I need help in identifying an old-ish sci-fi book which I read in my college library a long time ago.  The story started building as follows -  There were robots which came from nowhere and started helping humans. They did everything considered risky for humans.  Because of this humans ran out all ways of feeling any kind of thrill and became very frustrated.  I don't remember the mid of the story.  There was a scientist who was explained to be of weak health and balding.   Later in the book due to extreme circumstances he was able to create physical things (a room which he remembered) simply by imagining them.  By the end it was mentioned that the scientist (sort of) didn't succeed in his mission of disabling the aforementioned robots and was nursed back to health by the same robots. He was surprised by how well he was nursed back to health and even his hairline was restored.
These androids show up day in suburban USA and start offering all their services for free - they are much better than the robot helpers that cost money - the protagonist is a salesman of the latter.   Soon, the 'helpers' are everywhere, and human beings effectively cannot do anything without these things keeping people 'safe'. Humans become infantilized and controlled.   Eventually it's discovered that one man created them, and he's been kept prisoner by them to prevent for his own safety.   This seems remarkably similar to the conclusion of the I, Robot movie.
Is tipping mandatory at Restaurants and Bars in Germany? The layman's question. Is there a maximum temperature that can be reached by air on Earth due to global warming? For example, one that would prevent living organisms from functioning? I read somewhere that with the increase of the sun's brightness by 10%, the average temperature on our planet will be 47 C. This, however, only for about 600 million years. Would global warming enable reaching such a high average temperature? What does the author mean by 'back to back' and 'hidden city' ticketing hacks? Sum of (example: 0+1+2+3 = 6 , 0+1+2+3+4+5+6+7 = 28 and so on) Least squares problem with constraint on the unit sphere It is easy to find the minimum of $\|Ax-b\|_2$, when $A$ has full column rank. But how is the case when we add the constraint $\|x\|_2=1$? Or, to be explicit,  $$\min_{\|x\|_2=1}\|Ax-b\|_2=?$$  My idea is to construct the corresponding Lagrange function  $$L(x,\lambda) = (Ax-b)^T(Ax-b) + \lambda(x^T x - 1)$$  Differentiate the function with respect to $x,\lambda$, we have  $$A^T A x - A^T b + \lambda x = 0$$  $$x^T x=1$$  However, I find it hard to move forward to get the answer. Could anyone help me? Thanks a lot! Signature/date line with fixed width Get specific GPS location somehow on windows 8 Solve for $x$ in $6x^2-25x+12+\frac{25}{x}+\frac{6}{x^2}=0$ I simplified to get $6x^4-25x^3+12x^2+25x+6=0$  Or $6 (x^2+1)^2+25x(1-x^2)=0$  Then I substituted $z=x^2+1$, to get $6z^2+25\sqrt{(z-1)}(2-z)=0$  I can't find a way to proceed further. Shorten title on each beamer slide In a beamer presentation the title is long but ok for the first slide. The problem is that when the title appears below on each slide it is very long and I would like to use here some sort of running or shorter title, how can this be done? List of PDOStatement::bindParam data_type parameters Does it make any difference for SEO benefits to buy dropped and already available domains other than backorder domains that are expiring soon?  I heard somewhere that whois gets deleted after being dropped. But I didn't find any confirmation if it's true or not.  Anybody can tell me if there are benefits of one against the other, if yes what? This question is a possibly harder version of: .  Question.  Let $f,g :\mathbb R\to\mathbb R$, such that \begin{align} f(x-y)=f(x)\, g(y)-f(y)\, g(x), \tag{1}\\ g(x-y)=g(x)\, g(y)+f(x)\, f(y), \tag{2} \end{align} for all $x,y \in \mathbb{R} $. If $g$ is continuous at $x=0$ and not identically zero, then there exists an $\alpha\in\mathbb R$, such  $$ f(x)=\sin \alpha x\quad\text{and}\quad g(x)=\cos \alpha x. $$ Is there a pair of discontinuous $f$ and $g$ satisfying $(1)$ and $(2)$?  Update. If $\ell :\mathbb R\to\mathbb R$ is a linear functional over $\mathbb Q$ (i.e., $\ell(qx+ry)=q\ell(x)+r\ell(y)$, for all $x,y\in\mathbb R$ and $q,r\in\mathbb Q$), then $$ \sin\big(\ell(x)\big), \quad \cos\big(\ell(x)\big), $$ satisfy $(1)$ and $(2)$. Discontinuous such functionals do exist, and they are obtainable using Zorn's Lemma (equivalently the Axiom of Choice.) This takes care of the second question. Why are There No "Triernions" (3-dimensional analogue of complex numbers / quaternions)? Since there are  complex numbers (2 dimensions) and quaternions (4 dimensions), it follows intuitively that there ought to be something in between for 3 dimensions ("triernions").   Yet no one uses these. Why is this? Vi on Linux: show ^M line endings for DOS-format files On Solaris, if you open a file in vi that has Windows line endings, this shows up as ^M at the end of every line.  On Linux, vi is cleverer and understands the Windows file format, and does not display ^M.  Is there a setting to make Linux vi behave the same as Solaris in this respect?  A common problem for us is copying a shell script off a (Windows) dev box and forgetting to dos2unix it, and then being confused when it doesn't work properly. On Solaris the problem is obvious as soon as you vi the file, but not on Linux.  Thanks. How can I take a self-portrait without using a remote?  My camera is a Canon Powershot SX210 IS. I do not have a remote, but I do have a tripod. How do I programmatically get the field type of a specific field? How to split a string with any whitespace chars as delimiters How did "but" mean "only"? : Old English butan, buton &quot;unless, except; without, outside,&quot; [...]  I don't know Old English. From the étymons overhead, how did but  to mean    |adverb| = 1. No more than; only  ? What can explain the semantic shift? I didn't understand , because English is not my first language  :   In sense: Only. An elliptic development of the conjunction: see .  a. By the omission of the negative accompanying the preceding verb (see ), but passes into the adverbial sense of: Nought but, no more than, only, merely.    I understand Shakespeare's use in . Thank you all. Moment of inertia of a cylinder about its base I've tried to find the moment of inertia of a cylinder rotating about an axis parallel to its base (i.e about the 'End diameter') as one can see  . But when I checked my results with different references ,I've found that it's incorrect!.I need a help to figure out where I did it wrong. since $$I=\int\limits x^2.dm$$ $$dm = \rho.dv$$ where $$dv= r.d\theta . dr .dh$$ &amp; $$\rho=\frac{M}{\pi R^2 H}$$ $M$:cylinder total mass. $H$:total height of cylinder. $R$:the radius of the cylinder. The distance of each infinitesimal element from the axis of rotation would be : $$\sqrt{r^2+h^2}$$ Therfore, $$I= \frac{2M}{ R^2 H}\int\limits_{0}^{R} \int\limits_{0}^{H}\, r(r^2+h^2)dh\,dr$$ and this gives a result of : $$\frac{M~H^2}{3}+\frac{M~R^2}{2}$$ Which is obviously wrong since the second term should be multiplied by a factor of $1/2$. Density of ring of algebraic integers in $\mathbb C$ Clearly, $\mathbb Z$ is not dense in $\mathbb Q$ (and not dense in $\mathbb C$).  But why is the ring of algebraic integers $\overline{\mathbb Z}$ dense in $\overline{\mathbb Q}$?  In particular, if this is so, it is dense in $\mathbb C$.