Formula for rotational work

Question: I read online that rotational work is defined as
$$W =\int \tau \mathrm{d} \vartheta$$
which is not exactly the same as
$$W = \int \vec{F} \cdot \mathrm{d}\vec{r}$$
So i was wondering if it possible to give a little more general formula for rotational work that resembles the one with the dot product. If I consider a force not perpendicular to the axis of rotation, can I use the infinitesimal displacement vector $\mathrm{d} \vec{\vartheta}$ and write this?
$$\mathrm{d}\vec{r} = \mathrm{d}\vec{\vartheta} \times \vec{r}$$
Doing so would allow me to write
$$W = \int \vec{F} \cdot \mathrm{d}\vec{r} = \int \vec{F} \cdot (\mathrm{d}\vec{\vartheta} \times \vec{r}) = \int (\vec{r} \times \vec{F}) \cdot \mathrm{d}\vec{\vartheta} = \int \vec{\tau}\cdot \mathrm{d}\vec{\vartheta}$$
and keep a perfect symmetry with the other definition of work. Where is my mistake?
Comment: What makes you think you made a mistake? Especially if you realize that ${\rm d}\vec{\vartheta} = \vec{\omega} {\rm d}t$ just as ${\rm d}\vec{r} = \vec{v} {\rm d}t$. In the end you have $W = \int P {\rm d}t$ where $P=\vec{F}\cdot\vec{v} = \vec{\tau} \cdot \vec{\omega}$ is power.
Comment: @ja72 Well, online I didn't found this formula, only the one without the dot product and I found it very strange because of the symmetry with the non rotational case, so I thought that there might be some mistake in my reasoning.
Comment: The key world here is symmetry. Actually it is called duality usually in rigid body mechanics.  There is something [intriguing in this symmetry](https://physics.stackexchange.com/a/390753/392) between linear and rotational quantities. Some quantities in pairs represent [lines in space](https://physics.stackexchange.com/a/375222/392) (line of action, line of rotation, percussion axis) and the rules that govern them are identical. (See included link)
Comment: Also read [this answer](https://physics.stackexchange.com/a/387263/392) on angular momentum, to see that geometry (and symmetry) in mechanics.
Comment: @ja72 Thank you for the answer and the links.
Answer: It is easier to derive 3D power, and then assert that work is the time integral of power.
Consider a moving rigid body, with a force $\boldsymbol{F}$ applied and a torque $\boldsymbol{\tau}_C$ applied at the center of mass. The body is instantaneously rotating about some point such that the velocity of the center of mass is $\boldsymbol{v}_C = \boldsymbol{\omega} \times \boldsymbol{r}_C$. Additionally the equipollent torque at the rotation center is $\boldsymbol{\tau} = \boldsymbol{\tau}_C + \boldsymbol{r}_C \times \boldsymbol{F}$.
Let us look at power at the center of mass and at the center of rotation. The two should be identical because power should be coordinate invariant.
$$\require{cancel} \begin{aligned}
  P & =  \boldsymbol{F} \cdot \boldsymbol{v}_C + \boldsymbol{\tau}_C \cdot \boldsymbol{\omega} & &\mbox{at center of mass} \\ \hline
  P & =\boldsymbol{F} \cdot \cancelto{0}{\boldsymbol{v}} + \boldsymbol{\tau} \cdot \boldsymbol{\omega}=(\boldsymbol{\tau}_C + \boldsymbol{r}_C \times \boldsymbol{F}) \cdot \boldsymbol{\omega} & &\mbox{at rotation center} \\
 & =(\boldsymbol{r}_C \times \boldsymbol{\omega}) \cdot \boldsymbol{F} + \boldsymbol{\tau}_C \cdot \boldsymbol{\omega} = \boldsymbol{F} \cdot \boldsymbol{v}_C + \boldsymbol{\tau}_C \cdot \boldsymbol{\omega} & &\checkmark
\end{aligned} $$
So the rule for power (and hence work) is:
At any arbitrary location A, dot product the force with the linear velocity and the torque with rotational velocity to calculate power. Work is the time integral of power.
$$ P =  \boldsymbol{F} \cdot \boldsymbol{v}_A + \boldsymbol{\tau}_A \cdot \boldsymbol{\omega} $$
 $$ W = \int P {\rm d}t $$
Pick the center of rotation and $\boldsymbol{v}_A \rightarrow 0 $, or the line of action of the force and $\boldsymbol{\tau}_A \rightarrow 0$ and the above simplifies to just one inner product.

Formula for rotational work


Can I daisychain multiple Arduino Nanos to a single USB port (specialized purpose)

Question: I need to have several Nanos on one USB port. They will have separate power, so power constraints won't be a concern. I need them all to go through the same serial port. They will never get anything sent to them, and should never send data simultaneously. Each one is connected to a switch, and upon pressing the switch, will send an 8-digit serial number over serial. I want to have a VB.NET application which listens over this shared serial COM for numbers, and collects them all, displaying them in a history list. Can this work?
Comment: No, they can't all share one data line.  What you'll need to do is either connect all of the switches to one Arduino or connect all of the Arduinos to one "master" arduino which will communicate with the computer.
Comment: The single Master Arduino is what I'll go with. "Master" and "Slave" boards, reminds me of IDE drives lol
Answer: For a USB topology to operate one needs a USB controller which knows about all the different USB protocols necessary to communicate with all the different USB peripherals (this is why a USB controller is usually a fully capable computer) all connected through a USB hub.  It is unlikely a USB network could be created using only peripheral USB devices which were wired directly together.
To communicate between several Arduinos and a computer it would be much easier to use a serial bus made for multiple drops like RS485. There are many RS485 to USB converters available like this one for computers that do not have an RS485 port.


Values not coming in Dropdown in PowerBuilder 12.5.2

Question: I have recently migrated to PB 12.5 from PB 10.5. I am facing an issue now in PB 12.5 where i try to fetch the values in Drop down which is placed on a Data window. As of today i have below code in place where i first insertrow in Data window and then establish SQLCA connection. This used to work fine in PB 10.5 but it stopped working with PB 12.5. When i debug the code and i execute the statement for establishing SQLCA connection first then insertrow it works fine with PB 12.5 but not the other way round.
<code>dw_5.InsertRow(0)
dw_5.SetTransObject (SQLCA)
</code>
How i can resolve this issue ?
Answer: When you say 'values in a Drop down' my assumption is a drop down datawindow (dddw) column in a datawindow which itself is populated by another datawindow object which retrieves values from the database.
You need to establish the database connection prior to inserting the row.  This is how it should have been done in your v10.5 code.
Alternatively you can use the GetChild method on the dddw column in your dw_5, set the transaction object on the child datawindow, then issue a retrieve on the child dw prior to inserting the row in the parent dw (dw_5 in your example).


Can I take tax deductions for a second residence where my son lives?

Question: I own a small second residence where my disabled son lives. He is unable to pay any rent and probably never will. For income tax purposes, can I depreciate the house, deduct property taxes and anything else? I also pay for all utilities; are these deductible?
Comment: Are you claiming your son as a dependent on your tax return?
Comment: yes I am claiming my son as a dependent
Answer: Yes.  This would be considered your secondary residence and you can deduct mortgage expense and property taxes.   Since you don't draw income from the property, it would not be advisable to treat it as investment property where you can deduct other maintenance expenses and depreciate the house.


Is it possible to know the address of a cache miss?

Question: Whenever a cache miss occurs, is it possible to know the address of that missed cache line? Are there any hardware performance counters in modern processors that can provide such information?
Comment: MetallicPriest, you can start from simulating the cache hierarchy with vallgrind's tool cachegrind - http://valgrind.org/docs/manual/cg-manual.html
Comment: And there was project to profile data addresses from Pentium4 PEBS - http://www.lifl.fr/west/courses/cshp/doc/profguide/node10.html  = http://sourceforge.jp/projects/hardmeter + ADAPTOR
Comment: @PeterCordes - the PMU also provides the data address on recent implementations as part of it's "memory PEBS" events. It also tells you if the access was an L1 hit, LFB hit, whether it was locked, what the TLB behavior was, and lots of other goodies! This is exposed on Linux as part of `perf mem`.
Comment: You can of course get the address *of the instruction* that caused the cache miss, using perf counters.  So on Linux you can `perf record -e L1-dcache-loads ./a.out` and then `perf report -Mintel`.  Often you know what array an instruction is accessing, so in many cases this is enough.  (There are counters for other levels of cache, too.  Get `ocperf.py` and use `ocperf.py list` for the full set of supported HW counters).
Answer: Yes, on modern Intel hardware there are precise memory sampling events that track not only the address of the instruction, but the data address as well. These events also includes a great deal of other information, such as what level of the cache hierarchy the memory access was satisfied it, the total latency and so on.
You can use perf mem to sample this information and produces a report.
For example, the following program:
#include <stddef.h>

#define SIZE (100 * 1024 * 1024)

int p[SIZE] = {1};

void do_writes(volatile int *p) {
    for (size_t i = 0; i < SIZE; i += 5) {
        p[i] = 42;
    }
}

void do_reads(volatile int *p) {
    volatile int sink;
    for (size_t i = 0; i < SIZE; i += 5) {
        sink = p[i];
    }
}

int main(int argc, char **argv) {
    do_writes(p);
    do_reads(p);
}

compiled with:
g++  -g -O1 -march=native   perf-mem-test.cpp   -o perf-mem-test

and run with:
sudo perf mem record -U ./perf-mem-test && sudo perf mem report

Produces a report of memory accesses sorted by latency like this:

The Data Symbol column shows where address the load was targeting - most here show up as something like p+0xa0658b4 which means at an offset of 0xa0658b4 from the start of p which makes sense as the code is reading and writing p. The list is sorted by "local weight" which is the access latency in reference cycles1.
Note that the information recorded is only a sample of memory accesses: recording every miss would usually be way too much information. Furthermore, it only records loads with a latency of 30 cycles or more by default, but you can apparently tweak this with command line arguments.
If you're only interested in accesses that miss in all levels of cache, you're looking for the "Local RAM hit" lines2. Perhaps you can restrict your sampling to only cache misses - I'm pretty sure the Intel memory sampling stuff supports that, and I think you can tell perf mem to look at only misses.
Finally, note that here I'm using the -U argument after record which instructs perf mem to only record userspace events. By default it will include kernel events, which may or may not be useful for your. For the example program, there are many kernel events associated with copying the p array from the binary into writable process memory.
Keep in mind that I specifically arranged my program such that the global array p ended up in the initialized .data section (the binary is ~400 MB!), so that it shows up with the right symbol in the listing. The vast majority of the time your process is going to be accessing dynamically allocated or stack memory, which will just give you a raw address. Whether you can map this back to a meaningful object depends on if you track enough information to make that possible.

1 I think it's in reference cycles, but I could be wrong and the kernel may have already converted it to nanoseconds?
2 The "Local" and "hit" part here refer to the fact that we hit the RAM attached to the current core, i.e., we didn't have go to the RAM associated with another socket in a multi-socket NUMA configuration.
Comment: you should mention that PEBS = precise event-based sampling.  I didn't find a good URL about PEBS itself, just pages that mention it as something used by a specific profiler.
Comment: Oddly enough, I was just looking for a good link specific to PEBS memory profiling, but I didn't find one. The SDM covers it in detail of course.
Comment: @PeterCordes - I gave up trying to find a good link and just removed PEBS.
Comment: You missed a 2nd occurrence.  Just write "PEBS (precise event-based sampling)" the first time you use it.
Answer: If you want to know the exact virtual or physical address of every cache miss on a particular processor, that would be very hard and sometimes impossible. But you are more likely to be interested in expensive memory access patterns; those patterns that incur large latencies because they miss in one or more levels of the cache subsystem. Note that it is important to keep in mind that a cache miss on one processor might be a cache hit on another depending on design details of each processor and depending also on the operating system.
There are several ways to find such patterns, two are commonly used. One is to use a simulator such as gem5 or Sniper. Another is to use hardware performance events. Events that represent cache misses are available but they do not provide any details on why or where a miss occurred. However, using a profiler, you can approximately associate cache misses as reported by the corresponding hardware performance events with the instructions that caused them which in turn can be mapped back to locations in the source code using debug information. Examples of such profilers include Intel VTune Amplifier and AMD CodeXL. The results produced by simulators and profilers may not be accurate and so you have to be careful when interpreting them.


how to establish a connection between an arduino and a web server?

Question: I want to establish a connection between my arduino mega ( which is connected to an ethernet shield so internet access is available) to a web server. Any idea how the code should be?
I searched for it but all I found was a local host connection establishment.
Thanks in advance.
Comment: None of the examples in the IDE help you?
Comment: That's the one thing i forgot to check. I'll get to it right now.
Answer: The answer of this was already existing in the arduino examples which I forgot to check at first. Thanks Majenko for making me notice.
Comment: @jsotola - actually this is an answer, as it resolves the question.  When a solution is posted as a comment, summarizing it in an answer is permitted; short of closing the question (as subsequently happened here) it's typically the only way the system can be convinced to consider the issue resolved and avoid having it bubble back up every few months to annoy everyone.


How can I reassign a comment in Google Docs?

Question: Is it possible to reassign a comment to another person? For example, to assign the comment to a person who commented on the comment thread as well.
Comment: But then I am losing the entire comment history.
Answer: You can achieve reassigning a task from an existing comment thread by adding a new comment starting with +[email address] of who you want to assign/reassign the item to.
As you fill in the email address of the designee, Google Docs will show a checkbox prompting you to "reassign" the comment/task.
Below is an example screenshot of Google Docs prompting you to assign/reassign a task.
Comment: for some reason I do not see this checkbox after entering such comment
Comment: I tested the feature on November 20, 2018 and can confirm this description still applies.  I updated original answer with a screenshot
Answer: You can only assign a comment thread to a person by mentioning them in the comment text using the +[email] notation (tip: you can use the @ sign during typing and it will be replaced with the + sign). When you do so, on the bottom of the comment Window you will see a checkbox appear to assign the thread to that person (before you save).
If you mention multiple people in the comment, the checkbox will be completed with a dropdown where you can select the person to whom you want to assign the thread, chosen from the ones you mention in the comment. A thread can only be assigned to one person at a time.
This works both in a new comment (to assign) or in a reaction on an already assigned thread (to reassign). You don't need to be the assignee in order to reassign the thread, you just need to reply.
However, if the initial message was not assigned, there is no way to assign the thread afterwards. Not even by editing the original message. This also makes it so that you cannot assign threads linked to suggestions, since the initial message (the suggestion) is not assigned.


Is Skype available for the Motorola Xoom?

Question: Is Skype available for the Motorola Xoom?
Comment: See alist of the various available Android Skype versions and where to get them from on this previous question http://android.stackexchange.com/questions/9664/can-i-install-skype-on-my-xperia note that because a lot of phone networks don't like Skype, it may be your network or country that stops you seeing it in the Market, not just your phone type.
Comment: Please, give some more details. A quick guess... If Skype is unavailable in Market, then probably you need to uncheck "Settings->Application->Fast boot" option.
Comment: I just want to use Skype on Motorola Xoom
Comment: I just want to help you. Could you please answer my questions above? I mean, provide some more details.
Answer: I recently (two nights ago) installed Skype on my Xoom, and it appears to work fine, with chat, video, and audio calling available.
This was on the UK market, Wifi version (so no provider issues), stock 3.2.
This is the market item I have installed.
Answer: Yeah, it is compatible, but depending on which country you're in and how tight the laws are there, you may not be able to download Skype. However, there is an app called Market Helper which is for ROOTED devices which allows you to fake your location and download the app.


What is the Data value of plus sign in Path

Question: How to draw plus and minus signs in using data property in Path object.
This is my triangle path object. I need to change it to plus symbol.
<Path x:Name="trianglePath"  Data="M 0 8 H 12 V 15 Z"/>

Answer: Here, I've created a plus and minus sign which is 10 x 10 pixels using XAML path markup syntax:
<Path Margin="10" Stroke="White" Data="M0,5 H10 M5,5 V10Z"  StrokeThickness="2" Height="10" Width="10" />

<Path Margin="10" Stroke="White" Data="M0,5 H10"  StrokeThickness="2" Height="10" Width="10" />

When experimenting with designing your path drawing, it's helpful to set the path element's height & width first.  To better understand  XAML path markup syntax, see MSDN.
Comment: For plus it should be "M0,5 H10 M5,0 V10" i suppose.
Answer: You might find it easier if you draw them out on a piece of graph paper and then label the vertices with the values needed to reach it from the previous one.
Then copy this into your code.


Can Remote Site Settings whitelist IP addresses instead of/in addition to domains?

Question: I'm just wondering: We make a number of callouts from Salesforce to different APIs, and so obviously we need to whitelist their respective domains with Remote Site Settings.
However, I'm wondering whether it is possible to whitelist specific IP addresses in this way, in order to protect against DNS spoofing that could make calls to https://api.domain.com go to a malicious IP address instead of the real one?
Answer: Yes you can put IP addresses in there as well. We've been doing this for years.
Do note that salesforce does a 1:1 comparison between the domain name used in the callout and the Remote Site Setting. So you will have to use the IP address in the callout as well (and not the literal domain name).


AFHTTPRequestOperation returns cached SOAP WSDL file, testing in browser does not

Question: I have been working on this issue for hours now, and I cannot figure it out.
My server creates a WSDL file which a user can update with new functions and the WSDL file will update to reflect those changes. I am using an AFHTTPRequestOperation with GET to grab that file so I can check which functions exist in the file.
For some reason, after a user updates the file and regenerates it, the AFHTTPRequestOperation is still seeing the old version (cached?), but if I view that same URL in my browser, not logged into my site or anything, it shows the new version of the file. Even trying wget grabs the new copy.
I am making sure to use NSURLRequestReloadIgnoringLocalAndRemoteCacheData on my NSMutableURLRequest but it doesn't seem to matter:
// Setup the connection
NSString *wsdlURL = [NSString stringWithFormat:@"%@?WSDL", site.soapURL];
NSURL *serviceUrl = [NSURL URLWithString:wsdlURL];
NSMutableURLRequest *serviceRequest2 = [NSMutableURLRequest requestWithURL:serviceUrl cachePolicy:NSURLRequestReloadIgnoringLocalAndRemoteCacheData timeoutInterval:60.0];
[serviceRequest2 setHTTPMethod:@"GET"];

// Create the operation
AFHTTPRequestOperation *operation2 = [[AFHTTPRequestOperation alloc] initWithRequest:serviceRequest2];
[operation2 setCompletionBlockWithSuccess:^(AFHTTPRequestOperation *operation2, id responseObject2) {

    // Convert data to string
    NSString *wsdlStr = [[NSString alloc] initWithData:(NSData *)responseObject2 encoding:NSUTF8StringEncoding];

} failure:^(AFHTTPRequestOperation *operation2, NSError *error) {
    failure(error);
}];
[operation2 start];

Does anyone know why it would be getting the old copy of the file? And the browser shows the new one?
Answer: I realized I needed to add the following to the request:
[serviceRequest2 setValue:@"no-cache" forHTTPHeaderField:@"Cache-Control"];


how to change the existing bundle id from itunes connect with new bundle identifier from project

Question: Changed project name before submitting to AppStore. So that changed bundle identifier too in the project. In iTunes connect it shows old bundle id how do i change it with a new one.
Answer: how you create a new AppID without deleting the existing one?
Answer: Just make another AppId (that will reflect your new bundle id) and set it to your provisioning profiles (dev and distr). Then refresh the profiles in xcode and try signing your app with the new profiles.


Lagrangian Torus of a symplectic manifold

Question: Suppose $(M,\omega)$ is a $2n$-dimensional symplectic manifold. Consider the $n$-torus $\mathbb{T}^n=\mathbb{R}^n/\mathbb{Z}^n.$ Then $\mathbb{T}^n$ is a Lagrangian submanifold of the symplectic $2n$-torus $\mathbb{T}^{2n}$, equipped with the unique symplectic form that pulls back to the canonical symplectic form on $\mathbb{R} ^{2n}$. Now, how does it follow that there exists a Lagrangian submanifold of $M$ that is diffeomorphic to $\mathbb{T}^{n}$?
Comment: How is $M$ related to the torus? Are you asking if *any* symplectic $2n$-manifold admits such a submanifold?
Answer: The fact that $\mathbb T^n$ is a Lagrangian submanifold of $\mathbb T^{2n}$ plays no role. Indeed, by Darboux's theorem, for any symplectic manifold $(M^{2n}, \omega)$ and for any $x\in M$, there is $U_0 \subset \mathbb R^{2n}$ and a local coordinates chart $\phi : U_0 \to U$ so that $\phi^* \omega = \omega_{std}$ and $x\in U$, where $\omega_{std}$ is the standard symplectic structure on $\mathbb R^{2n}$. Since it is easy to find Lagnrangian in $(U_0, \omega_{std})$ diffeomorphic to $\mathbb T^n$: choose $p =(p_1, \cdots, p_n)\in U_0$ and $r_1, \cdots, r_n >0$ small enough, then
$$ \mathbb S^1 (p_1) \times \cdots \times \mathbb S^1 (p_n) $$
is such an example.
Of course this also shows the existence of infinitely many Lagrangian tori on any symplectic manifold.


Extruder clogs with HIPS

Question: I've got a Prusa i3 MK3. I have printed with PLA, PETG and tried HIPS. Haven't had any clogs with PLA and PETG, but with HIPS I've got a weird problem.
My first three test prints in HIPS went fine, but then I got a very bad clog (required total disassembly of the extruder) twice. And every time, it was at the same moment during a print. The object I was printing was a hollow cylinder. The walls were about 5 mm thick, getting thinner near the top edge. At the moment the walls started getting thinner, the problems started.
I've read that HIPS can clog if the filament moves too slow through the hotend. At the moment the clog occurred, the printer was printing a very narrow part, and the extruder had to move around a lot. Is it possible that, at that moment, the filament moves too slow and the problems starts? I have also printed two copies of the object in a single run, and then the problem didn't occur.
I hope my explanation makes sense, but here's what it comes down to: Does HIPS clog easily when the filament moves too slow, and if it does, what can I do to solve this?
Answer: This has been sitting for a long time without an answer, so let me answer with an experience I've had with PETG rather than HIPS.
PETG seems to be a relatively soft plastic.  It isn't soft like TPU, but it is softer than PLA or ABS.  The HIPS filament (which I have but haven't used) appears to also be softer, so it is possible that my PETG problem could relate to your HIPS problem.
I was printing and re-printing an object with PETG that had worked fine with PLA.  Three times in a row, I got a filament jam in about the same place.
The problem was that the filament was retracting, returning, retracting, and returning many times within a very small amount of extruded plastic.  My extruder was set for high pressure between the drive roller and the idler.  When the filament went back and forth through the extruder, it flattened enough that it would jam from being too wide to fit through the next stage (in my case, a Bowden tube).
When I reduced the compression of the filament in the extruder, the problem stopped.  I also reduced the retraction distance, and increased the minimum travel before the slicer would do a retract.  Both were intended to reduce the number of times any single bit of filament would pass through the rollers.
Answer: HIPS does better with a wider nozzle; try a 1mm nozzle.

Extruder clogs with HIPS


Nexus 5x - No one can hear me on the phone

Question: I've had this phone since November and it's still in great condition. From the start though call quality hasn't been amazing, friends often tell me that I'm very quite (I'm not actually speaking quietly). In the last few days though absolutely no one can hear me unless I have my headphones plugged in but even then it's not ALL the time that it works. The headphones don't have a mic so it's nothing to do with them I imagine. I've made a few videos to check that it was still recording sound and it works perfectly still. It's really left me baffled. While the phone is still in warranty I really do want to avoid sending it to LG as I don't have a backup phone.
Does anyone have any idea what could be causing this? I'm running stock vanilla 6.0.1  I don't have a case on the phone (I've seen a few people complain their case covers up their mic), neither I've muted the call (I've tapped the mute button a few times to make sure).
Comment: I had a similar problem which I eventually traced to a bug in an app that routed calls over WiFi when available.  It dropped the volume whether on WiFi or not.  If you have such an app, try disabling it for a while as a test.
Answer: I had this same issue with my HTC One. It turned out that the background noise cancellation software build into the phone canceled out too much (thus cancelling out my voice). This especially happened when it was windy outside.
That being said, I haven't heard of this being an issue with the Nexus 5x. I would start with contacting Google support.


How could the varying multiple colorful skin colors of a Fantasy race be explained?

Question: In my Fantasy story I have decided to integrate gnomes which are about 2ft tall and have human intelligence, but most notably come in a variety of skin colors and hair colors. You have gnomes with light blue hair/skin, subtle red skin/hair, purple hair/skin and other colors which don't don't exactly neon or superficial looking. My influence of this was seeing how colorful tropical birds and poison dart frogs are, and seeing how this natural vibrant colors would work on a fairly human creature. I thought of multiple ways to explain the variety of vibrant colors, such as the gnomes are poisonous or they come from a very colorful biome (maybe a coral reef type place on land?) but this wouldn't explain why they come in a variety of colors instead of one. I was also thinking the gnomes could dye their skin to show which tribes they come from, but I wanted to see other people expand on these ideas or come up with more interesting ones. Also note that magic does exist but in a much weaker and sometimes undependable form.
Comment: Charles Darwin, [*The Descent of Man, and Selection in Relation to Sex*](https://en.wikipedia.org/wiki/The_Descent_of_Man,_and_Selection_in_Relation_to_Sex) (1871). Sexual selection is a very powerful force of beautification. Just make sure that the ancestors of the gnomes had good color vision.
Answer: Look at humans; hair color and eye color vary among the population, while having little to no direct effect on fitness. Different eye colors aren't much selected against, so evolution doesn't stop them from happening.
So you don't need a grand reason for the gnome colors. Like hair color and eye color, just random variation in the population can explain it.
If you want a more specific reason, perhaps the gnomes long tended to choose unusually-colored gnomes as mates. Over time this could result in sexual selection like the peacock's tail, only instead of a large tail, the selected trait is having random and bright coloration that's different from other gnomes.
Comment: While generally true, albinoism and vitiligo do affect health. If these fantasy races have entirely different skin pallete tones (not from feathers or fur) it may imply they do not produce melanin, or if they lack rosy pink skin types it could imply their blood isn't red, and their blush wouldn't be pinkish. They may not suffer the same skin or blood diseases.
Answer: Color evolves for a few reasons.
Camoflauge is one obvious one. A being that lives in a background of a particular sort of color will have a huge advantage if they blend in. Perhaps gnomes live in a very colorful area.
Another reason is attraction of mates. Peacock feathers and baboon rumps are two examples. Perhaps they are more colorful at some point in their reproductive process because "blue-and-silver-armed guys get all the girls."
Another reason is identification especially at a distance. Baby gnomes can spot momma gnome by her distinguishing color pattern, and know to go to her and not the other gnomes who will not feed them. The boss gnome has just this particular pattern so you can spot him coming.
Another reason is as a marker of age. Maybe very young gnomes have one color, young adults another, middle aged another, and old another. Think silver-back gorilla or the fledgling colors of many birds. Knowing that this lady gnome is a good healthy pink color may mean she is just the right age to ask out for a cup of whatever gnomes like to drink. But if she starts to get those orange streaks, then she is the one to ask for sage family advice from an elder.
Another reason is that some animals allow themselves to be (or cannot avoid being) colonized by microscopic life. Fungus in the fur, bacteria growing under the nails, etc. As Sid the Sloth said, when he migrates south and the fungus in his fur dries out, he starts to look pretty sharp. Maybe gnomes allow such colonization because it makes them taste really terrible to predators. Or maybe they can't avoid it in the place they live.
Some animals get color from the things they eat. Flamingos that don't eat their usual food can be white. Maybe the food gnomes eat is multi-colored. Or different colors in different regions. Or during different times of the year.
Answer: They use structural coloration.
Gnomes, like squids, use small structures to give them their vivid colours, ones that diffract light in a variable way.
As they age, their ability to change camouflage tends to weaken, and so most fixate on a particular colour when older.


Is there any reason to carry 700cx23-32mm inner tubes as spares for 25mm tires?

Question: If I know that when I need a spare inner tube, I'll need a
700c x 25mm
inner tube, what would be the point of buying
700c x 23-32mm
inner tubes?
Related

Pros and cons of using 20-25mm inner tube in a 32mm tire?
How much can a 700x23 inner tube stretch?
Inner tube kink
Answer: There can be a reason: you have several bikes with tires in that range and one set of roadside repairs tools. Having a tube that can take a wide range of widths allows you to have one spare tube in your kit that will work with several bikes. Note that this reasoning is also true if you want to simplify the spare parts management at home, have several bikes, and be able to use the same spares with as many bikes as possible.
Otherwise, the answer to the question might not be in the intrinsic characteristic of the tube, but to commercial considerations (=why is such product on the market).
In the comments, there's a reference over an entry-level Decathlon tube. This product is a low cost proposition (I don't mean it the bad way), meant to an audience that is not primarily interested in performance, but in a price point. Decathlon might want to sell such tube instead 2 references with a 5mm range from commercial reasons: it allows them to order/manufacture larger quantities of the same item (economies of scale), and having less references also simplifies inventory management, which contributes to meeting the price point.
On the other side of the spectrum, there are also TPU tubes that offer that range. First, high-end manufacturers are also interested in simplifying inventory management and in economies of scale, and second the benefit should be noticeable. I see for example that a 23-32 TPU tube weights 35g, which is ridiculously light. They may make a version that would be rated for 23-28 tires, but if it weights 34g instead of 35g, it may just not be worth the hassle of keeping 2 product sizes.
Now if weight or performance is your concern, the question should rather be focused on the material the tube is made from, rather than the range of size it is rated for, as the two are also linked.
Comment: Re: "I don't mean it the bad way" Thanks for stressing this. All too often in cycling (as elsewhere) uncritical folks will use "cheap" to signal "of poor quality", which only leads to gratuitously dear products. That said, 23-32mm is not exclusive to  budget-priced or generic products of unknown provenance. Pirelli, for one, also produces such an inner tube.
Answer: Actually, I am not sure there is such a thing as a 23-32mm inner tube. That is an immense size range. 23mm tires have much less internal volume than 32s. If you told someone from the era when 23mm was the accepted standard that people were contemplating 32mm tires on road bikes, and on aerodynamic wheels to boot, they would either laugh, or cry, or laugh and then cry.
On a cursory Google search, I saw one listing for 18-23mm tubes. That's not a huge difference, and I bet butyl for a narrower tube can stretch. In any case, almost nobody makes tires under 23mm anymore - I have a feeling that 23 is soon to become a casualty of the move to wider rims. I've seen tubes rated for 25-28mm or so. I used a latex tube with that size rating in a 23mm tube, and it was an acceptable fit, and I experienced no problems.
I see one Tubolito tube rated for 18-28mm tires. That's a TPU tube. It may be fitted for a very narrow tire and still be able to stretch to a 28mm tire. I have no inside knowledge. It seems like bad practice if they really meant 25-28mm, only we'll just list narrower sizes since who even rides those anymore.
Otherwise, I've seen listings for tubes for 28-32mm tires, which seems like a plausible range.
25mm tires are not very wide at all. If you had a tube that could expand out to 32mm, it would probably be too wide to fit into a 25mm tire. I wouldn't feel comfortable using it, anyway.
Conversely, I have said that standard butyl tubes for 23mm tires have been used in cyclocross tires in the past, and it was fairly common practice. Yes, it exceeds the tube rating, but it seems that in practice it was ok for a few races - with the caveat that I wouldn't do this to light butyl or latex tubes.
Comment: Partly regarding of @Criggie's point there's a non-technical factor:the rareness of 18mm means a specialist product, probably for a weight-conscious rider, but a small amount of inherent stretch means it's OK up to 23. A tube thick enough to stretch to 32 but still thin enough (when new) to fit 23 covers the vast majority of road bikes. That means a non-specialist shop can cover more uses with one product line
Comment: Re: "I am not sure there is such a thing as a 23-32mm inner tube." Here is one https://www.decathlon.com/products/presta-valve-inner-tube-700-x-23-32-48-mm that's sold worldwide.
Comment: @Criggie Maxxis makes an "ultralight" 33-50mm tube, that's a 51% increase. I've used them in 42mm tires.
Comment: @oscu0 fascinating - clearly "percentage increase" isn't a linear metric.   Perhaps it's exponential ?
Comment: Re: "If you had a tube that could expand out to 32mm, it would probably be too wide to fit into a 25mm tire," well, that's exactly my question!
Comment: It's quite a percentage increase - 18mm to 23mm is 28% increase, whereas 23 to 32 is a 39% increase.
Answer: Most tubes are sold in compatible ranges rather than specific "one-size" configurations, I guess that would make product portfolios a mess since many brands even offer multiple valve configurations and you have 3 different lengths for Presta valves, a "light" model, latex tubes, extra puncture protection, etc... tires got wider over the years and the cycling community was never running just "one size" for a long time, so you always needed some flexibility in tube size, that's not just the recent trend of running 28-30 mm on many full-road configurations.
So, you should be fine with a 23-32 mm offering for your 25 mm tires. I run 20-25mm-specified tubes on 25 mm tires for years and had no problems except unavoidable punctures.
These "ranges" are a calculated and tested tolerance in which the tube is stretched out flush on the lower end but also not stretched beyond the material's capabilities, so safe to ride. Just try inflating an old tube without tire casing and see how large it gets before it finally explodes.
Just don't exceed these ranges and fit something that doesn't even include your tire size, maybe except from a 23-mm spare tube as a lifesaver on big ride (but I would back off from something too large because it might not sit well well and won't last too long without puncturing, anyway)


interpretation of the transition probability of a brownian motion in terms of the Wiener measure

Question: Let $W(t)$ be a standard brownian motion in $E \triangleq \mathbb{R}^d$.
The transition probability from a state $x \in E$ at time $t$ to a state $y \in E$ at time $T$ is
$$
p(x,t;y,T) = \frac{1}{\sqrt{2 \pi (T-t)}^d} \exp \left ( -\frac{1}{2} \frac{\|x-y \|^2}{T-t}\right ).
$$
Using the Chapman-Kolmogorov equation, it is clear that for all $n \geq 0$ and for all finite sequence of states $x_0 = x, x_1, ... , x_n, x_{n+1} = y$ and
$t_0 = t < t_1 < ... < t_n < t_{n+1} = T$, we have
$$
p(x,t;y,T) = \int_{E^n} \frac{1}{\sqrt{2 \pi}^{nd}} \exp \left ( -\frac{1}{2} \sum_{i=0}^{n} \frac{\|x_{i+1}-x_i \|^2}{t_{i+1}-t_i}\right ) \prod_{i=1}^n \frac{d x_i}{\sqrt{t_{i+1}-t_i}^d}.
$$
I am not so sure that the limit as $n \to \infty$ makes sense in the right hand side above but I believe that it can be interpreted in terms of the Wiener measure on $\mathcal{C}([0,\infty);E)$
and
$$
C(x,t;y,T)
\triangleq
\{ \omega \in \mathcal{C}([0,\infty);E) \: | \:  w(t) = x, \: w(T) = y \}.
$$
(if no mistake) how to interpret
$p(x,t;y,T)$ in terms of $\mu$ and $C(x,t;y,T))$?
Comment: That would be a better question for Math.SE.  But you are asking about $P(\{B_t = x\} \cap \{B_T = y\})$.  The random variable $B_t$ has a nondegenerate Gaussian distribution, which is a continuous distribution, so $P(B_t = x)=0$ for any $x$.
Comment: This isn't really correct.  Your set $C(x,t;y,T)$ has Wiener measure zero.  The "transition probability" is really a probability density and needs to be understood as such.
Comment: Thank you Nate, could you help me to show that  $C(x,t;y,T)$ has Wiener measure zero?
Answer: I have find in [equation 1.1.51, page 24,Chaichian M, Demichev A. Path integrals in physics, vol I : stochastic processes and quantum mechanics. Bristol (Philadelphia): Institute of Physics Publishing; 2001] that
when $N$ goes to $\infty$, then
$$
\lim_{\Delta t \to 0,\\ N \to \infty}
\exp \left ( -\frac{1}{2} \sum_{i=1}^N \frac{(x_i-x_{i-1})^2}{t_i-t_{i-1}}\right ) \prod_{i=1}^N \frac{d x_i}{\sqrt{2 \pi (t_i -t_{i-1})}}
=\\ ``\exp \left ( -\frac{1}{2} \int_0^t |\dot{x}(s)|^2 d s \right ) \prod_{\tau=0}^t \frac{d x(\tau)}{\sqrt{2 \pi d \tau}}"
$$
thus, if $A_y$ is a non-empty open set containing $y$,
$$
\mathbb{P} (x(T) \in A_y | x(t) = x) = \int_{A_y} p(x,t;y,T) d y\\
= "\int_{C(x,t;A_y,T)} \int_{E^\infty}\exp \left ( -\frac{1}{2} \int_0^t |\dot{x}(s)|^2 d s \right ) \prod_{\tau=0}^t \frac{d x(\tau)}{\sqrt{2 \pi d \tau}}"
$$
Here we don't really know what's inside the integral but, if no mistake, what should be correct is to write
$$
\mathbb{P} (x(T) \in A_y | x(t) = x) = \mu (C(x,t;A_y,T)).
$$


Call JavaScript function from workflow

Question: I want to call a JavaScript function from a workflow. I want to create a SharePoint Designer workflow with a pause. How do I call JavaScript functions from a workflow?
Comment: which workflow you are using? Designer workflow/ custom workflow using VS/ Third party workflow ?
Answer: Calling a JavaScript function is not supported by any kind of workflow manager which means that you cannot call your java scripts functions in workflow. Now if  you want to perform something in list, you have an option of using Web Service. So you can research more on web service instead of calling java script
Answer: You can not call JavaScript function but you can call web service from SharePoint workflow.
Working with Web Services in SharePoint 2013 Workflows using SharePoint Designer 2013
Comment: Dipongor is correct. Workflows are running server side. On a .net environment Javascript functions can only be run on the client side.
So, no, it is not possible to call a javascript from a workflow.

Call JavaScript function from workflow


Why didn't Shirohige rescue Ace when he was still in Impel Down

Question: The news of Ace capture is quite long time before the execution. And surely it will be much easier to save Ace when he was still in Impel Down (or maybe Enies Lobby). Is it because Shirohige is to far away? Can't he ask one of his subordinate or his alliance to save Ace? Where exactly was he at that moment?
Answer: Good question and a bit difficult to answer. I think the following things might have influenced White Beard to not save Ace in Impel Down:

The whole Whitebeard crew, including alliance partners, are said to be in New World, not in Grandline. And to come to Marineford, the only way is through Fishmen Island, and mobilizing such large pirate group does take time.
As we now know, the weather of New World is too unpredictable to travel quickly. Although it is not known whether Whitebeard was far away, but weather must have affected his travel time significantly.
Ace was 2 division commander of Whitebeard pirates. So if such a strong character can be captured, then I don't think Whitebeard would risk any more of his family to intercept/rescue Ace in Impel Down or Enies Lobby.
Reaching Impel Down/ Enies Lobby is considered to be difficult as it has natural protection in the form of circular waves which are used exclusively by marine only. Marineford is the remaining area where one can reach easily without going through the circular waves.
Also it is not known but as Kaido tried to block movement of Shanks, a marines tried to stop Whitebeard, so there must be other factors which tried to stop Whitebeard from moving, which stalled Whitebeard from coming quickly.
If he would have been able to save Ace earlier, then there won't be any fight and Ace would be alive right now. And that's not how Oda imagined it to be. ;)
Comment: 1. any source that say whole White beard crew including alliance partners are in New World? 3. how come whitebeard wouldn't risk any more of his family if after that he attack marine HQ with his full crew? and I don't understand your fifth point
Comment: well cant think of any particular source, but some dialogues come to mind. 1- some marine says that all new wold pirates came to support whitebeard just bore whitebeard's entry (also point 5). 3. i meant here that if 2nd division commander can be caught then anyother person less powerful would be able to have any impact. 5. Marines send warships to stop whitebeard from moving in new world. so he must have fought some marines before coming to save ace which took some time so he couldn't come early to save him.
Answer: My reasons would be,

Impel Down is surrounded by Sea Kings, they may deal with them easily but they still will pose a distraction. Their ships are not layered with Kairoseki, hence the sea kings will attack them. Someone has to wait outside to protect the ships against their countless numbers.
Straw Hat Luffy's physical strength is comparable to an average Division Commander (if not more), and he had to use Second Gear for the 4 Demon Guards (Awakened Zoan). If I were Whitebeard, I wouldn't attack such powerful Devil fruit users under such extreme conditions.
Imper Down's chief warden Magellan is Doku Doku no Mi Devil fruit user, a powerful fruit in any's hands. Obviously, no one would want to fight someone who can produce a,

mixture of poisons whose antidote hasn't been created.
more powerful version of poison, "Kinjite", which forms the "Venom Demon: Hell's Judgment".

Impel Down is the Great Underwater Prison in the middle of the Calm Belt, build to keep most dangerous criminals and pirates. No one in their right mind would try to take chances with this place (my opinion: Straw Hat Luffy doesn't have a right mind).
Comment: magellan's poison's antidote was there with Ivankov as he saved luffy . not the red one though.
Comment: @Sp0T that was not an antidote, [Emporio Ivankov](http://onepiece.wikia.com/wiki/Emporio_Ivankov) used his [devil fruit](http://onepiece.wikia.com/wiki/Horu_Horu_no_Mi)'s ability "Emporio Chiyu Hormone" to release his body's immune system's full potential, but the chance of survival is mostly based upon the individual's will to live.
Comment: Shiryu did have an antidote though. He saved the Blackbeard Pirates with it.
Comment: @PeterRaeves Only for [Hydra](http://onepiece.wikia.com/wiki/Doku_Doku_no_Mi), Luffy faced all his poison attacks while fighting Megallen, ;)


Has anyone found logical error or inconsistencies in the writings of Hegel in the book Phenomenology of the Spirit?

Question: Has anyone found logical error or inconsistencies in the writings of Hegel in the book Phenomenology of the Spirit? Since so few people understand it perfectly, you would assume even the writer himself could have made some kind of error during the writing of the book. Did anyone ever find out any inconsistencies or error in his book?
Comment: Welcome. It seems that I am among the many who do not understand it perfectly; e.g. I have always wondered how he managed to take phrenology seriously and to devote some pages to it. And in general I think that dialectics is nothing more than claiming to be right because you are contradicting yourself..
Comment: The method consists of a narrative building up through stages with stipulations being made at each stage and the conclusion building the foundation of all previous claims while being their natural outcome at the same time. The point is not whether he made mistakes, but why he wrote it the way he did and whether his means to do so are deficient. This approach, ie. that the means of description must be adequate to the object or else the object will be whatever your means allow it to be, is quite antithetical to core principles of analytic philosophy.
Comment: Nobody understands it perfectly. Phenomenology is valuable for offering ideas and viewpoints, often obscurely yet expressively, it does not offer a problem to solve or criteria by which the solution is to be judged. It is a guided trip towards Hegel's worldview from the ones received. With a style like that what is error, and how is one to distinguish between lack of understanding and error? It is as Wittgenstein said about private language, "*whatever is going to seem right to him is right. And that only means that here we can't talk about 'right'*". We can take what helps and drop the rest.
Answer: Kierkegaard once said that he couldn't understand most of Hegel, but he comforted himself that neither did Hegel.
It's pretty easy to make fun of the obscurities in Hegel or Heidegger or many other Continental philosophers. But it may be misplaced to ask if he "made errors." Anecdotally, he is said to have predicted that there could not be a planet between Mars and Jupiter, but many argue his meaning here was misunderstood. And he famously asked if it was possible that animal species evolved out of one another, but then added a footnote saying that was unlikely.
Another "error" attributed to him by leftists is his implication that the development of history reached a high point in the Prussian state, though once again this was probably not his meaning. He is often criticized for the mystifying idealism of "the real is the rational and the rational is the real." But this, in my view, is quite defensible if translated as the "rational becomes the actual and the actual the rational," with the development of computer software-hardware as a good example.
Generally, modern philosophers would simply condemn him for ill-defined metaphysical concepts like Geist and pronouncements that, without any standard of falsifiability, are meaningless or "not even wrong" as Pauli once put it. Many find his whole project of a totalizing rational system overweening and a dangerous precedent for totalitarian politics, but totalitarianism gets along just fine without Hegel.
As for "inconsistencies," Hegel simply isn't operating by the traditional or modern logical standards, which actually is a great part of his value. He was quite familiar with Aristotle's logic, of course, and developed his own dialectical logic in stupefying detail. This dialectical logic jettisons principles of contradiction and accepts mutual contradictions as equally valid prior to their resolution or Aufhebung into some new order of resolution.
Anyway, the short answer to your question is that many philosophers think everything in Hegel is an error! Here is the pertinent quote from Russell:
"Hegel thought that, if enough was known about a thing to distinguish it from all other things , then all its properties could be inferred by logic. This was a mistake, and from this mistake arose the whole edifice of his system. This illustrates an important truth, namely, that the worse your logic, the more interesting the consequences."
Comment: "*this, in my view, is quite defensible if translated as "the rational becomes the actual and the actual the rational"*".Your proposed translation would distort Hegel's proposition. In *Elements of the Philosophy of Right* Hegel employs the verb "to be" (sein, conjugated *ist*) rather than "to become" (werden, conj. *wird*). Hegel's choice of verb is consistent with chapter VI, section B of *Phenomenology*, where the German text reads "*Was nicht vernünftig ist, hat keine Wahrheit, oder was nicht begriffen ist, ist nicht*", therewith reinforcing his assertion that "the rational *is* the real".


Bialetti Moka Express Pot

Question:
Hi all! I am a new owner of a Bialetti Moka Express Pot! I have only had this little guy for maybe a month, and I am noticing that the water chamber is starting to look like this. Does anyone have any advice on fixing this issue or what I should be doing differently?
Comment: Have you tried cleaning it? If so, what did you use?
Answer: This may be an anecdotal answer, but it's coming from a friend that really cares that their aluminium moka pot stays in a prime condition as long as possible:
If you want to minimize visual changes in your moka pot, make sure to rinse it (do not use soap) right after use, wipe it with a dry cloth afterwards, and do not reassemble it until it's dry (as it will trap the remaining moisture in the chamber which causes the aluminium to oxidise, changing the colour). That should slow down the process significantly.

Bialetti Moka Express Pot


How to safely cut old lumber with old nails in it?

Question: A friend gave me a bunch of really old lumber (the late 1800s, early 1900s) and they have a bunch of old handmade nails in them which I tried pulling out but half of them broke off in the wood. I would love to use this lumber but I don't want to ruin my blades in the jointer/planer or trigger the SawStop so is there a way I can safely mill these boards or should I scrap them?
Comment: If you aren't willing to laboriously locate pretty much every nail (using a metal detector!) and dig it out, by whatever means necessary, then yeah, you might have to abandon the idea of milling the wood down to get fresh-looking stock. Without seeing numerous photos it's hard to advise further, but are the nails all over the place in most of the boards or are they positioned usefully in fair straight lines so the affected strips could be safely ripped off? You might be able to cut around them and still end up with a decent yield, just not in the lengths and widths you were hoping for.
Comment: I suppose it's worth mentioning that carbide-toothed TS blades are capable of cutting though staples, brads and even the occasional nail without harm. This isn't to say it's 100% safe to do so (for the operator or the saw) but it is a fact of life that every now and then you'll saw through a fastener without meaning to. Now nobody should *recommend* this, and of course it's not something to be cavalier about, but it is possible to get away with it. If you want a bit more info Stumpy Nubs did a video on this very subject maybe 2 months back, the thumbnail is easy to spot because of the sparks!
Comment: @AloysiusDefenestrate - and, I would add, will trigger the OP's SawStop, which will definitely finish the job on the blade that the nails started.
Comment: Were the nails substantially rusted out? If there is a lot of rust and little iron remaining, that's going to be a lot easier on carbide tools than metallic iron. Jointing and planning though would still be a no go unless you have a junk hand plane blade you can sacrifice.
Comment: There may be a local mill that specializes in milling "urban" timber. This basically means they will accept timber with fasteners probably embedded in it, and you will pay accordingly. Other mills will never accept such timber.
Comment: @AloysiusDefenestrate, I'd hoped it was clear that I was saying that this *could* result in no harm, rather than it coming across as me stating it *won't* (which is just as bad as saying it *will*).
Comment: @Graphus -- "without harm" might be overstating it. Chipped and prematurely dulled teeth is what I've experienced. Maybe it's fair to say, "you can get away with cutting through the occasional nail..."
Comment: @WalnutClose, *"and, I would add, will trigger the OP's SawStop"* >_< it might be best to do just a bit of research before making absolute statements like that (and the one in your Answer incidentally). The video I mentioned to the OP specifically addresses both points so you might want to start there!
Comment: @Graphus - I'm well aware that SawStop says nails don't generally trigger their safety mechanism.   I also know that from personal experience that they can and do not infrequently trigger the mechanism.   Staples and brad nails don't.   Fat old iron nails, though, often do.
Comment: @WalnutClose, yes but the point is **will** versus **might**. Not to mention Bypass Mode, naturally. I'm not trying to, ah, trigger an argument (haha, see what I did there) but unconditional statements, like proscriptive advice, tend to be far less helpful than intended.
Comment: Yes. This whole conversation is about the risks incurred, and how to assess those risks. There is very little "will happen for sure" when milling urban timber. It might even be low-risk in general. But, just as generally, these low-risk situations probably incur a high probability of something unwanted. Even if that is a chunk of hot carbide hitting your sandaled foot. Ask me how I know.
Answer: Before you start, rather than just winging it as many do when faced with the prospect of using reclaimed wood (I'm very much including pallet wood here for some of the direct parallels) it might be worth consciously looking at it this way:
potential value of wood to you / (the cost of your time + cost of 1-2 useful tools)
Everyone will do this calculation differently. If you're an amateur you might value your time at zero as many/most amateurs do, in which case it becomes only a matter of how much effort you're willing put into the boring preparatory stages, along with the cost of any of a few tools you might need to make this wood safe to process in your normal manner (but see bottom for an alternative).

New Yankee Workshop used reclaimed wood numerous times so that might be something to go hunting for to see someone working start to finish with wood that might be quite similar to what you have there. Sorry I can't give you even a starting point for the search like project titles, or even which seasons to look in, because in writing this I realise it's been 20 years since I watched NYW!
As Norm shows quite well (better in later episodes IIRC) you start by meticulously de-nailing the boards before any further processing.
Find the metal, remove it
Using a metal detector is considered a must here, so that's an expense to factor in. Be methodical. Do both sides. Mark each location with pen, chalk, or carpenter's pencil.
Do not be guided purely by the staining you might see, or obvious holes; although of course they are a useful starting point chunks of iron can be surprisingly well hidden on old, especially weathered, wood. I've missed a few on boards that were merely rough-sawn and a bit dingy!
You might read you can use a stud finder for the metal hunt but, eh, not really. Ditto a strong magnet. Both are capable of finding some of the metal in wood for sure, on thinner boards especially for obvious reasons. But they both lack the sensitivity you want for thicker material and to reliably find smaller chunks, like just the tip of a nail that gets left behind after pulling.

I tried pulling out but half of them broke off in the wood

It may be possible to successfully pull/prise out the pieces that remain e.g. by drilling to either side and then using needle-nosed pliers. This can take far longer than you expect, and it means leaving a much bigger gouge in the wood than you were hoping for. But remember you can always use tinted epoxy or a Dutchman for defects like this, and either can add an attractive touch to something obviously made from old wood.
Assuming you aren't willing to just rip cut out entire nail lines, and/or trim off the ends where the nails mostly lie, the only alternative to prying out is some type of coring tool or plug cutter which will leave a more uniform hole that you might or might not prefer (note that the larger the holes are the harder it is to plug with face-grain wood, so you might prefer to convert the round holes to any of the more traditional Dutchman shapes).
After you've worked your way along a board from one end to the other, ticking off every marked location, check the wood again with the metal detector. Dollars to doughnuts you'll find at least one piece that got overlooked or left behind.
It should be impossible to miss any piece of metal worth noting if you check a second time but.....
What if I do miss a piece?
Assuming you don't go a different route on initial breakdown the first major power tool to see the wood will be your table saw. Since you're using a modern saw I think it's safe to assume your blade is carbide-tipped :-) and as I mention in the Comment above, carbide-toothed TS blades are capable of cutting though staples, brads and even the occasional nail without harm1. And just to be clear, by without harm I don't mean no apparent damage I mean no damage at all that anyone can notice; you'll confirm this for yourself during your due diligence.
This shouldn't be that surprising since mild steel and wrought iron are relatively soft, and carbide is hard2.
Now the flesh-sensing technology on the SawStop adds a further complication because sawing though a bit of metal can on occasion trigger it, which means new brake and new blade, obviously something you want to completely avoid. You can turn the saw into a dumb saw, as an owner you'll know Bypass Mode is specifically provided for this purpose as and when needed, and some users make use of it on a regular basis. So this isn't at all an unreasonable option, but it's up to you if that's something you would be comfortable doing.
Once you get done with the saw cuts the wood should be as safe as you could hope for, and suitable for running over a jointer or thickness planing.
Alternative approach
Do the processing by hand, exclusively or mostly with hand tools. So, starting with rip and crosscut panel saws, possibly a hatchet (for wasting edges and splitting off), and a scrub plane or other roughing plane.
Because of the pace of work, and the nature of the tools themselves, it can be almost risk-free to process wood with nails in it manually; I have planed down to staples, brads/nails, and even a hard modern screw once or twice, without ever doing unrecoverable damage to the plane3, although admittedly others have had different experiences including chipping the rear of the mouth opening.
I suppose the primary power tool you could use to help with this process is a jigsaw4. And at worst you'll trash a jigsaw blade or two, not an unreasonable expense for what you're getting at the end of the day (even if this is 'only' softwood).

1 Do your due diligence here. Because of how relevant it is to your situation the video I referred to above in the Comments would make a great starting point; the original title was different but it's now What did a tiny nail do to my $10K table saw? As you might expect there's quite a bit on the forums related to this topic, and probably much more on YouTube.
2 But not necessarily as brittle as you might have been led to believe. This is one area where you can expect to notice the quality of your blade's carbide, since tungsten carbide is by no means a single, uniform, entity as so often implied (just like HSS isn't, as you might already know if you have a lathe and have tried various makes of turning tools). This is one of the genuine reasons for some saw blades costing a lot more than others, rather than it just being a name premium or the maker recouping their fat advertising budget :-)
3 Other than one deep scratch to the sole (which doesn't affect function in any way) the worst I've had to deal with is a minor nick in an iron and a worse, but still superficial, gouge to the leading edge of a cap iron.
4 I suppose you could use a reciprocating saw for this, as they're used for demo work their blades are most definitely up to the task (I doubt you'd even notice sawing through these nails as far as increased resistance goes) but this type of saw may be too uncontrollable for what you need here. A jigsaw is slower, safer and has much greater potential future utility to the average woodworker.
Answer: Short answer for this: no, there is no way using ordinary wood shop equipment to safely mill wood with embedded iron in it.   Jointer, planer, and bandsaw blades will be ruined by even small amounts of iron.   Carbide table saw blades will survive some cutting of steel or iron, but will be dulled significantly, and may experience damage.    Iron also may trigger your SawStop if it's a big enough fragment, if you don't disable the mechanism for each and every cut.
If there is a relatively small number of nails to deal with, I would remove the remaining bits of iron by coring the nails with a small bore carbide or bimetal hole saw, then plug the resulting holes with cores cut from near the end of the timber (to minimize shortening of the resulting boards), then mill it.   If there are very many, I wouldn't bother.
Comment: @FreeMan - I don't know.  I've used a lot of recycled wood in my day.   You can get some beautiful wood out of old barn beams and the like.   But even being careful, I've wrecked the occasional jointer and bandsaw blades.  It is not just urban trees, by the way, that sawyers have to be careful of.   Trees from fencerows in farm country are frequently full of steel - wire, nails, and even the odd steel fence post or plow share.  I ran into an elm log not long ago that had grown completely around a steel T fence post.  Totaled my chain saw chain.
Comment: Interesting that this has 2 up votes and 2 down votes. It seems perfectly reasonable to me and I'd be curious to know what parts the DV's disagree with and why. This seems to line up with all the conventional wisdom I've ever heard on dealing with recycled lumber and _precisely_ why many lumber mills don't accept urban trees - there's too much of a chance of running into embedded metal, thus destroying expensive bandsaw blades.
Answer: First, evaluate the boards and figure out how you want to use them. If they're old and they have a lot of hand cut nails, maybe it'd be nicer to leave them in their current state as much as possible to preserve their character. That'd save you some work, and you might end up with a project that's one of a kind.
If you do decide to mill the boards, you need to get rid of the nails. There are a lot of good tools for that out there, and you may need more than one. A Crescent Nail Puller is a great tool for something like this -- the harder you pull on it, the tighter it holds the nail. A flat pry bar and a cat's paw might also be handy. As others have suggested, a wand-style metal detector can pay for itself in the cost of replacement blades in just one or two uses.
If you don't think you can get the nails out, sometimes you can push them farther in. For example, if you've broken the head off a nail, you may not be able to get a hold on it to pull it out. You can try to excavate around it, but at some point you're just going to make a mess of the board. Instead, insert a small punch in the hole and use a hammer to drive the nail a little further into the wood, so you can safely surface the wood without hitting the nail.
If you just want to surface the wood but don't need it absolutely flat, a belt sander is a good option. Even if you hit a nail, the sander will probably just sand it down along with the rest of the board. Worst case, you might have to change the belt, which isn't a big deal.
Carbide-tipped table saw blades will cut right through most nails and screws, and hand cut nails are probably softer than today's steel nails. Even so, you don't want to subject your best blade to nails, so buy a cheap blade for this project. I bought a rip blade at Home Depot recently for about $16. I think the brand is "Avanti," and it actually works pretty well. The teeth aren't exactly beefy, and I doubt it'll stay sharp for as long as a better blade would, but it's probably perfect for the kind of boards you've got.
If you're going to use your SawStop and want to avoid tripping the brake, just put the saw in bypass mode. Check your manual for instructions, but it's basically just a matter of turning the key as you start the saw. Just remember that the brake WILL NOT FIRE when the saw is in bypass mode, so use the blade guard and an extra dose of caution.


Driving Solenoids from Arduino

Question: I was wondering what the best way to run a solenoid would be from an Arduino board. I was thinking about using a MOSFET that runs into a relay to turn on the solenoid but am not sure how to go about it.
Answer: You can drive the solenoid using only the MOSFET (or a bipolar transistor)
It would help to know what type of solenoid you wish to drive so we can select suitable components. Here are a couple of circuits to give you the general idea for MOSFET/Bipolar:

The resistor can be ~10k - 100k (the range can be wider as Steven notes, e.g. 1k\$ \Omega \$ - 10M\$ \Omega \$ - too high a resistance and you risk susceptibility to noise though), it's to make sure the gate is pulled to ground if the input is floating. The diode can be almost any general purpose diode capable of handling a reasonable amount of current.
Darlington Version:
Comment: Oli, I don't think noise will be an issue. Even when driven from an open drain output the pull-up will provide a low impedance. The resistor is just there in case the gate would float for some reason, but if the driver is disconnected/defective the device won't work properly anyway, and by the way, a 10 M\$\Omega\$ resistor generates only 400 \$\mu\$V Johnson noise at room temperature over a 1 MHz bandwidth.
Comment: @Steven - I wasn't thinking of Johnson noise, rather just in the (unlikely) event the input is left floating in a noisy environment (as mentioned). You could say the resistor is not needed at all if you're sure it's always driven properly (e.g. uC pin active before solenoid supply active)
Comment: Agreed, and IMO initializing I/Os should be (one of) the first thing to do after the uC is reset. Leaving the gate floating for a ms won't hurt it (even when the solenoid's power is already active).
Comment: @stevenvh 10 years on :-). No harm in most cases. I was designing a multi track tape deck drive (in 1977) and there was a brief glitch at startup for this reason. This latched a fast-rewind commend into the deck and it despooled the tape. Nothing in the code explained it :-) . Solution was both good pulldowns and a ***STOP!!!*** commend as soon as the system initialised :-)
Answer: If the solenoid needs an AC drive you'll indeed need the relay, otherwise you can directly drive the solenoid with the MOSFET. They're the same kind of load.

Oli suggests 10 kΩ to 100 kΩ for R2, but you can even use a 1 MΩ for this.  Make sure that you have a logic FET. Other FETs may need a too high gate voltage to turn on. A relay may need around 50 mA or less, a solenoid probably a couple of hundreds of mA. Select a FET with a low \$R_{DS(ON)}\$, so that even at higher currents dissipation will be low. FETs with an \$R_{DS(ON)}\$ of less than 200 mΩ are perfect and well available.
If the relay/solenoid needs 24 V or less the Si2304DS is a possibility: \$R_{DS(ON)}\$ is less than 200 mΩ, so even at 1 A it will dissipate only 200 mW. Can drive more than 1 A at 3 V gate voltage.
Comment: Why would you use a depletion-mode MOSFET (shown) instead of an enhancement mode MOSFET?

Driving Solenoids from Arduino


What is the purpose of the Tort Claims Act?

Question: Generically speaking and presuming federal and state are essentially the same;  What is the plain language purpose of the Tort Claims Act aka who does it cover in what capacities, etc?
Answer: I am curious why you say "and presuming federal and state are essentially the same," because they really are not.
Nonetheless, the FTCA operates as follows: first, there is a doctrine of sovereign immunity which disallows citizens from suing government entities without that government entities express permission. The FTCA provides the guidelines by which one can in fact file

specific types of lawsuits against a federal government entity and federal employees who have acted within the scope of employment while causing injuries, but certain strict rules must be followed.

Essentially, one must first file an administrative claim with the government entity that allegedly wronged him or her. Once six months pass with no answer or an unsatisfactory answer, the suit, pursuant to its various rules and exceptions, may then go forward.
[This is not and should not be considered legal advice. Rather, it is general educational info derived from the linked site].
Comment: Ok, just to be clear... you can sue the government if the employee did whatever *while within the scope of employment*, **IF** the claim falls under the requirements of the Torts Claims Act. If the person is acting outside the scope of their employment, like say assaulting you while drunk at a bar, I believe you would just sue them as an individual (could be different by jurisdiction - not legal advice!).
Comment: I believe the phrase is "all things being equal".
Can a private party sue a government employee for injuries done under color of law but which were outside the scope of their employment without going through the TORT Claims Act?

My original question may have been overly broad because it ask to explain a law which is ever changing and excessively ambiguous.
Comment: If it was outside the scope of employment, the Torts Claims Act will be of no help. The Act requires that the action be done within the scope of employment. Likewise, independent contractors working for the government cannot be a vehicle through which one sues the government, unless the government "treats" them like an actual employee.
Comment: OK so that is just what is so confusing.  I have read where government can not be held liable for acts of their employees done within the scope of employment.  So, how would one sue a government employee that acted outside their scope of employment?
Comment: @j.howdee as I understand it, which is really very superficially, federal sovereign immunity is one reason why lawsuits generally name federal officers and employees personally, but "in their official capacity."
Answer: The purpose of the FTCA is basically to allow people to sue the government for money damages for certain narrowly defined torts, notwithstanding sovereign immunity, which are closely analogous to actions of non-sovereigns, where a uniform rule for governmental and non-governmental actors would be useful, while regulating carefully the manner in which those suits are carried out.
The reason for sovereign immunity in the first place is that the government has such broad power that at some level, a sufficiently imaginative set of lawyers and judges could hold the government responsible for just about anything.
So, FTCA basically takes responsibility for certain kinds of routine car accidents, slip and fall situations, medical malpractice and the like, while excluding uniquely governmental discretionary functions.
The FTCA is the "exclusive means by which a party may sue the United States for money damages . . . in tort" pursuant to 28 USC § 2679, but this is really something of an exaggeration as there are lots of constitutional and statutory grounds upon which the United States government can also be sued for money damages that naively appear tort-like, such as a reverse condemnation action under the 5th Amendment to the United States Constitution.
The FTCA does not bar suits for breach of contract, does not bar suits for injunctive or declaratory relief, and does not bar suits against government employees for money damages for intentionally violating someone's civil rights (even though some union contract indemnify and defend government employees for civil rights violations, in practice, converting tort liability of an individual into contractual liability of the United States government). It also does not bar tax refund lawsuits.
In general, the FTCA relates only to the vicarious tort liability of the entity, the United States government, on a respondeat superior theory, arising from an agency or employment relationship some some other person or entity that acts on its behalf. This is because the United States government, like many entities, can't take action without acting through some other person or entity. The general agency law of state respondeat superior law determines when the action of a person or entity is attributable to the United States government or not.
Most states have similar governmental immunity statutes, although their exact details differ. The FTCA is particularly vague. Many state governmental immunity statutes are much more specific.
The FTCA itself does not govern the liability of the employee or entity which committed the tort for which the United States government is being held responsible. Not infrequently, an employee or agent who actually committed a tort (e.g. causing a car crash) can be sued in addition to a suit against the United States government under the FTCA.
Suits against the federal government for breach of contract for money damages must often be brought in the court of claims which is governed by a parallel process.


Bitcoin arbitrage using ripple

Question: Can someone smarter than me please give me step-by-step instructions on how to make money taking advantage of the disproportional BTC values across exchanges? I think using ripple could make the turnaround time faster but I'm not sure.
Answer: There are multiple distinct types of arbitrage possible with Ripple (there may or may not be financial terms for these, I'm a software developer not a finance person).
Within Ripple
Ripple has a built-in exchange between any pair of currency+issuer. Depending on market conditions it's possible to find arbitrage opportunities that can executed near instantaneously.
For example, given USD issued by gw1 (an example Ripple gateway) and CAD issued by gw2 and the various order books (USD/gw1:CAD/gw2, USD/gw1:XRP, CAD/gw2:XRP, etc) a trader may discover that they can trade USD/gw1 for XRP, then XRP for CAD/gw2, and finally CAD/gw2 back to USD/gw1 and get more than they started with. With Ripple this can be executed by a series of trade offers that are fully processed within seconds limiting the risks; or even by a single payment transaction with a custom path routing through the appropriate order books executing atomically (note: doing fully circular payments to do this in a single transaction is currently possible but non-trivial).
Since Ripple itself attempts to find the cheapest path possible for each payment made, such arbitrage opportunities may be short lived for currencies with large volumes of payments (e.g. someone making a CAD payment using their USD should automatically take the best USD:CAD or USD:XRP:CAD offers as appropriate and vise versa).
Between Ripple and a Ripple Gateway operating as an Exchange
Several Ripple gateways are existing Bitcoin exchanges and as such have their own established markets and order books, often with better spreads and volume than the internal Ripple order book for the same currencies. Depending on the speed and reliability of the Ripple gateways' issuing/redeeming process this can be a low risk arbitrage opportunity.
For example, Bitstamp was one of the first Ripple gateways for BTC and USD and has a good volume of BTC:USD trade on their own exchange. A user with BTC sitting in their Bitstamp exchange account can move some of that to BTC/Bitstamp within Ripple, trade to USD/Bitstamp, move that back to their Bitstamp exchange account and use Bitstamp's exchange to trade that back into BTC. The speed at which this can occur is dependent on Bitstamp's Ripple integration; when functioning well it only takes a minute or so but there can also be long delays occasionally (Ripple is in beta and any specific integration such as Bitstamp's can experience issues).
In addition to taking existing trade offers within Ripple (to limit the overall time of the above cycle and lower risk) traders can place offers on Ripple and on Bitstamp to capture larger differences in the spread over longer time periods but at the risk of price changes.
Inter Gateway Arbitrage using external paths
This is likely a general case that covers the original question.
A trader can profit on price differences between different gateways by moving funds between the gateways outside of Ripple. For example, the USD/SnapSwap:XRP market may be consistently trading at different prices from the USD/Bitstamp:XRP market. A trader with a US bank account may find it profitable to send an international USD wire transfer to Bitstmap, transfer that to USD/Bitstamp, trade to USD/SnapSwap (either directly of via XRP) and redeem that back to their US bank account. Since this uses the existing banking system it can be slow and expensive so it would only be profitable if the USD/SnapSwap and USD/Bitstamp markets differed significantly (which it often does).
Another example of this is a Canadian user wiring USD funds to Bitstamp and then trading into CAD/RippleUnion which they extract to their Canadian bank account. Recently the CAD/ru:USD/bs orders on Ripple have differed enough from the banks' exchange rate to cover the banking fees and make such a transfer profitable (if slow).
Specifically what the original question appears to be asking about is an example of this where the two gateways are also Bitcoin exchanges. For example, Bitstamp and The Rock Trading. Without Ripple an arbitrage trader can move Bitcoin between their Bitstamp and TheRock exchange accounts fairly easily and cheaply but it's usually expensive and slow to move their USD. With Ripple, someone can quickly move their USD to/from each gateway from/to USD/Bitstamp or USD/TheRock within Ripple. As long as the market on Ripple has sufficient liquidity they may then be able to trade USD/Bitstamp:USD/TheRock (or do a conversion payment in which Ripple will search for the cheapest conversion path, possibly USD/Bitstamp:XRP then XRP:USD/TheRock for example). This allows such a user to move USD between the exchanges very fast (but possibly not any cheaper, it all depends on the current Ripple markets).

Bitcoin arbitrage using ripple


Zero stress boundary conditions for the acoustic wave function

Question: When is it appropriate to use zero normal stress boundary conditions when solving the acoustic wave equation. That is when the pressure is equal to zero.
Answer: Strictly speaking: never. Outside the idealized models there are always at least a bit of radiation impedance so the pressure on the boundary is not truly zero.
But let's focus on idealized models. Usually the zero pressure boundary condition is used for open ends of the waveguides or for the free surfaces of solid bodies.
Typical illustrative example would be the loose end of the string: there is nothing (e.g. no bridge) which can provide a support for string stretching. Therefore the tension (analogy of pressure) must be zero and all the energy goes into displacement.
Comment: How accurate is the p=0 approximation for open ended waveguides?
Comment: If you seek for a standing wave, than is is sufficient. But if you want examine the radiation, then you need to be more careful. Study the wave reflection at the borderline of enviroments. It would be almost the limit case.
Comment: So I have a somewhat tangential question. Do standing waves even exist in real life? It seems like they're just an idealization that approximate a situation with low dissipation.
Comment: Let's say it is a highly useful model, very well valid in significant amount of cases. Of course, there are no pure infinite impedance to make the total reflection and so on.


Event PCP IDs mismatch in the civicrm_pcp_block table

Question: An oddity discovered in WP/CiviCRM 5.70.0: an Event "Personal Campaign" tab  displays non-editable fields

Campaign Type "Contribution" (mustn't be "Event" ? )
Online Contribution Page : empty (supposed to allow an Event selection I believe )

Partially confirmed on the https://wpmaster.demo.civicrm.org/ - the tab comes empty & with the infamous "Network Error Unable to reach the server " message.

A temporary band-aid:in the "civicrm_pcp_block" table, find the block corresponded with the event and manually change the "target_entity_id" from "contribute" to "event" (the "contribute" appears to be the default choice for every "event" record in the table).
This makes the  "Online Contribution Page" label disappear and fixes the rest of it.
Possible related deprecation message:
<code>[warning] attempt to access invalid property :_eventId Caller: CRM_Core_Form::getVar
Array
(
[civi.tag] => deprecated
)
</code>
Answer: A temporary band-aid:in the "civicrm_pcp_block" table, find the block corresponded with the event and manually change the "target_entity_id" from "contribute" to "event" (the "contribute" appears to be the default choice for every "event" record in the table).
This makes the "Online Contribution Page" label disappear and fixes the rest of it.
Comment: If you're getting the same thing on wpdemo, please create an issue at https://lab.civicrm.org/dev/core/-/issues describing your problem and your solution.  And if you can, a PR would be great


Quick method to create a curved dagger vector (without the handle)

Question: Does the blade on this dagger have to be created using the pen tool?
Are there easier ways to do so in Illustrator or Photoshop (CS6 if possible)?
Answer: With the pen you can draw the outline of the blade. You can cheat and draw only the upper edge. You can make the edge by clicking few times and then adjusting the edge more precise:

In Inkscape the pen should be in spline mode, so the clicks generate a smooth curve. Doing the clicks takes about ten seconds, but the result probably is too coarse. The final edge form is made by moving the curve (by moving the spline nodes) with the node tool. That can take few minutes, but it shouldn't be an obstacle even for a beginner.
Finally you have good enough edge. Make a duplicate, flip it and insert the left and right end segments. The edge must be converted to path (Bezier curve) before making joints or other path operations because Inkscape turns unstable if one asks it to do something complicated. Trying path operations with splines is one such task.
The resulted outline may be good enough, but to be more exact you can draw the whole blade outline. In the next image the bottom edge was made by flipping a duplicate:

The outline is not much more than an empty paper if you want an image which looks like it has the original 3D form and metallic texture - shiny metal or rusty. Drawing the 3D-like shading, possible glosses and maybe some engravings or rusty texture will be 99% of the work. Many of us would try to get it easier, for ex. by making a 3D model and getting a high resolution photo of rusty metal + mapping it on the model. But learning to use properly a capable enough 3D program is at least as tricky as learning to use all available tools in Inkscape or Illustrator.
If the intention is to make a non-shaded line drawing (for ex. to be used as a tattoo) inserting a few lines to visualize the sharpened edge is not difficult. Drawing the numerous details of the hilt needs much more care and skill.
If you just want to avoid drawing the outline manually you can make in Photoshop a selection which contains the blade. The quick selection tool in legacy PS follows the wavy edge quite well after making a few insertion and subtraction clicks. The selected blade area can be pasted to Illustrator and traced:

Expanding the tracing, removing the black fill and inserting a thin stroke shows that the resulted curve isn't more complex than the manually drawn. The bottom edge is not especially accurate because the original photo has been shot in poor light. It's not at all clear which pixels are the blade and where the shadow starts.

Little more: A whole new vectorized version of the dagger can be made with very low effort. The surface details are, of course, all distorted to unrecognizable due the low resolution, but it's a vector.
Answer: Forget Photoshop, it's not the right kind of software.
One method for Adobe Illustrator CC would be to use the width tool on a simple stroke. If you need to convert to an actual shape afterwards, do Object > Expand Appearance
For example

If you don't have a recent version of Illustrator, not to worry, the same is also possible in Inkscape (which is free). In Inkscape it's called the Power Stroke Live Path Effect. If you need to convert to an actual shape afterwards, do Path > Object to Path.
Answer: Adobe Illustrator
Note: I did not focus on the image in the question. There was zero attempt to match the number of curves or degree of curvature in the question image. Here, I'm just showing how you could create a similar shape without really using the Pen Tool.

You can do this with just a triangle. You will need to use the Pen Tool a bit, to add or remove anchors, but you don't have to create any curves or anything.

Draw a long triangle (You can simply use the Polygonal Tool set to 3 sides)
Remove the right path segment (in my rectangle below)
Choose Effect > Distort and Transform > Zig Zag and play with setting to get some good curves. Then click OK
Choose Object > Expand Appearance so the effect gets "baked in" and you have actual paths to work with.
Remove the anchor points where the paths overlap. The easiest way to do this is to use the Direct Selection Tool (white arrow) to click-drag and select those end anchor points. Then hit the Remove Anchor Points button () on the Control Bar across the top of the screen.
Use the Pen Tool to add ONE anchor where the tip should be.
Again use the Direct Selection Tool to click-drag that new anchor to the left (in my image) to form more of a tip or point.


Signature instead of PIN, Visa card

Question: Most of the credit cards require PIN to authorize transaction. Recently upon a transaction the merchant required my signature and not my PIN. I understand this is another sort of authorizing the transaction. But this is more to held me accountable , if i denied the payment.
It doesnt offer the security of a PIN since anyone obtaining my card can ran away with the money. The transaction was less than 100$.
 Moreover , i remember my father 10-15 years ago paying for bigger sums with just his signature, before the PIN arrived i guess.
Does this means whoever has either my card / or photograph of my card (both sides with CCV code) can withdraw as much as he wants?
Comment: It is worth noting that in the US, we still only use a signature for transactions.  It all depends on what your merchant bank (the bank that your account is with) will allow your card to be used for.  You would have to ask them for details on their policies for what they approve.
Comment: Related: [An amusing prank involving credit card signatures](https://web.archive.org/web/20130120184305/http://www.zug.com/pranks/credit_card/), or lack thereof, from the now defunct zug.com
Answer: Payment protocols have many variants. However, they mostly boil down to the three following:

The card number is just a reference, to be printed on paper. The owner signs with a pen on the paper. The paper may be printed with several technologies, some of them quite primitive (credit cards are embossed so that their number can be copied to paper efficiently with a purely mechanical device).
The card number is obtained by a payment terminal (e.g. with a swipe of the magnetic strip); the payment terminal then talks to the bank. The PIN code is used to authenticate the user (it is sent to the bank for validation).
The card is a smart card; the chip contains some secret value which is used to authenticate the transaction (with a MAC or a digital signature). The PIN is sent to the card and is used to convince the card that its true owner is indeed allowing the operation.

In any case, the point is not exactly to prevent fraud, but to reduce it to tolerable levels. The merchant does not really mind a fraudster running with the money, as long as he will be refunded by the bank. The bank sees the big picture and does not feel invested with the sacred mission of catching all thieves; the bank wants the total fraud cost to be as low as possible, and that's not the same thing.
Banks usually prefer it when the PIN code is used, because it lowers fraud level (by as much as a factor of ten, as I heard). However, this requires a PIN-aware terminal; with solution 2, a network connection must also be maintained with the bank; with solution 3, the card must have a chip (smart card deployment was long delayed in the Americas because banks waited for the 1986 French patent on smart cards to expire). Merchants are not usually cooperative for changes (they must pay for the new terminals) and card deployment is not fast (since each card is valid for several years), so the "first type" payment method (with a pen-based signature) is still possible in many shops. It should gradually disappear, though, because it allows for easier frauds, which makes banks uncomfortable.
Ultimately, this is a question of relative strength between banks (who want to enforce the systems which will ensure the least possible amount of total fraud) and merchants (who want to have the automatic refunding at the least cost for them). The card owner himself does not have much to say... however, legally speaking, the card owner is "protected" as long as he follows the official rules from his bank. As long as the bank does not forbid him to pay with a signature, the bank must refund the user if a fraud on his account occurred.
(Whether bank clerks will make the operation easy is another question.)
Comment: How is  least possible amount of total fraud achieved when according to http://www.bbc.co.uk/news/technology-25398408 is so cheap to obtain credentials is the subsequent question then.
Comment: In solution 3 the transaction is authenticated by the chip. How are the transaction resp. the validity of the card authenticated in solution 1 and 2?
Answer: What I think you'll find is that if you're in a country with Chip+PIN deployed, if a merchant takes a signature instead (usually because their Chip+PIN system is down) then the fraud liability moves from the customer to the merchant.
So if you have fraudulent transactions on your card where the merchant doesn't have the PIN you can just dispute them and the onus will be on the merchant to prove that they are legitimate, rather than on you to prove that they're not.
Answer: It likely depends on what network is being used to process the card.  If the network is EFTPOS-like, a PIN is typical.  However, if the network is credit-like, a signature is typical (at least, before EMV existed).
A lot of cards are dual-branded, and how they are processed can depend on the configuration of the merchant's terminal.  It's not likely to be a question of backup, though it's conceivably possible that a PIN might be required only if online authorization is being done.
A photograph of a card isn't often all that helpful, because usually a CVV code (different from the CVV2 code on the back) is stored on the magstripe and is not easily derived without a 128-bit DES key and knowledge of the card service code.  Just having a picture of the card, even of both sides, will usually only enable you to use the card for card-not-present transactions.
Really, the specifics of the security features on some particular card are best asked of the card issuer.
Comment: Card-not-present transactions could be an online purchase for a big sum of money though, so where is the layer of security with CVV2 going
Comment: Hmm?  Nowhere?  The point of a CVV2 is to provide a value that isn't normally stored alongside the card (so that magstripe cloning and pictures of the front of the card are not as useful).  It can be used in card-present transactions but that use is less common.
Answer: Signing for a credit card transaction is still quite common in countries where they use the magnetic strip on the side rather than the embedded smart card chip (which uses a PIN code). Note that this is a choice of the credit card company. A pin is indeed more secure, but for usability reasons not enforced everywhere (in Europe it is quite common these days).
The maximum sum is the same for your pin card as for the magnetic swipe. If they indeed have your CCV code then they can just use your card (although I know a lot of payment gateways check if the chip&pin is present for that card and they will require you to sign the transaction digitally).
If they find a gateway that does not do this check, then yes, they can withdraw money with your card (until its limit is reached). However most credit card companies will reimburse you for the damages suffered if fraud (malicious transactions) are discovered with your card.
Comment: I was talking about the very same card ,the card sometimes needs PIN and others not. Is like having a backup security method less secure than the primary one. E.g. setting a password in your tablet and having as backup mechanism face 'recognition' which is less secure. My question is why have the PIN anyway if you can still take money without using it
Comment: Because it's not always supported, in Europe they are banning the magnetic strip and prefering the chip. However for backwards compability (so until everyone is using chip&pin) you will still have the magnetic strip available.

Signature instead of PIN, Visa card