightarrow V$ such that $A(x)=f(x)\ \forall\ x\in B$  How can I prove this lemma? (This is not a homework problem.) Prove that for any finite sequence of decimal digits, there exists an $n$ such that the decimal expansion of $2^n$ begins with these digits. Random number generation and probability If I have a Windows executable, how can I find out which dlls it will load?  I'm just talking about which ones that will be loaded statically, not ones it might load dynamically with something like LoadLibrary. Notation: Why write the differential first? What is the difference between Gödel's completeness and incompleteness theorems? Any open subset of $\Bbb R$ is a countable union of disjoint open intervals Let $U$ be an open set in $\mathbb R$. Then $U$ is a countable union of disjoint intervals.    This question has probably been asked. However, I am not interested in just getting the answer to it. Rather, I am interested in collecting as many different proofs of it which are as diverse as possible. A professor told me that there are many. So, I invite everyone who has seen proofs of this fact to share them with the community. I think it is a result worth knowing how to prove in many different ways and having a post that combines as many of them as possible will, no doubt, be quite useful. After two days, I will place a bounty on this question to attract as many people as possible. Of course, any comments, corrections, suggestions, links to papers/notes etc. are more than welcome. Reduce Spacing In $$ In math, one often needs to put a letter inside the symbols &lt;&gt;, e.g. to denote a cyclic group &lt;x&gt; generated by some element x. However, plain text displays the symbols &lt; and &gt; as an upside down exclamation point and an upside down question mark, respectively, while math type displays a large space like so:  &lt; x &gt;    Is there some way to reduce this spacing? Problem with the header/ footer width I have recently started using the geometry package to format the margins of my documents. Although, I've noticed that the width of the header/ footer remains the same. How can I correct this?    Here's a MWE:  \documentclass{article}  \usepackage{geometry} \usepackage{fancyhdr}     \pagestyle{fancy} \usepackage{blindtext}  \lhead{} \chead{Header} \rhead{} \lfoot{} \cfoot{Footer} \rfoot{\thepage} \renewcommand{\headrulewidth}{1pt} \renewcommand{\footrulewidth}{1pt}  \begin{document}  \newgeometry{margin=0.5in, bottom=1in, top=1in} \Blinddocument  \end{document} Elmah: How to get JSON HTTP request body from error report Limit of $\lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{\sqrt {n^2 +i} }$ Direct way leads to nowhere.  $$\lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{\sqrt {n^2 +i} } = \lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{n \sqrt {1 +\frac{i}{n^2}} } = $$  $$ = \lim_{n\rightarrow \infty} \frac{1}{n} \cdot \lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{\sqrt {1 +\frac{i}{n^2}} } = 0 \cdot \sum^{n}_{i=1} 1 = 0 \cdot n $$  So, I tried to apply squeeze theorem:  $$\lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{\sqrt {n^2 +i} } \leq \lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{n}  = 1$$  Could you help me to figure out the lower bound? Beamer -- not indenting itemize in a single environment The output in the MWE posted at the end of this post is shown below. Notice how the default indentation from itemize gives an asymmetric slide w.r.t the spacing to the left and right of the itemize environment. How can I push the bullet points to the left so that the spaces to the left and right are the same? Such a solution would ideally be:   implementable on a one-off basis, so that it is applied when necessary (since some itemize environments should be given the default indentation) independent of the margin size, so that the solution doesn't need to be changed when the margin size is changed     \documentclass{beamer}   \begin{document}  \begin{frame}{A title} \begin{itemize} \item Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod \item tempor incididunt ut labore et dolore magna aliqua. \item Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi \item ut aliquip ex ea commodo consequat. \begin{itemize} \item Duis aute irure dolor in reprehenderit in voluptate velit esse \item cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat \end{itemize} \end{itemize}    \end{frame} \end{document}