Laws applying to Homemade Tricycles

Question: I am a freshman in high school who is planning to build his own recumbent tricycle.  However, I would be very disappointed if my creation was illegal to ride on bike paths and sidewalks.  I have already perused the Wisconsin State Statutes, and there is nothing that would apply to even a store-bought tricycle.  Is anybody aware of laws from other states covering tricycles, so that I may be aware of them before I start building?
Comment: I don't know about Wisconsin, but it's illegal to ride any bicycle on the sidewalk where I live. It's worth noting that riding on the sidewalk is one of the leading causes of collisions.
Comment: You might send a query to the [Bicycle Federation of Wisconsin](http://bfw.org/), or peruse their site.
Comment: Building your own bikes at 15? Good for you buddy!
Comment: Ask local Dept of Transportation and/or your city constabulary.
Comment: If you call the police and ask about tricycle law, they'd probably think it was a prank call. lol
Comment: I'm relatively sure that the law in most states considers a "bicycle" to be any vehicle that is human-propelled and within certain size/weight limits, regardless of wheel count.  But the Wisconsin laws should be online, and it's a good exercise to learn how to look up the rules for yourself.
Comment: @DanielRHicks I have looked at the Wisconsin laws pertaining to bikes, and it has to do with the number of wheels more than anything, as far as I can understand it.
Comment: Shyish 14 year old...  ._.    Whats a constabulary anyways?
Comment: @CodeAdmiral, "a constable" = "a police officer", "the constabulary" = "the police".
Comment: @MikeSamuel Makes sense :)
Comment: And in Wisconsin, we can ride on sidewalks
Comment: @Pete haha, first try at one anyways ^^
Answer: These are the Wisconsin State Bicycling Laws:
http://www.dot.wisconsin.gov/safety/vehicle/bicycle/docs/bikelaws.pdf
340.01(5) defines a bicycle thusly: "Bicycle" means every vehicle propelled by the feet acting upon pedals and having wheels any 2 of which are not less than 14 inches in diameter.
As it makes no mention of where or how the machine was manufactured, it sounds like your tricycle (and its rider) will be held to the same legal standard as any other bicycle. The wheel size requirement means that if two wheels are larger than 14 inches, it's a bicycle. My guess is that this is intended to rule out kids' "Big Wheels" and the types of tricycles that a 5 year old might ride.
That said, it's worth reading the entire document. I didn't bother because I don't live in Wisconsin.
It's also worth noting that local municipalities can pass further laws defining or restricting bicycles as long as they don't conflict with the state laws. So you'll want to check those as well. Those are sometimes hard to locate on the internet. If you have can't find them online, check out your public library. They usually try to archive local information like that.
Finally, as others have mentioned, the sidewalks are often illegal and even more often dangerous places to ride. If you do so, do so with great caution.
Comment: Alright, I will make it a priority to read this :)  Thank you!! +1
Comment: I find the size of the wheel interesting and amusing. How is a human pedal powered device with 12" wheels no longer considered a bicycle?
Comment: As I mentioned, I think it was meant to rule out children's "toys" that are intended to be pre-cursors to bicycles and not bicycles in themselves. A further consideration is the mechanical advantage offered by a bicycle. At some point (14 inches may or not be an arbitrary number, the specific math/physics are over my head) the mechanical advantage of a bicycle is lost with smaller wheels. Check here for more info: http://www.school-for-champions.com/science/machines_advantage.htm specifically, the section on "Distance Mechanical Advantage."
Comment: 14 inches is not a common bike wheel size.  12 and 16 inches are; perhaps 14 was chosen to avoid any need for a phrase like "larger than 12 inches and not including 12 inches"
Answer: In California a tricycle is a 'bicycle'.  For day time operations the only real requirement is that one wheel can skid.
39000. "Bicycle," for the purposes of this division, means any
device upon which a person may ride, which is propelled by human
power through a system of belts, chains, or gears having either
two or three wheels (one of which is at least 20 inches in
diameter) or having a frame size of at least 14 inches, or having
four or more wheels.

Equipment Requirements
21201. (a) No person shall operate a bicycle on a roadway unless it
is equipped with a brake which will enable the operator to make one
braked wheel skid on dry, level, clean pavement.

(b) No person shall operate on the highway a bicycle equipped with
    handlebars so raised that the operator must elevate his hands
    above the level of his shoulders in order to grasp the normal
    steering grip area.

(c) No person shall operate upon a highway a bicycle that is of a
    size that prevents the operator from safely stopping the
    bicycle, supporting it in an upright position with at least one
    foot on the ground, and restarting it in a safe manner.

(d) A bicycle operated during darkness upon a highway, a sidewalk
    where bicycle operation is not prohibited by the local
    jurisdiction, or a bikeway, as defined in Section 890.4 of the
    Streets and Highways Code, shall be equipped with all of the
    following:

(1) A lamp emitting a white light that, while the bicycle is in
    motion, illuminates the highway, sidewalk, or bikeway in front
    of the bicyclist and is visible from a distance of 300 feet in
    front and from the sides of the bicycle.

(2) A red reflector on the rear that shall be visible from a
    distance of 500 feet to the rear when directly in front of
    lawful upper beams of headlamps on a motor vehicle.

(3) A white or yellow reflector on each pedal, shoe, or ankle
    visible from the front and rear of the bicycle from a distance
    of 200 feet.

(4) A white or yellow reflector on each side forward of the center
    of the bicycle, and a white or red reflector on each side to the
    rear of the center of the bicycle, except that bicycles that are
    equipped with reflectorized tires on the front and the rear need
    not be equipped with these side reflectors.

(e) A lamp or lamp combination, emitting a white light, attached to
    the operator and visible from a distance of 300 feet in front
    and from the sides of the bicycle, may be used in lieu of the
    lamp required by paragraph (1) of subdivision (d).

In New York State you have to have a bell or similar device on your bike.
I would think the real question to ask yourself is "will a Police Officer think it is legal?".  If they think your tricycle is unsafe they will stop you whether it is legal or not, as they, most likely, should.

Laws applying to Homemade Tricycles


Whether to delete cases that are flagged as outliers by statistical software when performing multiple regression?

Question: I am performing multiple regression analyses and I am not sure whether outliers in my data should be deleted. The data I am concerned about appear as "circles" on the SPSS boxplots, however there are no asterisks (which makes me think they are not 'that bad'). The cases I am concerned about do appear under the "casewise diagnostics" table in the output - therefore should I delete these cases?
Comment: You should plot the predicted value of y (the one given according the model that you estimate) on the x axis and the residuals on the y axis. Instead of the predicted value of y, you could put one of your predictors/independent variables on the x axis. You could create several plots, each with a different predictor on the x axis to see which x value is leading to the outlier behavior. Again, I would caution against outlier removal; instead, analyze why the outlier is occurring.
Comment: @user603 No, you don't read me correctly. "Outlier" doesn't mean anything - especially when flagged by an automatic procedure in statistical software. There are just as many examples of the important findings of a study being in the "outliers". Whenever you have data you're deleting, it should be for a reason. "They're inconvenient" isn't a reason.
Comment: Echoing Charlie's statement, its the "why" that matters, rather than the "if", and I too would caution against their removal. I'm not familiar with SPSS, but whatever features you used to run the regression should be able to also give you a plot of residuals, or at least the value of them which you can use to make the plot Charlie suggests.
Comment: Thank you very much Charlie and Epigrad. Could you please suggest which graph in SPSS I look at to assess whether there are outliers in the residuals? The scatterplot looks quite messy!
I don't there is any problem with the data as such (as in they have not been entered incorrectly) I just think that some of my participants had much higher scores on some of my scales, i.e. because they were much more socially anxious that the rest of the sample.
Comment: @Anon I've merged your two accounts. Please register so that you can update and/or comment your question.
Comment: @EpiGrad: many outliers simply can't be "explained" in any scientific sense (except for attributing them measurement errors, miss imputation of data...). There are numerous notorious examples. Do I read you correctly that you would then advise letting such observations (even if they single handedly pull the resulting fit away from the majority of the data) in the sample?
Answer: Flagging outliers is not a judgement call (or in any case need not be one). Given a statistical model, outliers have a precise, objective definition: they are observations that do not follow the pattern of the majority of the data. Such observations need to be set apart at the onset of any analysis simply because their distance from the bulk of the data ensures that they will exert a disproportionate pull on any multivariable model fitted by maximum likelihood (or indeed any other convex loss function).
It is important to point out that multivariable outliers can simply not be reliably detected using residuals from a least square fit (or any other model estimated by ML, or any other convex loss function). Simply put, multivariable outliers can only be reliably detected using their residuals from a model fitted using an estimation procedure not susceptible to be swayed by them.
The belief that outliers will necessary stand out in the residuals of a classical fit ranks somewhere up there with other hard to debunk statistical no-no's such as interpreting p-values as measure of evidence or drawing inference on a population from a biased sample. Except perhaps that this one may well be much older: Gauss himself recommended the use of robust estimator such as the median and the mad (instead of the classical mean and standard deviations) to estimate the parameters of a normal distribution from noisy observations (even going so far as deriving the consistency factor of the mad(1)).
To give a simple visual example based on real data, consider the infamous CYG star data. The red line here depicts the least square fit, the blue line the fit obtained using a robust linear regression fit. The robust fit here is namely the FastLTS (2) fit, an alternative to the LS fit which can be used to detect outliers (because it uses an estimation procedure that ensures that the influence of any observation on the estimated coefficient is bounded).  The R code to reproduce it is:
library(robustbase)
data(starsCYG)
plot(starsCYG)
lm.stars <- lm(log.light ~ log.Te, data = starsCYG)
abline(lm.stars$coef,col="red",lwd=2)
lts.stars <- ltsReg(log.light ~ log.Te, data = starsCYG)
abline(lts.stars$coef,col="blue",lwd=2)

Interestingly, the 4 outlying observations on the left do not even have the largest
residuals with respect to the LS fit and the QQ plot of the residuals of the LS fit (or any of the diagnostic tools derived from them such as the Cook's distance or the dfbeta) fail to show any of them as problematic. This is actually the norm: no more than two outliers are needed (regardless of the sample size) to pull the LS estimates in such a way that the outliers would not stand out in a residual plot. This is called the masking effect and it is well documented. Perhaps the only thing remarkable about the CYGstars dataset is that it is bivariate (hence we can use visual inspection to confirm the result of the robust fit) and that there actually is a good explanation for why these four observations on the left are so abnormal.
This is, btw, the exception more than the rule: except in small pilot studies involving small samples and few variables and where the person doing the statistical analysis was also involved in the data collection process, I have never experienced a case where prior beliefs about the identity of the outliers were actually true.
This is by the way quiet easy to verify. Regardless of whether outliers have been identified using an outlier detection algorithm or the researcher's gut feeling,  outliers are by definition observations that have an abnormal leverage (or 'pull') over the coefficients obtained from an LS fit. In other words, outliers are observations whose removal from the sample should severely impact the LS fit.
Although I have never personally experienced this either, there are some well documented cases in the literature where observations flagged as outliers by an outlier detection algorithm were latter found to have been gross errors or generated by a different process. In any case, it is neither scientifically warranted nor wise to only remove outliers if they can somehow be understood or explained. If a small cabal of observations is so far removed from the main body of the data that it can  single handedly pull the results of a statistical procedure all by itself it is wise (and i might add natural) to treat it apart regardless of whether or not these data points happens to be also suspect on other grounds.
(1): see Stephen M. Stigler, The History of Statistics: The Measurement of Uncertainty before 1900.
(2): Computing LTS Regression for Large Data Sets (2006)
P. J. Rousseeuw, K. van Driessen.
(3):  High-Breakdown Robust Multivariate Methods (2008).
Hubert M., Rousseeuw P. J.  and Van Aelst S.
Source: Statist. Sci. Volume 23, 92-119.
Comment: This is good stuff (+1). However, I think you misuse conventional terminology and have co-opted "outlier" to refer to "influential observation." The concepts are both valuable, and you treat the latter well here, but they are not as interchangeable as you seem to indicate. For instance, an influential observation that *is* consistent with the majority of the data would fit your characterization of "observations that have an abnormal leverage (or 'pull') over the coefficients obtained from an LS fit" but would not be considered by most writers to be an "outlier" *per se.*
Comment: +1 Very nice example. Real data that shows two fits that are nearly orthogonal, and in which the highly-influential four in the upper-left won't have the largest residuals after an OLS fit.
Comment: @whuber: Good point. Indeed I consider, as do recent textbooks on robust statistics (for example, Robust Statistics: Theory and Methods. Wiley) such observations (so called 'good leverage points') as harmful. The justification is that they deflate the standard error of the estimated coefficients causing the user to place unwarranted confidence in the strength of the observed relation. Considering good leverage points as outliers also makes the formal approach more consistent: after all good leverage point do have an outsized influence on the s.e. which *are* a component of the LS/ML fit.
Answer: In general, I am wary of removing "outliers." Regression analysis can be correctly applied in the presence of non-normally distributed errors, errors that exhibit heteroskedasticity, or values of the predictors/independent variables that are "far" from the rest. The true problem with outliers is that they don't follow the linear model that every other data point follows. How do you know whether this is the case? You don't.
If anything, you don't want to look for values of your variables that are outliers; instead, you want to look for values of your residuals that are outliers. Look at these data points. Are their variables recorded correctly? Is there any reason that they wouldn't follow the same model as the rest of your data?
Of course, the reason why these observations may appear as outliers (according to the residual diagnostic) could be because your model is wrong. I have a professor that liked to say that, if we threw away outliers, we'd still believe that the planets revolve around the sun in perfect circles. Kepler could have thrown away Mars and the circular orbit story would have looked pretty good. Mars provided the key insight that this model was incorrect and he would have missed this result if he ignored that planet.
You mentioned that removing the outliers doesn't change your results very much. Either this is because you only have a very small number of observations that you removed relative to your sample or they are reasonably consistent with your model. This might suggest that, while the variables themselves may look different from the rest, that their residuals are not that outstanding. I would leave them in and not try to justify my decision to remove some points to my critics.
Comment: +1 Don't throw away data because its an outlier. Find out *why* some data are outlying.
Comment: this is terrible advice. It is very common for outliers to be so far away from the rest of the data as to pull the regression line towards them in such a way that they won't stand out on a residual plot (or worst: yield large residuals for the genuine data points). In fact, it can be shown that as soon as you have more than a single outlier, it cannot be reliably detected using a residual plot from a classical regression. This is called the [masking effect](http://www.jstor.org/stable/2289995) and i well documented notably in many real data examples.
Comment: By the way, this is also why i'd avoid using the Mars example: it illustrates a procedure that only works if you are dealing with a single outlier. In most application there are no such guarantee. It gives a wrong sense of confidence in a generally flawed methodology (which as statistician is really what we should thrive to prevent).
Answer: +1 to @Charlie and @PeterFlom; you're getting good information there.  Perhaps I can make a small contribution here by challenging the premise of the question.  A boxplot will typically (software can vary, and I don't know for sure what SPSS is doing) label points more than 1.5 times the Inter-Quartile Range above (below) the third (first) quartile as 'outliers'.  However, we can ask how often should we expect to find at least one such point when we know for a fact that all points come from the same distribution?  A simple simulation can help us answer this question:
set.seed(999)                                     # this makes the sim reproducable

outVector = vector(length=10000)                  # to store the results
N = 100                                           # amount of data per sample

for(i in 1:10000){                                # repeating 10k times
  X = rnorm(N)                                    # draw normal sample
  bp = boxplot(X, plot=FALSE)                     # make boxplot
  outVector[i] = ifelse(length(bp$out)!=0, 1, 0)  # if there are 'outliers', 1, else 0
}

mean(outVector)                                   # the % of cases w/ >0 'outliers'
[1] 0.5209

What this demonstrates is that such points can be expected to occur commonly (>50% of the time) with samples of size 100, even when nothing is amiss.  As that last sentence hints, the probability of finding a faux 'outlier' via the boxplot strategy will depend on the sample size:
   N    probability
  10    [1] 0.2030
  50    [1] 0.3639
 100    [1] 0.5209
 500    [1] 0.9526
1000    [1] 0.9974

There are other strategies for automatically identifying outliers, but any such method will sometimes misidentify valid points as 'outliers', and sometimes misidentify true outliers as 'valid points'.  (You can think of these as type I and type II errors.)  My thinking on this issue (for what it's worth) is to focus on the effects of including / excluding the points in question.  If your goal is prediction, you can use cross validation to determine whether / how much including the points in question increase the root mean squared error of prediction.  If your goal is explanation, you can look at dfBeta (i.e., look at how much the beta estimates of your model change depending on whether the points in question are included or not).  Another perspective (arguably the best) is to avoid having to choose whether aberrant points should be thrown out, and just use robust analyses instead.
Comment: Thanks for your comment, @user603; that's a thought-provoking position. Which procedures that I recommend are you objecting to: using, eg, dfbeta to *detect* possible outliers, or using robust analyses (prototypically Tukey's bisquare as an alternative loss function) as *protection* against their influence instead of choosing which data points to throw out?
Comment: *My intuition is that it would be pretty difficult not to notice outliers that are distorting your results* but unfortunately, the fact is that it ain't so. Also look at the example i provide in my answer.
Comment: The procedures you recommend only work reliably if there are at most a single outlier (regardless of the size of your dataset) which is an unrealistic assumption. Tukey calibrated the whisker rule to exclude roughly 1% of the observations on each end if the data is drawn from a Gaussian distribution. Your simulations confirm that. Tukey's opinion was that the losses caused by disregarding such a small portion of the data in those cases where the observations are well behaved is for all practical concerns inconsequential. Specially in regards to the benefits in the cases when the data is not.
Comment: thanks for pointing out the lack of clarity in my comment (i was constrained by the length limit). Of course, i specifically mean the first ones: *dfbeta* and cross validation (the latter is problematic only if the observations used to perform the cross-validation are randomly drawn from the original sample. An example of case where cross-validation could be used would be in so-called quality control setting where the observations used for testing are drawn from a temporally disjoint sample).
Comment: Thanks for clarifying, @user603. I'll have to play w/ these ideas to understand them more thoroughly. My intuition is that it would be pretty difficult *not* to notice outliers that are distorting your results; it seems like you would need to have outliers distorting your results on both sides equally, in which case your betas would end up approximately unbiased & your results would simply be less 'significant'.
Answer: You should first look at plots of the residuals: Do they follow (roughly) a normal distribution? Do they show signs of heteroskedasticity? Look at other plots as well (I do not use SPSS, so cannot say exactly how to do this in that program, nor what boxplots you are looking at; however, it's hard to imagine that asterisks mean "not that bad" they probably mean that these are highly unusual points by some criterion).
Then, if you have outliers, look at them and try to figure out why.
Then you  can try the regression with and without the outliers. If the results are similar, life is good. Report the full results with a footnote.  If not similar, then you should explain both regressions.
Comment: Even assuming one could reliable find outliers using such a procedure (and most of the time, one [can't](http://www.jstor.org/stable/2289995)) that still leaves strangely unaddressed the problem of what to do when you can't "figure out"/explain the outliers. I second the advice to stay clear of SPSS. –
Comment: Thank you very much Peter. I have inspected the Q-Q plots and the data do not appear to be outstandinly non-normal. When I delete the outliers, they don't seem to make much of a difference to the results. So, therefore, should I just leave them in? I would still be interested to hear others' thoughts on the casewise diagnostics table in SPSS. Many thanks.
Comment: Yes, I would then leave them in with a footnote something like "analysis with several outliers deleted showed very similar results"
Answer: (late add: this topic has some whiskers on it. But I'm just seeing it for the first time.)
I disagree strongly with some of User603's premises. Some of this reinforces what Charlie said above.
In the abstract, there is no OBJECTIVE definition of an outlier, UNTIL you mentally or formally propose a data-generating model. I view outliers as the gods possibly trying to tell me I'm not as smart as I think I am, unless I can attribute those outliers, with very high certainty, to measurement or data collection errors.
Tossing data that inconveniently does not fit your model is a very dubious practice, because it makes the model look stronger and more certain than it really is.
Even when explanation is the goal, if you suspect outliers may be present, then re-sampling 500 times is a good technique for demonstrating how certain/uncertain you really are with your model.
In a production mode for predictive models, I am opposed to tossing even KNOWN BAD DATA  from the training dataset ... UNLESS the cause of the bad data has been fixed, so that similar bad data will not be showing up in the future, in the data to be scored. Real world model performance tracking has to include how well your model does on bad data, as long as similar bad data is still flowing in as part of the data stream.


Rigorous approaches to quantum field theory

Question: I have been reading Quantum Mechanics: A Modern Development by L. Ballentine. I like the way everything is deduced starting from symmetry principles.
I was wondering if anyone familiar with the book knows any equally elegant presentation for quantum field theory. Weinberg's books start off nice with the irreducible representations of the Poincare group/algebra but the later chapters lose me with the notation. Also, most books I've read on QFT (Srednicki, Peskin and Schroeder, Mandl and Shaw) make a valiant initial attempt at a nice consistent framework but end up being a big collection of mathematical recipes and intuitive insights that seem to work but the overall structure of the theory seems to be sewn up. The relativistic equations crop out of rather flimsy arguments, the canonical anti/commutation relations are imposed out of density indeterminate air, functional methods are developed cause we know no better, infinities come about with renormalization theory to the rescue but it seems very alien from the initial context.
Is there any approach that ties all these things together in an elegant mathematical framework which accounts for all the patch up work that is needed? I am not talking about axiomatization just a global point of view that encompasses all the issues.
Comment: Robin Ticciati's *Quantum Field Theory for Mathematicians* might be what you are after!
Comment: This question is awesome I have been following the same path almost exactly.. Learnt QM from Ballentine, 2nd chapter of Weinberg now Haag. This question seemed very helpful.
Answer: I wish I could point to a single book that does what you want.  The best I can offer is this suggestion:  Read (or rather, skim) a few books on axiomatic field theory.  Just get a sense for what the physics being described by the axioms is.  Draw cartoons. Don't get too hung up on the topology.
I'd start with Haag's book, Local Quantum Physics.  Learn about nets of algebras, which are a way of encoding the idea that physical observables actually are located somewhere in spacetime.  Also does a nice job of explaining the idea that there's some sort of algebra of observables, and that states -- both pure states and density matrices -- are linear functionals on this algebra.  Notice how crucial the fact that spacelike separated observables commute is to matching up the product of operators with the product of observables.
The thing really missing in Haag's book, if you're reading axiomatics as a way of organizing you're thinking about the material in some particle physics book, is a notion of field.  The algebras in Haag's book really ought to be generated by 'local observables'.  There should be operator-valued functions -- or rather, distributions -- on spacetime, and you should get the algebras in Haag's book by smearing these operators with test functions and then multiplying them.  There is a language for this, which is nicely explained in Streater & Wightman's PCT, Spin, Statistics, and All That.   This book also explains a critical reconstruction theorem:  If you can write down all of the correlation functions of a QFT, then you can recover the Hilbert space & operators directly from these correlation functions.
Thinking of the basic local fields as generators of the algebra of observables is a good idea, but it's more complicated than you might think.  The product of two fields at a point is in general singular.  Equivalently, many of the correlation functions diverge as you approach the diagonals.  You can define non-trivial products by subtracting away these divergences.
It's worth reading Hollands & Wald's paper Axiomatic Quantum Field Theory in Curved Spacetime, at about this point.  They axiomatize QFT on globally hyperbolic spacetimes in terms of operator product expansions.  Hollands and Wald's point of view is very close to the modern Wilsonian point of view on QFT, which says a) that a QFT is a deformation of a conformal field theory, and b) that a CFT is a collection of local observables obeying an OPE which satisfies the bootstrap condition.  You could probably alter their diffeomorphism language to something involving conformal maps and get a definition.
It's also worth spending more time thinking about OPEs and CFTs.  Spend some time with diFrancesco et al's Conformal Field Theory or maybe one of the math books on vertex algebras (Kac, Vertex Algebras for Beginners or Frenkel-Ben-Zvi Vertex Algebras & Algebraic Curves)?
Then at last, the path integral.  It's not the most general definition of a QFT, but it's very useful. Basically, it gives you a way of writing down the correlation functions, and from the correlation functions, you can read off the OPEs, recover the Hilbert space, etc.  The basic idea is best learned first in lattice QFT; I like Montvay & Munster's Quantum Fields on the Lattice. This is also a good time to learn a bit about gauge fields.
The biggest annoyance of the path integral approach is that the funcrtions on field space which are integrable with respect to the continuum measure -- the ones that represent observables in whatever vacuum you're playing in -- can be hard to express in terms of variables that people typically use to construct the measure.  This is what renormalization is all about; it gives you a way of using stupid variables and then isolating the main contributions to the correlation functions you're after.
The standard mathematical reference on path integrals is Glimm & Jaffe, Quantum Physics: A Functional Integral Point of View.  Most of what you'll want is in Chapter 3,6, or Appendix A.  They spend most of the book grinding out a detailed construction of the correlation functions of 2d massive scalar field theory.  Figuring out how their constructions are related to standard renormalization language is a worthwhile exercise.
Answer: I have not read it myself, but did you take a look at Zee's book? I heard that while it is not very technical, it is great on a conceptual level.
Comment: It's an excellent book to get an overall feel for QFT, - it uses the functional approach quite extensively
Comment: Judging by the content the book tries to cover a lot of ground so, as you said, it probably doesn't go deeper in the mathematics. I'll have a look. Thanks.
Answer: I enjoyed Brian Hatfield's "Quantum Field Theory of Point Particles and Strings."  Part 1 of the book is great IMO, Part 2 is useless.  Also make sure to get the newest edition, there are many errors in the older editions, but the work is still good.
Comment: I like that part 1 of the book is rather concise and technical enough to build up a more mathematical view. But again, it seems to follow to same algorithm in writing QFT books as the ones I mention. For introductory purposes this is fine I guess but I'm not necessarily looking for an introduction, rather a restructuring under a small set of neatly justified ideas with associated mathematical objects that fit nicely together.
Comment: +1 one of the few books that deal with the functional Schroedinger picture
Answer: If you are looking for a book with an "elegant mathematical framework which accounts for all the patch up work that is needed" to build a realistic perturbatively renormalizable quantum field theory like the recently completed and validated Standard Model, its title could be : Noncommutative Geometry, Quantum Fields and Motives. It is written by Alain Connes and Mathilde Marcolli two mathematicians whose work is strongly inspired by quantum field theories .
The first chapter addresses for instance the conceptual understanding of the algebra (with their representations for particles) required to describe the gauge symmetries (and quantum anomalies cancellations) in the Standard Model as well as a "clear mathematical interpretation to the renormalization procedure used by physicists to extract finite values from the divergent expressions obtained from the evaluations of the integrals associated to Feynman diagrams". Unfortunately this book does not attempt to be instructional and it is clearly focused on a mathematical audience!
Nevertheless non commutative geometry is definitely a deep approach that ties important archipelagos of contemporary quantum field knowledge and could bring new insight for physicists but it is definitely a work still in progress just like M-theory I guess. On the opposite quantum mechanics appears to be built on old firm foundations (linear algebra, Hilbert spaces) elaborated mostly by mathematicians from the XIX century who distilled the models of heat transport and electromagnetic wave propagation imagined by Fourier, Maxwell and others...
Answer: I know you're probably aiming for a textbook, but I can recommend giving Coleman's original lectures (made available for all on the Harvard website). While he advances rather slowly, and some of the stuff is fairly outdated, he gives many delightful insights, and I find his manner of introducing Quantum Fields one of the most illuminating I have come across so far. Give them a try if you can find the time. In fact, there are accompanying lecture notes made available on the arXiv, linked to on the same page, if you find the actual lectures are moving a bit slowly.


Why was Beverly Crusher not on the second season of Star Trek: TNG?

Question: Berverly Crusher was replaced by Katherine Pulaski in the second season of Star Trek: TNG to become leader of a medical research faculty. My question is what were the show's 'internal' reasons to replace her? Did the producer doubt the character or wasn't the actress available in that year?
Comment: One hard fact that we have is that Gates McFadden played Cathy Ryan in the film *The Hunt for Red October*, which filmed during 1989. However it wasn't a large role, so I don't imagine it occupied her for an entire year.
Answer: As explained on the Sci-Fi SE:

Out-of-universe, according to some recent reports, there was some sort of problem between Gates McFadden and producer/writer Maurice Hurley. I've heard this characterized in some places as sexual harassment, but I'm not sure that's based on any actual allegations. Rick Berman did say he was at the center of it, though:

Gates McFadden fired at end of first season because head writer Maurice Hurley "he had a real bone to pick" with Gates and din't [sic] like her acting, Berman brought Gates back for 3rd season after Hurley left

(That quote is from the summary here.)
Comment: Does adding details to an unsubstantiated claim make it better or worse?
Comment: It would be nice to actually include some links to the 'recent reports'. It looks like the SFF answer doesn't have any either, but it bothers me that there's an unsubstatiated claim of sexual harassment without even mentioning who was involved, who the victim was, etc.
Comment: I realise I have difficulties accepting the answer given these allegations. They are interesting and maybe true or not but I cannot judge this so it's hard to decide this by accepting answer.
Comment: Further discussion unrelated to commenting on and improving this answer should be taken to chat please.


how to make shiny figures for cake decoration?

Question: I am wondering how are the little figures on this cute cake are made? Whats the material and where can you buy molds and casts to shape them? and how are they so shiny?
Answer: These figures are probably made with fondant.
I think the figures are handshaped. There are plenty of tutorials. You can even look for tutorials working with modelling clay.
Basically you only need a rolling pin, a knife and tweezers. Cans, forks, any food-safe utensil that has an interesting pattern are useful. Of course there are special molds for fondant but I don't think that you need them unless you want to make fancy things like laces. You can buy molds online but also in some larger hardware stores, supermarktes, or gift shops. It depends on where you are located.
Fondant is quite matt. To make fondant shiny you can

hold the fondant over steam or
apply shortening,
egg whites,
corn syrup, or
alcohol on the surface
Comment: Thanks @Ching Chong, I did not know there are techniques to make fondant shiny, all I had seen was kind of matt.
Comment: BTW,  , can you tell me what is the icing on the cake? (butter milk? cream? ) @Ching Chong
Comment: @fetah It's probably an ising that that has a low water content like [(American) buttercream](https://en.wikipedia.org/wiki/Buttercream#Types). If you use other icings like cream cheese icings or normal whipped cream the fondant will melt.
Answer: Ching Chong's answer is already very good. But note that everybody he said can also apply to marzipan figurines, not only fondant ones. This may increase your options, since I think marzipan is somewhat easier to shape.
Comment: thanks @rumstscho, I will try marzipan as well, although I don't like the taste
Comment: I totally agree with you, but in this case the figurines probably aren't marzipan, which is always slightly "grainy".


How to schedule shutdown of a phone?

Question: I want to use my phone as a wireless router. Since I am on a time-based data plan, I want the phone to automatically shutdown after a specified amount of time (or at least close the data connection after a specified amount of time).
Basically, I want to prevent to exceed the data limit, and the shutdown is a plus. The phone is running gingerbread but I will probably install cyanogenmod 7.2.
Answer: There are many 3rd-party apps available on the Market that allow you to set up actions (toggle cell data on/off, for example) at specified triggers (e.g. on a timer.)  Tasker and AutomateIt are great examples.
If you have a specific data limit on your plan (e.g. 3GB per billing cycle), a more advanced app like 3G Watchdog would be a better choice.  It allows you to set and monitor limits on cell data usage, and disable it when the usage gets to the threshold.
Comment: I'll try AutomateIt; however 3g watchdog is not useful for time-based plans.

How to schedule shutdown of a phone?


Did Walter have intentions of staying alive after he started making millions?

Question: At the beginning of Breaking Bad we observe Walt refusing to fight for his life and deciding to slowly wait for his last day. However, when he starts making "real" money, I think everything changes. But is there any true indication that Walter changes his mind and wants to live and use his money? I cannot imagine he was building his meth empire only to feed his ego or to support family.
Comment: Related: [Which is the first sign that indicates that Walt is not doing it for the family anymore?](http://movies.stackexchange.com/q/23601/49).
Answer: Walt starts the series as a dead man.  He has nothing beyond his family, despite a big potential (Gray Matter, billions etc).  The news of his impending demise allow him to slip off the mental inhibitor that allowed him to be a family man, but kept him in this nothing existence.
The provision for the family is an EXCUSE, not a driver.  Walt becomes Heisenberg, Walt's amoral image.  As this becomes more and more successful, the life returns to Walt, and he starts to care about trying to survive the cancer.  His ties to his family slip, Skyler has an affair, Walt jnr distances himself, and Walt takes Jesse as a surrogate son.
Only when Walt realizes that his immense talents cannot stop either his death, or the approaching car crash of his business, he begins to regain his moral compass, setting things right for his Family (via the Schwarzs), and by attempting to redeem himself by sacrificing himself to rescue Jesse.
It wasn't that he'd had intentions of staying alive, he just hadn't realised he was dead.
As Walt says to Skyler in his final meeting:

I did it for me. I liked it. It made me feel alive.

This isn't him trying to placate Sklyer to make her feel better by changing it from "I did this for you", it's just about the ONLY truthful thing Walt says to Skyler in the whole series, and only because he knows it'll be the final time they speak.
Answer: His family was Walt's main motivation for most of the series. Being rich was not. All of Season 1 and most of Season 2, Walter believes the cancer will kill him soon, until he finds out it is in remission. (Season 2 Episode 9 "4 Days Out"). At that point he immediately starts planning on leaving the drug game. (Season 2 Episode 10 "Over"). After his wife leaves him (when she learned Walt's a drug lord when he was babbling during his cancer surgery), Walt was basically planning on burning the million he got from Gus. (Season 3 Episode 1 ("No Más") He also turns down Gus's offer of 3 mil for 3 months of cooking.
The defining moment in this is how Walt explains it:

"I have money, more than I can spend" Walt says, declining. "What I don't have is my family."

There is more of the back and forth between Mr. And Mrs. White in season 4 and 5, but in the end, the theme follows the entire series. Walter White's main concern is his family. The Money was a means to an end of ensuring his family is well off. Even after beating cancer.
But Walt does transform through the series. His intentions at the beginning may have been completely pure, but eventually the power corrupts him more and more. He becomes less Walt the Science Loving Family Man and more Heisenberg the Drug Lord. By the end of Season 5, he even admits it to himself and Skyler, even as he still attempts to make sure she and his kids are well off financially.
Comment: "His family was Walt's main motivation for most of the series" - Actually I think this completely the wrong way about.  His family was Walt's main EXCUSE for most of the series.  Walt initially just wants to raise money to provide as he is a DEAD MAN WALKING already.  As the series continues and the old Walt (the brilliant/arrogant one who started Gray Matter) resurfaces, it becomes less and less about the family, and more about Walt.  This is then driven home in the final meeting with Skyler where he admits it.  Walt transforms, but back into the person he was before his family.
Comment: She doesn't really learn that he's a drug lord during his babbling, does she? He merely admits that he has a second phone. But it isn't till quite a bit later that he himself tells her the whole truth, no?
Comment: @TheWanderingDevManager the creator even says after the finale `he has managed to do the one thing he set out to do, which is a victory. He has managed to make his family financially sound in his absence, and **that was really the only thing he set out to do in that first episode. So, mission accomplished**."` From day one to his last breathe he did it for his family.
Comment: @cde - Yes but he also says "Walt is never going to redeem himself. He's just too far down the road to damnation".  The important part is "in that first episode", that was how Walt reconciled in his head why he was doing this, but that wasn't the real driver.  If I happen to be in Best Buy and splash out on a new laptop without telling the wife, I'll convince myself that I'm going to get x and y done by buying it. But really I'll just feel cool with my new toy.
Answer: I think there are two separate questions here -

a. Did Walter have intentions of staying alive after making millions?
b. Was he building his meth empire only to feed his ego or to support family?

I will start with "b". A lot of questions have already been asked here which all point to this same issue/topic.
The defining moment for this question is the scene from the series finale, where Walt meets Skyler for the last time and he tells her

I did it for me. I liked it. It made me feel alive.

When Walt entered the meth business, he had a number in mind, in order to support his family. He already crossed that number long long ago, but still continued anyway, because long long ago he stopped doing it for the family and started doing it for himself.
So I guess, this answers the part-b.
Now, part-a.
This is a little tricky.
I think Walt definitely wanted to stay alive, irrespective of whether he made millions or not. This is because inspite of all his vices, Walt was a family man, and he really loved his family, especially his kids. Any person who is in love with his family would definitely want to stay alive, but not to spend the millions he had made, but to simply be with his family.


40 days at the Kotel

Question: If someone is trying to pray 40 consecutive days at the Kotel, does beginning prayer one minute after sunset count for the day that's ending? For the day that's starting? Both? Neither?
Comment: Tuvya, welcome to Mi Yodeya! I recommend that you consult your rabbi for spiritual guidance regarding the best way to do and keep track of your special davening. We can't recommend how you, personally, should proceed in your particular situation, so I am editing the question to make it more general. If it's not consistent with your intent, please [edit] further. I sincerely hope your prayers are answered for the best.
Comment: It really just depends what the rules of your acceptance were. Anyone can accept to do anything with its own rules. What are you accepting to do?
Comment: If he is beginning prayer all 40 days one minute after sunset what difference does it make?
Answer: As the question you linked to states, this is a recent custom and essentially it depends on why you are doing 40 days at the Kotel.
If you made a vow, then it would depend on what you had in mind. If you didn't think about this trick then it would go by how most  people would interpret it. Most people assume (as far as I know) that 40 days at the Kotel mean you have to make the effort to go 40 consecutive days to the Kotel.
This is called: בִּנְדָרִים הַלֵּךְ אַחַר לְשׁוֹן בְּנֵי אָדָם
But even if you had in mind to simply pray 40 consecutive days at the Kotel, with on 20 trips, you probably can't do it right before & after sunset.
I have been taught that the Yerushalmim consider the first 13 minutes after sunset as day (and in a pinch you can Daven Mincha then).
18 minutes after sunset you can already daven Maariv without repeating Shma. I assume the 5 minutes between are Bein Hashmashot - twilight.
So if you want to do 40 days at the Kotel in 20 days, you probably need to pray for a few moments before sunset (or within the 13 minutes thereafter in emergency), and then again 18 minutes after sunset.

40 days at the Kotel


How does one edit and save clips once and reuse in multiple videos with Adobe Premiere?

Question: I have many clips which all need basic editing such as adjusting the start and end. I would also like to reuse these same clips in multiple videos without setting the start and end again. I would like a portfolio of these basic edits once and simply use them as is. Of course inside premiere i would edit them again if necessary and so on without affecting the original settings. Is this possible if so how ?
Answer: Within a new project, create a sequence/timeline; call it 'Basic Edits' if you like, and make your trim edits on the source clips there. For each of your multiple videos, create a new sequence and copy-paste the trimmed clips from the first sequence.
Or if you want to use these clips in another project, you can import the sequence by the File -> Import menu dialog.
Of course, I presume that by Adobe Premiere, you don't mean Premiere Elements - the lite version - which doesn't feature multiple sequences in a project, as far as I know.
Comment: Thnx will try! i was hoping there was a formal way rather than "messy" copy/paste but the second para seems to be on the money...
Comment: The import option seems to imply all my clips get imported. I was hoping that a panel of "edited" clips could be built up and then i pick one by one without "importing".
Comment: In the import dialog, you can choose to import the entire project or selected sequences. Just gather your reusable clips in a single sequence and import just that. Or if even that's too much, you'll have to create a sequence for **each** source clip and then import just that. More trouble than it's worth, IMHO.


Where does Toad's slime power come from?

Question: Where does Toad's ability to spit thick, instantly hardening, suffocating slime come from, you know that slime he used on Jean Grey in the first Bryan Singer X-Men film? I've seen it in some of the X-Men shows and comics, but this was after the Ray Park character was introduced.
Comment: To clarrify ... you are asking what is the origin of Toad's slime or what is its power? I'm not seeing a defined question here.
Comment: Origin. Makes me wonder, do any real toads sling slime like that?
Comment: That said, Xmen evolution Toad also had the spitting. That show premiered in 2000 just ahead of Xmen the movie. So it's atleast that old.
Comment: Toads are (historically) supposed to spit poison to incapacitate their prey. It's actually a myth.
Comment: To cde- I realize about the show; however, this show aired 4 months AFTER the film. Also, to Paulster2, I am looking for the origin of the slime.
Comment: Poking around, I haven't found any commentary by the director, or by Ray Park, on the change in powers.
Comment: I know that it was originally scripted in an early draft of the film (which involved Pyro, Blob, & Beast before budget cuts) as Toad surprising Jean and licking her face, causing the slime to transfer from his tongue to her face. This occurs in the novelization of the film as well, but no word on where it changed to a spit attack with no surprise factor.
Comment: Did a bit more poking around. Found a very early script where Toad spit, and I quote, 'thick, black spittle' at Warren Worthington III, covering his face; however this COULD be coincidence since the black spittle burns Angel and the green slime cuts off Jean's oxygen.
Answer: To the best of my knowledge, the first Bryan Singer X-Men movie is the first instance of Toad having this power.  Previously, he had only displayed the powers of agility, wall-gripping, and an extended, flexible tongue.
I cannot speak to why it was decided Toad should gain this power, but it did serve as an effective plot point - it helped split up the heroes so that there could be moments for each one to shine and character development (such as it was).  It also helped set up for Storm's line about toads and lightning (which I can only imaging was supposed to sound much cooler than it did).
Following the movie, this power proved popular enough that it was incorporated into other media.  It appeared in the X-Men Evolution TV show (which used many designs/influences from the Singer films) and eventually migrated to the comics as well.
Answer: Toad gained the power to spit the resin after tinkering with his own genetic makeup using the Stranger's technology.
Source: http://marvel.com/universe/Toad
Answer: If you check out the old X-Men Animated Show, there is an episode in where Toad actually creates slime from his hands and can throw it, but also the slime has a side effect, that it can put people in suspended animation, as the slime has similar effects as curare.


MongoDB Hosting: MongoLab vs MongoHQ vs MongoMachine

Question:
Possible Duplicate:
How to find web hosting that meets my requirements?

I looking for a MongoDB managed hosting solution, here are 3 I found comparable.
Has anyone have some insights in which one to use?
Answer: When we started to evaluate MongoDB hosting, I tweeted about our initial results (DB size was reported differently) and whilst MongoHQ replied on Twitter to explain the differences in reporting, the MongoLab folks reached out to me directly and asked about our business needs and seemed to genuinely care about working with us.
We continued our initial tests against the free accounts on both hosts for a while but MongoLab's ongoing engagement and interest in our data volumes and patterns made us feel much more comfortable with using them for our business so we now have a dedicated two server (+ arbiter) replica set hosted at MongoLab.
MongoLab staff also spent time on conference calls ensuring everything was set up the way we wanted and helped us do extensive failover testing before we went live. We were very impressed.
For a fully managed solution, backed by enthusiasm, expertise and a demonstrated willingness to engage and assist their customers, we think the pricing is very competitive (compared to managed data center servers which cost us about double).
Answer: No noticeable difference on the technical side of things after using both MongoHQ and Mongolab. However I really appreciate mongolab's eagerness to correspond with its customers, quick replies to emails, and the overall good feeling that results from talking with them.
Answer: Well i'm using MongoLab, free account for development.)  Works perfectly
Comment: Me too, the support is better compare to MongoHQ. MongoLab replied in no time, but I am stilling waiting to get my questions answered by MongoHQ. However, my concern is MongoLab pricing goes from Large at $40 to custom DB (7.5GB RAM) at $600-$700, which is a huge jump. Whereas MongoHQ seems more granular.
Answer: Johnny...sorry about that. Lots of good stuff happening at MongoHQ right now so we have gotten a bit behind in responding to non-emergency requests. Our offering includes replica sets, user controlled backups and powerful web tools on top of arguably the world's largest provisioned MongoDB data layer. We have been around since the pre 1.0 days and have certainly learned over the last few years how to effectively run MongoDB in the cloud.
Also, we recently acquired MongoMachine. So, we are building our solutions for their customers as well. Busy but exciting!
Happy to help.
Jason
MongoHQ
Answer: Since hosting MongoDB in the cloud is new, both companies are likely to go through some growing pains which may or may not be a true indicator of which is the better provider for you.
We used MongoHQ for some of our early beta apps for Connect.Me and are getting ready to launch with MongoLab on a dedicated replica set. Ultimately, we chose MongoLab after corresponding with their technical support and getting comfortable with their roadmap and approach to customer service. For our needs at the moment, good support is critical so we can stay focused on building our app instead of managing infrastructure.
We also talked to a number of Heroku customers who ran into issues with MongoHQ. Of course, there's always the caveat that every service provider has issues at one point or another. Not to mention that cloud hosting customers often complain about provider issues when it's actually issues with the underlying technology and not the host.
I'll let you know how things go with our launch and MongoLab.
Answer: What is your major consideration? Price? Uptime?
From my experience, I consider the price at first but I adjust my through afterward.
For traditional SQL database environment, the database version doesn't come out so fast. Mongodb is other stuff which is fast growing. I used to include some new feature in my application of every mongodb release. The version transparency so look important for my starup company situation.
For mongohq shared plan, there are little transparent of what version they are using, their planing to update. In their FAQ, they just mention version 1.6.x / 1.8.x, and you may find some more thing in their twitter. May be their Dedicated Plans, have better support and version control.
For mongolab, their support seems better, at least self support. You may know what is happening in their support page.
10 gen has release mongodb version 2.0 and planing to release 2.1 at Oct 12, 2011. The version gap of mongohq/mongolab is huge, or at least provide a latest environment for my testing. This version gap force me to setup a local development db with latest version and pending my application to release.
The reason I would like to choose a cloud db service like mongohq/mongolab is I would be a dub! I am lazy to learn something about version, maintenance, setup etc.


Genre of "Meant To Be" by Arc North

Question: What is the genre of the main tune in the foreground of Arc North's Meant To Be, and who are other artists working in this style?
Answer: The style of music used in this track is a genericized form of House Music that is quite prominent in pop music today.
The original House Music stye has been highly influential to a lot modern music, and has evolved to include a plethora of sub-genres, so identifying a specific sub-genre will be difficult.
Deep House is one common sub-genre of House Music that seems to align with your reference track, primarily due to the relatively low BPM of ~105, but also due to the general sound of artists in that genre.
As for other artists working in this style, they are too numerous and broad to try listing. Search for Deep House music, and you'll likely find tracks that are appealing.
Answer: Beatport labels this track as electronica-downtempo. See the side bar using previous link for similar artists and tracks. Another answer suggested Deep-House, though that genre usually has BPM's around 120, not 105.

Genre of "Meant To Be" by Arc North


What qualities characterise girlish Japanese handwriting?

Question: In English, handwriting is generally seen as girl is the mini. caps are almost as large as the maxi. caps, the edges are rounded out, and if the dots are replaced with little cirles reminiscent of the japanese period (。). What characteristics are common of handwritting considered 'girlish' in Japanese?
Answer: Generally in Japanese handwriting the more feminine something is the more rounded out and cute it will be. If I think of girly English writing I think of neat bubbly letters while guys tend to be sloppy and angular. This carries over to Japanese.

Additional reading:
http://guideline.livedoor.biz/archives/51130942.html
http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1142672631
Comment: I'm embarrassed that even though I'm a boy I write Japanese kana like that, almost exactly! (honestly, though, except for the か and the お and the わ which are a bit weird) Though my kanji is more of a sloppy imitation of 楷書...I never learned how to write roundish kanji.
Comment: Same here, I think it looks a lot nicer and legible, more enjoyable to read. Any ways, thank you for the information and picture!
Answer: Legible and accurate writing is just good handwriting. What's 'girly' about is only that girls will write like this more often than boys. If we keep calling it girly then us males are going to keep excusing ourselves from proper handwriting! I'm male and I don't think sloppy and angular should just be necessary qualities of 'boyish' handwriting. But circles instead of dots, yeah I suppose that could be a feminine stylistic feature.
Comment: Someone's always watching O_o


How should I delete a CiviCase or a Case Type

Question: If I need to delete a CiviCase Type or a CiviCase it can be confusing given that 'deleted' Cases are not actually removed from the db.
Answer: Civi Case Types cannot be deleted while there are Cases of that Type. Cases can be changed to a different Case Type which can then permit you to delete a Case Type with no Cases.
But if you just want the Civi Cases gone then note that Civi Cases themselves, when 'deleted', remain in the system for audit purposes.
To delete a Civi Case entirely it is necessary to do so either via the API Explorer (at /civicrm/api/explorer) or via sql.
Via API Explorer use
CRM.api('case', 'delete', {'id' : xxx});
Via MySQL use
<code>DELETE c, ca, a FROM
civicrm_case c LEFT JOIN
civicrm_case_activity ca ON c.id = ca.case_id
LEFT JOIN civicrm_activity a ON ca.activity_id = c.id
WHERE case_id = xxx;
</code>
and this should take care of any case_contacts data and any rows in civicrm_relationships that have case_id
Comment: also need to deal with case_contacts and rows in civicrm_relationships that have case_id


Partitioning a Linux based system

Question: I am using Linux Mandriva OS. During installation my friend suggested 2GB for the swap partition and the remainder as the root partition. What is the use of providing a separate space for root? Instead of providing 2GB should I go with 4GB, or more?
Answer: Like it has already been said, swap is just like a spare-wheel RAM, to which the system resorts in case of shortage of physical memory. Like an insurance, in that sense. The common advice is to make the swap partition as big as two times your RAM, but actually that is the "old way". With RAMs the size we have today, having a x2 swap would waste too much space on your hard disk with a useless partition, as you would much unlikely need that much extra memory (again, given RAMs the size we have nowadays). But the advice remains this way there's no fixed advisable size for swap, it depends on your RAM. If you want to hibernate, you surely want to make your swap size as big as your memory, allowing your system to save the whole RAM to your hard drive. That could happen also in a dedicated file in a normal partition, avoiding making a separate one just for this, the way Windows does, but is better not, like the fact it's Windows' way suggests. By separating hard drive sectors according to this much different usage you contribute to your system stability, and you have a double insurance you'll always get some RAM backup space, and not (even for how much unlikely it is) steal its space for regular usage and find yourself without it when you need it.
As for the root (/) partition, it's the one that contains everything, so of course you wanna make it a separate one (also if I don't get what you mean, separate from what? From swap?). It's like basic Windows C: partition, it's gonna contain your operative system as well as every indispensable library and default programs, and every software and game you install not specifying a different path. Also every device and partition you get running in your system refers to root, as your system is based on it. Of course, that does not mean that they get physically copied into it and you must have enough free space for them, just that directory shortcuts are created in that, like pointers, so absolute path for them start with a / too.
What many people create a separate partition for is home (/home/username) folder, in which the big part of your personal data is stored. You wanna do that also if you are gonna boot multiple systems into your computer and have files like documents, music, pictures, videos and movies, downloads and so on in common between those, in an impartial partition that does not belong to any system, but it's accessible by every one of them the same way. But again, there's another better way of doing it which I recommend, as having shared home folder between more systems can create conflict with personal settings (due to user and group ids), which are stored in hidden folders in your home for Linux systems. You can just have a separate data partition (if you have a Windows system already installed with a D: storage partition, that is) and just create symbolic links in your home with simple terminal commands, so that you have the heaviest files into a dedicated big partition shared among your systems, and you get access to them directly from your home without having them actually stored there. This way there's no conflict as you have a separated home for each system (with your user settings safe there), which contains link to all your personal files.
Making a short summary, this is the way I recommend a Linux partitioning:
Root partition: your system main one, ext4 filesystem, around 20 Gb size;
Swap partition: your RAM extension, linux-swap filesystem, as big as your RAM;
Data partition: if you don't already have it, a big partition containing all your documents, images, music and so on, shared among all operative systems, filesystem FAT32, as big as you can.
Hope everything is clear, ask for any doubt!
Answer: During hibernation the system saves an image of the current state to swap.  This image is loaded on awakening.  Swap space also acts to supplement and optimize the systems physical memory.  Inactive items are moved to the swap to make space for active items.
It is commonly recommended that the swap space be about the same size as physical memory on the system.  Swap space can be either a file or separate partition.  Designating a partition as swap space serves to prevent fragmentation of a swap file.
Answer: Yes, you can provide more than 2 GB space to swap.
To read more about swap space, follow: All about Linux swap space
Answer: A swap partition is used for the case when the system runs out of RAM, it starts moving unneeded information in RAM into this SWAP area.
If you don't have a swap area, the system will report that it ran out of memory and new processes won't be able to start.
You can use as much swap as you want, but generally, 2 GB are enough (on my 2G RAM system i never used more than few hundred MBs of swap, and most of the time less than 100 MB).

Partitioning a Linux based system


beschränken vs einschränken – is there a difference?

Question: What is the difference between verbs beschränken and einschränken? Do these two words have the same meaning or maybe they mean something different?
Answer: beschränken is something to happen, e.g. @splattne

Dieses Angebot ist beschränkt auf Kunden mit Wohnsitz in der Schweiz
  meaning: This offer is only for  Customers living in Switzerland  (also: limited to)

beschränken thus is more of passive for the one experiencing it (the customers either live in Switzerland or not), and generally refers to the object of the sentence as experiencing party.
The subject of the sentence in is the beschränkende/restricting party, meaning it takes action to reduce the freedom of action of the object.
the result of this sentence is the same as above but gives more of the active impression:

Der Verkäufer beschränkt das Angebot auf Kunden in der Schweiz
  The seller limits the offer to customers in Switzerland

einschränken is more of reflexive active, meaning: someone restricts his own freedom of action for some reason, again see @splattne:

Nach dem Herzinfarkt musste er sich beruflich sehr einschränken
  meaning: he had to restrict himself in career terms after the heart attack

opposing to;

Der Herzinfarkt beschränkte ihn beruflich
  meaning: the heart attack restricted him in career terms

einschränken is usually in a reflexive context with sich,
beschränken is usually used with etwas and restricts someonewho does not take action
Of Course you can use einschränken in an active context, and beschränken reflexive, but this is not as common.
In general the meaning is the same and they can be used synonymously, but einschränken in general stands with reflexive sich and beschränken in general stands with a dativic object etwas
@Emanuel:
as correctly added by Emanuel, both words in past participle are often(?) used as adjectives: eingeschränkt and beschränkt.
In this example the words are replaceable:

Die Nutzung von 32-bit Programmen auf 64-bit Systemen ist nur eingeschränkt möglich (also: beschränkt)
  The usage of 32-bit programs on 64-bit systems is limited

While here a replacement would change the sense of the sentence

Die Überwachung des öffentlichen Raumes ist nur eingeschränkt möglich
  Public area surveillance is only possible within certain (not further clarified) borders

The Surveillance itself has no borders, but these borders cannot be fully exploited, as some other circumstances define a smaller exploitable area

Die Überwachung des öffentlichen Raumes ist nur beschränkt möglich
  Public area surveillance is limited (due to the high price of cameras or whatever reason)

The Surveillance itself is limited, and not "restricted" by external influences, but in itself.
At least is this my interpretation. i think you could start a debate about that, which is not my target.
Here the correlation between "restrictor" and "restricted" inverts, opposing to the verbal use. --> eingeschränkt refers to external restrictions and beschränkt to internal.
Comment: "The difference is, einschränken is activity by the one losing freedom of action, and beschränken is more passively accepting restrictions that are externally given, at least in general." This is a bold claim, but I just don't think it is true (I'm a native speaker of German). Do you have any support for this? Also, your answer completely neglects the uses of the participle 2 forms as adjectives for both verbs. This is very common though and certainly reflects the very semantical differences the OP was asking for. An explanation completely based on the "mode" of the verb misses the point.
Comment: @Emanuel thanks for your critic, please provide an example for your claim concerning the mode. also thank you for directing my view to the past participle form of these two verbs when given as adjective. i must admit i do not often use that, maybe this is a regional difference? FYI i am native speaker, 17 and Abiturient ;) please do not expect a linguistically correct explanation from me. in my eyes the main difference lies in the "main" mode of the verb  and its constructions, but maybe that is just the diference in lifetime?
Comment: So by "mode" I meant the "passive" vs. "reflexive" you mentioned. I think linguistically this is not necessarily called mode but I didn't know what else to call it. As for the use... I don't use the participle 2 that often either but that is because I don't use those verbs very much anyway. I think in newspapers the p2 is very common. There is a difference in meaning between:

"- Die Wahlmöglichkeiten werden in Art. 2 eingeschränkt." and "- Gesellschaft mit beschränkter Haftung"   and  I think the key-difference between the verbs can be found in situations like these.
Comment: @Emanuel "passive" is a mode, "reflexive" is not a mode, but a sort of pronomen referring to the subject of the sentence (see wikipedia). the examples you provided are wonderful, i should have used them, i think i got the difference in meaning either way. the problem is, sometimes these two are replacible and somtimes not, the difference in situation is just extremely difficult to explain
Comment: If you need more of those example try out Linguee.com... here's the link: http://www.linguee.de/deutsch-englisch/search?source=auto&query=eingeschr%E4nkt   The English translations might also help flesh out the differences. In this case it looks like beschränken is more "to limit" while einschränken is shifted toward "to restrict" :)
Comment: if that is the case, my example no.2 is not correctly translated and not well chosen ;) thanks for the link, i'll look at it
Answer: Though the two are mostly synomymous, there is a slight difference between the two and there are cases in which only one of the two is used. However, it is really difficult to pinpoint the difference (even for a native speaker). I will try anyway:
einschränken is the only option, if the limitation is in respect to some reference:

Der Schnee schränkt den Verkehr ein. – The snow impedes traffic. Here the reference are the normal conditions for traffic.
Die Funktionen des Druckers sind eingeschränkt. – The features of the printer are limited. Here the reference are other printers. The printer in question might, e.g., lack network capability.
Dank der Hinweise konnten wir die Liste der Verdächtigen weiter einschränken – Thanks to te clues we could further reduce the list of suspects.

beschränken is the only option, if the limitation can be directly expressed in form of a clearly defined threshold or area:

Die Celsius-Skala is nach unten beschränkt. – The Celsius scale is bounded from below. Here the threshold is −273 °C.
Das Angebot ist auf Deutschland und Österreich beschränkt. – The offer is limited to Germany and Austria.
Die Nutzung der Rutsche ist auf Kinder unter 12 Jahren beschränkt. – Usage of the slide is limited to children under 12.
Answer: The two words are synonyms, but you can't simply exchange the one with the other in every case because they are often used in phrases, for example

Dieses Angebot ist beschränkt auf Kunden mit Wohnsitz in der Schweiz.

or

Nach dem Herzinfarkt musste er sich beruflich sehr einschränken.

Here are the the definition of both words in Duden online with some examples:
beschränken

einschränken, begrenzen, einengen
sich mit etwas begnügen
sich erstrecken, gültig sein

einschränken

a) verringern, reduzieren; auf ein geringeres Maß herabsetzen
b) in etwas einengen

aus einer Zwangslage heraus, um etwas zu erübrigen, die Ausgaben für den Lebensunterhalt klein halten, sich mit wenigem begnügen; bescheiden leben


Can I use one string gauge for standard D and drop B tuning?

Question: I've been using 10 - 48 gauge strings for standard E tuning for 3 years, but I want to change to standard D tuning. I read somewhere that I should use 11 - 58 or 10 - 58 gauge strings for this tuning; is that correct? I don't want the strings to be too slack. And can I use one string gauge for standard D and drop B tuning ?
Comment: Tuning down by 5 semi-tones is pretty insane. May I recommend that you switch to a seven-string at some point, if you're certain you want to play lower pitches.
Answer: I agree with what you heard that if you drop all the strings two frets you want to go up at least one step in string gauge. Perhaps two. I played two frets down in one band and I ended up stringing 12s for that, so to me, 11s certainly make sense.
Drop B is a big difference for the lowest string. It's gonna be floppy, but unless you get a custom gauge string, it will be floppy. If I were in your shoes I would just deal with the floppy feel and learn to work it. Another option is pick up a second hand guitar that isn't too expensive and customize the strings for drop B and switch for those songs. A string that's not floppy for drop B will be too tight for standard D tuning.
Comment: Can floppy string hurt the guitar neck ? if not I can use d tune string gauge for drop b because I am not a big fan of drop b tune (I just like slipknot songs )
Comment: @amirmehr - floppy strings probably won't hurt the neck - although the neck relief and action may well change with floppy strings. They'll rattle more, and be easier to press out of tune (sharp) and maybe they'll give a different feel to themselves when you play them.
Answer: You don't say what the guitar is - Les Paul versus Strat means different tensions for the same string gauge and tuning, so it's not that straightforward.
It makes sense that whatever tension you are already used to, that same tension, approximately, is retained for each string in the new tuning regime.
You need to experiment a bit, by going up in gauge as a particular string goes down in pitch. There are individual strings available to facilitate this.
One set of strings for two rather different tunings isn't going to be anything but a compromise. As Todd says, a second guitar is a far beter option if you want to do that. Apart, faffing about re-tuning, unless done smartly, always sounds so amateur, and wastes a lot of time. Then after, the same faffing to re-tune..!
40 odd years ago, I made the same sort of decision, and from then use a hybrid set on several guitars - unfortunately not avaiable as a complete set of strings off the shelf - but in standard tuning, it works for me. Others hate it, and it means I'm so used to the feel, it's not pleasant playing others' guitars, but there we have it. We can set up our own guitar action, (or have it done for us), so why not have a bespoke set of strings to boot?
Comment: While there are more guitar styles than LP and strat, I agree with the notion that the guitar plays an important role. If you happen to have a tremolo system that is suspended by springs, changing (adding/removing/replacing) springs in the back of the guitar can help accomodating for different tension due to tuning.
Comment: @Ian - I was thinking more about the scale lengths, but, good point about springs v. strings.


What is a good small bicycle bag to store your gear and/or personal things?

Question: I'm looking for one that attaches to your bike and easily detaches so you can take it with you.  I usually ride with a small Timbuktu messenger style bag (really small, it's about the size of a large book) and I carry my wallet, phone, keys and stuff in it.  Is there something for bikes so that I can easily attach and detach from the bike?
Comment: Changed gear tag to equipment to avoid confusion.
Answer: Saddle Bag

It may seem too small at first. But check what I can fit in with my Specialized Saddle Bag:

Two spare inner tube boxes
Cell phone
Keys
Money
Train travel card
3 tire levers
Small toolset
Comment: Accepting the answer of Saddle Bags. These have the form factor that I'm looking for. I also found one and posted below.
Answer: I just picked up a Timbuk2 Handlebar Bag, and so far am loving it.  Has a nice velcro-down pouch, and attached to the bike via two velcro strips.  It is on the bike well enough to hold my daily lunch, u-lock, glasses and a few other things.  It also has straps to turn it into a fanny-pack style bag.
Comment: I have a Timbuk2 messenger bag I use when I need my Netbook, and I can verify that it's well built.
Comment: Well built and has a nice bit of waterproofing.  Wont help from the sides, but will probably work great in a heavy rain.
Comment: I love Timbuk2 bags. I like the fact that it can be used as a fanny pack, but it seems a little big for that.
Answer: I actually just found this great bag that got high reviews.  Avenir Bigmouth Velcro Seat Bag. It easily attaches/detaches. According to one reviewer, it takes less than 15 secs.
This is large enough for my stuff and a few essential tools that were recommended here in this forum.
Answer: You might want to look into pannier bags (if you have a rack on the back of your bike).

There are all sorts of sizes, styles, and types of bags, including those large enough for groceries. I got a pair from Walmart (I can't remember which brand) for about $25 that I use to commute to and from work. They're big enough to carry all of my work clothes, lunch, and water plus some extra. They're also water-resistant, which is nice when I get caught in a sudden rainstorm (happens a lot in Colorado). I always have a spare ziploc bag to toss my phone into, just in case.
My bags hook on to the edge of the rack and have an elastic strap that runs around the bottom of the bag and the "leg" of the rack. I have a set of bungie cords that strap everything down tight so they don't bounce loose. It takes me about 30 seconds to take the bags off, and mine came with shoulder straps, which makes them easy to carry into the office.
Performance Bicycle has a nice selection of pannier-style bags.
Comment: I think he's looking for a smaller bag. A saddle bag is probably what he needs.
Comment: Look at the clips that hold a pannier onto your rack, the best clips are very quick to operate and always holds the pannier securely.   I have lost a cheap pannier (it fell at some point) due it is "bend bit of metal" clip that did not possibly grip the underside of the rack.
Answer: I find that handlebar bags are the ultimate in convenience.
From your description, a medium-sized handlebar bag might do the trick if you can mount one. I love my Ortlieb Ultimate handlebar bag, but it's not a cheap item; here are some others. FOr maximum convenience, look for something that clips onto and off of the bike quickly.  Most bike shops carry handlebar bags.
Comment: Those are pretty cool.  I like the little waterproof map attachment!


Is there a way for a user to tell if their Android device is encrypted or not?

Question: There is a semi-relevant thread on SO https://stackoverflow.com/questions/12640708/check-if-android-filesystem-is-encrypted
that explains how a developer would determine if full-disk encryption is enabled, but is there an easy way for a user to know? I tried encrypting (I'm on 4.4.2) and it seemed to fail at some point but did not throw an error, just dropped me back to the homescreen at a certain point.
Comment: That's not conclusive (as you said), you can set a PIN without encryption
Comment: I have a Galaxy S6 that I attempted to encrypt, I started the process and took a shower. When I came back to check the results I could not tell if it was successful. The only difference is that there is no longer a choice to encrypt. That does not conclusively indicate that the phone is encrypted.
Answer: On Oreo 8.0.0
Settings → Security & Location → Encryption & Credentials & it shows phone encrypted
Better method
Using adb command adb shell getprop ro.crypto.state ( works on unrooted devices also) returns encrypted or unencrypted
Output examples

Oreo ( Unrooted, encrypted)

Vostro1510 ~ $ adb shell getprop ro.crypto.state
encrypted

Marshmallow ( Rooted, unencrypted)

Vostro1510 ~ $ adb shell getprop ro.crypto.state
unencrypted

Source - Adb command to check if the device is encrypted
Note : Original question refers to Full Disk Encryption which has been replaced by File encryption from Nougat onwards. See this for details
Edit Instead of adb you can install Termux and type getprop ro.crypto.state to get the result - works on unrooted device also
Comment: @guettli guess you missed the app alternative towards the end of the answer
Comment: +1. Is there a way to know if the device uses full-disk encryption or file based encryption?
Comment: @Firelord Thanks. Yes, we have an answer here https://android.stackexchange.com/q/195713
Comment: You call it "Better method". Unfortunately I don't know how many people have adb installed or not. I guess (but don't) know that most devices don't have adb.
Answer: Same place where you start the encryption:
In (I am on 4.3) Settings -> Options -> Security,
the first entry will report the status and offer decrypt (if encrypted)
or encrypt (if not).
Comment: I could be wrong but isn't there a difference between FDE and system encryption? I think the one you mention is only system level.
Answer: If your phone came with Android 5 or above, the storage is encrypted by default. You can verify this by going into Settings > Security & lock screen > Encryption & credentials. It should say Encrypt phone - encrypted and it won't allow you to turn it off.
Hovewer, the safety of the encryption depends on several factors. Most importantly, you should be using a strong password. PIN codes can be brute forced easily - Android allows you to try 5 different passwords every 30 seconds. That means brute forcing a 4 digit PIN takes less than 17 hours.
Another factor is whether you have the bootloader unlocked and what kind of encryption your phone uses.
File-based encryption
Android 10+, some devices with Android 7 - 9.
Android with FBE enabled encrypts the master key by a combination of the device key and your PIN/password. A device like this is NOT decryptable without your password even if one can run arbitrary code* on the device.
You can quickly verify if your phone is using FBE by restarting it. If it asks for PIN/password with a default-themed keyboard, it's using FBE.
A more reliable way is running adb shell getprop ro.crypto.type. You'll get the response file for FBE.
Full-disk encryption
Android 4.4 - 6, some devices with Android 7 - 9.
The master key is encrypted using only the device key by default. If you can run any code* on the device, your data is as good as unencrypted. To encrypt the master key with your PIN or password, you need to enable "secure startup" (Settings > Security & location > Screen lock > PIN or Password and tap Yes when it asks if you want to use Secure start-up). That makes the master key encrypted with the device key AND your PIN/password.
If you get a black screen with a prompt "To start Android, enter your PIN/password", then your phone is using the secure start-up. If it boots normally and asks for PIN/password with your customized keyboard, your phone is NOT using the secure start-up.
You can check if the device is using FDE by running adb shell getprop ro.crypto.type. You'll get the response block for FDE.

* you can run arbitrary code if the bootloader is unlocked, the device manufacturer (or possibly a very determined hacker) can likely do this even with bootloader locked
Read more about Android encryption here: https://source.android.com/security/encryption/
Comment: some weird exception (forced by chinese government?) https://android.stackexchange.com/q/241934
Comment: @alecxs You can verify this by launching TWRP on an Android <=9 device and being able to read the contents of the device without entering a password/PIN. If the key was encrypted, this would be impossible. What would it be encrypted with anyway? I tested this on a Mi A1 (tissot) when "secure start-up" was not enabled.
Comment: Using the passphrase "default_password" is as good as having an unencrypted key, but I'll change the wording to reflect that.
Answer: Try changeing default storage to SD Card
Settings -> Memory -> Default Location -> SD Card
if your phone is encrypted than you'll get a warning stating that internal memory is encrypted. Of course its only a hint, not a proof.
My P9 Lite (Android 7) behaves like that, and this is consistent with user guide page 193

Full-disk encryption |  All data on the memory chipset is
  automatically encrypted


What was the price of a horse around 1750?

Question: I'm looking for the average price of a horse, in British Pounds, around the year 1750. I'm interested in draft horses (they pull carts), not riding horses, but the difference in price between those two wouldn't hurt. And I'm more interested in colonial America rather than Europe, although I have no idea if the prices will be very different.
Answer: Prices are occasionally mentioned in mid-18th century journals; for example, David Zeisberger's journals, available here: Diary of David Zeisberger : a Moravian missionary among the Indians of Ohio.  In this one you will discover that a buck skin is worth a dollar, which is repeated in various frontier sources between 1750 and 1800 that I have read; this is probably the origin of the colloquial "a buck is a dollar"!
Though less interesting to read, a more direct source are the estate inventories that were required when probating an estate. In researching early Detroit under the Americans, 1780-1830, I've studied many of these in the original. Godfroy Corbus, along with many others beginning in 1797, is available (free) on FamilySearch. These are digital images, but the records have only a primitive index.
Godfroy Corbus was a farmer; he had moved to Detroit from Pennsylvania; probably of Scots-Irish descent. His widow is one of my aunts.
On this record, Wayne County Probate file #67, from 1807 one finds:
One bay horse $30; one grey horse $45; one bay mare $45; one sorrel ditto $45; One bay mare $45; one colt $10.
One yoke of oxen $50; one yoke and ring $1; One young yoke $30; one red cow with white $12; etc. A side saddle, for his wife? is listed at $10. The entire estate is worth $732.85.
The usual pound used at Detroit was the New York pound, worth $2.50. Some records list values in shillings and pounds as well as dollars, right up to 1830.
A probate record from 1825, the estate of Jesse Hicks, Wayne County Probate file #299, we find:
2 horses and plough harness $100; 1 yoke of oxen with yoke $45; 4 cows $44; 1 yoke of steers three years old $20.
Note that a yoke of oxen can do the plowing, but a team of horses does more work in a day, but also requires more care and is more expensive to feed. The yoke of three year old steers is only worth $20 because they are not yet fully trained or fully grown: they'll be called oxen when they are four years old and fully trained as a team, left and right.
From these records you can see that the price of a horse is stable during this period, but responds to the local demand. You should be able to find similar records for your region of interest.
Another source is military supply records, which are numerous for the Revolutionary War period. Every penny counted, and on the frontier they had to buy cattle and horses on a regular basis. See Frontier Advance on the Upper Ohio, 1778-1779, which includes transcriptions of many original documents, with sources.
Comment: Those are some pretty cool sources, especially because of the ergonomic book-reading interface. It's way better than Google Books. However, I checked your last one and searched for "horse". All hits did not show any prices. Am I missing something?
Comment: Also try looking for "team", "mare", and various terms for cattle and oxen. The prices of oxen and horse teams are often proportional.  There are five books in this series, and I ran across a lot of cattle, steers, hogs, flour, and whiskey -- the men had to be fed!  But they also had drovers and men on horseback, so I expect that there are a few horses listed also.
Comment: At $5 per pound sterling, a typical exchange rate prior to 1914, your prices of $30 to $45 for a horse are rather close to what I have estimated below as 8 pounds sterling..
Comment: @Pieter Geerkens: the gold value of the US dollar was inflated several times during the 19th century; after the panic of 1837, during the Civil War, etc. In 1800 to 1820 the New York pound was $2.50, and the Halifax pound was $4.00. Both were used in commercial accounts in Detroit.
Comment: This site provides time-series [exchange rates for US Dollar and British Pound](https://www.measuringworth.com/exchangepound/#). Plugging in 1800 to 1837, the lowest rate was $3.62 for 1812, and the highest was $5.22 in 1816: bracketing the War of 1812.
Answer: This list of medieval prices indicates the price of a draught horse in the 13th century to be between 10s and 20s,, while this estimate of global inflation shows prices in 1750 being 8 or 9 times what they were 500 years earlier.
I note that the steady inflation from the early modern era is due to the influx of American silver into the European economy by Spain.
Also, I suspect that draught horses would be less expensive in the English colonies than in London, for example, and for the same reason that cost of living today is higher in New York City than in Hoboken.
Putting this all together gives an average price of about 80s (or 4 pounds sterling) for a draught horse in 1750, This will go up or down depending on the age and condition of the individual horse of course - don't look a gift horse in the mouth as they say. Harness  and tack would all be additional, just like GPS and A/C in modern cars.

"pounds sterling" means exactly that - translated, 20 silver shillings, which was a silver coin slightly larger than a modern U.S. or Canadian dime I believe
. From Wikipedia, pertaining to the 1816 "new" standard reminting of the shilling: "New silver coinage was to be of .925 (sterling) standard, with silver coins to be minted at 66 shillings to the pound. Hence, newly minted shillings weighed 87.273 grains or 5.655 grams.". Prior to 1816 the mintings were irregular.
Comment: @DrZ214: "*pounds sterling*" means exactly that - translated, 20 silver shillings, which was a silver coin slightly larger than a modern U.S. or Canadian dime I believe. From Wikipedia (https://en.wikipedia.org/wiki/Shilling_(British_coin)#History), pertaining to the 1816 "*new*" standard reminting of the shilling: "*New silver coinage was to be of .925 (sterling) standard, with silver coins to be minted at 66 shillings to the pound.[8] Hence, newly minted shillings weighed 87.273 grains or 5.655 grams.*". Prior to 1816 the mintings were irregular.
Comment: Good point about silver. By any chance, do you know the going rate for silver in 1750? How many pounds stirling would 1 troy ounce of pure silver cost?