What's the difference between:     I'm amazed that he could paint such a piece.      I'm amazed that he can paint such a piece.   Context: A guy painted a painting and some people liked it and said the first sentence but I want to know what's the difference between could and can in these sentences.
Can you please explain this to me?          Could you please explain this to me?   I am unable to figure out which to use which situation. I did google, and some posts say they are both the same, even if the second one is more formal. Other posts say could is the past tense of can, but in the above example, I don't think could is used as past tense of can.  What is correct way to use these words?
When an air-filled balloon is released without its opening tied up, it moves in a circular path rather than a straight line. Why is that? For files within a specific folder, I would like vim to never touch "modified" timestamp at all.  The background is that I use  for blogging, which uses plain text files in ~/bloxsom as source of all articles.  The article date (and therefore order of appearence) is based on modification date of the text file. I don't want article pop up like if it's new whenever I just fix a typo. (I do lots of them... :D)  So far, vim changes timestamp and the original stamp is lost forever.  This is OK and I want to keep it that way for most of files on the system.  But I don't want that for the blog files - I can always touch the file if I need.  Any ideas on how to tweak vim into this behavior? Index notation Lorentz transfromation matrix I just did a clean install of 20.04 and I noticed that no key shortcuts for files manipulation work when my focus in on Desktop (not in Nautilus).   When I have copied a file to clipboard, I cannot Ctrl+V it to Desktop, when I click on a file on Desktop, I cannot Ctrl+C it, or I cannot Delete it with keys. Only ways to do it is either navigate to the Desktop folder in Nautilus, or right-click the file on the Desktop and copy/move to trash/paste...  Sorry if I'm missing something obvious, all the key shortcuts worked normally for me in 18.04. What HTML tags are allowed on Stack Exchange sites? Let $\alpha$ be an irrational real number and let $a_j$ be a sequence of rational numbers converging to $\alpha$. Suppose that each $a_j$ is a fraction expressed in lowest terms: $a_j = \alpha_j / \beta_j$. Prove that the $\beta_j$ tend to $\infty$  Attempt: AFSOC that $\beta_j$ does not tend to infinity, then it is bounded by some $M$. We can also find an interval $\alpha \in (k, k+1)$. Let $\epsilon &gt; 0$, $\exists N_0$ such that for all $N &gt; N_0$ we have $|a_N - \alpha|  &lt; \epsilon$. So $|\frac{p_N}{q_N} - \alpha| &lt; \epsilon$. We try to use the fact that $q$ is bounded but fail to derive a contradiction. I do not know how to use the fact that $\alpha$ is between two integers, although it might not be relevant at all.  Ideas? Underscore doesn't work in Coffeescript's console Straighten Vertices Along a Line On a line, I need to line up the bottom vertex points in relation to a top reference vertex point. How could I reset the X Y and Z coordinates of these vertex points to essentially line them up all through use of the vector of the reference point vertex.  I do not have access to Mesh -> Transform -> Scale on Axis for aligning vertices along a line. Using Either a Comma or a Semicolon My teacher was explaining how sometimes a comma isn't enough to make a sentence correct, and that sometimes you have to use a semicolon. I am having trouble figuring out when you should use which.   Can someone please explain? Suppose $K \subset L$ is a finite field extension of degree $m$. Is it true that there exists some natural $n$ such that $L$ is isomorphic to a subfield of $M^{n\times n}(K)$, the ring of $n\times n$ matrices with entries in $K$? What is the smallest dimension (as a function of $m$) for which an isomorphism exists?  The example I had in mind was the 2-dimensional extension $\mathbb{R} \subset \mathbb{C}$ with $\mathbb{C}$ being isomorphic to $\{ \begin{pmatrix}a&amp;-b\\b&amp;a\end{pmatrix} : a, b \in \mathbb{R}\}$. I am looking for the name of a sci-fi cartoon. Key plot points  There were Space ships flown by some American voiced crew. They were some kind of rescue squad or maybe space police. In one episode they went to an orange tree farm in a canyon which used mirrors on the canyon walls to direct sunlight to the oranges. They had a force field that protected the canyon but some bad guys came and shot the mirrors. The heroes came back and saved the day. Another episode was set in an underground ancient tomb of some kind that was covered by a sandstorm once they escaped.  Chronology and other relevant information It had kind of 80s or 90s animation. I don't think I ever saw it on TV. I only ever watched the same 3 episodes on VHS. What should I look for when buying chain lube / lubricant? In the past, I personally have only used WD-40.   However, I have occasionally had my bicycle looked over at the locally run, free service sessions and most of the mechanics there use a hand applied type of greasy gel (I forget the name).  Questions:   Is WD-40 suitable for bicycle chains? Would alternatives provide better chain longevity? When shopping around for lubricant, what are the most important things to look for? What do you use and why?  (optional added extra) Any tips for reducing chain wear? Given a DateTime representing a person's birthday, how do I calculate their age in years? Let $(X,d)$ be a metric space. How to prove that for any closed $A$ a function $d(x,A)$ is continuous - I know that it is even Lipschitz continuous, but I have a problem with the proof:  $$ |d(x,a) - d(y,a)| \leq d(x,y) $$ for any $a\in A$ - but we cannot just replace it by $|d(x,A) - d(y,A)|\leq d(x,y)$ since the minimum (or infimum in general) can be attained in different points $a\in A$ for $x$ and $y$, so we only have that $$ |d(x,A)-d(y,A)|\leq d(x,y)+\sup\limits_{a,b\in A}d(a,b) $$ which does not mean continuity. Is there any hint that some of the beings in Tolkien's lore may have survived into "our" times? In Tolkien's lore, they are many very old beings. Is there any indication that some or even one would have been truly immortal and survived into what we would call "our" history or Age? Galadriel, Cirdan, Ingwe, Bombadil, Ungoliant, or any Maia or Ainur? Anyone or anything? Seems there must be some kind of carry-over seeing as how "man" existed in this time. Dryer Outlet - 4 prong to 3 prong Our new dryer has 3 prongs vs. 4. We are changing to the new 3 prong dryer outlet, but want to make sure we are grounding. The wires coming from the wall our white, red &amp; black - the the copper wire. Do I need to ground it?? Thank you! Molly How to see download count of an Android app on Google Play store? I cannot see the download counts of one app on Google Play.   How can we know that number of one app? I flew a long range flight carrying my laptop, a quite heavy one, inside a neoprene briefcase in the passenger cabin. The recommendation by the aircrew was to place it in the overhead compartment or under the seat in front of me. However, during take-off and landing, the vibrations on the plane are quite strong and, as a result, it received minor damage.   Placing them in the overhead compartment might be equivalent to placing it on the floor under the seat, with the added issue of additional luggage in the compartment shifting.  I considered the alternative of holding the laptop by the handle while sitting, so it won't be any contact with the aircraft's floor. This is impracticable during cruise, but I thought it could be better during the take-off and landing segments. Another option I considered is to wrap it with completely with bubble wrap before boarding the plane.   Which is the safest way to transport a laptop during flight? Wubi with 14.10 doesn't work - failed to partition the selected disk I tried to install Ubuntu 14.10 on my computer with Wubi. The installation appeared to work in Windows, and told me to reboot.   After rebooting the Ubuntu installer continued the installation, until it stopped with an error message: Failed to partition the selected disk with the detail This probably happened because are too many primary partitions in the partition table. Does the Planck scale imply that spacetime is discrete? On a quantum scale the smallest unit is the , which is a discrete measure.  There several question that come to mind:   Does that mean that particles can only live in a discrete grid-like structure,  i.e. have to "magically" jump from one pocket to the next? But where are they in between? Does that even give rise to the old paradox that movement as such is impossible (e.g. )? Does the same hold true  for time (i.e. that it is discrete) - with all the ensuing paradoxes? Mathematically does it mean that you have to use difference equations instead of differential equations? (And sums instead of integrals?) From the point of view of the space metric do you have to use a discrete metric (e.g. the ) instead of good old Pythagoras?   Thank you for giving me some answers and/or references where I can turn to.  Update: I just saw this call for papers - it seems to be quite a topic after all: Is Reality Digital or Analog? FQXi Essay Contest, 2011. , , . One can find some pretty amazing papers over there.