Do elements actually transmute in nuclear reactions?

Question: Whenever a nuclear transmutation happens, do we get a new element or do we have the same element with chemical properties of a different element?
Isn't it very much against the intuition?
Answer: By definition, a nuclear transmutation involves transformation of one element into another. This means the element has undergone some sort of change in the nucleus (either by nuclear reaction or nuclear decay), hence a change in atomic weight and/or number.
Whether or not this goes against intuition depends upon what experiences one's intuition is based on.
Comment: To me, a 'transmutation' requires a change to the number of protons in the nucleus, which clearly changes the electronic structure, which in turn changes the chemistry. Nuclear reactions such as neutron absorption only change the neutron number, and do not change the chemistry (well, except for hydrogen isotope chemistry where the mass difference can cause chemistry differences, particularly biochemistry). So, I will disagree with Encyclopedia Brittanica that neutron capture is a transmutation event...


Title Hero or titular/eponymous hero?

Question: Jane Eyre is the title of a novel. The hero of the novel is called Jane Eyre. Can you say "Jane Eyre is the title hero of the novel"? I know that titular hero or eponymous hero is correct, however I'm focusing on the noun+noun phrase here. Any input welcome :-) Thanks!
Comment: You can say it and people will know what you mean, but adjectives exist for a reason. Titular exists, why force title?
Comment: Sorry, that wasn't the warmest welcome. Welcome!
Answer: Title is the noun and titular is the adjective, as you know and (subjectivity warning!) I would encourage using adjectives as adjectives and nouns as nouns*.
There is, however, precedent for using the noun-noun construction.
Since the 1960s use of titular hero has declined while title hero has increased.

This perhaps follows the use of title hero which is far more common than titular character and has been for a long time.

*I would appreciate comment, edit or additional solution which addresses the part of speech of title in title hero. I expect it is not a noun marauding as an adjective, but I am not well enough versed in grammar.
Comment: Thanks, that helped a lot - interesting statistics, how did you get them?
Comment: Whoops didn't link. They're from Google Ngrams—really fun tool. Questionably reliable but gives a good rough picture. Graph of word use in Google Books. Check it out!

Title Hero or titular/eponymous hero?


Profit And Loss

Question: If a trader sells two articles at the same price, one at a loss of x% and the other at a profit of y%, then the trader makes approximately what profit or loss.
How to got about solving this??
Answer: If the two selling prices are each $p$ and the costs were $c_1$ and $c_2$ then $$p = c_1\left(1-\frac{x}{100}\right)$$ and $$p = c_2\left(1+\frac{y}{100}\right)$$ so you can calculate the overall percentage profit (or loss if negative) from  $$\left(\frac{2p}{c_1+c_2}-1\right)\times 100. $$

Profit And Loss


Is it possible to make a group a site collection owner in SharePoint Online?

Question: I have a SharePoint Online site collection and I have a SharePoint group on the main site in that site collection that I would like to make a site collection owner. Is this possible, maybe through PowerShell?
Answer: I do not think so.
Site collection admin should be Azure AD identity (group or user). It exists at tenant level.
SharePoint group exists within SharePoint site.
Instead you should be able to create an AAD Security Group (login to https://portal.azure.com/, then Azure Active Directory, Groups, + New Group), wait ~10 minute, then you can

manage group membership
use this group in your site
Answer: Unfortunately for Sharepoint groups no, and this has been a long standing caveat with Site Collection Administrators - they can only be defined users.
You can use Azure AD / Office 365 Security Groups though.
This link to previous question explains this well this very well.
Answer: There is no way to make a SharePoint Group as site collection administrator. As a workaround, you could make an offcie 365 group as site collection administrator.
Create a Office 365 group and add users to it. Then go to SharePoint admini center, choose the site and click permissions. Add the Office group as admin.


api.fda.gov is failing security check

Question: This server couldn't prove that it's api.fda.gov; its security certificate is from *.fr.cloud.gov. This may be caused by a misconfiguration or an attacker intercepting your connection.
Comment: Please detail how you are connecting, whether it is the first time you try, or from when it started happening.
Answer: We had a series of brief outages last week while adapting our networking to support an upstream change. The issue is now resolved and uptime is restored to our normal consistency. Thank you for your patience and my apologies for any problems this created for our users.
Regards,
Violet Wren
openFDA Tech Lead
Answer: I'm experiencing the same issue. I'm accessing the API through the Python requests module. I fixed the issue by adding the argument verify=False in my request (full code below). I'm pretty sure this is bad practice, but I think it's fine for a trusted source like the FDA for a small number of API calls (which is my case). Someone please correct me if I'm wrong. The following is my call for information  about a particular NDC, which generated the error you've mentioned.
r = requests.get('https://api.fda.gov/drug/ndc.json?search=packaging.package_ndc:{NDC}')

When I change it to:
r = requests.get('https://api.fda.gov/drug/ndc.json?search=packaging.package_ndc:{NDC}', verify=False)

it works. Hope that helps until they fix the issue.
EDIT: It seems to work now. No need to have verify=False if you're using requests in Python.

api.fda.gov is failing security check


No GRUB after Ubuntu install

Question: The main issue of the problem is that i can't load Ubuntu 12.10 desktop - i386 after install near win7basic (windows 7 was preinstalled on my laptop). I've tried manual reconfiguring of file system, have tried automatic one. also tried to install ubuntu 12.04 - destop - amd64. None of errors were noticed during the installation process. But after install windows 7 starts automatically. seems to me that nothing changed within winloader. I know that not so much info i put in here, but i'll answer any questions.
Comment: So you're saying you don't get the option to boot Ubuntu? It just goes straight to Windows?
Comment: Yes. Just like that.
Comment: Can you give us some hardware information?
Comment: Well. Don't know where to start... Asus n76vz, intel corei7-3610qm, intel 76 chipset... what else?
Comment: That should be all we need.  I think this is a problem with UEFI.
Comment: possible duplicate of [How can I repair grub? (How to get Ubuntu back after installing Windows?)](http://askubuntu.com/questions/88384/how-can-i-repair-grub-how-to-get-ubuntu-back-after-installing-windows)
Comment: to Web-E - i think, not, because first was win7, ubuntu comes after...
Comment: to iSeth: yes. Boot-Repair said smth about that.
Answer: Your problem is that you're attempting to mix BIOS-style and EFI-style booting. Windows 7 is installed in EFI mode, as indicated by the use of a GUID Partition Table (GPT) with an EFI System Partition (ESP) as /dev/sda1 that contains Windows EFI boot files such as EFI/Microsoft/Boot/bootmgfw.efi. Your Ubuntu installation is in BIOS mode, though, as indicated by the presence of GRUB code in the MBR, the presence of a BIOS Boot Partition (/dev/sda5), the lack of any Ubuntu EFI boot loaders in the ESP, and the fact that you attempted to install the i386 version.
The cleanest solution is to wipe your current Ubuntu installation, download an AMD64 version, and install it in EFI mode. Unfortunately, the Ubuntu installer doesn't make it clear that you're running in EFI mode vs. BIOS mode. To make that determination, you should open a shell and look for the directory /sys/firmware/efi. If it's present, you've booted in EFI mode; if it's absent, you've probably booted in BIOS mode. If you boot an AMD64 installer and find that this directory is absent, try again, but use whatever tool your computer offers to select the boot device, and be sure to select the one for your CD or USB flash drive that includes "EFI" or "UEFI" as part of its description.
Another solution is to install my rEFInd boot manager in Windows. Edit the refind.conf file so that the scanfor line is uncommented and includes the hdbios item. rEFInd should then give you boot options for Windows and for a generic BIOS option. The latter should launch GRUB, which in turn will take you to Linux. Using two boot managers complicates the startup process, so it's better to install a 64-bit version of Ubuntu unless you've got a compelling reason to use a 32-bit version. (Such compelling reasons to go 32-bit are rare these days.)
Yet another solution is to use your computer's own boot manager, which you typically access by pressing F2, F8, or some other function key during startup. You should have options to boot Windows in EFI mode or to boot from your hard disk in BIOS/legacy mode. (The exact names used vary from one installation to another.) This is likely to be the most awkward solution in the long run, but you might consider it acceptable, especially if your firmware has a better-than-average boot manager.
Comment: Ok, i got it. Fortunately, i've found the right way to solve the problem. Didn't know anything about EFI before today, so thank you for some piece of explanation. Besides, i had one-minute trouble with loading win7 loaders (Invalid EFI filepath error), but somehow this issue was solved by one-time running BootRepair.  After that, just as you told, now i'm offered of three or so variants in GRUB. But for now i have no inconvenience with that.
Comment: Although `/sys/firmware/efi`existed, the GRUB didn't show up on reboot. Seems this is not guaranteed to work.
Answer: You didn't install Ubuntu bootloader to MBR.
To restore GRUB follow this link:
https://help.ubuntu.com/community/RecoveringUbuntuAfterInstallingWindows
If restoring fails, see the first answer:
How can I repair grub? (How to get Ubuntu back after installing Windows?)
If it still fails, try again but install GRUB to your Ubuntu partition:
if it is in /dev/sda7 enter
grub-install /dev/sda7

and NOT
grub-install /dev/sda

to install, then use EasyBCD and add an entry for your Ubuntu partition.
Comment: Now have just tried Boot-Repair. If someone's interested: http://paste.ubuntu.com/1467542/
Comment: Is EasyBCD used just for cases when ubuntu installed first and then comes Win7 loader that destroys grub?
Comment: While this might answer the question, it is preferred that you include the essential parts of the answer here. Thanks!
Comment: @user116845 EasyBCD is used for editing Windows Vista+ Bootloader Entries. To add an Ubuntu entry you must install GRUB to your Ubuntu partition.
Answer: Helo
Try this metode if you've grub installed:
In Terminal:

sudo update-grub
edit by NANO or vii /etc/default/grub  and modify if in GRUB_TIMEOUT= 0 modify for ex 5 and SAVE; easier in Midnight Commander (apt-get install mc)(sudo -s ENTER, mc ENTER)!!!/etc/default/grub and F4!!!!(sudo -s ENTER, mc ENTER)
again
sudo update-grub
Close the terminal and RESTART or REBOOT

No GRUB after Ubuntu install


When to use the Bridge pattern and how is it different from the Adapter pattern?

Question: Has anyone ever used the Bridge pattern in a real world application? If so, how did you use it? Is it me, or is it just the Adapter pattern with a little dependency injection thrown into the mix? Does it really deserve its own pattern?
Comment: The [GoF book](https://stackoverflow.com/a/60067236/1371329) answers this question directly.
Answer: There's a combination of Federico's and John's answers.
When:
                   ----Shape---
                  /            \
         Rectangle              Circle
        /         \            /      \
BlueRectangle  RedRectangle BlueCircle RedCircle

Refactor to:
          ----Shape---                        Color
         /            \                       /   \
Rectangle(Color)   Circle(Color)           Blue   Red

Comment: @vainolo because Color is an interface and Blue, Red are concrete colors
Comment: Why would you do inheritance for colors?
Comment: This is just a refactoring. Bridge pattern intent: "Decouple an abstraction from its implementation so that the two can vary independently." Where is the abstraction and where is the implementation here?
Comment: @clapas , Abstraction is "Shape.color" of property ,therefore class Red and class Blue is implementation,and Color interface is bridge.
Comment: I read tens of unappropriate examples which simply misuses inheritance, i.e. something which naturally feels like 'has a' is presented as 'is a'. This is the best answer I have found. Bravo! Short, informative, outlined.
Comment: Is not Rectangle(Color) a more abstract one that the BlueRectangle thing?
Comment: @clapas you're puzzled just as i was. those examples are poor because they deal with properties (like color). Bridge pattern is about _behavior_
Answer: The Bridge pattern is an application of the old advice, "prefer composition over inheritance".
It becomes handy when you must subclass different times in ways that are orthogonal with one another. Say you must implement a hierarchy of colored shapes. You wouldn't subclass Shape with Rectangle and Circle and then subclass Rectangle with RedRectangle, BlueRectangle and GreenRectangle and the same for Circle, would you? You would prefer to say that each Shape has a Color and to implement a hierarchy of colors, and that is the Bridge Pattern. Well, I wouldn't implement a "hierarchy of colors", but you get the idea...
Comment: I do not think a color is a good example for an implementation hierarchy, it is rather confusing. There is a good example of the Bridge pattern in "Design patterns" by the GoF, where implementation is platform dependent: IBM's PM, UNIX's X etc.
Comment: See also Anton Shchastnyi diagram below for a graphical illustration of this explanation.
Answer: When:
        A
     /     \
    Aa      Ab
   / \     /  \
 Aa1 Aa2  Ab1 Ab2

Refactor to:
     A         N
  /     \     / \
Aa(N) Ab(N)  1   2

Comment: I think it's very pragmatic approach to patterns: 1) describe suboptimal straight-forward design 2) refactor design/code to better factored one
Comment: Use maths concept to explain the Bridge design pattern. Very interested.
Comment: This is just a refactoring. Bridge pattern intent: "Decouple an abstraction from its implementation so that the two can vary independently." Where is the abstraction and where is the implementation here?
Comment: John puts it nicely in a [blog](https://simpleprogrammer.com/design-patterns-simplified-the-bridge-pattern/) post. Found it to be a good read for high level overview.
Comment: nice, do you have diagrams like this for other patterns?
Answer: A classic example of the Bridge pattern is used in the definition of shapes in an UI environment (see the Bridge pattern Wikipedia entry).  The Bridge pattern is a composite of the Template and Strategy patterns.
It is a common view some aspects of the Adapter pattern in the Bridge pattern.  However, to quote from this article:

At first sight, the Bridge pattern looks a lot like the Adapter pattern in that a class is used to convert one kind of interface to another. However, the intent of the Adapter pattern is to make one or more classes' interfaces look the same as that of a particular class. The Bridge pattern is designed to separate a class's interface from its implementation so you can vary or replace the implementation without changing the client code.
Comment: Bridge has nothing to do with Template or Strategy. Bridge is a structural pattern. Template and Strategy are behavioral patterns.
Answer: In my experience, Bridge is a quite often recurring pattern, because it's the solution whenever there are two orthogonal dimensions in the domain. E.g. shapes and drawing methods, behaviours and platforms, file formats and serializers and so forth.
And an advice: always think of design patterns from the conceptual perspective, not from the implementation perspective. From the right point of view, Bridge cannot be confused with Adapter, because they solve a different problem, and composition is superior to inheritance not because of the sake of itself, but because it allows to handle orthogonal concerns separately.
Answer: Adapter and Bridge are certainly related, and the distinction is subtle.  It's likely that some people who think they are using one of these patterns are actually using the other pattern.
The explanation I've seen is that Adapter is used when you're trying to unify the interfaces of some incompatible classes that already exist.  The Adapter functions as a kind of translator to implementations that could be considered legacy.
Whereas the Bridge pattern is used for code that is more likely to be greenfield.  You're designing the Bridge to provide an abstract interface for an implementation that needs to vary, but you also define the interface of those implementation classes.
Device drivers is an often-cited example of Bridge, but I'd say it's a Bridge if you're defining the interface spec for device vendors, but it's an Adapter if you're taking existing device drivers and making a wrapper-class to provide a unified interface.
So code-wise, the two patterns are very similar.  Business-wise, they're different.
See also http://c2.com/cgi/wiki?BridgePattern
Comment: @zgulser, yes, you do use polymorphism. The Bridge pattern describes one kind of usage of subclasses to decouple implementation from abstraction.
Comment: Hey Bill. I don't understand why we necessarily use Bridge pattern in device drivers. I mean we can easily delegate implementation (of read, write, seek etc.) to the correct class via polymorphism right? Or with a Visitor perhaps? Why it's have to be Bridge? Thanks in advance.
Comment: You meant decoupling Shape implementation (ie. Rectangle) from let's day Color abstraction right? And I believe you're saying there're variety of ways to do it and Bridge is just one of them.
Comment: Yes, subclassing has other uses. This particular way of using subclasses is what makes it the Bridge pattern.
Comment: And the decoupling I mean is from the abstract Shape interface to a concrete Rectangle implementation. So you can write code that needs an object of the "Shape" type, even though the concrete object is really some subclass of Shape.
Comment: It's important to point out that the Bridge pattern can be implemented different ways depending on the capability of the language / system.  Any language that allows definition of a class must necessarily have a way to define the interface of that class.  But not all languages allow interface definitions independent from classes.  For those that do (C# for example) the Bridge pattern can be implemented directly using such interface definitions and skip at least one layer of subclassing and private-object instantiation in doing so.
Answer: I have used the bridge pattern at work.  I program in C++, where it is often called the PIMPL idiom (pointer to implementation).  It looks like this:
class A
{
public:
  void foo()
  {
    pImpl->foo();
  }
private:
  Aimpl *pImpl;
};

class Aimpl
{
public:
  void foo();
  void bar();
};

In this example class A contains the interface, and class Aimpl contains the implementation.
One use for this pattern is to expose only some of the public members of the implementation class, but not others. In the example only Aimpl::foo() can be called through the public interface of A, but not Aimpl::bar()
Another advantage is that you can define Aimpl in a separate header file that need not be included by the users of A.  All you have to do is use a forward declaration of Aimpl before A is defined, and move the definitions of all the member functions referencing pImpl into the .cpp file.  This gives you the ability to keep the Aimpl header private, and reduce the compile time.
Comment: If you use this pattern then the AImpl doesn't even need a header. I just put it inline in the implementation file for the A class
Comment: Your implementor is private. I have a new question in regards to this, see http://stackoverflow.com/questions/17680762/bridge-pattern-should-the-implementor-be-private
Answer: To put shape example in code:
#include<iostream>
#include<string>
#include<cstdlib>

using namespace std;

class IColor
{
public:
    virtual string Color() = 0;
};

class RedColor: public IColor
{
public:
    string Color()
    {
        return "of Red Color";
    }
};

class BlueColor: public IColor
{
public:
    string Color()
    {
        return "of Blue Color";
    }
};

class IShape
{
public:
virtual string Draw() = 0;
};

class Circle: public IShape
{
        IColor* impl;
    public:
        Circle(IColor *obj):impl(obj){}
        string Draw()
        {
            return "Drawn a Circle "+ impl->Color();
        }
};

class Square: public IShape
{
        IColor* impl;
    public:
        Square(IColor *obj):impl(obj){}
        string Draw()
        {
        return "Drawn a Square "+ impl->Color();;
        }
};

int main()
{
IColor* red = new RedColor();
IColor* blue = new BlueColor();

IShape* sq = new Square(red);
IShape* cr = new Circle(blue);

cout<<"\n"<<sq->Draw();
cout<<"\n"<<cr->Draw();

delete red;
delete blue;
return 1;
}

The output is:
Drawn a Square of Red Color
Drawn a Circle of Blue Color

Note the ease with which new colors and shapes can be added to the system without leading to an explosion of subclasses due to permutations.
Answer: You're working for an insurance company where you develop a workflow application that manages different kind of tasks: accounting, contract, claims. This is the abstraction. On the implementation side, you must be able to create tasks from different sources: email, fax, e-messaging.
You begin your design with these classes:
public class Task {...}
public class AccountingTask : Task {...}
public class ContractTask : Task {...}
public class ClaimTask : Task {...}

Now, since each sources must be handled in a specific way, you decide to specialize each task type:
public class EmailAccountingTask : AccountingTask {...}
public class FaxAccountingTask : AccountingTask {...}
public class EmessagingAccountingTask : AccountingTask {...}

public class EmailContractTask : ContractTask {...}
public class FaxContractTask : ContractTask {...}
public class EmessagingContractTask : ContractTask {...}

public class EmailClaimTask : ClaimTask {...}
public class FaxClaimTask : ClaimTask {...}
public class EmessagingClaimTask : ClaimTask {...}

You end up with 13 classes. Adding a task type or a source type becomes challenging. Using the bridge pattern produces something easier to maintain by decoupling the task (the abstraction) from the source (which is an implementation concern):
// Source
public class Source {
   public string GetSender();
   public string GetMessage();
   public string GetContractReference();
   (...)
}

public class EmailSource : Source {...}
public class FaxSource : Source {...}
public class EmessagingSource : Source {...}

// Task
public class Task {
   public Task(Source source);
   (...)
}
public class AccountingTask : Task {...}
public class ContractTask : Task {...}
public class ClaimTask : Task {...}

Adding a task type or a source is now much more easier.
Note: Most developers would not create the 13 classes hierarchy upfront to handle this problem. However, in real life, you might not know in advance the number of source and task types ; if you have only one source and two task types, you would probably not decouple Task from Source. Then, the overall complexity grows as new sources and task types are added. At some point, you will refactor and, most often, end up with a bridge-like solution.
Answer: The key difference between the Adapter and Bridge design patterns lies in their intents. From Design Patterns, chapter 4, section 'Bridge', paragraph 'Related Patterns' (Gamma et al. 1994):

The Adapter (139) pattern is geared toward making unrelated classes work together. It is usually applied to systems after they're designed. Bridge, on the other hand, is used up-front in a design to let abstractions and implementations vary independently.

The word 'independently' means that the Bridge design pattern applies in this situation because shapes and colours are independent:

             ------Shape-----                           Shape       Colour
            /                \              Bridge       / \         / \
       Circle                Square         ----->  Circle Square  Red Blue
        / \                   / \
RedCircle BlueCircle  RedSquare BlueSquare

But it does not apply in this situation because colours depend on shapes:

             ------Shape-----
            /                \
       Circle                Square
        / \                   / \
RedCircle BlueCircle  RedSquare GreenSquare

And it is useless in this situation because there are a single shape and a single colour:

Shape
  |
Circle
  |
RedCircle

Tabular representation of situation 1:
| Shape  | Colour |          | Shape  |  | Colour |
| ------ | ------ |          | ------ |  | ------ |
| circle | red    |  Bridge  | circle |  | red    |
| circle | blue   |  ----->  | square |  | blue   |
| square | red    |
| square | blue   |

Tabular representation of situation 2:
| Shape  | Colour |
| ------ | ------ |
| circle | red    |
| circle | blue   |
| square | red    |
| square | green  |

Tabular representation of situation 3:
| Shape  | Colour |
| ------ | ------ |
| circle | red    |

Thus the Bridge design pattern in object-oriented programming is equivalent to normalisation to projection–join normal form, denoted PJ/NF (Fagin 1979), in relational databases.
In situation 1, the relation schema R(Shape, Colour) has the multivalued dependencies ∅ ↠ {Shape} (independent shapes) and ∅ ↠ {Colour} (independent colours) which are not implied by the set of key dependencies {KEY({Shape, Colour})}, so it is not in PJ/NF. Its projections are in PJ/NF because R1(Shape) has the trivial functional dependency {Shape} → {Shape} which is implied by the set of key dependencies {KEY({Shape})} and R2(Colour) has the trivial functional dependency {Colour} → {Colour} which is implied by the set of key dependencies {KEY({Colour})}.
In situation 2, the relation schema R(Shape, Colour) has the trivial multivalued dependency {Shape} ↠ {Colour} which is implied by the set of key dependencies {KEY({Shape, Colour})}, so it is already in PJ/NF.
In situations 3, the relation schema R(Shape, Colour) has the functional dependencies ∅ → {Shape} (single shape) and ∅ → {Colour} (single colour) which are implied by the set of key dependencies {KEY({Shape, Colour}), KEY(∅)}, so it is already in PJ/NF.
Answer: I'll give you one new example for a bridge pattern if you get board of the same old Shape and Color example.
Let's say you have different ways to make payments like Card payment and net banking. And there are different payment gateways like CITI bank and HSBC bank.
Then you can just add the payment gateway member to the payment modes. And at runtime pass this information to the payment mode object. And make the payment.
So for example it will make the Card payment on the CITI bank payment gateway.
Answer: for me i think of it as a mechanism where you can swap interfaces.  In the real world you might have a class that can use more then one interface, Bridge lets you swap.
Answer: Bridge design pattern we can easily understand helping of service and dao layer.

Dao layer -> create common interface for dao layer ->
public interface Dao<T>{
void save(T t);
}
public class AccountDao<Account> implement Dao<Account>{
public void save(Account){
}
}
public LoginDao<Login> implement Dao<Login>{
public void save(Login){
}
}
Service Layer ->
1) interface
public interface BasicService<T>{
    void save(T t);
}
concrete  implementation of service -
Account service -
public class AccountService<Account> implement BasicService<Account>{
 private Dao<Account> accountDao;
 public AccountService(AccountDao dao){
   this.accountDao=dao;
   }
public void save(Account){
   accountDao.save(Account);
 }
}
login service-
public class LoginService<Login> implement BasicService<Login>{
 private Dao<Login> loginDao;
 public AccountService(LoginDao dao){
   this.loginDao=dao;
   }
public void save(Login){
   loginDao.save(login);
 }
}

public class BridgePattenDemo{
public static void main(String[] str){
BasicService<Account> aService=new AccountService(new AccountDao<Account>());
Account ac=new Account();
aService.save(ac);
}
}
}

Comment: I downvoted because I feel this is a convoluted, poorly formatted answer.
Comment: Totally agree, how can you post answers on this site without a minimal attention to code indentation and clearness


Why are ground and neutral bonded at the main panel?

Question: I realize that the only time the grounds and neutrals can be bonded is in a main panel, not a sub-panel. What I can't figure out is why could it be allowed in the first place? What were to happen if the neutral somehow were to get broken, wouldn't the current flow through the smaller ground into a grounding rod and burn it up? I also realize that the resistance of the earth is greater, but isn't that still dangerous? Thanks.
Comment: Does this answer your question? [Why doesn't current return via the grounding conductor when it's connected in the panel?](https://diy.stackexchange.com/questions/150856/why-doesnt-current-return-via-the-grounding-conductor-when-its-connected-in-th)
Comment: You would be amazed at how much current a number 6 grounding electrode conductor can handle. If the neutral opens there are other things that will be going wrong the neutral is earth grounded at the transformer so depending on the distance and the quality of the ground you may not even know until a very large imbalance starts swinging the voltages most notice the lights dimming or going bright when this happens.
Comment: Does this answer your question? [Since neutral is connected to ground how is current kept off of ground?](https://diy.stackexchange.com/questions/36516/since-neutral-is-connected-to-ground-how-is-current-kept-off-of-ground)
Answer: The reason they're allowed to be mixed in a main is a convoluted tale.
In principle they're supposed to be separated there too; however panels need a feature to keep 120/240V power from floating at some unnaturally high voltage to earth, e.g. 9600V from a transformer leak. That would cause problems for insulation in devices.  So they take one of the active conductors, name it "neutral", and bond it to earth. The transformer then forces the other conductors to be the appropriate distance (120V) from earth.  This bond is called the Neutral-Ground Equipotential Bond.
It would be perfectly OK if neutral and ground were merely close; so for instance a 1-volt transformer would be a fine N-G bond, giving neutral a 1-volt bias from ground and the other legs 121V and 119V biases.  That is certainly better than the alternative, a 9600V, 9720V and 9840V bias from ground!  However a piece of copper is the cheapest available bond.
At that point, manufacturers said "Wait, since they're all connected anyway, why not just let people use all the same bar?"  There was no reason why not, so NFPA allowed it.
You're absolutely right; in a lost neutral situation, which happens a lot, current starts flowing across the N-G bond into the earth to the transformer's ground rod and back to the transformer.  However the grounding electrode wires are plenty large enough that the limiting factor will be the conductivity of the earth.
Answer: The reason is to provide a path to trip a breaker when the first fault develops and to limit (control) voltage to ground. The secondary of a transformer is isolated from ground, if left in that state a single fault on a line conductor on a 120/240v service would make one leg measure 0v to ground, 120v to ground on the neutral, and 240v to ground on the other leg. One fault in one house would effect all houses being served by that transformer. No overcurrents would exist, so no fusing would trip. Somebody could be in contact with a metal frame of a faulted appliance and wouldn't know it. Then when a second fault occurred someone could get shocked, or at very least a breaker would trip and you could be looking for two faults hidden in four or more houses.
Trouble really starts to develop when you start dealing with multiple transformers like large multifamily or commercial building with multiple 277/480 3Ø, 120/208v 3Ø and 120/240v 1Ø transformers, all could have faults that could create multiple seemimgly random voltages to ground, and again it would take two faults before an overcurrent device would trip.
Comment: I have had *exactly* that happen: a bolted fault on a 120V load on L1 and no N-G bond.  In fact, the site had been haunted by faults like you describe, because both 120V services had been moved onto the same 480 phase, and their neutrals bridged together.   That's probably because they had circuits where outlets were taking hot from service 1 and grabbed a random nearby neutral which was on service 2.


How the Tablets were written - all at once or letter by letter?

Question: In my previous question the Torah says explicitly that the Tablets were written by G-d's finger.
Does it mean they were written letter by letter, as one finger can do, or all at once?
Answer: This is how Or HaChaim sees it (here):

"כתובים באצבע אלהים": והודיע הכתוב אופן כתיבת הלוחות במה נכתבו ואמר כתובים באצבע אלהים.
  פירוש כי היה ה' מצייר צורת האות באצבעו כביכול.
  פירוש בחינת אור אחד מאורו יתברך בדמות אצבע כנגד הלוח כשיעור שטח אברי האותיות כדי שלא יהיה חרות אלא את אשר יצייר כנגדו ולצד עוצם תוקף אורו יתברך לא היה אור של הלוחות יכול עמוד בכל המקום אשר יכוין כנגדו אצבע אלהים והיה נאכל או מתצמצם לצדדין והיה נשאר כל אשר יצטייר כנגדו חלול ולזה נכתבו משני עבריהם"...
The words: "written with the finger of G'd" mean that G'd drew the shape of the letter with His "finger," i.e. using one of the kinds of light at His disposal. It (the light) assumed the appearance of a finger opposite the Tablets corresponding to the dimensions of the requisite letter G'd wanted to inscribe. G'd did this in order to ensure that no more and no less than the letter should be engraved on the Tablets themselves. Seeing that the light G'd used to do this with was more powerful than the light the Tablets were made of, the light of the "finger" penetrated the requisite area of the Tablets. We may perceive of that area on the Tablets as having either been devoured or pushed aside. What remained were holes forming the letters G'd had engraved. Thanks to the superior power of the light of the "finger" the inscription became visible from either side of the Tablets. This is what is meant when the Torah wrote in 32,16, that the Tablets were written from both sides, i.e. that the inscription was deeply engraved. The Torah uses the expression חרות על הלוחות "engraved on the Tablets," instead of saying חדות בלוחות, engraved in the Tablets. This is the allusion to G'd having placed His finger "on" i.e. opposite the material of the Tablets as we have explained.


"Give up" versus "give in"

Question: Do give up and give in imply different meanings?
Comment: @Kim, maybe "have" would have been a better word choice here, but "imply" is not really a fancy word, is it? It means to [express indirectly](http://www.merriam-webster.com/dictionary/imply).
Comment: Yes, but more importantly, words don't "imply" but "have" meanings. Please don't use fancy words where they aren't needed.
Comment: Wether it's fancy or not surely depends on the context. Compared to "have", "imply" is very fancy. ;)
Comment: How about the use of both in the Florence and the machine song "Never let me go" where by she say she's "its over, i'm going under. I'm not giving up i'm just giving in" describing the fact she's drowning.
Answer: Give up and give in do have similar meanings that are very close to surrender. However, compare the examples of give up and give in from the Merriam-Webster dictionary:

don't give up on the project
forced to give up his job
refused to give up her efforts
give in and have some chocolate
after withstanding hours of begging, their father finally gave in and let them go to the amusement park
give in his resignation

Notice how the examples of give in express something that happens after insistence or entreaty. This doesn't happen in the examples of give up, where the meaning is closer to quit and abandon.
EDIT:
It should be noted that the last example of give in above ("give in his resignation"), in particular, is actually a case where it means deliver, submit or hand in. It therefore illustrates a definition of give in that is very different than give up. Another example of give in with that meaning, from dictionary.com:

please give in your timecards
Comment: As mentioned, `give up` is synonymous with `abandon`; a synonym to `give in` might be `succumb`.
Comment: I think your last example of `give in his resignation` is a different `give in` than the others. In that case, he's just handing something in, which in this case is his resignation.
Comment: @Claudiu, you're right. I'll edit my post to clarify that. Thanks
Comment: Was watching Dark Knight and Batman was shouted at - "You can not give in". Was it wrong usage and should have been "You can not give up" ?
Answer: give up is used for quitting a habit or withdrawing from something.But give in is letting something happen or give way for something.
Comment: sorry its 'an important ..
Comment: I think you mean *quiting* (not *quieting*). But , no, importance has nothing to do with the difference between *giving up* and *giving in*. See the other two answers.
Answer: Give up indicates cessation as well as forfeiture, whereas give in denotes surrender to something (perhaps temptation in the chocolate example above) or a person or persons (the children in the example of the father above).

"Give up" versus "give in"


Hyperbolic harmonic oscillator

Question: The classical harmonic oscillator can be associated to the differential equation:
$$y''+\omega^2y=0$$
and solutions
$$y=A\cos(\omega t)+B\sin(\omega t)$$
or $$y=A\cos(\omega t+\delta)$$
The harmonic oscillator is associated to springs and/or small oscillation problems, or Hooke law force motion. What about the hyperbolic version of this equation? That is:
$$y''-k^2y=0$$
with
$$y=A\sinh(kt)+B\cosh(kt)$$
What are the physical problems associated to this equation?
Remark: A "Wick-like" rotation in $\omega$ transforms the HO into the hyperbolic one at the level of the solutions.
Comment: The inverse pendulum is a trivial example; how any perturbation increases exponentially with time is pretty evident from those solutions
Comment: Looking at the Kapitza Pendulum might give you some insight.
Answer: Yes, there are many physical problems that do follow such equations. You even mentioned one of them in your question.
A pendulum held against gravity near to its unstable equilibrium point locally follows such an equation
The differential equation that governs the motion of a pendulum is given as
$$ \dfrac{d^2\theta}{dt^2}+g \sin(\theta) = 0$$
But if you let $g \rightarrow -g$ (reverse the direction of gravity) then the equation would read as
$$ \dfrac{d^2\theta}{dt^2}-g \sin(\theta) = 0$$
The transformation which I did transformed the equations in such a way that the pendulum is now near its unstable equilibrium point i.e. the initial position of the bob of the pendulum is more near the angle $\pi$ than to $0$. And now if we assume $\theta <<1$ then what we essentially have is (the nearer it is to $\pi$ the more accurate the solution)
$$ \dfrac{d^2\theta}{dt^2}=g\theta$$
Hence this physical situation has a local solution (around its unstable equilibrium point) as
$$\theta (t) =A\cosh(gt) +B\sinh(gt)$$
Another interesting way to come up with the same solution is to transform $\theta \rightarrow -\theta$ instead of $g \rightarrow -g$, this is an equivalent transformation and if we transform both $\theta \rightarrow -\theta$ and $g \rightarrow -g$ the differential equation remains unchanged. I'll leave this to you to figure out why this happens.
Answer: I had a professor give a really good homework problem that demonstrated the similarities of the two situations. The math is obviously important but the picture is what's helped me build an intuition for harmonic (and exponential) motion:
Imagine a plank of wood resting on two rollers on either side of the center of mass so as to hold it up (located at $\pm a$, say). If the plank is moved slightly, the torques provided by the (currently unmoving) rollers must stay the same since the plank doesn't start rotating. Because the lever arms (distance from the CM to the rollers) changes, this means the normal force must be greater on the side with shorter arm. So if the plank moves to the right, the normal force at $+a$ has a greater magnitude than that at $-a$.
1) If the rollers are now spinning inward, they generate a frictional force pushing the plank back to the center whose magnitude is proportional to that of the normal force from the roller. If the plank is at the center, these frictional forces are equal and nothing happens. If it moves slightly to the right, the roller at $+a$ has a greater normal force $\to$ it's frictional force to the left increases and the plank returns towards its original position. If you work out Newton's laws, you'll find the CM of the plank undergoes exactly harmonic motion.
2) If the rollers are spinning the opposite direction (away from the center) and you move the plank to the right the exact opposite effect happens. Again, the normal force from the $+a$ roller is greater and so its frictional force to the right will be greater and the plank will continue accelerating (exponentially) to the right. As it accelerates to the right, the difference in frictional forces becomes greater so it seems reasonable to expect you would have an exponential motion of the plank.
Answer: This equation would correspond to the physical situation where you had a force that was repulsive and somehow grew proportionally to the distance you are from the equilibrium point $y=0$. As such, the particle in question will be accelerated to ever increasing speeds away from $y=0$ and this motion is not bounded. Eventually relativistic effects would kick in, and you would have to modify your framework. I know of no real physical system that follows this equation. And in fact, the energy of this problem is unbounded just like the trajectory, so the source of this force field would have to be able to provide infinite energy to your particle.
Also, such a system is not an oscillator as it does not oscillate. It just goes off to infinity.

Hyperbolic harmonic oscillator


What is the purpose(s) of JavaScript build tools

Question: Lately I have been studying Node.js. In this time,I have heard a lot about using Gulp or Grunt in as a build tool. Now I am interested in learning how to use Gulp. I have heard it was a build tool, but I am not sure what all that covers. What would I do(what kind of tasks) with a build tool like Gulp that would assist me in development? Some examples would be nice.
Answer: Gulp ( and Grunt ) allows for task automation.
Pretty much anything you find yourself doing repeatedly in a project, can be automated with gulp and it's plugins, and if you can't find a plugin to do the job for you, gulp is just a Node.js app, so you can quickly write your own code to do the job.
As far as examples, since I myself am an Angular web developer. I will give you examples from the Front End Development land, but don't think gulp is only limited to this area. Here are some examples :

Automate your build process (some subtask examples here)

Take all your projects HTML, JavaScript, CSS, concatenate them and minify them
Automatically inject dependencies into your HTML files

Listen to file changes and run tasks when a file changes

Every time you add a JavaScript file, you need to add include it to your HTML files. this can be automated
Every time you save a JavaScript file you want to run jshint on it, to warn for errors
Every time you save a CoffeeScript file, you want it to be automatically converted into a JavaScript file, and have that javascript file included to your HTML files

Deleting files automatically
Thousands of other things

Another interesting benefit you get with JavaScript build tools specifically ( as opposed to Java's Ant or Rails's Rake ) is that most of all web applications out there use JavaScript, so if your back end is in Java or Rails or C++ your front end people always rejoice under JavaScript. Which means that, no matter what language you use, you still use JavaScript which makes tools like gulp very interesting, because JavaScript and JavaScript experience is guaranteed to exist in any web development team.
I guess I'll update this in time to make it clearer. Until then have a look at: http://gulpjs.com/plugins/ to get an idea of some of the easy to obtain functionality you can get with gulp.
Here's a quick code example, of a gulp task, that takes your project's images, and moves them into your dist folder:
gulp.task('images', ['clean'], function () {
  return gulp.src('/src/assets/images/**/*')
    .pipe(gulp.dest('dist/assets/images/'));
});

Tasks can be chained together and rely on each other. Notice how the task 'images' depends on 'clean' . That means that if you want to run 'images' your 'clean' task will automatically get called before. This allows you to chain tasks together for very powerful reusable task sequences. Here's an example of how 'clean' could look like:
gulp.task('clean', function (done) {
  del(['/dist'], done);
});

Here's some random page i found with a google search. It contains a very clear CoffeeScript file with examples of gulp automation tasks in a front-end project: http://pem-musing.blogspot.ca/2014/02/a-gulp-of-coffee-your-gulpfile-in.html.
Comment: So, would `npm install` be an ideal task to run via gulp?
Comment: I can't see why that would be a problem, but don't take my word for it ... Why would you think that could be a problem ? And why would you need npm install in a task ?
Comment: Thanks, @Cosmin, for explaining the concept in simple plain English. Appreciated. :)
Answer: Gulp JS is a Javascript based tool which allows you to automates the tasks of your workflow. Automation can literally increase your production. Whether you're a developer or a designer who creates HTML wireframes now and then, we recommends to dig into that.
http://www.jshive.com/getting-started-gulp-task-runner/
Answer: Build tools are an asset to application development. Few years back, it was common for project managers to run behind the developers asking them to clean up the code, lint the code, increase the performance of the application etc.
The usual modus operandi of developers was to make a copy of the 'Development' environment code for the Production environment and do the required operations. Developers would use third party software or apps that helps in cleaning up the code like removing unnecessary comments, minifying to decrease the overall size of the file and thereby the application, concatenating the files so that you decrease the number of hits to the server, perform unit tests, to name a few.
What build systems like Gulp and Grunt have done is that it automates all the above mentioned tasks in a span of few seconds. These build systems have specific plugins that does concatentation, minification, linting, environment specific development etc. All these tasks run in one go performing the required operations, in turn running the application from the newly formed production code.
The advantage of using build system is that it accelerates your application's page load time to a greater extent. Your code is cleaner, smaller in size and at  the same time adheres to the best coding practices. And in turn , you save a lot of time which was spent doing each of these tasks.
They are pretty easy to work with and should be used in application development. :-)


I'm here to run the official Go-Ethereum repo. How can i do that?

Question: I want to run  go-ethereum in my own PC. Is there any instruction about this? How they deployed it?
Answer: If you want to make project from resource

install go
you need clone go-ethereum
make it

More details in official documentations: https://geth.ethereum.org/docs/install-and-build/installing-geth#windows
If you are needed only executable client go to https://geth.ethereum.org/downloads/


Minecraft TNT Mining

Question: I've got some TNT and a way to set it off, but I'm scared I might destroy precious minerals like diamonds, redstone or gold. Is there a way to set it off, but in a safe way? I know water stops it but then the TNT wouldn't do anything.
Comment: I am tempted to say this is a duplicate of [this](http://gaming.stackexchange.com/questions/29357/do-explosions-destroy-stuff)
Comment: [This](http://gaming.stackexchange.com/a/18216/10616) could cover it as well.
Comment: It's a good way to get deep. But once on the right level, TNT should not be used. What do you mean by "set it off" ?
Answer: If by a safe way you mean one where the TNT wouldn't destroy valuable resources, then no.
TNT is somewhat impractical for mining, because only about 30%-ish of the destroyed resources actually drop as items (wiki). So if you don't want to risk destroying diamonds and such, don't use TNT — at least when you're deep enough for the resources to occur.

Minecraft TNT Mining


Is it possible to find the area of a shape from its perimeter?

Question: Is it possible to find the area of a free form shape knowing the perimeter?  An example would be a clover leaf shape.  If the perimeter is 96 how would I know what the area would be?
Comment: No, it's not possible to determine area from perimeter.
Comment: Yves brings up a good point. By "clover leaf shape" do you mean you know the shape precisely up to similarity (i.e., the shape but not its size)? If so, the answer is yes, and you can easily write down a formula given the perimeter and area for any particular size of that object. If you simply have a perimeter, then the answer (as indicated by several answers) is no.
Answer: Contrary to all other answers, I say yes you can find the area $a$ of a known shape (clover leaf) from the length of its perimeter $p$.
Taking a similar model of the clover leaf, measure its area $A$ and perimeter $P$, using a curvimeter and a planimeter. You can also do that from a digital image (photoscan), but I don't know of ready-made tools for that.
Then, for any clover leaf (of the same shape), this proportionality rule holds:
$$\frac aA=\left(\frac pP\right)^2,$$
so that
$$a=A\left(\frac pP\right)^2=F_{clover}p^2.$$
For any shape there is a corresponding conversion factor that you can compute once for all.
For instance, with the picture below, you can estimate an area of $19852$ pixels and a perimeter of $750$ pixels (this is an inaccurate measurement).
Then $F_{clover3hearts}\approx0.0353$, and your leaf has an area of $325$ square units.
Answer: This is impossible.  We can prove this by constructing two shapes with the same perimeter but different areas.
Consider, for instance, the unit equilateral triangle, with perimeter $3$ and area $\sqrt{3}/4$, and the square with side lengths $3/4$ and area $9/16$.  Since these two shapes have the same perimeter, but different areas, one cannot uniquely determine area from perimeter.
Answer: Perimeter is basically arc length. You could just as easily have a line segment of length 96 as a square of perimeter 96. Then the side length is 24, and so the area is $24^2.$ On the other hand, if the circumference of a circle is 96, then $96=\pi d,$ so that means that $r=96/ 2\pi$. This means that the area is $(96/2)^2,$ which is different from $24^2.$
Answer: In general, no, though the Isoperimetric Inequality gives and upper limit on area: For a bounded region in the plane with perimeter $L$, the area $A$ must satisfy
$$A \leq \frac{L^2}{4 \pi},$$
and equality holds iff the region is a circle. By constrast, if the region is a square, we have $A = \left(\frac{L}{4}\right)^2 = \frac{L^2}{16}$, which (since $\pi < 4$) is smaller.
If you know the shape of the boundary, you can compute the area of the region by computing an integral just over the boundary, for example, with Green's Theorem. This is the principle exploited by the planimeter, a machine which does exactly this.
Answer: No, this is not possible, because you can easily increase the perimeter of any polygon (while retaining its area) by modifying its edges like this:

(Source: http://en.wikipedia.org/wiki/File:Quadratic_Koch_curve_type2_iterations.png)
You can even use this technique to create fractals with an inifinite perimeter, such as the "Minkowski Sausage".
PS: As Yves Daoust and Travis have noted, this answer only applies if the shape is unknown.
Answer: If "perimeter" is the lenght of..., is impossible, as already answered. But if the form is know is possible calculate the area using Green's theorems. The Planimeter is an application of this fact.
Answer: The answer strictly speaking is no. take a US quarter for instance has a perimeter (circumference) of 3 inches exactly. A Circle has the maximum area for a given perimeter for a shape. A US Quarter has a width of 0.955 inches so its total area (for one of its circular faces) has an area of 0.7163 inches^2
As an example, a shape known as a reuleaux triangle can have the exact same width at any given axis (0.955 inches), the exact same perimeter (3 inches), and have an area of 0.643 inches^2 (rounded). There's a whole infinite group of "reuleaux" shapes that could be created from the shared area of intersecting circles of radius 0.955 inches centered on the vertices of equal-sided polygons that would all also have the exact same width on any given axis and the exact same perimeter. The more vertices of the corresponding polygon, the closer the area becomes to that of a circle.
On the other extreme, a 1.5inch line can also be said to have a perimeter of 3 inches but an area of 0 (zero) inches^2 if you think of it as a rectangle with a width of 1.5inches  and a height of 0 inches.
Interesting yes?


Who won the Leipzig Debate between Martin Luther and Johann Eck?

Question: Who won the Leipzig debate between Martin Luther and Johann Eck? What was the final conclusion? How did it affect to the Reformation? Is a transcript of the debate available online?
Comment: I think you need to be more specific on what resources you like beyond the [wikipedia entry](https://en.wikipedia.org/wiki/Leipzig_Debate) so you get what you want.
Comment: "Eck came off victorious, exposed Luther's heresy, and won over as a loyal adherent to the Catholic standard, George, Duke of Saxony."
~ Catholic Encyclopaedia: Johann Eck
|
If you're interested in the debates of the time, you should read cardinal St. Robert Bellarmine's De Controversiis. He demolishes the Protestant position.
Comment: @GratefulDisciple I need its transcript or related posts, books etc. Because I find it difficult to get resources on this subject.
Comment: I incorporated your further detail from [the other question](https://christianity.stackexchange.com/q/92447/10672) and vote to close the other question as duplicate.  In the future, rather than leaving the further details in a comment, you need to edit it into the Q itself.
Answer: I only know of one source, which I have here, on the table, in the form of a published book. I will extract quotes from it, to give a flavour of what the author says about the Leipzig debate between Martin Luther and Johann Eck, a professor from the University of Ingolstadt, held between 4th and 14th of July, 1519.

"On the appearance of Luther's theses [Eck] had leveled against them
an attack under the title Obelisks, the word used to designate
interpolations in Homer. Luther replied with Asterisks. Eck's attack
was galling to Luther because he was an old friend, not a mendicant,
but a humanist, not "a perfidious Italian" but a German, and not the
least because he was formidable... he was a man of prodigious memory,
torrential fluency, and uncanny acumen...
[Eck] openly baited Luther by challenging his alleged assertions that
the Roman Church in the days of Contantine was not above the others,
and that the occupant of the see of Peter and the vicar of Christ - in
other words, that the papacy was of recent and therefore of human
origin... [Then comes Luther's response to that]
Luther set himself to prepare for the debate. Since he had asserted
that only in the decretals of the previous four hundred years could
the claims of papal primacy be established, he must devote himself to
a study of the decretals. As he worked, his conclusions grew ever more
radical. To a friend he wrote in February: 'Eck is fomenting new wars
against me. He may yet drive me to a serious attack upon Romanists. So
far I have been merely trifling.'..." Here I Stand - Martin Luther by Roland Bainton, pp 107-109, Lion 1988 reprint

Once all the preparatory letters had been sent back and forth, the debate proper started in July, 1519. A description in the book follows, of the ceremony, the pomp, the personnel, what the choir sang while the town piper played lustily, all prior to dinner. Then the preliminary skirmishes over the rules of the verbal tournament are mentioned. The only point of note (for your purposes) is that Eck said 'No' to stenographers as that would chill the passion of the debate, but he lost. Melanchthon said, "The truth might fare better at a lower temperature."
The debate takes eight pages to detail, including the statement of an eyewitness, but if you find the foregoing interesting, you might like to obtain the book. It is to be recommended as a scholarly, well written work. The entire section is from pages 107 to 120. You would need to consult Catholic sources for their version of events.
It goes without saying that Catholics would largely tend to say Eck won the debate, while Protestants would say Luther won it. As the book I quote from is written by a Reformed Protestant scholar, it forms the latter conclusion.
Answer: I will give a Lutheran perspective. An online source, from this perspective for the debate can be found here. The highlighted quotes that are brought out in this response comes from that online source.
It is interesting that to begin with, the debate took place during a time in which Luther held to a belief in purgatory. For example:

In his ninth thesis Luther had assumed, with the scholastic theology
of the times, that there is a purgatory, but had claimed that it is
not settled whether the souls in purgatory are certain of their future
salvation, and whether divine grace is effecting a reformation in
them.

In reading what transpired during the debate, the nature of the debate followed what Eck requested:

Eck demanded that no one should be permitted to read anything from a
paper, but every speaker must speak ex corde.

Melanchthon wrote how Eck:

… thought that the nature of the debate precluded its being reported,
for that the force of the debaters was increased by speaking ex
tempore and would be decreased by the delay of writing, that while
minds were stimulated by rapidity, they would be enervated by delay.

These rules of engagement set the stage, early in the debate, for Carlstadt to flounder:

At this point Carlstadt began to speak haltingly and admitted an
activity of man's free will that is communicated by grace, but he
claimed that activity is as when a wagon is set in motion : it is
really grace alone that operates. Melanchthon had meanwhile slipped a
paper to him from which Carlstadt tried to read, when Eck protested
that this was against the rules of debate on which they had agreed. He
also charged that Carlstadt had brought a private notary into the
meeting who was carefully taking down Eck's remarks, and then helped
Carlstadt at his lodging to prepare his replies for the next day,
while he, Eck, was compelled to rely solely upon his memory and had to
speak ex tempore.

Sadly, the Lutherans broke the rules of engagement. The author writes about Eck's comments following the debate:

[Melanchthon had passed a note to Carlstadt during the debate, which
Eek resented], three doctors of law, several professors who aided him
privately and publicly even in the course of the debate. But I alone,
with nothing but right on my side, withstood them.

The author of what transpired, during middle of the debate, adds his comments:

Nature and grace had not favored Carlstadt. Over and against the tall,
portly Eck with his dapper appearance and jaimty airs the little
sallow professor from Wittenberg with his hollow, monotonous voice,
his poor memory, and his nervous and irritable temper made a very poor
showing. He was habitually confused, had to hunt among his notes for
the remark which he was going to make when his turn came to speak,
always came into the hall with a load of ponderous tomes, which he was
incessantly searching without finding what he wanted,

He notes how Luther wrote about Carlstadt:

He dishonored, instead of honoring, our cause. He is a most unhappy
debater, of an appallingly dull mind." The Wittenbergers were hanging
their heads in shame during this ordeal. Thus matters stood on the eve
of July 4, 1519.

On the other hand, the author writes about Luther debating Eck after Carlstadt:

It is a queer fact, which a close study of the protocol of this debate
reveals, that Eck winced more under the patristic than under the
Scriptural arguments of Luther. He was noticeably weak in his
Scripture-proofs, while Luther massed his striking texts for a
powerful charge upon his opponent. But that he would have to consider
himself defeated also by arguments from the fathers was an unbearable
thought to Eck.

The author writes about
Luther saying:

Eck's assertion-that the Greeks are arch-heretics he declared
extreme,...

Here are a couple of more comments about the debate. After one session, the author notes:

In the afternoon Luther continued to speak of the condemned teachings
of Wyclif and Hus, and said that there were among these teachings some
that had a right Christian ring; for instance, that there is a Church
universal, that it is not necessary for salvation to believe that the
primacy of the Pope exists by divine right. Many of the old fathers
had believed thus and had gone to heaven.
At this statement of Luther Duke George was observed to lean forward,
put his arm akimbo, and exclaim excitedly, "The pest take the man!"

At another session, he writes about Luther:

... Continuing in German, he said that he
did not deny that human right of the papacy, and then proceeded with
his argument in Latin, stating that the majority of the fathers do not
understand the rock to signify Peter, while the rest are undecided.
The Asiatic bishops, Irenaeus and others, he said, had reprimanded the
Pope, and the best of the Greek fathers had never been under the Pope;
Gregory the Great had opposed the absolute primacy. In John 21, 16 no
supremacy is conferred on Peter, at least, no such authority as the
present Pope has, but he is merely exhorted for the love of Christ to
do and to suffer all things in behalf of the Church. Now, where is
there such a pope? Luther asked. He proceeded to emphasize cordial
love as the great duty inculcated in this text, and this love, he
said, concerns all teachers. A wicked teacher, also a wicked Pope,
must either mend his ways or be deposed.

And:

Here the session of Friday afternoon was adjourned.  It was reported
that many in the audience had become  offended at Luther's statement
that the schismatic Greeks are saved.

The author notes how Loughlin comments:

... the Leipzig Debate was the last occasion on which the ancient
custom of swearing to advance no tenet contrary to Catholic doctrine
was observed. In all subsequent debates between  Catholics and
Protestants the bare text of Holy Writ was taken as the sole and
sufficient fountain of authority. This, naturally placed the
Catholics in a disadvantageous position and narrowed their prospect of
success.

Who won the debate? As time goes on the Roman Catholic Church appears to no longer view those in the Greek Orthodox as "not saved." I believe that some day there will be re-approachment and the division at the time of the Reformation will be healed.
The author writes about the conclusion of the debate:

Eck remained in Leipzig nine days longer, gathering laurels and
enjoying himself after his fashion. He deported himself as the
unquestioned victor; but there were  men who questioned, and some who
openly denied, his victory. They were few, it is true, but it meant much in papal  Leipzig
that there should be any who believed that the disputants from
Wittenberg had won in the famous argument.  Carlstadt returned
directly to Wittenberg, and the crowd of  visitors carried the news of
the great things which they had  seen and heard to many parts of
Germany. For the rest of  that year the correspondence of the learned
men in Germany,  Prance, and Italy is filled with references to the
Leipzig  Debate.


Is the flatness of DC output of a typical ATX power supply unit worse than a power adapter?

Question: I converted an ATX power supply unit (Seasonic, 330W) into a standalone power adopter (by adding load, etc.), to which I connect multiple things. When I plugin a computer and a monitor each to a 12VDC line, they work fine, but when I also plugin an audio speaker to another 12VDC line, it gives a noise that is at an unusually bad level. If I, instead, just plugin the speaker to an ordinary AC-DC switching power adopter, then, the noise dissapears. I was wondering if the flat level of the DC output of an ATX PSU is that bad. I had though that switching adaptors should be worse than a power transformer (which is used in ATX PSU) with respect to flatness, but the reality seems to be the opposite. Am I wrong?
Answer: The ATX power supply is a switching power supply. It's important to be sure of the difference - a switching power supply switches the voltage at a much higher frequency (e.g. 65kHz) so smaller transformers can be used (transformers work more easily at higher frequencies)
The downside is high current switching can easily cause EMI problems if not dealt with properly, and often in cheap power supplies (e.g. ATX) the filtering is very basic and may not always meet regulations.
A "standard" supply uses the 50Hz or 60Hz mains frequency to change the voltage, so the transformer for the same amount of power would be much larger. The supply size will likely be over twice as big for the same rated output. However with low frequency and (usually) linear regulation, these supplies are usually quieter. Are you absolutely sure your "AC/DC" supply is a switching supply?
It is relatively easy to make a quiet supply using either design though, so you may find a well made SMPS (can include linear regulation after initial switch regulation)  is quieter than a cheap (possibly unregulated) standard supply.
I think your noise may well be present all the time, and causing issues with the sensitive (active I assume :-) ) analogue speaker circuitry. It may be (as mentioned previously by Madmanguruman) from the PC/monitor plugged causing problems with regulation, or could be a grounding problem of some sort. Depending on the frequency (be good to know roughly how high/low it is) it would be easier to guess at what is causing it. An scope on the lines would tell the full story.
Answer: We have a few ATX units converted in the office, we didn't try with an big external load but loads we use are around 3W. When we build the things we looked at the output with a scope in AC coupled there was noise (more than bench supply) however it was at an acceptable level. Perhaps only 30-40% more then bench supply for a given voltage output.
Sounds like speaker is not well designed as some high frequency noise creeping back into the output. In this case, I guess supply noise may be the issue, but the speaker should be able to cope with it, it sounds like it is not well designed.
Comment: not a bead but a decoupling cap. If he puts a 10nF and 1nF and potentially 100nF between the supply and ground, I suspect those caps will suck the living daylight out in terms of noise. those caps need to be close to the speaker.
Comment: Do you think that sawa could fix that with a ferrite bead or something similar on the power supply to the speaker?
Answer: ATX supplies specify their ripple to be 1% of the rail voltage. What I suspect is happening is that the other loads are disturbing the rail and the speaker is picking up the disturbances. Even though there may be multiple connections to 12V, I suspect that there's only one feedback loop for all the feeds, so the noise coming from the other loads is enough for the speaker to transduce.
Try the speaker on the ATX supply without the monitor and/or computer and see if there's an effect.
Answer: I assume you are refering to noise on the audio output of active speakers. The power supply itself could also directly produce audible noise, which is a different problem.
The noise could be caused by a ground loop.
In this case, the difference of the two power supplies could be that the output is connected (or not connected) to ground in a different way.


German employee with stock options for a NASDAQ-listed company: eligible for Tax Treaty Benefits?

Question: I am a German employee (German citizenship, living and working in Germany, no connections to the US) of a NASDAQ-listed company and have received stock options (more exactly RSUs, Restricted Stock Units) for the company. Am I eligible for Tax Treaty Benefits according to the treaty between the US and Germany?
Comment: what taxes are you required to pay in the US and why?
Comment: @littleadv: none that I know of, but that's part of my problem - logic tells me that I won't have to pay US taxes when selling these shares, but tax laws are not always logical...
Comment: Generally RSU grants are held through brokerages who are well aware of all the potential complexities. Have you been asked for a W8/W9 form?
Comment: @littleadv: unfortunately my company is only providing a  website/app ("Global Shares"), and to sign up for that I have to specify if I want to claim Tax Treaty Benefits. The app's support only told me that I won't be able to change this setting later - both they and my company's HR department are taking the position that they are not allowed to offer me tax advice, and to ask my tax advisor. I don't have one, but one colleague I asked talked to their tax advisor, and they couldn't provide a definite answer either...
Comment: I'm not a tax advisor either :) I'd suggest that you say that yes, you do want to claim treaty benefits. The tax treaty provides that you only pay taxes on your proceeds/gains in Germany (article 12(5) for gains and article 15 for grants)
Answer: I'd suggest that you say that yes, you do want to claim treaty benefits. The tax treaty provides that you only pay taxes on your proceeds/gains in Germany (article 13(5) for gains and article 15 for grants)
Comment: In the treaty I linked above, article 12 refers to "royalties" (5 is "permanent establishment") and 15 refers to "dependent personal services". Not sure how these relate to my situation? Article 13 refers to gains, but there is no article for "grants" (at least not using this term). I thought the most relevant article for me would be 13 ("relief from double taxation")?
Comment: @rob74 sorry, you're right - I was referring to 13(5). Your grant is essentially a salary (paid for dependent personal services) that is paid in stocks (which you later sell, aka alienate, hopefully for a gain).
You would probably want to pay someone to provide you guidance since you're actually asking for legal advice here. I'm not a lawyer and not a CPA.


My new Western Digital Blue 2TB shows "Reboot and Select Proper Boot Device or Insert Boot Media in Selected Boot Device and Press a Key" error

Question: I just got my new Western Digital Blue 2TB 3D NANDA SATA 3.0 SSD but whenever I tried to run the PC into the Windows login screen, it always shows the terminal which reads "Reboot and Select Proper Boot Device or Insert Boot Media in Selected Boot Device and Press a Key." I then shut down the PC, go into the BIOS Settings and change the first Boot Priority and the Boot Override to my SSD. I checked several times to see if I had selected the correct SSD and tried to run it again. My brother incorrectly installed the SSD frame by taping it onto the actual PC rather than screwing it onto the PC, but I don't think this is the cause because all of the cables are correctly connected. There are two slots inside the SSD which you have to connect the cables to. Both are easily recognizable by the L shape which is on the cable. All I know is that the smaller cord connects the the Memory and the larger cord connects to the Power Supply. My brother taped the original SSD to the PC after screwing everything back onto the frame and plugging the cables back in and the original SSD worked perfectly. One thing my brother told me was that I many need to install windows onto the SSD. I don't know if this is true or not so I cannot be sure. Please leave me suggestions so I can finally use my SSD!
Answer: Your brother is correct.
You have an empty SSD. There is nothing on it. That is how they come out of the packaging.
So your computer is very helpfully telling you to install an operating system (like Windows) on it so it becomes a proper boot device.
Normally, at this point, you would install the new SSD side by side with the old drive.
Then you use disk-cloning software (which isn't part of Windows, but often comes together with the new SSD for this purpose) to copy the old drive content to the new SSD.
Then you can remove the old drive and boot from the new SSD.
(Or you leave the old drive in there and re-format it for use as a data-drive.)
This cloning of the disk was apparently not done.


Feed Me: Feed inside the feed

Question: I have just started using Feed me to import a festival schedule, and I have run into an issue with how their API is set up. The URL I have to use for the feed (with the token) outputs only a <link>URL.xml</link> to a temporary XML-file with a unique filename each time. So there's pretty much a feed inside the feed. Any way of getting Feed Me to look at the linked XML-file, or any other suggestions on how to solve this?
Answer: There's no current way for Feed Me to handle this I'm afraid. My best suggestion would be to write a module to fetch the XML from your first URL, parse that, find the <link> note, fetch and parse that, and output the XML. You'd then point Feed Me to that URL, with the actual content of the feed that's required.
It could be a Craft module, a standalone PHP script, or even JS - whatever you're comfortable work.
It's a bit of extra work, but custom development would be the only option for the moment.
EDIT: The other option you could create a template (let's say my-feed.xml) in your templates directory with:
{% header "Content-Type: application/xml;" %}

{% set params = {
    url: 'http://path.to/feed/',
    type: 'xml',
} %}

{% set feed = craft.feedme.feed(params) %}

{% for node in feed %}
    {# Find the node that contains the link #}
    {% set link = node.myLinkNode %}

    {# Get the raw data and output it #}
    {% set xml = craft.feedme.getDataTypes().getRawData(link) %}

    {{ xml }}

Comment: I see, could you give me a very quick summary on how you would solve this with JS? No code, just a few words to push me in the right direction. I was hoping that I could create a separate feed and save the xml as an asset, but it looks like Feed Me only handles image files.
Comment: When I mention JS, I'm probably referring to server-side JS with Node, doing the same thing, fetching, parsing, then fetching, parsing again. Any language you'd be comfortable with, but just needs to be a "middle-man" between your original feed and Feed Me. I've also just added another method above
Comment: Is craft.feedme.getDataTypes().getRawData() something that should work out of the box?

Feed Me: Feed inside the feed


Fundamental concepts of ESRI Javascript API

Question: I am building a Web Application for the first time using the ESRI's Javascript API and wanted to know the basic fundamental concepts that I should keep in mind?
Comment: Suggest this should be a community wiki, since the poster "wants to understand more about the kind of questions that can be asked in interviews"
Comment: To clarify my last comment, there may be multiple "correct" answers.
Answer: Your question is vague so it's hard to know where to start or when to stop but here are some things I wish I did when I started my project.

Decide if OpenLayers is a better choice
Get a good understanding of dojo
Build unit tests from the beginning
Create an automated build process
Avoid the temptation of putting everything in one js file
Locate the JSAPI examples and become familiar with them
Download JSAPI locally and beautify it...it's still a nightmare but it helps
Comment: +1 to Avoid temptation of putting everything in one js file
Answer: Here are some questions that should be asked when designing any web-mapping app. The questions are inter-related, in that the answers to either will affect the others.

What is the purpose of the map/application?
Who is the intended audience?
What capabilities need to be included in the application, e.g.

can users edit features;
is a buffer tool needed;
is a zoom slider sufficient or does the audience expect/require zoom boxes?

What browsers/platforms need to be supported? (note that this isn't as relevant to your question, since you've specified the JS API)
What basemaps and feature data will be shown?
Where will the data come from and are the data services available to the environment where the application will be hosted (e.g. intranet vs. public internet)?

Here are some other questions specific to a JS API.

Is there intellectual property in the application tools or design that would be detrimental to expose via JavaScript?
Is the web-map going to be part of an application that is built in a different JS framework, e.g. jQuery or EXT JS? If so, what extra work will be needed, or considerations will need to be made?
Will it be suitable to call the API from ESRI's servers, or should it be served locally from the application's servers?
Comment: Thanks @Kevin that was very insightful. Could you elaborate a bit more on the intellectual property? Most of my tool is from the Javascript API gallery and sample code. Does that comprise of intellectual property?
Comment: The tools in the API gallery/samples are not your intellectual property (IP). However, the design, branding, and custom tools of your application may be considered IP. A JavaScript application means the source-code is visible to anyone with access to the app, potentially exposing any IP included in the app.
Comment: Well presently only the IP of the ArcGIS server would be visible when I adding the basemap.


"." on numPad no longer centers view on selected

Question: Numpad . no longer centers the view on the Selected Object, but on the Cursor. I must have changed something in the settings unwittingly. Does anybody know how to reset it?
Comment: perhaps you've centered the view so many times that your numpad is wearing out?
Answer: Make sure numlock is activated on your numeric keypad.
Numeric keypad have different flavors as well.
I have two numeric keypads attached.
Comment: Stupid me, I incidentally checked the "lock to cursor" box in the properties shelf.
Comment: Hmmm.  That probably wont make even the 99 most irritating and time consuming errors yet to come.  You got lucky!
Answer: TavernSenses Thank you!
Your mistake help me to find my mistake, it was the same! Somehow I made that lock with: ⇧ ShiftNumpad . (View Lock to Active), which centers the view to the last selected active object, overriding other view alignment settings.


ITerm2 Closes Immediately After Opening

Question: My iTerm2 closes right away when I click on the icon in an attempt to open it. I have seen that this is a known issue with iTerm2, but the solutions I found involve editing preferences through the menu. However, I can not access the menu items. Also, I can not resize the window to get the alert to move out of the way so now I can't read the information displayed. Finally, I don't see any error logs. Any ideas?
iTerm2 build 3.3.12 running on Mojave 10.14.6
Comment: In general see the answer. But I notice that login shell begins with /usr so I don't think you have the default. Perhaps you have removed the shell you use and might be fixed by putting it back
Answer: Move the following directories and files somewhere else to back them up.
<code>~/Library/Application Support/iTerm2
~/Library/Preferences/com.googlecode.iterm2.plist
~/Library/Preferences/com.googlecode.iterm2.private.plist
</code>
See if iTerm2 starts up without crashing.  You may need to redo all your settings or attempt to decipher them from the backed up files. You can open the PLIST files in Xcode in an easy to reference view.
Answer: I just encountered this same issue, and found that by checking the Suppress this message permanently box and restarting iTerm, I was able to access the Settings menu again.
Turns out the Settings menu is not grayed out because of the crashing iTerm application, but instead by the dialog message itself. While my terminal window instantly crashed again, iTerm remained open so I could update those settings.
I believe this solution is easier than removing/relocating preference files!
Answer: I just saw this upon upgrading my version of macOS, and reinstalling iTerm resolved the problem.

ITerm2 Closes Immediately After Opening


Why does hot oil explode when pouring water on it?

Question: What is the reason that hot oil makes sound and explodes when water is poured on it?
Answer: The liquid water changes phase when heated above the boiling point, namely it becomes a gas. When water vapor in cavitation bubbles escapes fast, it makes a mess. The sound of splashing aside, notice that nothing happens if the oil is cold.
Related fun fact: The pistol shrimp is so loud, it kills other fish by snapping with its claw.
Comment: Please give him this [incriminating evidence](http://meta.stackexchange.com/questions/258892).
Comment: @babou: You'll hear from my lawyer.
Comment: And I got an **excavator** badge for it. Repaying debts is always rewarded.
Comment: Actually there is more than I said. I consider voting moderately intelligent, and downvote generally stupid. Hence I want my activity free from downvotes. The other point was for me to check whether I can actually change a vote after editing the post. The answer is yes, and adding a blank space at the end seems to be the minimum change required. But you can unroll that now, so that it disappears :)  Unexpected result of the experiment: a new badge. Always fun to conduct new experiments. I am actually interested in the socio-technical working of SE.
Comment: I downvoted by accident, but I cannot undo it, unless you do some editing ... even adding a single space. Sorry. Let me know if you edit by replying to this comment.
Comment: @babou: I was being serious, you could get into [Max Stirner](https://en.wikipedia.org/?title=Max_Stirner)s works.
Comment: @babou: I don't understand what you say here. The *s* at the end is also not part of his name, did you even look at the linked page?
Comment: @babou: What do you mean by the Masters line here?
Comment: @babou: If you actually read [his main work](https://en.wikipedia.org/wiki/The_Ego_and_Its_Own), you'll find that Gods are by far not the only Master figures. Start with **[the first page here](http://www.df.lth.se/~triad/stirner/theego/theego.pdf#17)**, it's written in an entertaining way, too.
Comment: Let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/24953/discussion-between-babou-and-nikolajk).
Comment: Fastest edit I ever did.
Comment: @babou: "debt". I feel honestly saddened you didn't listen to me at all.
Answer: The essential basic fact is that the boiling temperature of oil is very much above that of water, known to be $100^\circ\;\mathrm{C}$ at atmospheric pressure (by definition).
For oil, the boiling point varies, but is very often above $200^\circ\;\mathrm{C}$: $197^\circ\;\mathrm{C}$ for olive oil, $246^\circ\;\mathrm{C}$ for corn oil (depending on quality, it can vary significantly), and around $300^\circ\;\mathrm{C}$ for refined motor oil. Actually, organic oil may smoke, i.e., decompose chemically, much before it boils, but nevertheless at very high temperature such as $191^\circ\;\mathrm{C}$ for olive oil (extra virgin, higher for other qualities).
Thus hot oil may mean much hotter than the boiling point of water. Whatever the heat capacity of oil, or more precisely its specific heat, which is actually about half that of water, the very high temperature can provide considerable heat that will cause an instant change of state from water to steam, creating instantly a considerable change in pressure, thus in volume, i.e. an explosive behaviour for each drop of water.
Following on a comment by mikuszefski, there is also an issue of
relative density, water being denser than oil. The effect depend on
the amount of water being poured.  If it is only a few drops, they
either vaporize instanly, of are kept buoyant by the steam pressure as
the bottom vaporizes first.
However, if the amount of water is more important, the buoyance will
be insufficient (it is proportional to the square of the water blob
size, while the weight is proportional to the cube), and the denser
water will fall into the oil, while continuing its explosive
vaporization, which may then carry some of the oil with it.
Comment: Can you add to you answer the influence of specific weight. Namely, if water would stay on top, it would just evaporate, but as it sinks into the oil (oil goes on top of water) the rapid volume change results in an explosion "ejecting" oil. Otherwise, I think this is the most complete answer.
Comment: @mikuszefski Thanks for the remark and edits. I did not keep all the edits, as my feeling is that pressure is the first to increase, thus producing the change in volume. My idea is that you need the pressure to move the molecules so that they will occupy more volume, if the enclosure will let them.
Comment: Pressure change leads to volume change; agreed.
Answer: Oil heats up faster than water because it has a lower specific heat capacity.
As it reaches past boiling point of water as the water is denser than oil so its at the bottom.
Then it turns into steam and the steam expands splashing the oil everywhere.
As for dropping water into already being  hot oil
its pretty much the same. Its interface determines the rate of heat flow.
Answer: Oil boils at a higher temperature than water which means that when water is poured into boiling oil it is heated to, and past, the boiling point very quickly.  Oil is also less dense than water meaning that the water will sink to the bottom of the pot.
Water at the bottom of the pot being heated very rapidly forms a gas at the bottom of the pot underneath all of the oil.  The gas takes up much more volume than the water previously did and also is now less dense than the oil and so it shoots up creating a fountain of oil and steam out of the pot.
This fountain creates a fine mist of the very hot oil, this greatly increased surface area coupled with the already hot oil causes it to ignite which then ignites surrounding droplets until the entire batch of oil that was displaced from the pot is a huge fireball.
http://en.wikipedia.org/wiki/Deep_frying
You can also find pretty cool videos on youtube about this exact thing
Answer: Shrapnel.
The oil is analogous to the container that holds the explosive (water-->steam) .
Answer: Yes, its pretty much the same. More precisely, its due to the difference in their temperature and due to vigorous transfer of thermal energy from hot oil to cold water where water instantly changes its state into vapour.
Answer: The water heats up and expands as it is falling through the oil, due to density. the water is covered up and expands into steam blowing the oil away. boom.
Answer: Due to abrupt  transference of heat energy from hot oil to cold water drop.
Comment: This really isn't much of an answer; it would be better if you could expand this to cover what heat transfer does (e.g., the rapid change indicates X).


Does $\tan x\cdot \cos x$ equal $\sin x$?

Question: Is it true that $\tan x\cdot \cos x = \sin x$? If I put $x=30$ in my calculator then I don't get the same answer as $\sin 30$, why is this? Don't the two cosines cancel out? I'm probably missing something really stupid here.
Comment: A properly functioning calculator used properly will return the same value for $\tan 30\cdot\cos 30$ as for $\sin 30$ regardless of whether it is set on degrees or radians or any other unit, except when the unit is so chosen that the number $30$ represents a right angle or other value for which the cosine is $0$. However, I said "used properly" and I've noticed students sometimes getting really confused about that and entering things like $\tan(30\sin30)$ instead of $\tan30\cdot\sin30$, etc.  Maybe some explicit report on the sequence of key strokes could shed some light on what's going on.
Comment: You might want to double-check that your calculator is on degrees. They both give sin(30), but only with degrees do you have sin(30)=1/2.
Comment: Have you inputted $\tan(30^\circ)\cos(30^\circ)$ or something that will give you $\tan(30\cos(30))$? Also this is not true for $x=(90^\circ$ plus multiples of $180^\circ$).
Comment: (But tanx*cosx=sinx, yeah. Assuming tanx is defined.)
Comment: It is possible only when $\cos x$ is non-zero
Comment: You need to double check the precedence rules used by you calculator to evaluate expressions.
Answer: By definition,
$$
\tan x=\frac{\sin x}{\cos x}
$$
but in order to give sense to this definition, the $\cos$ must be nonzero, i.e. $x\neq\frac{\pi}2+k\pi$. Hence $\tan$ is defined only for $x\in\Bbb R\setminus \{\frac{\pi}{2}+k\pi\}$. For these values you can multiply both sides for $\cos$, obtaining $\tan x\cos x=\sin x$.
But pay attention: this holds only for the values I wrote! Otherwise $\tan$ is not even defined, so it wouldn't make sense to consider the relation.
Now in your case, $x=30°$ is the same as $x=\pi/6$ in radiant and in this value the $\tan$ is defined. So the relation holds.
You must had a bad work with your calculator, that's all.
Answer: As tan(x)≡  Sin(x)/Cos(x), you are right in that Tan(x) * cos(x) ≡ Sin(x). This is by definition of the Tan function, which is defined as Sin(x) / Cos(x). If it helps consider the right angle triangle from the unit circle, where cos(x) = Hypotenuse / adjacent and Sin(x) = opposite / hypotenuse, so Tan(x) as equalling opposite / adjacent is easy to see by dividing one by the other since the hypotenuse will cancel in both.  However, it is worth remembering that for certain values, where x is either an odd multiple of 90 degrees or odd multiples of Pi/2 if dealing in radians, this simply does not work as Cos(x) = 0 ( it is easy enough to see that at 90 degrees, this leads to 1 = 0 which is obviously nonsensical).
However, it is easy enough to prove that since Sin(30) = 0.5 and Cos(30) = root(3) /2, then tan(30) = 1 / root(3). Multiplying this by cos(30) does in fact lead us to 0.5 again, so this is right here (luckily the normal rules of communativity apply here.) However, I can see how with approximation in the calculator it would not work. If you try using the exact answers this should be proven to be true.
Answer: Without doubt,
$$\tan30°\cdot\cos30°=\frac1{\sqrt3}\cdot\frac{\sqrt3}2=\frac12=\sin30°$$
$$0.57735026919\cdots\times0.86602540378\cdots=0.5$$


What is $f(n)$ in $NTIME(n)\subseteq DTIME(f(n))$ if $CIRCUITSAT$ is in $P$?

Question: If $CIRCUITSAT$ in $n$ variables and $m$ gates has an $O((nm)^c)$ algorithm for a fixed $c>0$ then $NTIME(n)\subseteq DTIME(O(f(n)))$ for large enough $f(n)$. What is the smallest $f(n)$ in $NTIME(n)\subseteq DTIME(O(f(n)))$?
Answer: I'm not 100% sure on this, but I believe that the best known bound on this comes from the construction used for the best known bound on creating oblivious Turing machines. See this Gödel's Lost Letter blog post on the relationship between circuit size and oblivious Turing machines, and in particular the "Open Problems" section.
Given an arbitrary deterministic Turing machine that runs in time $T(n)$, it is known how to construct an oblivious deterministic Turing machine that accepts the same language in time $O(T(n) \log T(n))$. I believe that this implies $\operatorname{NTIME}(t) \subseteq \operatorname{DTIME}(t^{2d} \log t)$, where $d$ is the CIRCUIT-SAT exponent from the question (the 2 coming from the fact that you wrote $(nm)^d$ instead of $(n + m)^d$). However, I have not verified the details myself.


What Type of Mortar do I need for a Glass Block Shower?

Question: I have a glass block shower that was not installed properly. I need to know the proper way to regrout. The mortar is disintegrating. I was told I need a water-resistant mortar and to add an agent to make sure it's waterproof. Does anyone know the proper way?
Comment: Are you going to start fresh or try and repair and reseal the existing mortar?
Comment: Glass Block Mortar is a common pre-mixed type that you will find at home stores.
Comment: "What type of *grout*..." - if anyone answers the title, @me, because I have no idea how, or with what, to *set* glass block.
Answer: Any fortified thin set will work. I have used colored grout with add mix several times for glass block shower walls. Once the mortar is cured I then seal it the same as any tile job. There are pre mixed glass block mixes it is usually white.


Can we have electronics with charge carriers OTHER than electrons?

Question: Ions perhaps? Or other elementary particles with charge?
Answer: Depending on your view, there is electronics with other charge carriers. It is commonplace to have semiconductor devices where the relevant carriers are holes!
Furthermore, batteries and electrolysis relies heavily on ions as charge carriers (but hardly count as electronics). I guess genuine electronics with ions will be difficult as charge carrier mobility will be much lower in solid state systems (and high carrier mobility is highly relevant for effective devices).
Furthermore, we are beginning to build electronics, where not the charge, but the spin carries the information ("spintronics"). Some spintronics devices are already in production, namely read-heads for hard disk drives based on the giant magnetoresistance.
Another topic in research is functional replacement for electronics based on optical signals. Signals in optical fibres are already amplified actively without transferring the signal to electrical current (by pumping a dotant, usually Erbium in telecommunication applications, in the fibre, that then emits photons by induced emission when the signal passes). There even are optical transistors.
Comment: You're right.  Batteries are not _electronic_.  "Electronic" usually applies to circuits that process or use electric, information-carrying _signals_.  Thus an old-fashioned flashlight with batteries and a switch and a light bulb would not be considered _electronic_, but a current-regulated LED flashlight would be _electronic_ because of signals that are internal to its power supply.
Answer: Can we have electronics with charge carriers OTHER than electrons?
Yes, see what Sebastian said above. And see the physicsworld article Taming light at the nanoscale:
"Look around, and you will probably see numerous electronic and optical gadgets, such as mobile phones, personal digital assistants, laptops, TVs and digital cameras. These may all do different things but they have one thing in common: in the electronic circuits that drive these devices, charged particles flow through components and impart power via what is known as the conduction current. But is the motion of charged particles the only current we have available? Those with a good memory for Maxwell's equations of electromagnetism will remember that in addition to the familiar electric field, E, there is also a displacement field, D..."
You can contrive "electronics" using displacement current rather than conduction current. And get this: displacement current doesn't necessarily involve charge carriers, because "it is not an electric current of moving charges, but a time-varying electric field". The article is to do with "taming light" because light involves a time-varying electric field, because light is in essence alternating displacement current. That's why we talk of vacuum impedance:
$$Z_0 = \frac{E}{H} = \mu_0 c_0 = \sqrt{\frac{\mu_0}{\varepsilon_0}} = \frac{1}{\varepsilon_0 c_0}$$
It isn't the same thing as impedance in a conduction-current A/C circuit, but it isn't totally unrelated.
Answer: You need something that can be conducted along the wire to power electronics; if you were to get protons, rather than spreading from atom to atom you'd just end up changing the element of the atom or splitting it. The closest thing that you can do other than add electrons is chemically charge it, as in replace the batteries.