Why the reference for kilogram has to be round in the Avogadro Project? The question popped into my mind after reading  and the corresponding . From what I've understood (please correct me if I'm wrong), they wanted to redefine the Kilogram. So they made the roundest object on earth whose mass is exactly $1$kg. But why they went through all the trouble for making a $1$kg perfect sphere?  I mean, couldn't it be an easier-to-make shape? Or why it's shape should be perfect? From a layman's point of view, when you want to make something a perfect $1$kg and a perfect sphere simultaneously, these two perfectnesses may compensate each other. You may smoothen some surfaces to make it more round but instead you might lose some material, or vice versa.  Here are the reasons that I could think of, which did not sound totally convincing:   The object is intended to be a reference for kilogram, which is the base for all weight measurements. This kind of object is surely a special one, so it should be special in some other ways as well to make it unique. Being the roundest object serves this purpose. To illustrate some technological advancements. I mean, if they are showing their ability to make such a perfect silicon sphere, it indicates that they can handle making some ultra-sensitive devices as well, such as ultra-accurate gyros and other stuff. This would justify the expenses in the long (or even short) term. The molecular structure of silicon in its monocrystalline form is spatially symmetric. So the sphere shape is more compliant with this crystal form than other shapes. (Sorry for possibly inaccurate terms, I'm not so familiar with the details).   These reasons are not so related to physics except somehow the last one. Here are my questions:        Are there any other physics-related or technical reasons for the spherical shape of the kilogram reference?   Wouldn't it be better to put more focus on the accuracy of the weight and be less worried about its perfect shape?      P.S. Some side-notes:  I tried my best to add relevant tags, but since I am not so familiar with this site and this is my first question, some tags might be missing or irrelevant. Please feel free to edit and improve the question.  I am also having trouble understanding why the kilogram should be redefined at first place and what was wrong with the good old platinum-irridium alloy. Since this was not so relevant, I didn't mention it directly. But a really perfect answer may shed some light on this matter as well.
Why is the prospective new kilogram standard a sphere? I can understand the choice of material, silicon 28, but why is it a sphere rather than (say) a cube? Article   I would have thought that a sphere would have been the hardest shape to machine accurately.
Where does a spinning figure skater's energy go when she slows down? In sampling without replacement the probability of any fixed element in the population to be included in a random sample of size $r$ is $\frac{r}{n}$. In sampling with replacement the corresponding probability is $\left[1- \left(\frac{1}{1-n}\right)^r\right]$.  Please help me show how this is proved. I am having trouble adding an image picker to a block form defined in a custom module.  If I create a custom block type I can define an image field as entity_reference and in the block's form view tell it to use entity_browser and media_entity_browser.  This provides me with an picker with which I can select my image:    I am trying to recreate this in a block provided by my custom module, without much success  // /src/Plugin/Block/MyCustomBlock.php  function blockForm($form, FormStateInterface $form_state)  {     ...      $form['image'] = [       '#type' =&gt; 'entity_browser',       '#entity_browser' =&gt; 'media_entity_browser',       '#title' =&gt; $this-&gt;t('Image'),       '#default_value' =&gt; $this-&gt;configuration['image'] ?? null,       '#weight' =&gt; '0',     ];      ... }   This gives me the following.  Note the lack of the bounding box, title and option to edit remove items:     Exporting the configuration files for the working form view gets me this:  // core.entity_form_display.block_content.lead_block.default.yml      ...  field_image:     weight: 1     settings:       entity_browser: media_entity_browser       field_widget_display: rendered_entity       field_widget_edit: true       field_widget_remove: true       selection_mode: selection_append       field_widget_display_settings:         view_mode: default       open: false     third_party_settings: {  }     type: entity_browser_entity_reference     region: content   ...   But if I try and use 'type' =&gt; 'entity_browser_entity_reference' in my blockForm function the field disappears altogether.  Looking into various core files I can see that entity_browser is a @FormElement and entity_browser_entity_reference is a @FieldWidget but I don't really understand the difference.  As you might guess I am fairly new to Drupal and I feel like I am missing something fundamental.  I (think I) understand that custom block types are actually nodes internally and that they are subject to different rules to blocks which I define in my custom modules, but I don't fully grasp what the differences here are.  Is is it possible to use the entity browser in my custom module block form in the same way as it is used in the form which I build through the admin's custom block type builder?  Thank you. $\textit{Why}$ the cases in 4 $\nmid n^2 - 3?$ (bases cases in modular induction) This question has already been answered . My question is, when we suppose the hypothesis is not true (proof by contradiction), namely that $4 \mid (n^2 - 3)$, we get $n^2 - 3 = 4k$ for some integer $k$ and then we have two cases. But where does the two cases come from? In addition, why does putting them into two cases work to prove the statment? My thought process would be to try to prove this statement by contradiction and somehow figure out a way to produce a contradiction similar to how $\sqrt{2}$ is proved by contradiction. Any help is great! Let me know if I need to clarify more! Why does as.factor return a character when used inside apply? What is the difference between the GNU Makefile variable assignments =, ?=, := and +=? Can anybody give a clear explanation of how variable assignment really works in Makefiles.   What is the difference between :   VARIABLE = value  VARIABLE ?= value  VARIABLE := value  VARIABLE += value   I have read the  in GNU Make's manual, but it still doesn't make sense to me. After my suspension period, my reputation was not returned On Stack Overflow, I have a suspension period of 7 days which ends today. But my actual reputation has not been returned to me as one of the moderators said it would. I have a message like this by @Andrew Barber:     Once your suspension period is over, you will be returned to your   correct reputation level, minus the votes from the accounts which have   been deleted. At that time, you are more than welcome to return, and   continue contributing your knowledge, and gaining legitimate   reputation points. Just please keep our rules in mind when you do.      Regards      Andrew Barber, Stack Overflow moderator   Can any moderator here help me or tell me what the rules are of getting back my reputation?  How can I get the attention of a moderator so that they can resolve my problem? I would like a way to convert a document from HTML to LaTeX on a Windows platform. What is my best option? Make CMD-Delete a keyboard shortcut in Apple Mail to move a message to the archive? How do you show that $e^{-1/x^2}$ is differentiable at $0$? Define the real valued function $f(x)$ by $f(x) = e^{-1/x^2}$ if $x \ne 0$ and $0$ if $x = 0$.    How do you show that $e^{-1/x^2}$ is differentiable at $0$? How do you show that this function is infinitely differentiable? Electric potential is related to Electric Field by negative integral of Field with distance.If charges move away from the positive terminal (Assuming conventional flow) why is there no drop in electric potential even though the charges are moving in the direction of electric field?  Some of the answers I read for the similar question said that the electrons in wires rearrange themselves in a way to make the electric field uniform in the wire.However,this doesn’t explain the absence of potential drop in the wires (due to electric field) since the field is still there. Why won't closing the lid sleep my MacBook Pro with external monitor attached after upgrading to Lion? AutoHotkey Equivalent for OS X? Is there an equivalent product/method for AutoHotkey. For those that don't know, its a product that allows you to program your mouse movements and keyboard. This allows me to "macro" certain functions on programs instead of having to do it manually. In the old days they used to call them keyboard stuffers. But that is only half of the solution as I need a "mouse movement" stuffer as well.  Is there such a beast? Why is negative times negative = positive? Someone recently asked me why a negative $\times$ a negative is positive, and why a negative $\times$ a positive is negative, etc.  I went ahead and gave them a proof by contradiction like so:  Assume $(-x) \cdot (-y) = -xy$  Then divide both sides by $(-x)$ and you get $(-y) = y$  Since we have a contradiction, then our first assumption must be incorrect.  I'm guessing I did something wrong here. Since the conclusion of $(-x) \cdot (-y) = (xy)$ is hard to derive from what I wrote.  Is there a better way to explain this?  Is my proof incorrect?  Also, what would be an intuitive way to explain the negation concept, if there is one? Where were the cannons in final fight in Wakanda in Infinity War? In Black Panther, Ulysses Klaue describes his arm cannon as a leaf blower in comparison to the cannons/weapons that Wakanda has.  Infinity War comes after the events of Black Panther, so the weapons should exist. During the final fight with the children of Thanos and Space Dogs (as Rocket refers to them), Wakandans could have used these powerful cannons, pointing them at the opened section of barrier. Instead they chose a fist fight.  Even M'Baku says that it would be the end of Wakanda, so the magnitude is huge and risks are very high. Why were these powerful weapons not used?    Edit 1: I watched the movie again and planes are there in the fight. But they were only used to destroy the spaceships that crashed. Can I get a postdoc in China more than 3 years after having received my PhD? Ping a site in Python? How to acknowledge a deceased advisor’s contributions to a paper? One of my advisors suddenly passed away while I was in graduate school.  We had some discussions and ideas about future publications, but he passed away before any of the work was completed.  When the work was finally completed and published, I and my co-authors were therefore presented with an ethical dilemma about how best to acknowledge his contributions to the ideas behind the paper.  Should we list him as a co-author?  Put him in the acknowledgements?  Listing him as an author would give credit for the original idea, however, we would have no way of knowing if he actually approved of—and would want his name attached to—our methods and writing.  In the end my co-authors and I decided to list him as a co-author with a footnote stating that he passed away before publication.  I’m interested to hear from others who have been in similar situations and/or suggestions on what constitutes “co-authorship” when one of one’s collaborators passes away before the publication or work is complete. Sorting an array of an array of objects in PHP by key value Basically I have a setup like the following:  Array (  [0] =&gt; Array ( [0] =&gt; stdClass Object ( [nid] =&gt; 1 [title] =&gt; title1 [uid] =&gt; 1 [parent] =&gt; 0 [weight] =&gt; -15 [name] =&gt; name1 [value] =&gt; 0 )                [1] =&gt; stdClass Object ( [nid] =&gt; 2 [title] =&gt; title2 [uid] =&gt; 1 [parent] =&gt; 0 [weight] =&gt; -7 [name] =&gt; name2 [value] =&gt; 100 )                [2] =&gt; stdClass Object ( [nid] =&gt; 3 [title] =&gt; title3 [uid] =&gt; 2 [parent] =&gt; 0 [weight] =&gt; -1 [name] =&gt; name3 [value] =&gt; 0 )                [3] =&gt; stdClass Object ( [nid] =&gt; 4 [title] =&gt; title4 [uid] =&gt; 2 [parent] =&gt; 0 [weight] =&gt; 1 [name] =&gt; name4 [value] =&gt; 80 )               )   )   What I need is a way to sort all the arrays inside the parent array by the [value] key in the Object. I've been trying for about 2 days now with usort and different methods but I just can't seem to get my head around it. The [value] key will range anywhere from 0 to 100 and I need all of the arrays sorted in decreasing order (IE: 100 down to 0). Punctuations with relative pronouns Sogou is a Chinese search engine, which can search text, images, music and maps.  Is a comma required before "which" in the above sentence?