Can a child release his own work into e.g. the public domain?

Question: I (15 years old; living in Germany) write software now for ~four years and wondered whether I can release it into the public domain or under some free software license without having to ask somebody.  I know that I have to ask my parents for many legal acts and that my father's employer (he is a professional software developer) has some rights about his software.  Have I to ask my parents (as for many legal acts), my school (my "employer" :)) or somebody entirely different?  I had searched the web very often but I always only find what the legal status of schools are.
Comment: As a general rule, if you are employed but write software on your own time which is not related to your employer's business, then it is your software and your employer has no rights to it at all. (Unless there is an employment contract term to the contrary, in which case it gets complicated). But as amon says, your school is not your employer.
Answer: In Germany, there is no concept that corresponds directly to public domain. You automatically hold the Urheberrecht (~ copyright) for all creative works that you make, and it can't be given up or transferred (§29 UrhG). The work only enters the Gemeinfreiheit (~public domain) 70 years after your death. You can however license Verwertungsrechte (economic usage rights). When you make creative works in the course of employment (see §43 UrhG), your employer automatically gets the Verwertungsrechte necessary in the context for the work, which is typically an exclusive right (no one else, not even you, can use the work).
Your are not in an employment relationship with your school, so it has no rights to your works and cannot prevent you from publishing them on copyright grounds. When you see advice on the internet to check with your school first, that is U.S.-specific advice.
Since you're still a minor (7–17), you only have limited capacity to enter contracts or legal transactions (bedingte Geschäftsfähigkeit). While you are able to make transactions involving your own means (e.g. buying something with your pocket money) or make transactions that are only to your benefit (such as accepting a gift), other transactions are schwebend unwirksam (~ pending ratification), until your parents agree. The relevant law is in §107 and §108 BGB.
This is a problem with open source licenses. If you publish software under a license, this license is schwebend unwirksam. Someone might start using the software under the license. But then if your parents refuse ratification, the license would be invalid, and everyone would have to stop using your software and destroy any derivative works they made. This is a bit of a problem, especially since open source licenses are otherwise assumed to be irrevocable.
So if you want to offer a license (including open source licenses), please give legal certainty to the recipients of the license and ask your parents for their consent first, possibly even in writing. Per §107 BGB, the license you offer with their consent will be valid.
Comment: @DPenner1 That sentence is indeed ambiguous in the original German as well, but its meaning is well established through case law: Germany has a mild variant of the "work for hire" concept, just with an implicit license grant instead of a copyright transfer. That the surrounding subsection still applies means that details about adequate remuneration also reach into the employment relationship, e.g. an employed author may be able to re-negotiate royalties in surplus of their original salary if their work is very profitable.
Comment: Not directly relevant to the question but it seems that §43 UrhG actually says the opposite, the employer does not automatically get rights absent a contract to the contrary (my German isn't great, I used the English translation the Justice ministry provides: https://www.gesetze-im-internet.de/englisch_urhg/englisch_urhg.html)
Comment: There might be a relevance of the school, if you programmed in class. (I never really understand the law there and suspect it is complicated and controversial.)
Comment: slight nitpick: youth work is strictly regulated and deserves a mention in this regard.
Comment: @K-HB: I don't think the school counts as an "employer" in this case - but that would make a good separate question :-).
Comment: Actually, this has already been asked (and answered): [When submitting coursework to a university does the author retain copyright?](https://law.stackexchange.com/questions/8069/), and [Who are the copyright holders of softwares that students develop during their studies?](https://law.stackexchange.com/questions/48484/).
Answer: We would have to look exactly at what happens if a 15 year old publishes their own work under the GPL license. USA and Germany are not identical but similar.
In the USA, you can absolutely publish your work under the GPL. However, you or your legal guardian can cancel this at any time up to and slightly after your 18th birthday. If that doesn't happen, then everything is fine.
But if you void the GPL license, it just is not valid anymore. That would mean trouble for everyone using it. They suddenly lose their license, and they are committing copyright infringement by using the software. That would be my risk that I take if I use gpl-licensed software that was licensed by a 15 year old. For you, there is no risk.


How to add reference numbers instead of names in citations in MS word?

Question: I am using the citation feature of MS word. When I add a citation it is added as (Author Name,year) and the references at the end of the document are not numbered as well. I want to change the citation to a reference number and add include numbers with all citations at the end of the document.
Comment: Are you talking about reference numbers to a footnote? Or only reference numbers to the works cited?
Answer: easiest out-of-the-box solution in Word is to select the IEEE citation format
■ in the CITATION and BIBLIOGRAPHY segment on the REFERENCES tab
■ use the STYLE dropdown box to select the IEEE style
That style will provide a bracketed number inline (ie [5]) and when you insert a BIBLIOGRAPHY will format your citations and refer to the inline numbers.  Individual references are added with the INSERT CITATION and numbers are automatically assigned and resequenced as necessary as you edit (which can be a downside, since your reference numbers will be dynamic and your bibliography will be in the order of the inline references)
Only thing I don't like is that the inline references aren't superscripted and when I tried to format then when I refreshed the bibliography they reverted back to the paragraph style where they were embedded.  Other than that, seemed to work well and meets your need for sequentially numbering the references.


Brazil IR swaps and help with new holiday

Question: Brazil has a pending new holiday that is expected to be official in the next month, for date Nov 20.
Existing BRL interest rate swaps contracts have a clause that fixed accruals are not impacted by new holidays, but float accruals are impacted.
How do I adjust my BRL swap accrual calculations once the holiday is official?
I thought I could just adjust the initial (PV) notional and day count, but that would impact both legs.
Answer: New non-business days, one-off or annual, appear on various calendars pretty often even in developed markets. Recent examples come to mind: the Queen's funeral in London, the new King's coronation in London, the day of mourning for President George W Bush in 2018 in the U.S., and probably the same for Jimmy Carter any day now.
Fixed income markets have ways of dealing with new  non-business days. If a previously scheduled payment or settlement falls on such a day, then it gets rescheduled like any other, according to the term sheet / documentation. If the interest amount is daycounted, then it too as adjusted for a new number of actual days.
But Brazil is special in that the interest of some instruments accrues only on business days. My understanding is that they don't want the interest amounts to change when the calendar changes. For that, you'd need to have two calendars - the one frozen as of the instrument's inception, to calculate the number of days of interest accrual as planned at inception; and also the current calendar still, to schedule coupon payments and settlements on current business days, like in all markets.


Is it possible with Python to code G key to move channels up and down in the Dopesheet editor?

Question: Just like we are able to translate most elements in Blender, it would be really nice to be able to do it there. Is it possible?
Comment: Well, in the form you've asked it, the answer is "yes," but that's probably not what you're looking for. Incidentally, the answer to any question that starts with "is it possible to write code that would..." is almost ALWAYS "yes." It is possible. A better question is "would it be worth it." The BEST question would be "What Python command sets a new hotkey in Blender," or "how do I get my Blender script to listen for a keypress without it just running all the time?" Try to be specific.
Comment: Actually, "yes" would be enough, thank you! Sometimes I think something is possible, then look for a way to do it, and after a lot of time invested, turns out it isn't possible. Also, every little usability improvement is always worth it if you repeat the same task every day, even if I have to expend a ridiculous amount of time figuring out how to implement it. P.S.: I'm sorry if the question bothered you!
Comment: Are you asking if you can use python to make dope sheet channels drag+drop with the G key to change their position in the list?
Comment: You can move the position of channels within each Action group up and down using the Page Up/Down keys, not sure if you already knew that.
Comment: I know about the keys, I want indeed to drag+drop with G key.
Answer: Yes, the default keys are ⇞ Page up and ⇟ Page down, the setting can be found in keyboard input under Animation Channels.

The python path is bpy.context.window_manager.keyconfigs.active.keymaps['Animation Channels'].keymap_items['anim.channels_move'] with the property type being the key used, properties.direction is the direction the selected item is moved. You will want to loop through the keymap_items as you will find four keymap_items['anim.channels_move'] entries, up one line, down one line, to the top and to the bottom.
You should look at adding keymaps to an addon to make the changes properly.


Rating based off play level?

Question: Is there a program that can tell your rating based off how well you play in the game? (NOT based on result). Thanks.
Answer: This is called Intrinsic Performance Rating.
There has been a Kaggle Competition in which the winner predicted the Elo on the basis of a single game with an average error of 150 points.
As far as I know there is no single piece of software that gives you these predictions, but the Kaggle Competition provides links to the code used by the participants.
Comment: +1 brilliant. I didn't know there was such a competition. Thanks for sharing!

Rating based off play level?


ExtJS 4 building component from jsonp response

Question: Here is my situation. I have a JSONP feed that I want to render as an ExtJS component. I'm not sure the best way to go about this. There is the Ext.CompontentLoader feature, but is that applicable to this scenario? The alternative is to use an Ajax call to get it. However, I cannot figure out so far which API call makes JSONP possible. Ext.Ajax doesn't seem to support JSONP in ExtJS 4.
Answer: First question I'm not too sure what are you going to achieve, but for the JsonP, you can probably check out Ext.data.JsonP class.


Localizing at the primitive polynomials?

Question: For any UFD $R$, the concept of a primitive polynomial (gcd of the coefficients is 1) makes sense in $R[x]$. The product of two primitive polynomials is primitive (Gauss's Lemma), and certainly 1 is a primitive polynomial, so the primitive polynomials form a multiplicative subset $S$ of $R[x]$ - hence we can form the ring $S^{-1}R[x]$. What can we say about it? What does this look like geometrically?
Answer: A prime ideal of $S^{-1}R[X]$ is the extension of a unique prime ideal of $R$, so that the morphism $Spec(S^{-1}R[X])\to Spec(R)$ is a bijection, and even an homeomorphism. All the extensions of residual fields induced are pure transcendental of transcendence degre $1$.
As an example, if you look at the case $R=\mathbb{Z}$, the morphism of schemes you get "puts in family" the extensions of fields $\mathbb{F}_p\hookrightarrow\mathbb{F}_p(X)$.
Comment: In the first sentence, I think you mean "A prime ideal of S^{-1} R[X] is generated by elements of R".  In fact, you could say that every ideal of S^{-1} R[X] is the extension of a unique ideal of R.  This would show you that the map between spectra is a homeomorphism.
Comment: Yes of course ! Thanks for pointing out the inaccuracy !
Comment: Thanks for the explanation! I'm still a novice with schemes, but I think I get the gist of your answer. Let me see if I understand the argument: Let $\phi:R[x]\rightarrow S^{-1}R[x]$ be the canonical map (injective since $R[x]$ is an integral domain). Because $R[x]$ is a UFD, every polynomial factors uniquely into a product of irreducibles of $R[x]$, which are either irreducibles of $R$ or irreducibles $f\in R[x]$, $f\notin R$. Each irreducible $f\in R[x]$, $f\notin R$ is necessarily primitive, so that $\phi(f)$ is a unit in $S^{-1}R[x]$.
Comment: Thus, for $I\subset R[x]$ an ideal, $S^{-1}I$ is generated in $S^{-1}R[x]$ by $\phi(I)\cap R$ (where we have identified $R$ with $\phi(R)$). Thus, $S^{-1}I$ is the is the extension of the ideal generated in $R$ by $\phi(I)\cap R$, and the injectivity of $\phi$ shows that this is the only ideal of $R$ which $S^{-1}I$ is an extension of. Finally, the fact that preimages of prime ideals are prime and that extension of a prime ideal is its image under $\phi$, establishes the bijection.
Comment: So, this answer definitely depends heavily on $R$ (and hence $R[x]$) being a UFD, especially with "each irreducible $f\in R[x]$, $f\notin R$ is necessarily primitive". Out of curiosity, any ideas on the case of non-UFD $R$?
Answer: Google "Kronecker function ring". This is the germ of the idea behind Kronecker's divisor theory. An elementary historically-minded introduction can be found in Harold Edward's book "Divisor Theory".


Singularities and Horizons

Question: Well, the Morris and Thorne article on wormholes states that the function $\Phi(r)$ of metric
$$
     ds^2 = -e^{2\Phi(r)}c^2dt^2 + dr^2/(1 - b(r)/r)+r^2(d\theta^2 + sin^2\theta\hspace{0.1cm} d\phi^2)
$$
must be finite for all values of $r \geq r_0$ to avoid singularities, but I did not understand why this avoids singularities ($g_{tt}$ being finite), while $b(r_0) = r_0$, which implies that $g_{rr}$ is not finite at this point, does not produce a singularity. What is the difference?
Answer: $b(r_{0}) = r_{0}$ is a coordinate singularity rather than a true physical one, in the sense that you could define a new set of coordinates such that the patch of physical spacetime you cover is different, and that singularity is avoided. A common simpler example of that is de Sitter space. Consider the global coordinates with closed slicing which cover the entirety of the manifold by embedding it in $\mathbb{R}^{1,4}$:
\begin{equation}
\begin{split}
x^{0} &= \ell \, \sinh{t} \\
x^{1} &= \ell \, \cosh{t} \cos{\chi} \\
x^{2} &= \ell \, \cosh{t} \sin{\chi} \cos{\theta} \\
x^{3} &= \ell \, \cosh{t} \sin{\chi} \sin{\theta} \cos{\varphi} \\
x^{4} &= \ell \, \cosh{t} \sin{\chi} \sin{\theta} \sin{\varphi} \\
\end{split}
\end{equation}
The metric is then given as:
\begin{equation}
ds^{2} = -\ell ^{2} \left ( -dt^{2} + \cosh ^{2} {t} d\Omega _{3} ^{2} \right )
\end{equation}
where $d\Omega _{3} ^{2}$ is the metric of a unit 3-sphere. As you can see, no singularity there. By contrast, if you choose the static coordinates:
\begin{equation}
\begin{split}
x^{0} &= \sqrt{ R^{2} - r^{2}}  \, \sinh{\left (\frac{t}{R} \right )} \\
x^{1} &= \sqrt{ R^{2} - r^{2}}  \, \cosh{\left (\frac{t}{R} \right )} \\
x^{2} &= r\sin{\theta} \cos{\varphi} \\\
x^{3} &= r \sin{\theta} \cos{\varphi} \\
x^{4} &= r \cos{\theta}
\end{split}
\end{equation}
then your metric acquires a coordinate singularity at $r=\pm R$:
\begin{equation}
ds^{2} = -\left ( 1- \frac{r^{2}}{R^{2}} \right ) dt^{2} + \left ( 1- \frac{r^{2}}{R^{2}} \right )^{-1} dr^{2} + r^{2} d\Omega _{2} ^{2}
\end{equation}
These coordinates cover only the region of dS space which is in causal contact with a static observer. The coordinate singularity in turn describes the two event horizons that appear (future and past) which is a feature of dS space. You can readily see this in the relevant Penrose diagram:

with the future and past horizons being $H^{+}$ and $H^{-}$ respectively, and the region covered by static coordinates is region I.
For your case, it might take some work to figure out exactly an appropriate coordinate system where the singularity is lifted, but from its form it seems that it is doable. On the other hand, $\Phi(r)$ can only be removed via a conformal/Weyl transformation, hence the stipulation that it is finite is necessary to keep the metric non-singular.
Comment: Thank you for your response. I don't have a good understanding of Penrose diagrams yet, but I will study more. Anyway, I will look into the differences between a physical singularity and a coordinate singularity, thank you very much.
Answer: I am afraid I cannot explain it better as Francisco S. N. Lobo in his paper "Exotic solutions in General Relativity: Traversable wormholes and 'warp drive' spacetimes" therefore I quote him here verbatim:
(...)
Consider the following spherically symmetric and static wormhole
solution
\begin{equation}
ds^2=-e ^{2\Phi(r)} \,dt^2+\frac{dr^2}{1- b(r)/r}+r^2 \,(d\theta
^2+\sin ^2{\theta} \, d\phi ^2) \,, \label{metricwormhole} \tag{1}
\end{equation}
where $\Phi(r)$ and $b(r)$ are arbitrary functions of the radial
coordinate $r$. $\Phi(r)$ is denoted the redshift function, for it
is related to the gravitational redshift, and $b(r)$ is denoted
the shape function, because as can be shown by embedding diagrams,
it determines the shape of the wormhole (Morris and Thorne). The
coordinate $r$ is non-monotonic in that it decreases from
$+\infty$ to a minimum value $r_0$, representing the location of
the throat of the wormhole, where $b(r_0)=r_0$, and then it
increases from $r_0$ to $+\infty$. The proper circumference of a
circle of fixed $r$ is given by $2\pi r$. Although the metric
coefficient $g_{rr}$ becomes divergent at the throat, which is
signalled by the coordinate singularity, the proper radial
distance
\begin{equation}
 l(r)=\pm\,\int_{r_0}^r{{dr}\over{(1-b(r)/r)^{1/2}}} \,,
                                                 \label{eq:PD} \tag{2}
\end{equation}
is required to be finite everywhere. Note that as $0 \leq 1
-b(r)/r \leq 1$, the proper distance is greater than or equal to
the coordinate distance, i.e., $|l(r)| \geq r - r_0$.   The metric
(1) may be written in terms of the proper
radial distance as
\begin{equation}
ds^2=-e^{2\Phi(l)}dt^2 + dl^2
 + {r^2}(l)({d\theta}^2+ {\rm sin}^2\theta\,{d\phi}^2)\,. \tag{3}
\end{equation}
The proper distance decreases from $l=+\infty$, in the upper
universe, to $l=0$ at the throat, and then from zero to $-\infty$
in the lower universe. For the wormhole to be traversable it must
have no horizons, which implies that $g_{tt}=-e^{2\Phi(r)}\neq 0$,
so that $\Phi(r)$ must be finite everywhere.
(...)
Comment: Thank you for the article recommendation, it has been very helpful.
Comment: I am glad I could help. Another possibility to understand it is to notice that Einstein field equation in that case are on $e^{\phi}(r)$ and $1-b(r)/r$ functions which both are finite. See the work out in https://physics.stackexchange.com/a/679431/281096

Singularities and Horizons


Can red eye in only one eye be a sign of cancer?

Question: I noticed on a photo I did of a client that only one of their eyes turned red on a photo. I remembered reading that this could be a sign of eye cancer (see http://www.chect.org.uk/cms/index.php/signs-and-symptoms)
I wanted to double check what other things could cause this before I worry a client. It has never happened in my work before, but I don't know if this is a common occurrence.
Comment: Would you take medical advice from a random stranger?
Comment: @SVilcans If that person said to you, "Hey, it looks like you may have a symptom of retinoblastoma," it might be enough to get you to ask your doctor.  Better safe than sorry.
Comment: The link in the question is broken, but here's a similar page from the same source: https://chect.org.uk/about-retinoblastoma-2/whiteeye/
Comment: In very young children, it can be, yes.  Note that retinoblatoma is most commonly seen in infants, and very rarely in anyone over five years old or thereabouts, so if you're saying that the person paying for your shoot is showing these symptoms, then either you have some very lax child labor laws where you live or it probably isn't retinoblastoma, statistically speaking.  :-)
Answer: If you take a lot of flash photos, with the flash pointed directly at the subjects, you'll notice that eyes only sometimes go red: it depends on the angle of the eye with respect to the flash & lens. If the eye is facing off to one side, or outside the main area painted by the flash, it may not appear red.
Having one red eye could happen if, for example:

the person is quite close to the camera
off to one side of the frame
not looking directly at the flash/lens
has a lazy eye (or is otherwise pointing their eyes in different directions)

I would recommend checking more photos of the person (if you have more), to see if they consistently have just the one red-eye (the same one each time).
If in doubt, I would suggest to the client that 'it can be a symptom of eye problems, you might want to get it checked by a GP', rather than suggesting cancer straight up. The link you provided doesn't suggest it's unequivocal evidence, and pretty vaguely suggests that (for one red one black eye) "This can also be a sign that something is not right".
Answer: There's a famous rule taught to med students:  "If you hear hoofbeats outside the window,  don't think 'zebra' when it's almost certainly a horse."  (reverse the species if you live in Africa, I guess :-) ).  The point is that observing a single possible symptom which might correlate with a disease has very little to do with proper diagnosis.  You need to be able to Rule Out  the myriad other conditions which also correlate with the symptom in question, as well as weighing the relative probabilities.
It's like having a coughing attack and thinking lung cancer.  There are lots more likely and common reasons to cough, and several other symptoms which a lung cancer victim would be presenting.
Comment: Okay so passing by to mention that there are about 750,000 zebra https://defenders.org/zebra/basic-facts  and 4,500,000 horses (https://stud.epsilon.slu.se/7676/17/khadka_r_150305.pdf)  in Africa. Plus I think the zebras are more likely to be in larger herds futher away from windows... I should get out more...
Comment: See also [Occam's razor](http://en.wikipedia.org/wiki/Occam's_razor), and [Bayes' Theorem relating to medical tests](http://vassarstats.net/bayes.html).
Comment: Off-topic, but this is why folks with EDS sometimes call themself zebras (that and their skin).
Answer: The optical axis of eyes change with the distance the person focuses at. So they do not look in the same direction most of the time. If the person is facing you completely, then there is better chance that the two optical axis have the same angle to you and your camera. Still, one eye may be a tiny bit off, that is natural. Or it can be waaay off - those people still see well.
So the only information that you can deduct from only one red eye is: only one eye was directed towards the camera. But even you can do that. E.g. have someone photograph you from 5 meters when you have a pencil between your right eye and the camera, you look over the top of the pencil and directly to the camera, and focus on the pencil with your both eyes. The pencil should be 50 cm far. Then your right eye will look directly into the camera, and the left will definitely not look into the camera.
However, you might as well spotted some eye problems, and a quick check with an eye doctor is not a bad idea. (Usually 10 minutes, they just check if the two eyes are properly aligned). My bet is: eye cancer? Nah. Some minor axis error? Small chance.
Answer: I quite regularly end up with red-eye in only one eye.  I do a lot of casual, candid shots where people don't know I'm taking a photo and it happens all the time.  While red eye most typically happens when people are looking directly at you, it can also occur regularly when they are not.  If someone is looking to the side, the side of one eye will still reflect enough light back while the other will not.
Note that this principal is the same as the tidbit about cancer being detected through red-eye.  If cancer is causing a deformation of the eye, then it won't reflect light back in the expected way and you won't get red-eye.  This should occur even when directly facing.  It may still be possible to have the same occur for many other reasons though to, so it is just a very small possibility to be the cause.
Answer: They could have an artificial eye that would not react to the flash.
Comment: Or be a heterochrome.
Comment: Heterochromia affects the color of the iris, not the pupil or lens.


How are LTI systems related to Toeplitz matrices?

Question: I am having trouble understanding why the system matrix of an LTI system is Toeplitz. I am following an Edx online course by Professor Richard Baraniuk of Rice University, named discrete-time signals and systems. In the course, the instructor showed that given a system matrix $H$, $H(n,m) = H(n'+q,m'+q)$ where $n'=n-q$ and $m'=m-q$, which is obvious. But, from that, he claimed the general Toeplitz structure $H(n,m)=H(n+q,m+q)$ and this is where I am getting lost.
Comment: Take a look at [this](https://dsp.stackexchange.com/a/44439/21075)
Comment: Take a look at the first few pages of Gray's [Toeplitz and Circulant Matrices](https://ee.stanford.edu/~gray/toeplitz.html)
Comment: [Related](https://dsp.stackexchange.com/q/54206/21075)
Comment: [Related](https://dsp.stackexchange.com/q/15096/21075)
Answer: LTI systems are related to Toeplitz matrices via convolution:
The output of an LTI system is the convolution of the input with the system impulse response.
Assuming matrix equations are understood, observe how time domain convolution can be written as a matrix product, applicable to finite duration impulse responses. The resulting matrix $A$ with each column as a shifted copy of $r[n]$ is a Toeplitz matrix.
Comment: Could someone post a link to the definition of "System matrix" in this context?  I would have taken the term to mean the _state transition matrix_, which is clearly not the case here.  I mean -- yes, it's the convolution operator, in matrix form, but it would still be nice to see the context in which it is defined.
Comment: Thanks, I understand that, but what is not convincing to me is why the professor claimed H(n, m) = H(n+q, m+q) from the fact that H(n'+q, m'+q) = H(n, m) where again n'=n-q and m'=m-q.


Should "NaN" default to SNaN or QNaN

Question: I created a function to read floats (IEEE 754 binary 32-bit) from strings, for developers. I have everything finished and working perfectly, except i'm wondering if a user/or programmer enters a string such as "NaN" that does not specify QNaN or SNaN, what should it be considered? or should "NaN" be considered an invalid input and only accept "QNaN" or "SNaN"?
Comment: That's going to depend on the context. Which one do the users most likely want? What are the possible consequences of them getting the one they *don't* want, without realising? Could you provide options for *them* to decide?
Comment: So long as the caller has a means to determine that you passed QNaN or SNaN, then they have everything necessary to convert as needed.  Pick the one they will most likely need, and provide adequate documentation.
Comment: @jonrsharpe Well, the function is for the general public of programmers. A library that anyone can use, so its not for any specific purpose other than what someone else might decide. there will definitely be documentation of the function. Providing an option to switch the behavior doesn't seem necessary to me. Perhaps someone has an opinion on that?
Answer: First of all you should note that the signaling NaN (SNAN) is behaving the same as the quiet NAN (QNAN) when floating point exceptions are disabled. Usually they are disabled.
If "NaN" in your file is supposed to mean "missing data" then use QNAN.
If "NaN" is your file is supposed to mean "this must be initialized with proper data later" the use SNAN.
In the latter case an exception would be generated (if enabled, of course) in case the data is (accidentally) read and fed into a computation. However, when doing it this way (exceptions enabled) you must ensure that all your other FP computations do not generate NaN during regular computation and/or you need to implement proper exception handling. There of course you loose the advantage of FP math of being algebraically closed, i.e. be able to work in an exception free manner.
One problem with FP exceptions is also that in most programming languages the exceptions are non-continuable, whereas in the FP world this is not necessary (after exceptions the code can be continued). This is a bit too restrictive.
Personally I would suggest you to use QNAN.
Comment: "Personally I would suggest you to use QNAN." Do you prefer that over "NaN" being considered invalid and enforcing ether QNAN or SNAN strings?
Comment: I would not distinguish SNAN and QNAN in a text format, just "NaN" which gets parsed as QNAN. One could add the feature that also the text strings "QNAN" and "SNAN" are parsed, but in any case I would read them as QNAN symbols. I cant think of any use-case that needs the user to enter a signaling NaN in the data. So I would ignore this. It might have unwanted side effects

Should "NaN" default to SNaN or QNaN


Booklet printing

Question: How would I print a booklet in Word 2016? Do I have to do 4, 1 then 2, 3 or is the order printed automatically as some people have said. I am doing it for my project and I am making a book so will I have to rearrange the pages 4,1 2,3 after i have done book-fold option in Word 2016 so that the reader will read it in correct order or not? Plus how do I add a gap in the middle of my page for book binding? I am going to try printing it normally without doing any page order changes and have not tried anything as of now.
Answer: So this process is called imposing and you are asking about printer spreads. What we usually look at when making a document is called reading order or reader spreads.
For any booklet with more than 8 or 12 pages, you are probably going to want to use reader spreads and have software handle the page ordering for you, since it gets kind of overwhelming.
Usually you are going to want to set the page size of the document the trim size (that is: the final size of the book), and then when you impose & print, the pages get printed 2-up, double sided on sheets that are the same height and twice as wide as the trim size. Double sided printing on consumer printers is called duplexing.
An additional consideration is creep which is an alignment adjustment made to account for the thickness of the paper: the inner sheets will stick out farther because the spine gets thicker as you stack pages.
Exactly how you get this done varies wildly depending on software. I usually rely on my print provider to do this for business, but for home projects, the simplest is to print or export to PDF, and the run the PDF through open source PDF-to-booklet software.
A few tips:
1) saddle stitch (fold and staple) booklets need to have page counts in exact multiples of 4: you are printing 2-up double sided and then folding in half. A single page (half sheet) will fall out of the book.
2) in keeping with #1, if you need to work out page order for a 16 page booklet, take 4 sheets of paper, stack them, fold them in half, and then take a marker and write "1,2,3..." in reading order. When you remove the sheets, you will see the required layout of the pages.
3) google using the bolded terms above. One of the main differences you may find in page ordering is for perfect bound books: for perfect bound you break up the book into mini-booklets called signatures and then stack them. See also: https://graphicdesign.stackexchange.com/search?q=booklet
Comment: So i get everything else but are you saying with word 2016 they do not do imposition FOR you because with all the videos i've seen along with the comments it certainly looks like word does imposing for you.

Booklet printing


They are going to rate/ or evaluate our working performance. Is there a difference?

Question: Is there a difference between the words evaluate and rate? For example, does a boss evaluate or rate one's work?
Answer: To rate a performance is to estimate the value of something on some quality scale.
e.g.

Rate this from 1 to 10.
We were rated the third-best of the presenters.
He rates as one of the best journalists in town.
That website rated the movie with a very low score.

To evaluate is to undergo a process of reviewing something, testing things and judgement to see a thing's worth, quality, or significance.

You will be evaluated on your skills on the exam.
The teacher evaluated the students' work and surprisingly, he failed three students on the assignment.
We are waiting for Luke to evaluate their performance to see how they're doing.
They are evaluating our paper to find out just how ground-breaking our discovery was.

The output of the evaluation doesn't have to be a rating or score; it could be comments on how to improve something as well!
Answer: He/She can do both.
Evaluate is used for things.
Rate is used for things or people.

1.— The boss evaluated the results.
2.— The boss rated your performance.
Comment: I can't find any such distinction in any major dictionary. The annual *employee evaluation* is a much-dreaded and much joked-about topic in American corporate culture, and if anything, to *rate* employees sounds much harsher and hierarchical to my ears than to *evaluate* them.
Answer: In this situation, they are pretty much interchangeable. Here are the nuances:
to rate
This verb has neutral formality, I could see this being used in casual contexts and formal papers alike. The underlying "quality" exists on a scale of ratings.  Ratings are orderable: For any two different ratings X and Y, either X is greater than Y, or X is less than Y.
In the United States, films are rated G, PG, PG13, R, in terms of audience maturity
In finance, bonds are given AAA, AA, A, BBB, BB etc. ratings for how likely the borrower will pay the money back.
to evaluate
This verb is more formal. For example, you can casually say

My fashion magazine rates this season's outfits as "hot or not"

but it would be out of place to use "evaluates" here.
Also, the underlying "quality" is not necessarily on a scale. Evaluations can be non orderable. For example, you could say

In our evaluation of employee A's performance, we found him to be uncooperative and slow to respond to emails
In our evaluation of employee B's performance, we found him to be very productive but unethical

It isn't clear which evaluation is "better".


Diplacusis - possible to tell which ear is normal?

Question: Diplacusis is a hearing disorder in which the two ears hear the same sound as different pitches. Suppose we know that someone with diplacusis has one normal ear and one ear that is slightly off. Using simple sine waves sent through headphones, it is possible to have the person adjust the pitch being sent to one ear until the sound is identical in both ears, which would tell us by how much the ears are offset (at that frequency). But is it possible to devise a test which could detect which ear is normal?
Comment: "which ear is normal" cannot be decided, human ears are not gauged to a absolute frequency scale, but hearing gives a subjective pitch. There is no way to tell which pitch is "the right one".
Comment: @SebastianRiese - what if multiple pitch offsets are considered? For example, suppose the person is a musician. If a scale is played that sounds perfect in one ear, but in the other ear one or more pitches sound like they are slightly off the scale, then that could be an indicator. Or perhaps the same note 4 octaves apart played simultaneously that sound like the same note in one ear but out of tune in the other. I guess this would depend on how pure the offset curve is...
Comment: In such cases this could certainly be possible, I guess. This is, however, not pure pitch offset between the ears, but also inconsistency of the pitches reported by a single ear. The doubling of the frequency corresponds to the change of pitch by one octave quite exactly. But even then you cannot specify, that the pitch one ear produces for a 440Hz sine wave is the correct one.
Comment: Why would you want to even if you could?  All you need is a frequency-shifter applied to either ear (assuming the offset is constant) to make the subject hear "properly."
Comment: @CarlWitthoft - if you know which ear is the problem, it could help with diagnosing the cause.
Answer: From a physics perspective: No. Relative differences can be detected as you point out, but in order to test which ear is normal, you need a reference. In the case of pitch difference, you can use one of the ears as reference for the other. In your case, the absolute reference scale is missing. And you can't get it from another person, because perception is subjective (is the pitch I perceive the same as the one you do? Why don't we have the same frequencies we don't like?). Maybe there is something objectively wrong with one of the ears or the brain tissue processing the signals - but for that, I guess you'll need to ask physicians and not the physicists. But note: "objectively wrong" here means that it is different from the majority of ears of the human population. Now you have a reference!
The underlying problem you are facing lies at the heart of experimental physics: For most experiments, you are trying to measure something on a (for all practical purposes) continuous scale: You might be measuring a frequency, a time, a distance, etc. All of this is only possible by comparison with a reference scale. In a continuum, there is no absolute scale until you fix one. This is why it is so very important to have good definitions of units: we need good absolute scales which we can compare our experiments with. Luckily, nature is in many ways discrete and has some fundamental constants that are dimensionless - and we can use that to define our scales objectively (time is defined by number of oscillations of a Caesium atom, mass will probably be defined by the number of atoms in a crystal at a specific temperature).
Comment: I'm not 100% convinced that there is no way to get an absolute reference, but I agree that if one exists it is the physician, not the physicist that can answer that. My current line of thinking is to learn more about how cochlear implants work. Perhaps someone who is deaf in one ear and has a cochlear implant, and can hear fine in the other ear would be able to tell us if this is possible. If the implant needs to be *tuned* to the user's preference, then perhaps the electrical signal is not absolute. Seems like a stretch anyway that the signal would be interpreted the same way by everyone.
Comment: @TTT: Even if you can extract a reference in the case of a cochlear implant, that wouldn't be much help for any other case. I have no idea about medicine, but a priori, there can be two ways for the pitch shift to occur: There is a failure of the mechanical parts of the ear to transmit the frequencies faithfully (if this is the case, if you'd replace the bad ear by a cochlear implant, you'd notice), or there is failure of the brain to process the information correctly (in which case a cochlear implant can't tell you whether the other ear is "normal"). But we agree, that's not physics.
Comment: I fully agree. I'm making the assumption that the failure is (usually?) mechanical rather than the processing. I suppose this is true of eyes as well. Now that I think about it, this question could be entirely repeated for eyes instead of ears. Many people see slightly different colors or shades in each eye. I would assume the answer would the same.
Answer: When the afflicted subject listens to a single tone, he will hear one pitch in one ear and another pitch in the other ear. The difference between the pitches will be clear, but for the answer to be "yes", the subject would need some other piece of information to discriminate between the two. Otherwise, they won't know if their left ear is incorrectly shifted up, or their right ear is incorrectly shifted down.
So, for the great majority of the populace who cannot listen to a single tone and tell whether it's "right" or "wrong", there's no way to tell which ear is wrong. But, those with absolute pitch CAN listen to a single identified tone and tell whether it's wrong. So, an unfortunate musician with this condition may be able to play $A$ on a piano and tell whether one ear is wrong, and which one.

As an aside, about ten years ago I had an ear infection which gave me exactly this problem. Everything sounded like dissonant chords, which (as a musician) was a serious bummer. (I knew which ear had been infected, so I knew which one was mis-hearing.)
As a software engineer, I decided to measure the condition, and so wrote a simple Macintosh application called ToneTester. It played a pitch in each ear and let you adjust the two until they seemed to match. I couldn't play the pitches simultaneously, since audio leaks from one ear to the other and you could hear the tones beat against each other and tell that they were wrong. So, my app alternated playing one tone in one ear and the other tone in the other ear. Using this I found that one of my ears would hear pitches about one and a half semitones higher than the other.
Over the following year my ears adjusted, and I once again heard clearly. I haven't updated ToneTester in a long time, and it won't run on anything later than OS X 10.6.8.
Comment: I think you're making a big leap about perfect pitch and how the brain processes it.  You're implying that somehow the brain "knows" that the bad ear is "reporting" a different value than the good ear.  It would be interesting to track down someone who's got both perfect pitch and diplacusis to see what happens, but my bet is they'll recognize pitches just fine with either ear.
Comment: Interesting point about playing the tones simultaneously and having beating.
Comment: @CarlWitthoft Nope. Someone with real absolute pitch (not me) can listen to a note and tell you whether it's an A or an A flat. If they play an A, and hear A in the right ear and A flat in the left, then they'll know the left ear is hearing wrong.
Comment: @DanielGriscom, that assumes that the person had perfect pitch before getting diplacusis, otherwise they would never have been able to learn which ear was correct to begin with.
Comment: I doubt people are born with diplacusis; otherwise their brains would never train to hear pitches differently in each ear. Wikipedia supports this, although not explicitly.


Can I cast Shield against an attack that hits me during a Time Stop?

Question: Suppose an enemy casts Time Stop and then makes an attack against me, rolling a 20 to hit against my 16 AC. Normally, I could cast Shield to cause this attack to miss. And of course, this attack also ends the Time Stop. So, does time start flowing "soon enough" for me to cast Shield against the attack that ends the Time Stop spell?
Comment: Though I did close this question, I could certainly see the argument made that the linked question never mentions the *shield* spell which is an exceptional enough spell to warrant its own question (after all, we have a **lot** of questions about *shield*)
Comment: @Medix2 Yeah, it's a bit ambiguous. Unfortunately the accepted answer kind of glosses over the details of the interaction between *Time Stop* and *Shield*.
Answer: Yes, you can cast Shield
Time Stop says:

This spell ends if one of the actions you use during this period, or any effects that you create during this period, affects a creature other than you or an object being worn or carried by someone other than you.

As soon as the caster Attacks or creates some effect that affects a creature other than itself, the spell ends. Once the spell has ended, you can act normally, allowing you to cast Shield with your reaction, turning a potential hit into a miss.
Comment: If the attack misses, how does it affect you?
Comment: @MarkWells It affects you by making you a target. Whether or not you were successfully hit is irrelevant, as long as you were targeted.


Would using Websockets cause PCI compliance failure?

Question: Would utilizing WebSockets cause an issue with obtaining or maintaining PCI compliance?
Comment: In and of itself I can't see the use of websockets contravening PCI, I'm definitely not aware of a specific mention of it in the standards.

However it's entirely possible that an application implementation which made use of websockets could be non-compliant.  If you provide some more details it may be possible to give a better answer :)
Comment: @RoryMcCune - this was a general water cooler question that came up in the office today, no application implementation. Thank you for the words.
Comment: You would naturally need to use TLS-protected WebSocket protocol (`wss:`) for any communication including sensitive data like PANs.
Answer: Not in and of itself; however, like any network connection, it is subject to PCI DSS rules such as the following:

1.1.5.a Verify that firewall and router configuration standards include a documented list of services, protocols and ports necessary for business—for example, hypertext transfer protocol (HTTP) and Secure Sockets Layer (SSL), Secure Shell (SSH), and Virtual Private Network (VPN) protocols.
  1.1.5.b Identify insecure services, protocols, and ports allowed; and verify they are necessary and that security features are documented and implemented by examining firewall and router configuration standards and settings for each service.

So you'll need to document that any services you set up using WebSocket are necessary and secure; pretty much just the way you would as if it was vanilla TCP.

1.2.1.a Verify that inbound and outbound traffic is limited to that which is necessary for the cardholder data environment, and that the restrictions are documented.

Again... document that it's needed.
I haven't used WebSocket, but it appears to be just an abstraction layer on top of TCP, and so for PCI purposes does not introduce any inherent insecurities over the set pre-existing in TCP (...until proven otherwise, natch).  Obviously for PCI purposes you'll want to pay attention to encryption and make sure that's enabled most places.


Sony HDR AS30 detect device on imac

Question: Does anyone know for sure if Sony HDR AS30 is only compatible with macOS 7 and up?
I know from reading docs it's only compatible for 7 and up for wifi setup but it's hard to know for desktop because there is software current for mac but no ability to input without device detection. I can see the USB connection on the mac and camera but the software is not detecting a camera.
Answer: Ok finally worked it out haha
Do not be a dummy like me and insert the memory stick upside down!
You will know when it is correctly inserted because a red light will come on indicating ready to record.

Sony HDR AS30 detect device on imac


WCF and n-tier architecture and serialization performance

Question: When working with 5-tier architecture (front-end => interface tier => business tier => database tier => database) using WCF service as the interface tier, having the client applications calling it's methods, should I use also WCF service for the business and database tiers? I ask because of all the serialization / deserialization that will be going on between the 3 services is probably going to consume a lot of CPU for the server, and have a performance impact on the application as a whole, or am I wrong?
In the case of running all 3 component layers on a single machine, is it better to build the business and database tiers as simple class libraries, and leave only the interface layer as WCF?
Tks
Answer: Tiered architecture is a pre-SOA approach, although we still build logical tiers in our software today. But physical tiers, if more than one (apart from UI and database), will cause you pain and heartache. Sometimes you end up having two but I personally advise against it.
Trend is using parallel/decoupled processing using Service Bus or similar methods and building serial services are not recommended.
You have pointed out the serialisation overhead. But that is just the beginning, you have method execution delay, more points of failure, degradation of performance since layers talk out of process, maintenance overhead, ...
So do not be apologetic about having only one middleware physical layer, that is not an asset it is a liability.
Answer: WCF is useful for communication between physical machines.  Although you can use WCF to communicate intra-process there are simpler and more efficient ways to accomplish the same thing.  You would only use WCF intra-process if you were thinking about putting the different layers on different machines at some point.  As far as using WCF for the database tier, you wouldn't: you would use the classes in the System.Data.xxx namespaces (ie System.Data.SqlClient if you are using a SQL server database; or possibly the Entity Framework).
Edits:
When people talk about 3-tier architecture they are mixing two concepts into one: physical tiers: a client machine, a middleware machine and a Database machine; and logical layers in the software architecture: client UI code, Business logic code, and data access code.  When code from two different logical layers that reside on the same physical machine need to communicate the simplest model is one class calling into another, the amount of decoupling depends on your requirements.  You want to use the simplest model that satisfies your requirements.  Rockford Lhotka has an excellent description of this in the first chapter of his book Expert C# 2008 Business Objects
Comment: What are the simpler and more efficient ways? Could you elaborate a bit? And in case of chosing to build the 3 tiers in WCF, is the overhead in performance too big? Is there a way to minimize it? Tks


Modeling incoming solar radiation

Question: I want to write a model for estimating incoming solar radiation for a specific latitude on earth but I am struggling to find an appropriate source which shows the required equations for doing so. Would anyone be able to provide me with a link to where I can find equations for estimating solar radiation (irradiance) given a specific cloud cover, latitude, time of day, and day of year?
Comment: Are you only interested in the direct irradiance or do you also want model scattered light? Are you interested in a specific wavelength region (or spectral irradiance) or the total irradiance in the full spectrum?
Comment: @Kate This is of interest to people studying and manufacturing photovoltaic solar cells. They talk about solar radiation at 1A (one atmosphere), 1.5A (one an a half atmospheres) etc. The following link can be a good starting point, but you might have to download the whole article in order to read it. http://www.mendeley.com/catalog/evaluation-high-altitude-solar-radiation-platform/#page-1
Comment: Take a look at the SMARTS atmospheric model and associated documentation, it might have the clues you need. http://www.nrel.gov/rredc/smarts/
Comment: @jkej I am interested in direct irradiance, where the mainaim of the model will be to estimate short wave radiation with wavelengths in the visible (VIS), near-ultraviolet (UV), and near-infrared (NIR) spectra.
Answer: Ok, I'm still not sure on what level you want to do this, but I will start you off with some basics. The most important factor is probably the solar elevation angle, $\theta$. As described on the wiki-page it can be calculated using this formula:
$$\sin\theta=\cos h\cos\delta\cos\Phi+\sin\delta\sin\Phi$$
where $h$ is the hour angle, $\delta$ is the solar declination and $\Phi$ is the latitude. The trickiest to calculate of these is the solar declination. A few different formulas to calculate is can be found here. Which formula you use will depend on the accuarcy you need. I suggest starting with this formula:
$$
\delta=-\arcsin(0.39789\cos(0.98565(N+10)+1.914\sin(0.98565(N-2))))
$$
where $N$ is the day of year beginning with $N=0$ at 00:00:00 UTC on January 1 (prefereably calulate $N$ as a decimal number to increase accuracy). Note that this formula uses degree-based trigonometric functions.
Now, if we totally ignore atmosperic effects, total solar irradiance (of all wavelengths) incident on a horizontal surface will be:
$$
E=A\sin\theta
$$
where $A$ is the solar constant which approximatley has the value 1360 W/m$^2$ (on average, it varies by roughly 7% over the year due to the ellipticity of Earth's orbit).
Since this ignores atmospheric effects, the actual irradiance on the ground will be lower due to scattering and absorption. These effects will also depend on the solar elevation angle, since a lower angle gives a longer light path through the atmosphere.
Maybe, starting from this, you can explain what further aspects you need to model.
Comment: Nice explanation. Could you also provide your sources?
Answer: If you are interested just in the direct irradiance you can neglect the emmision and scattering terms in the Radiative Transfer Equation RTE wich can in this case be simplified to allow only for absorbtion and is known under the name Beer-Bougert-Lambert's law of absorption
$$
\cos\theta_{0}\,\frac{\partial}{\partial p}S^{i} =
-\frac{\kappa^i}{g}\,S^{i}
$$
Here I assumed pressure coordinates to parameterize the height above ground, $i$ is the index of the band if you have more than one, and $S$ is the solar flux in Wm$^{-2}$. The zenith angle $\theta_0(\lambda,\phi,t)$ varies with longitude, latitude, and time of the year which can be taken into account, by
$$
\cos\theta_0 = \cos\phi \cos\delta\cos h + \sin\phi \sin\delta
$$
where $\delta$ is the declination angle and $h$ the hour angle.
The Absorption coefficient con be calculated for example as the mixing ratio $\rho_a/\rho$ of the absorber times the band strength $K^i$
$$
\kappa^i = \frac{\rho_a}{\rho}K^i
$$
The only thing left to do for a simple parameterization of the solar radiation is to specify the upper boundery condition for each band you want to consider, for example
$$
\begin{eqnarray}
S^1(p=0) & = & C_{sun}\,\:UV_{O3}\,\cos \theta_{0}\\
S^2(p=0) & = & C_{sun}\, \:VIS_{O3}\,\cos \theta_{0}\nonumber \\
S^3(p=0) & = & C_{sun}\,\:VIS_{H2O}\, \cos \theta_{0} \nonumber \\
S^4(p=0) & = & C_{sun}\, \:UV_{O2}\,\cos \theta_{0} \nonumber \\
S^5       & = & C_{sun}\,\cos \theta_{0} \, -
\,\sum\limits_{i=1}^4 S^i (p=0)
              \nonumber
\end{eqnarray}
$$
Where $C_{sun}$ is the solar "constant" of about 1362  Wm$^{-2}$, $UV_{O3}$ for example is the relative part of the incoming solar energy that goes into the ozone UV absorber band, and the fifth band contains the radiation that is directly transmitted to the surface. With this simple parameterization you can calculate the solar radiation at the surface by integration the absorption law downward.
More comprehensive methods to solve the radiation problem in the shortwave regime include scattering on aerosols, clouds, and air molecules and allow for reflection
at the surface too. Non-LTE (most important in for the longwave regime in the middle atmosphere for example) in the SW regime can be established by considering appropriate
efficiencies for the conversion of absorbed solar radiation to kinetic energy of the atmospheric constituents.
In the approach of discrete ordinates, the appropriate RTE is solved for different discrete zenith directions.
The principle of invariance and the adding method apply some kind of ray tracing for the incoming solar beam
inside an atmospheric layer in order to  calculate the emerging radiation
at the upper and lower boundary of the layer.
These more comprehensive methods are explained for example here where you can find a more detailled explanation and treatment of both, longwave and shortwave radiative transfer in the atmosphere.
Comment: Good explanation of how absorption can be treated. However, can scattering terms really be neglegted? The fact that the sun is red at sunset is a clear indicator that scattering is important, at least for low sun angles. Also, your link to explain the calculation of zenith angle goes to the wiki-page on the solar *azimuth* angle.
Comment: @jkej yes thanks, I updated my answer a little bit.
Answer: Heinrich Morf, A stochastic solar irradiance model adjusted on the Ångström–Prescott regression, Solar Energy, Volume 87, January 2013, Pages 1-21, ISSN 0038-092X, 10.1016/j.solener.2012.10.005.
Keywords: Ångström–Prescott regression; Cloud enhancement; Photovoltaic fleet; Solar irradiance; Stochastic modeling
Heinrich Morf, The Stochastic Two-State Cloud Cover Model STSCCM, Solar Energy, Volume 85, Issue 5, May 2011, Pages 985-999, ISSN 0038-092X, 10.1016/j.solener.2011.02.015.
Keywords: Climatology; Cloud cover; Meteorology; Solar energy; Stochastic modeling; Vertical visibility
Heinrich Morf, The Stochastic two-state solar irradiance model (STSIM), Solar Energy, Volume 62, Issue 2, February 1998, Pages 101-112, ISSN 0038-092X, 10.1016/S0038-092X(98)00004-8.
Answer: If you need to estimate solar radiation from the cloud cover in Europe you can look at the R-package 'sirad'. It contains a functon su() which implements the Supit-Van Kappel model. The model requires daily cloud cover and daily temperature range for input.
Answer: I studied physics in the old days but then had a career in engineering.  I think it important to have experimental data to correlate with formulae and hypothesis.  Perhaps astronomers studying solar radiation have data over several frequency ranges, times of year, latitudes etc.  I think also interesting to know the amount of polarisation of the radiation according to the distance traversed, and its angle, through the atmosphere. IR reflective mirrors could redirect incident radiation vertically so that it would be lost to space with a minimum absorption and reflection by the atmosphere.

Modeling incoming solar radiation


C++ Exposed property for COM in idl is showing as lower case "all of a sudden"

Question: I have this old C++ COM component.  I took the latest code base, built it and found that one of the properties has become lower case.  For example, in the pre-compiled dll i have a property "Type", but when building from source it's called "type".  The idl shows that the property is called "Type".  So what could possibly be happening here?
Answer: COM is case-insensitive, so there is only one entry in the library's symbol table for the symbol "type". The version which is put into the symbol table is the first one that the compiler encounters.
Microsoft's advice on the matter is simply:

Make sure that the same name is not already present in the IDL file when introducing a new identifier.

You should stick to either Type or type in the IDL, for consistent results.
Comment: My problem was that parameter `value` in one method was breaking `Value` property
Answer: You discovered a quirk in the OS stock implementation of ICreateTypeLib, used by practically all tool chains on Windows that can create a type library.  It uses a rather crude way to deal with possible problems caused by languages that are not case-sensitive, VB/A being a prominent example.
At issue is the definition of an identifier with one casing, being referenced elsewhere in the type library with another casing.  Not a problem at all in, say, VB, big problem when the client programmer uses a case-sensitive language like C# or C++.
The "fix" it uses is to force the casing to be consistent everywhere in the library.  Unfortunately it is not very sophisticated about it.  Best example is a method declaration earlier in the type library that takes an argument named type.  Any identifier named Type in the rest of the type library will now get case-converted to type.
Repairing this problem is easy enough, just change the name of the identifier so it no longer matches.  You'll have to find it, not so easy, best to use Oleview.exe, File > View Typelib command.  Copy/paste the decompiled IDL into a text editor and use its Search command.
Comment: Actually I am simply talking about viewing the library in OLEVIEW so not .Net involved at this point.  However, possibly by some coincidence what you say is happening in this case.  I looked at recent changes.. a new method had been added with a param named "type".  I then commented this any the "Type" property was displayed correctly.  I then uncommented it.. and.. it works!?? huh? using VC++6 IDE for this component so not shocked, just a little frustrated.

Thanks for the quick response.
Answer: I had the same problem almost 10 years after this question was asked and I would like to share my solution (thanks for the help in understanding the problem).
First I would like to say that I had several names whose casing was changed by tlbimp and changing all the instances of these names to my expected casing in the IDL fixed all but one. I'm assuming that that name (Text) came from a different IDL I imported. I was also not happy with the solution of changing the names of parameters and the like since in the future someone else may change them.
The solution I found was to introduce a dummy interface with the casing I wanted. I did this before all other imports and then referenced it in the library section of the IDL. Note that both these details are required. If you don't put it in the library section it's ignored and if I defined it at the beginning of the library section after the imports it's too late.
import "oaidl.idl";
import "ocidl.idl";

[
    uuid(4EA92D5A-BF84-46C4-AA38-0F7DEADC69B),
    helpstring("Ensure that names used in interop have correct casing")
]
interface IAmHack : IUnknown
{
    HRESULT Space();
    HRESULT The();
    HRESULT Final();
    HRESULT Frontier();
};

// ...

library MyLib
{
    interface IAmHack;

    importlib("stdole2.tlb");


Linux ssh user connect

Question: I all, I have a linux Server (Ubuntu) where some user can be connect to by ssh.
Is possible to know who was connected to the server?
A sort of list of login by ssh of the past day.
Is possible to retrieve?
Answer: who will show you who is currently connected.
w will show you who is curretly connected, plus what command they're running.
last will show you all users logged in/out since /var/log/wtmp was last rolled.
The contents of /var/log/auth.log and/or /var/log/secure may also be useful, but the commands above will probably get you what you need to know
Comment: I don't want who is connect in that moment but who connected in last days. I'll see this file
Comment: I don't have /var/log/auth.log /var/log/wtmp and /var/log/secure no files.. :(
Answer: I don't know if this'll help but I came across the last command recently. It shows:

User name
Tty device number
Login date and time
Logout time
Total working time

For Example:

Also, If I'm not mistaken, remote login attempts are stored in the /var/log/secure logs as well.
Hope this Helps..
Comment: I don't have file or folder in var/log/secure. Secure isn't exist
Comment: Can you try the following -->

grep -ir ssh /var/log/* and grep -ir security /var/log/*
Comment: Nothing return to me

Linux ssh user connect


Can I legally transfer a font that comes with a Mac to a Windows machine?

Question: The American Typewriter comes by default on Mac machines, but not on Windows. If those in my agency who need to use this font on their PC, do they have to purchase a license for it, or could I just give them the font to use?
Answer: In terms of technology, likely no problem. Font file formats are mostly cross platform these days (OSX and Windows 7 can handle most font file formats). Legally, though, it's murky. The fonts that come with OSX are licensed with the purchase of the Operating system. Technically, you are allowed to use them with the operating system...but not on other machines.
Comment: The short answer is "yes, illegal." the long answer is: some/many fonts have clauses in the license to allow service bureaus to use on a per-job temporary basis your fonts for use in the production of your document. It depends.
Answer: You can't just give them the font to use. The OS X EULA doesn't allow that, so it would not be legal, but there is the practical point that the older TTC (TrueType Collection) format, which is how this particular font is store on the Mac, is both rare (although it's used on both platforms) and obsolescent.
There are so many advantages to OpenType, beside the simple fact of it being a truly system-agnostic wrapper for both Type 1 (developed by Adobe) and TrueType (developed by Apple and Microsoft) outlines, that I advise designers using any font in a production environment to upgrade. In your case, you would be best to use the OTF version in both environments so that you don't run into reflow issues moving documents from one platform to another. If you are likely to be creating documents in more languages than just English, or even if you have occasional need to set foreign words, you have even more reason to opt for OpenType.
Answer: Truetype or Postscript fonts are copyrighted works. You are not allowed to copy them without a license, and that obviously includes copying them to multiple PCs. The license coming with MacOS X actually says that you are not allowed to copy them, but even if it didn't specifically say that, as long as you don't find anything in writing that allows it, copying fonts is illegal.
Answer: The default Mac American Typewriter is a TrueType font. In most cases, TrueType and Postscript fonts are not compatible between the Mac OS and Windows. So the Mac TrueType font generally will not work on a Windows machine.
[Note: the Mac can use either a Mac version or a Windows version of almost any font. Windows is not that forgiving and can not use Mac versions of fonts.]
You'd be better off purchasing an OpenType version of the font for the number of seats you need. From here for example
The OpenType format will work on both the Mac and the PC and will be constructed much better than the default TrueType format which ships with the Mac OS.
Comment: TrueType and Postscript are fairly interchangeable across platforms these days. Not so much in the old days, but on OSX/Windows7, you really shouldn't have any technical issues. Also, opentype is a format for font information, but doesn't necessarily imply a better constructed typeface.
Comment: Opentype is a superset of truetype AFAIK, but it was developed with cross-platform compatibility in mind. I am in a situation where I have to deal very little with cross-platform, but one problem I have had in the past was that Mac users didn't have a grasp of the dual-fork nature of the max OS filesystem, and I would be given  the resource fork for the fonts (which is useless). I don't recall if OSX/Leopard/Lion etc still uses the dual-fork paradigm.
Comment: OSX still uses hidden files in the file system. It doesn't hurt Windows...it just means windows sees a few more files.


How does the hydraulic valve system work in excavators?

Question: There are many types of valves used in excavators. Two are important: the main valve and the pilot valve. Is the pilot valve is controlled by the operator and the main valve is controlled by the pilot valve? But I can't imagine this system properly. How can the pilot valve control the main valve? Additionally, I am not able to understand the flow of oil after pumping. Will it go to the main valve or the pilot valve?
Comment: How did you get on with the course suggested here? https://engineering.stackexchange.com/a/54548/10902
Comment: I asked the question here to get the accurate answer in a few lines. I dont want any course or book link.
Comment: I gave you that simple answer as the first line in my answer.
Answer: Think of the pilot valve as a "lever" to control the main valve.
If you obtain a system diagram then you can follow what happens.
There are many texts available that describe the functions of all the parts in a hydraulic system. I have the set of Hydraulic books by Mannesman Rexroth Sigma, now part of Bosch, so I don't know if they still produce them. Worth searching for and reading.
This is a link to one of the series (they were produced in several languages, in fact they also produced a technical dictionary across 6 languages which I still find useful):
enter link description here


While reviewing First Posts, should links for question or answers still be clickable?

Question: I'm not sure if this is a feature or a bug. When you are reviewing questions for first timers, in there are test questions. You are still able to click the links for the original questions, if that was really a test if the reviewer is looking on what is looking on, should this link be a dead link?
Comment: Though clicking the link *does* give away that it's an audit, it does not, however, sidestep the whole *gist* of audits: they are there to catch robo-reviewers, and a robo-reviewer will likely not actually click the link (they'll just straight away click the review button).
Comment: Whenever I felt the need, I've always found a quick way to get to the original question and add whatever contributions I felt were needed outside of the review system. And you can do edits inside the review, which for me is quite robust.
Answer: This is not a bug, this is the desired behavior.  It's not that uncommon for a reviewer to either need additional information on a post that can only be found by going outside of the review system, or to take an action that is not an option provided from within the review system.


How can I show the month for a Enterprise Custom Date Field in the Project Center for Grouping?

Question: I setup a Enterprise Custom Field for a Key Date that leadership wants to group by year and month. I thought I could just make 2 new Enterprise Custom Fields, one to parse out the Month and the other to parse out the year from another Enterprise Custom Field that is defined as a Project level date field that users pick from the calendar. I've tried several approaches using the following formulas and only get blanks in the target fields.
Field 1 = 2/2/2025
Field 1 Month = Month(Field 1) returns blank;
Field 1 Month = Mid(Field 1, 3, 2) returns blank;
Field 1 DateSerial(Field 1) returns blank;
I noted that in the Formula edit box that the Enterprise Custom Fields are not listed as available fields and am now wondering if the available fields are limited to system fields and no calculations can be performed on Enterprise Custom Fields. So, how can the month and year be parsed out of an Enterprise Custom date field? If I can get the month to work, the year should work the same by using "Year(Field 2)" but, I get nothing. Any help is appreciated.
Answer: From Add or edit enterprise custom fields in Project Server:
To add a field to the formula, click Pick field, point to a field type, and then click the name of the field that you want to reference. To reference an existing Enterprise Custom Field, point to a field type, point again to a custom field type (such as Custom Date or Custom Finish), and then click the Enterprise Custom Field that you want.


Why is there no 32 bit ISO for the new Ubuntu 18.04?

Question: Why is there no 32 bit ISO for the new Ubuntu 18.04?
Answer: There are 32 bit ISO from the new 18.04 LTS distro, but not standard Ubuntu. The community flavours have uploaded 32 bit iso files, and some of them are particularly suitable for old 32 bit computers, because they have light desktop environments,

Lubuntu
Ubuntu Budgie
Ubuntu MATE
Xubuntu

You can find them via the following link. Look for 'i386' in the name of the iso file.
releases.ubuntu.com/

You can use the Ubuntu mini.iso files in order to install Ubuntu in BIOS mode (but not in UEFI mode), and there is a 32-bit version with 'i386' in the name of the mini.iso file. See this link,
cdimages.ubuntu.com/netboot
So it is possible to install standard Ubuntu in a 32-bit computer, but in most cases it is better to use a community flavour of Ubuntu with a lighter desktop environment, because standard Ubuntu 'wants' more powerful hardware for graphics that what is common in most 32-bit computers.
However, there may be cases, when you want to run a 32-bit operating system in a 64-bit computer, for example if you have some application software, that only works with a 32-bit system, or because a 32-bit system uses less RAM for the same task compared to a 64-bit system.
Comment: This answer implies that there are no ISOs for 32 bit PCs of standard Ubuntu, which isn't the case.  There just aren't any *Live* ISOs.  The plain network installer ISO is still available in 32-bit.
Comment: @thomasrutter, I have tried to improve the answer by adding a paragraph about the Ubuntu `mini.iso` 32-bit version.
Answer: Wow.  A lot of misinformation here.
Ubuntu can still be run on 32-bit PCs and Ubuntu still provide 32-bit installers.  All Ubuntu have stopped doing is producing 32-bit Live installer images.  The other type of installer image - the network installer - is still available in both 64-bit and 32-bit (along with other architectures like arm64 and armhf which were never available as Live installers).
Network installer images can be found on the alternative downloads page.
The network installer images don't boot to a live Ubuntu desktop instance, just to a basic installer that you can use to install Ubuntu onto your machine.  If you've ever installed Debian, it's a bit like their installer.  They are small images because they fetch almost all packages from the internet during installation (this is why they are called a network installer).  This means that the installer can't be used without an internet connection.  That said, this is a perfectly convenient way of installing Ubuntu these days, since most people have a permanent internet connection and the installer is light weight and has no frills.
Note that if you have a 64-bit capable machine, and you are not severely limited in physical RAM (ie, you have at least half a gigabyte) there is no good reason not to run 64-bit Ubuntu on it.
Comment: I think I just discovered a good reason to run 32-bit Ubuntu. I'm trying to set up a virtual machine, and VT-x is disabled. VT-x must be disabled to run docker, so in spite of having a 64-bit capable machine and heaps of RAM, I think I need the 32-bit iso. Please correct me if I'm wrong.
Comment: @craq should be sufficient to disable it in bios
Answer: Go to Alternative downloads/Network installer and download 32 bit mini installer. Other files will be downloaded by the installer.
Answer: Ubuntu has decided to stop creating desktop builds for 32bit since 17.10
https://www.omgubuntu.co.uk/2017/09/ubuntu-17-10-32-bit-builds-dropped/amp
Comment: Not just Ubuntu. Every mayor company that creates operating systems.
Comment: They've stopped 32-bit desktop builds *of the Live CD image*, not of Ubuntu itself.
Comment: Yes you are right. That is also true.
Answer: Since nobody has explicitly said how to do a 32-bit desktop install for "regular" Ubuntu, you can run the mini.iso installer referenced (which is usually meant for network boot install.)   There're procedures to run this ISO off a USB stick, you don't have to burn it to CD.  Warm up that fast internet connection, the mini ISO is 62MB and the 64-bit desktop ISO is like 1.9GB so you do the math.... install the ubuntu base system, run "apt-get install ubuntu-desktop" and when you reboot you'll have an equivalent of the desktop CD install.  Run "apt-get install ubuntu-restricted-extras" if you want the equivalent of checking that box in desktop installer that's for installing mp3 support and such.  I also personally "apt-get install gnome-session-flashback" for a traditional desktop rather than Unity, but that's personal choice just like on 64-bit.
I only have 1 32-bit system, but on it so far the only packages I've noticed unavailable are chrome (google quit building it a year or more ago) so you can install chromium instead; and android development toolkit (it made sense to get rid of the 32-bit version, it was easy to make it try to exceed the ~2.5GB address limit and bail out.)


Is it legal to use a friend's online gambling account with their consent?

Question: In the United States, assuming a friend creates an online gambling account legally, and gives you full consent to use the account, are there any potential legal ramifications? It will likely be against the online casino's terms and conditions (giving them the right to ban the account, which is fine). But with written consent from the account owner, could this be considered identity theft or fraud?
Comment: Are you paying for the money you spend on the account yourself, or are you spending your friend's money?
Answer: It could be fraud
new-south-wales

192E Fraud
(1) A person who, by any deception, dishonestly--
(a) …, or
(b) obtains any financial advantage or causes any financial disadvantage,
is guilty of the offence of fraud.

The use is dishonest, however, whether financial advantage comes by reason of the deception is critical.
In R v Fletcher [2019] NSWDC 587, the accused was acquitted by directed verdict of using other people's accounts to bet on horse and greyhound races. The acquittal flowed from the fact that the deception gave him the opportunity to financially gain but it did not cause the financial gain - the horse or dog winning did that and that was unrelated to the deception.
In this case, if the casino games bet on are pure chance
like roulette or sic-bo then an acquittal on the same basis must follow. However, if the game is one of mixed chance and skill like blackjack or poker, then the identity of the player is arguably crucial information and the deception is material to the financial gain.
In other jurisdictions, fraud statutes might refer to a benefit or an opportunity, rather than a financial gain. In those jurisdictions the ability to place the bets would be fraud.
Notwithstanding, the online casino has more options than simply suspending the account. They will almost certainly have a contractural right to void any and all bets made through the fraud and they can probably do it selectively - they cancel the bets you won and leave the bets you lost.
Comment: Do you mean fraud against the casino? If I gain the ability to bet money, and win or lose depending on luck, would that be a financial advantage to me?
Comment: @gnasher729 corrected
Comment: The OP never suggested that win or lose, they might benefit.  I see this as a case where the account holder benefits from authorizing a third party to place bets on their behalf.
Answer: washington
It is not fraud (version 1). That crime is limited to a set of specific acts: forgery, obtaining a signature by duress, impersonation, false certification (about legal documents), mental health advance directives, and academic credentials. Version 2 of fraud (criminal statutes were split into two titles, 9 and 9a) gives an additional list of specific acts (substitution of child, real estate fraud, auctions, removal of property, measurement of commodities etc), none of which pertain to using someone's online account.
Laws pertaining to gambling are in Ch. 9.46 RCW, however these are designed to prevent crooks from running gambling operations. The "end-user" restriction is against "cheating", which is to

(1) Employ or attempt to employ any device, scheme, or artifice to
defraud any other participant or any operator; (2) Engage in any act,
practice, or course of operation as would operate as a fraud or deceit
upon any other participant or any operator; (3) Engage in any act,
practice, or course of operation while participating in a gambling
activity with the intent of cheating any other participant or the
operator to gain an advantage in the game over the other participant
or operator; or (4) Cause, aid, abet, or conspire with another person
to cause any other person to violate subsections (1) through (3) of
this section.

There is not uniform statutory definition of criminal fraud, therefore the common law definition would have to be applied to know whether a particular act constituted "cheating" by being "fraud". However, one of the fundamental requirements of fraud is "dishonesty", which is the assertion as true of a matter known to be false. In using another person's account, you are not asserting that you are the account-holder (analogously, when you use another person's credit card with permission, you are not falsely asserting that you are that person).
Comment: Is it analogous to lending a credit card? Banks don't care if you do this, as their risk of loss depends on the cardholder's creditworthiness, not the item purchased. Bookmakers very much do care because they ban players who win too much. They prohibit account sharing in the TOS, and actively enforce it when shared accounts are detected.


Ring of integers of $\mathbb{Q}(\sqrt[3]{6})$

Question: I am trying to find the ring of integers of $\mathbb{Q}(\sqrt[3]{6})$. Unfortunately, the discriminant of the basis $\{1, \theta, \theta^2\}$, where $\theta = \sqrt[3]{6}$, is equal to $2^2 (-3)^5$ (so it's not square-free). How can I proceed in this case to find the ring of integers? I could take the prime $2$, and analyze the expressions of the form $(a + b\theta + c\theta^2)/2$ for binary values of $a,b,c$, but maybe there is a more direct approach.
Answer: $Disc(x^3-6)= -27(-6)^2=3^a2^b$
Since $v_3(6^{1/3})=v_3(6)/3=1/3$ then $\Bbb{Q}_3(6^{1/3})/\Bbb{Q}_3$ is totally ramified of degree $3$ with uniformizer $6^{1/3}$
Similarly $\Bbb{Q}_2(6^{1/3})/\Bbb{Q}_2$ is totally ramified with uniformizer $6^{1/3}$
The uniformizers of the ramified completions are in $\Bbb{Z}[6^{1/3}]$ thus it is a Dedekind domain ie. $$O_{\Bbb{Q}(6^{1/3})} = \Bbb{Z}[6^{1/3}]$$
For $p\ne 2,3$ then $(p)$ is a product of distinct prime ideals of $\Bbb{Z}[6^{1/3}]$, for $p=2,3$ then $(p)=(p,6^{1/3})^3$.
The more elementary solution : check that $(p)=(p,6^{1/3})^3$ for $p=2,3$, since the unramified prime ideals are easily shown to be inversible, this implies every prime ideal is inversible, thus it is a Dedekind domain, thus it is integrally closed ($=O_K$). The point is that (in Dedekind domains) a prime ideal $P$ becomes principal $=(\pi)$ in $(O_K-P)^{-1} O_K$, the uniformizer is $\pi$, from which we obtain a discrete valuation and a $p$-adic completion.
Comment: In general, if the minimal polynomial of $\theta$ is Eisenstein with respect to the prime $p$, then the index of $\Bbb Z[\theta]$ in the ring of integers is coprime to $p$. If you know about extensions of the field of $p$-adic numbers this is straightforward, but maybe is less easy to prove from first principles. @Philomeno
Comment: I do not understand this solution; in my class we have not talk about uniformizer. Do you know a less technical approach different that the one I mentioned?
Comment: @LordSharktheUnknown I feel better already =).
Answer: If you are interested, a complete determination of the ring of integers $R$ of a pure cubic  field $\mathbf Q(\sqrt [3] m)$, where $m$ is a cube free integer written as $m=hk^2$, withe $h,k$ coprime and square free, can be found in chap.3 of D.A. Marcus' book "Number Fields".
In the general case of a number field $\mathbf Q(\alpha)$, where $\alpha$ is an algebraic integer of degree $n$, thm.13 therein states that $R$ admits an integral basis of the form {$1, f_1(\alpha)/d_1,..., f_{n-1}(\alpha))/d_{n-1}$}, where the $d_i \in \mathbf Z$ , with $d_1|d_2|...|d_{n-1}$, are uniquely determined, and the $f_i \in \mathbf Z[X]$ are monic of degree $i$. In the particular case of $\alpha=\sqrt [3] m$, everything becomes explicit. The (long) exercise 41 op. cit. shows that one can take $f_1(\alpha)/d_1=\alpha$, and $f_2(\alpha)/d_2=\alpha^2/k$ if $m\neq \pm 1$ (mod $9$), $\alpha^2\pm k^2\alpha+k^2/3k$ if $m\equiv \pm 1$ (mod $9$) .
Comment: For $h,k$ coprime squarefree the same argument as in my answer shows that $\Bbb{Z}[3^{-1},(hk^2)^{1/3},(h^2k)^{1/3}]$ is a Dedekind domain, thus it remains to find the uniformizer of  $\Bbb{Q}_3((hk^2)^{1/3})$ depending on $hk^2\bmod 9$.
Comment: Sure, but @Philomeno says that he's not familiar with local methods.


Professor doesn't reply to email even after I talked to him

Question: A professor pitched his project that needs research assistants at an event in my department on Monday. I talked to him after the event about 5 five mins, telling him my background and that I am really interested. I sent him my CV after the event on Monday evening. Now that Tuesday has passed. I still didn't get any reply from the professor. What should I do now? Email him again or go to his office directly (now it is the exam period so he probably doesn't have office hours anymore)?
Comment: Why are you so impatient?  Do you think this person only has your email in his or her inbox?
Comment: Sorry it is just because I got ignored a few times by other professors during this semester.
Answer: Wait. As Buffy said, a day is virtually no time at all. The professor may be trying to give others a chance to respond, or may just be busy with other things. While your zeal is admirable, overdoing it will raise red flags. If he invited applications on Monday, I would wait at least until Friday before following up. Depending on the local culture, dropping by his office in person on Friday (or the following week) may be a good idea; otherwise, I would (again on/after Friday) just send a brief e-mail saying that you are still interested and that you hope to discuss the position with him soon.
Comment: Thanks for your advice. But do you think it is appropriate to just show up in his office on Friday (now that it is exam period, he doesn't hold his usual office hours (Mondays) anymore)?
Comment: I guess I am just nervous. Because I get ignored a few times by other professors this semester (like cold call). And now that he has a project that needs RAs. I think I should have a good shot.
Answer: A day is no time at all during busy academic periods. But trying to find him is probably a good bet. Some things are best done face to face. He probably won't have made any decisions yet and a visit might help him decide.
But an immediate email probably won't get you anywhere.
Perhaps someone in the department office can set you up with an appointment.
But if a week passes and you haven't made contact, then email should be fine.
Comment: Thank you! So a follow up email restating my interest?
Comment: Also, is there a possibility that he missed my email? For example, he thought he would reply the next day but he ended up forgetting.


Geometric Interpretations of Homotopy Theoretical Constructions

Question: In homotopy theory there are lots of nice constructions that seem designed to have some effect on the homotopy of a space, i.e. completing, localizing, and taking various homotopy (co)limits. It seems like some of these (for instance Quillen's + construction) have moderately visual interpretations by attaching cells and things like that. In general, does anyone out there have interest in constructing such things geometrically, i.e. drawing a picture of what a sphere looks like after you, I don't know, complete it at a prime, or something like that? Are there sensible ways to visually represent mod p Moore spaces? Do such constructions usually cause things to have to leap into higher, non-visual, dimensions or something? Or is it simply that this kind of thing doesn't really serve any purpose, and we can just prove that it works and that it exists? In general it also seems very interesting to me to know what a sphere localized at a given homology theory might look like.
Comment: I like the spirit of this question: visual intuition is often crucial in topology and geometry, and I would certainly benefit from good answers.

However, I think it could be much improved if you focus on a question of the type: "are there good visual interpretations of homotopy theoretic constructions such as (blah), for instance by attaching cells?" rather than ask people whether they would personally find such constructions useful.
Comment: I think Kathryn Hess discusses how you might think of the rationalized sphere in her notes on rational homotopy theory. As is alluded to below, i don't know that it is helpful geometrically. (she presents it as a cell complex, but it is huge)
Comment: That's sort of what I thought might happen, you necessarily get really massive cell complexes or something. Geometric constructions of such things would be really interesting to see (in low dimensions at least).
Answer: Though it is often satisfying and useful to have an appropriate way to visualize a construction, in fact the real innovation in homotopy theory that lead to the constructions you mention, among many others, was the realization that you need not limit your attention to geometric, visualizable operations and spaces but can be content knowing only certain relevant properties.
This realization led to what Mike Hopkins (and perhaps others before him) called designer homotopy theory.  The simplest example of a designer homotopy type is the Eilenberg-MacLane spaces---once you convince yourself they exist, you don't concern yourself with what they look like (a horrendous infinite CW complex, perhaps), but use only their characteristic relationship to homotopy groups.  Needless to say this particular example led to spectacular advances in the hands of Serre and others.
Comment: Thanks, I think that's a really good answer, and sort of in the spirit of what I was thinking about.  I had not heard of the term "designer homotopy theory."  However, I should hope that, after swinging to the side of purely algebraic knowledge, in time, we could come up with nice ideas of what such things look like.  However, after writing this question it occurred to me, knowing what such a thing "looks like" may in some sense be the same as knowing AT LEAST its homotopy groups, which we don't always know!
Answer: Many operations on the homotopy groups of a CW complex can be realized by a "geometric" (rather, topological) construction on the space itself. A popular example is the rationalization, studied in rational homotopy theory.
The general idea is to write down a CW model for your space, with explicit attaching maps, and doing the construction on spheres, then re-glue by the attaching maps.
An easy example to look at is the following construction on the 1-sphere:
take the covering $z \mapsto z^n$ from the 1-sphere to itself. A path on the "lower" circle that generates the fundamental group $\pi_1(S^1,1)=\mathbb{Z}$ can be multiplied with $n$ (going around $n$ times) and then lifted to the covering space and there it corresponds to the generator. Attaching a 2-cell along this covering map kills this $n$-times going around map on the homotopy level (since it is liftable, so contractible in the newly attached 2-cell). The result on the fundamental group is that you get $\pi_1(S^1 \cup_{z^n} e^2) = \mathbb{Z}/n\mathbb{Z}$.
You can iterate this with a mapping telescope construction to get an inverse limit over these groups, thus the fundamental group becomes the profinite completion $\hat{\mathbb{Z}}$ of the integers.
Since you asked for how to visualize this, I tend to draw pictures on the blackboard and imagine the paths and the contractions quite visually.
To address the question whether this is useful or just good to know it exists:
Sometimes it can be crucial to know how many cells in which dimensions you need to attach to change the homotopy groups, and knowledge about the attaching maps can be important too. For example, from all attaching maps you can compute CW (co)homology, so you can look at how the (co)homology changes if you, say localize at a prime. Maybe the Quillen + construction is a good example for this, since one really has to attach only a 2-cell and then a 3-cell, to get it right.


Current sensing relay

Question: I have a 240v/30a table saw and want to automatically start my dust collector, 240v/20a by means of a current sensing switch and relay. I have a 30a double pole relay w/ 24v coil. A 24v transformer 40va,  and a Dwyer series ccs current switch,  amprage sensing range 0 -200a  ac,  switch rating 1a @ 240 vac. My problem, in my very limited understanding, is the switch voltage in the sensing unit. Can i use these items. If not what do i need?
Comment: Where are the links to the datasheets for the components? Put all the info **in the question** and not in the comments.
Comment: @RickC Have you made a good attempt at a circuit design?
Comment: Try an HVAC supply house. Such switches are commonly used to turn on a humidifier when the blower comes on. Or have you already exhausted that idea? If so, why?
Comment: Why not wire the collector in parallel with the table saw, after the power button?
Comment: Just Google "current sensing relay" and you will find many options including items for sale on Amazon and Ebay.
Answer: You can probably use them, but DON"T DO IT! You clearly know nothing about wiring practices, and your project has plenty of room for you to kill yourself or burn down your house.
If you must, this is the general approach

simulate this circuit – Schematic created using CircuitLab
The motor current closes the switch output, which applies 24 VAC to the relay coil. The coil contacts switch 220 to the blower.
A few caveats. First, although you have a 24 volt relay, you do not specify that the coil is AC. If it's a DC input, you're out ouf luck (unless you rectify the transformer output). Second, you do not specify the coil current requirement. If you need 2 amps on the coil, the power needed from the transformer is 2 x 24, or 48 VA, and your transformer is too small. Third, I recommend you get a spark arrestor for your relay contacts. If you don't, sooner or later your relay will fail from the transients involved with switching the blower.
Comment: Sorry, what dilemma? And all you need to do is put the blower switch on the appropriate load wire. The fact that this gives you trouble is another indication that you should not be messing around with this. Get an electrician.
Comment: Thanks for your quick response. I have been using a commercial unit that has accomplished the task for 11 years. It burned out, the business went under, and I can't find a unit to replace it. The circuit you drew is accurate, except the saw and the blower are on separate circuits.  Can you help me with this dilemma, with or without my parts?
Answer: There is an off-the-shelf solution for this problem for $75 that will save you designing a circuit yourself.
... as @Barry already indirectly suggested.

Current sensing relay