What is a word to describe holding two opposites at the same time as truth. To believe  and hold opposing truths or doctrines both as true at the same time, though they are completely in opposition.  Example.  "I believe that  women are  equal to men even though they are inferior to men."
I think some good words would be conflicted, or confused. As an example of context, think of someone who believes in freedom of speech, but, at the same time, they would support banning comedians who make jokes about certain issues that person cares about.
This is the proof, which I mostly understand except for one bit:  You have $h_1 \in H_1$ and $h_2 \in H_2$.   We also have $h_1^{-1}(h_2^{-1}h_1h_2) \in H_1$, because $h_2^{-1}h_1h_2 \in h_2^{-1}H_1h_2 = H_1$. Similarly, we have $(h_1^{-1}h_2^{-1}h_1)h_2 \in H_2$. Therefore  $$ h_1^{-1}h_2^{-1}h_1h_2 \in H_1 \cap H_2 = \{1_G\} $$  and so $h_1^{-1}h_2^{-1}h_1h_2 = \{1_G\}$. Let's first multiply everything on the left by $h_1$  $$h_1^{-1}h_2^{-1}h_1h_2 = \{1_G\}$$ $$ h_1 h_1^{-1}h_2^{-1}h_1h_2 = h_1 \{1_G\}$$ $$ h_2^{-1}h_1h_2 = h_1 \{1_G\}$$   Multiply both sides on the left by $h_2$ giving us  $$ h_1h_2 = h_2 h_1 $$  The bit I don't get is right at the beginning. Why is this correct: "We also have $h_1^{-1}(h_2^{-1}h_1h_2) \in H_1$, because $h_2^{-1}h_1h_2 \in h_2^{-1}H_1h_2 = H_1$." Why does shrinkage work? How do I use filenames that start with a dash "-" as command arguments? This may be a simple question, but how do I use files starting with "-" with command line programs?   For example,  I am trying to use pdfgrep on a file named -2013-01-01.pdf but it complains that there are no options defined for 2, 0, 1, 3 and so on.  Changing the filename to something that does not start with "-" solves it, but this is not an option since the files aren't created by me. I simply want to check for a specific change I know is coming. How to partially hide content in beamer latex? How can I send same email multiple times in iOS? I wanted to send a single email to different users. I save an email to drafts and send the email to a user and it goes to the sent box instead of staying in the drafts box. Is there a way I can send an email repeatedly from the drafts box? ERROR: cuvid requested, but not all dependencies are satisfied: cuda/ffnvcodec I am trying to compile FFMPEG with Nvidia Cuda support, on Debian 9.3. Parameters, what I am using:  --enable-cuda --enable-cuvid --enable-nvenc --extra-cflags=-I/usr/local/cuda/include --extra-ldflags=-L/usr/local/cuda/lib64 --enable-gpl --enable-libx264 --disable-x86asm --enable-libx265 --enable-libfdk-aac --enable-nonfree   Nvidia Cuda with drivers are installed. When I try to configure ffmpeg, it says:  ERROR: cuvid requested, but not all dependencies are satisfied: cuda   Newer ffmpeg will show a similar, re-worded message:  ERROR: cuda requested, but not all dependencies are satisfied: ffnvcodec   I absolutely don't know why I'm having this issue, because I am compiling ffmpeg on all of our trans-coding servers. Asking users to accept answer when they comment that it answers their question I've had a couple of answers today where the OP indicated via a comment that I solved their problem, but the question wasn't upvoted or accepted.  In both cases the person probably wasn't able to upvote since they were new, but they could have accepted my answer. I felt a little guilty asking them to accept the answer, but since it solved their problem I felt that it would help others who stumbled on the question trying to solve their own problem to know that my solution really was the answer. Is asking the OP to accept your answer when they've said that it solved their problem a reasonable thing to do or does that feel like nagging for reputation? Old Budrys(?) end-of-world/alien invasion of NYC story This one, from the late 1950s or early 60s (I think), features the last girl in NYC, who drives her jeep up the stairs of the main library (with the lions). She feels bad about breaking the lock, but what's a girl to do, if she wants something to read? In summertime, she drives topless and, the author writes, her bosom dances enchantingly on the steps. She lives in the boathouse on the lake in Central Park. Mysterious insect-like aliens are eating the buildings in the City.... I didn't recognize a title in Budrys or Bester's isfdb bibliogs, so I may be wrong about the author. But not about the story details: it's a memorable one. Thanks in advance for helping ID this one! Why could the pictures and paintings in Hogwarts talk and the photos of Harry's parents couldn't? How old is Chewbacca? Arrows linking table cells I'm currently trying to add arrows in my synthetic division example to show people clearly how synthetic division works. I'm working on Overleaf.   The code for my synthetic division right now is:  \begin{tabular}{c |r r r r r}     &amp;1&amp; 4 &amp; -1&amp;16&amp;-20\\   1&amp;&amp; 1 &amp; 5 &amp; 4&amp;20\\   \hline    &amp;1 &amp;5 &amp; 4 &amp; 20 &amp;\rule{3pt}{16pt}\;0\\   \end{tabular}   How would I add arrows to this? For instance, a down arrow going from the first 1 to 1, then an upwards arrow pointing right from 1 to 1, then an arrow pointing down from 1 to 5, etc. Basically I would like to add arrows that look like this: I am trying to run the following model:         I(week^2):mutation_status +         (week + I(week^2) | subject_id) ,          data = sim_dat)  This is the output I get from this model. The correlation between week and I(week)^2 is rather high (-0.95) and I was curious to know how I can change my data simulation code to lower that value. I am also having issues with convergence and would love to get thoughts on how to avoid issues regarding convergence. Thank you! Linear mixed model fit by REML. t-tests use Satterthwaite's method [lmerModLmerTest]  Formula: fetal_weight ~ week + mutation_status + week:mutation_status + I(week^2) +  I(week^2):mutation_status + (week + I(week^2) | subject_id) Data: sim_dat  REML criterion at convergence: 114  Scaled residuals:      Min      1Q  Median      3Q     Max  -1.9343 -0.3980 -0.0075  0.4168  1.9928   Random effects:  Groups     Name        Variance  Std.Dev. Corr         subject_id (Intercept)   1.51524  1.2309                          week         61.01832  7.8114   0.16                   I(week^2)   496.20236 22.2756  -0.19 -0.95  Residual                 0.05892  0.2427              Number of obs: 100, groups:  subject_id, 20  Fixed effects:                            Estimate Std. Error       df t value       Pr(&gt;|t|)     (Intercept)                  3.1331     0.4226  17.9961   7.413 0.000000713699 *** week                        -1.2465     3.5210  18.0053  -0.354          0.727     mutation_statusY             0.5061     0.5977  17.9961   0.847          0.408     I(week^2)                   34.5706    10.8146  18.0084   3.197          0.005 **  week:mutation_statusY       -1.0697     4.9795  18.0053  -0.215          0.832     mutation_statusY:I(week^2) 202.5521    15.2942  18.0084  13.244 0.000000000101 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  Correlation of Fixed Effects:             (Intr) week   mttn_Y I(w^2) wk:m_Y week        -0.160                             muttn_sttsY -0.707  0.113                      I(week^2)    0.145 -0.966 -0.103               wk:mttn_stY  0.113 -0.707 -0.160  0.683        mtt_Y:I(^2) -0.103  0.683  0.145 -0.707 -0.966  Code for data simulation: set.seed(123)  # set the seed J &lt;- 20  # number of individuals (clusters) cs &lt;- 5  # number of time points (cluster size) gam &lt;- c(0, 0.75, 1.34)  # fixed effects G &lt;- matrix(c(1.75, 0, 0,               0, 0.0125, 0,               0,0,0.0625),              nrow = 3)  # random effect variances (G-matrix) sigma2 &lt;- 0.08  mutation_status &lt;- rep(0:1, each = 5) mutation_status &lt;- rep(mutation_status, times = 10)  X &lt;- cbind(1, seq_len(cs),             (seq_len(cs))^2)  # for each individual X &lt;- X[rep(seq_len(cs), J), ]  X &lt;- X[rep(seq_len(cs), J), ]  X[,2] &lt;- X[,2]*0.05 X[,3] &lt;- X[,3]*0.05  # repeat each row cs times pid &lt;- seq_len(J)  # individual id pid &lt;- rep(pid, each = cs)   # Generate person-level (lv-2) random effects uj &lt;- lmf::rmnorm(J, mean = rep(0, 2), varcov = G)  # Generate repeated-measure-level (lv-1) error term eij &lt;- rnorm(J * cs, sd = sqrt(sigma2))  # Compute beta_j's betaj &lt;- matrix(gam, nrow = J, ncol = 3, byrow = TRUE) + uj  # Compute outcome: y &lt;- rowSums(X * betaj[pid, ]) + eij + mutation_status*X[ , 3]*10 + 3  # Form a data frame sim_dat &lt;- tibble(y, time = X[ , 2], pid, mutation_status) sim_dat &lt;- sim_dat[,c(3,2,4,1)] colnames(sim_dat) &lt;- c(&quot;subject_id&quot;, &quot;week&quot;, &quot;mutation_status&quot;, &quot;fetal_weight&quot;) sim_dat$week_2 &lt;-sim_dat$week*5 + 15  sim_dat$mutation_status &lt;- as.factor(ifelse(sim_dat$mutation_status == 0, &quot;N&quot;, &quot;Y&quot;)) sim_dat$subject_id &lt;- as.factor(sim_dat$subject_id ) #Model Building Viruses: Adaptation to a new host through repeated host jumps A friend told me, during a 3 minute discussion, that viruses that are endemic in host $A$ and make repeated jumps to host $B$ but can't be transmitted between individuals of species $B$, may slowly adapt (through these repeated jumps) to be able to be transmitted between individuals of host $B$ and become epidemic.  I don't know much about epidemiology. I don't understand how a virus population that is endemic to host $A$ may adapt to host $B$ with repeated jumps while the viruses that jump to host $B$ are dead end because they cannot be transmitted further more. Or Are these viruses able to jump back to host $A$ to bring back their newly acquired adaptations to host $B$?  Also, I might misunderstand the meaning of "repeated host jumps transmission". I first thought it meant repeated jumps from a reservoir population in host $A$ to host $B$, but it is also possible that it describes the dynamic of a virus population that is adapted to jump from species to species and they actually gain this ability by keeping jumping and jumping. But then, how could a virus species get adapted to jump from species to species? I'm a bit confused…. Can you give me some hints about this process of cross-species transmission through repeated jumps? Attribute editing in QGIS on geoJson file We have vector files in the format of geoJson files. We need to keep it in geoJson format as it is picked up by mobile devices via Restful services.  The problem is we want to change the attributes of the features in QGIS but it seems like this is not possible. We don't have to add or remove columns. We simply need to edit the existing data.  Is there a work around for this?  Are there any plugins that I can download that will allow me to do this in QGIS? How does gravity escape a black hole? Present and future of bots on Stack Exchange There are discussions on Meta already for some time now about the potential usage of bots on Stack Exchange (SE). The earliest I could find goes back to  , but there have been others , .  Here’s an  about having a bot that tries to answer “easy” questions. The scenario is that (almost) duplicate, simple questions are asked time after time, despite SE’s efforts to prevent this by listing related questions at posting time. This is where the bot could be of service: it could quickly retrieve and post an answer from a previous duplicate (or with smarter Artificial Intelligence - AI)  even from elsewhere on the web, like a user manual or a mailing list discussion). I imagine this might save some review time for moderators, and perhaps users would also enjoy not having to answer over and over again to the same question. Besides, answers would be very fast, which should make everyone happy if they are also of good quality.  This idea of “janitor” bots can have more use cases besides answering “easy” questions (see also discussion ), like suggesting missing tags and re-formatting what should have been code blocks, to name a few.  Yet, despite a long time since these discussions, better Machine Learning Classifiers (ML) and AI over the years, and   , it doesn’t seem that any such bots are among us (except maybe ). As part of a research project at the university, I am trying to understand why this is the case.  For this reason I’d like your opinion on the following:   Do you consider a bot “harmful” for the SE communities?   If yes, would you consider the bot harmful even if   it operates in an automatic manner only in limited scenarios (e.g. specific tags) it operates in a semi-automatic manner (namely with the supervision of a moderator who decides for posting or not the answer).  it operates only for a limited amount of time in a small community (e.g. here).   Would you consider it too risky to give a bot a try? Would you accept an answer provided by a bot?   If not, why ? (e.g. you don’t trust replies from machines)  Would you consider useless a “sloppy” answer by a bot, even if it is provided in just a few seconds? Answers may be not perfect, but they may link to other relevant threads that can help the asker to fix the problem without waiting extra time for a human response. What is wrong with my date regex? Should Java Objects be reused as often as it can be reused ? Or should we reuse it only when they are "heavyweight", ie have OS resources associated with it ?  All old articles on the internet talk about object reuse and object pooling as much as possible, but I have read recent articles that say new Object() is highly optimized now ( 10 instructions ) and Object reuse is not as big a deal as it used to be.  What is the current best practice and how are you people doing it ? $f$ bounded but $f'$ isn't How could a statement be true without proof? Godel`s incompleteness theorem states that there may exist true statements which have no proofs in a formal system of particular axioms. Here I have two questions; 1) How can we say that a statement is true without a proof? 2) What has the self reference to do with this? Godel sentence "G" can say that SUB(a,a, no prove) but could be this just arbitrarily judgement about non-provability of "a" because it may simply has a proof which is not yet revealed or discovered?