This is not a math question, this is a methodology and philosophy question.   Sometimes I see language describing things as "very statistically significant" because the p-value is extremely small.   But in the way that a p-value of 0.06 should not be called "almost significant",  I wonder if a p-value of 0.00006 should also not be called "very significant".
Why do statisticians discourage us from referring to results as "highly significant" when the $p$-value is well below the conventional $\alpha$-level of $0.05$?  Is it really wrong to trust a result that has 99.9% chance of not being a Type I error ($p=0.001$) more than a result that only gives you that chance at 99% ($p=0.01$)?
Can you play a Progress Card even when you get nothing from it? If I have a Progress Card for which initial preconditions do not hold, will I still be able to use it in order to discard it back to the pile? The goal is to prevent a spy from stealing it.  A few examples:   I am leading in victory points but I want to use Wedding card. I have Irrigation but I don't have any wheat hexagons. I have Blacksmith but I don't have any ore hexagons. The SPListItem being updated was not retrieved with all taxonomy fields Is there such a thing as a restore point in Ubuntu? Windows has this. Basically what I want is to record the state of the system either manually or periodically and then restore to that point if required. For example, before upgrading the distribution, or before installing a certain package.  What would be the easiest way to do this? What's the arc length of an implicit function? While an explicit function $y(x)$'s arc length $s$ is easily obtained as  $$s = \int \sqrt{1+|y'(x)|^2}\,dx,$$   is there any formula for implicit functions given by $f(x,y) = 0$? One can use the implicit differentiation $y'(x) = -\frac{\partial_y f}{\partial_x f}$ to obtain  $$s = \int\sqrt{1 + |\partial_y f / \partial_x f|^2}\,dx,$$  but that still requires (locally) solving for $y(x)$. Is there any formulation that does not require this, e.g. another implicit equation involving $s$?    Thoughts so far:  One could rewrite $s$ as  $$s = \int |\nabla f|\, |\partial_x f|dx,$$  or symmetrize to  $$s = \int |\nabla f|\, \underbrace{(|\partial_x f|dx + |\partial_y f|dy)}_{(*)}/2$$  where $(*)$ might be strongly related to $|df|$ I guess (though it's not identical due to the $|\cdot|$), but then? Is history expansion disabled in scripts? I understand the following error is due to ! used for history expansion:  $ echo "Hello!Tim" bash: !Tim: event not found   However if I put the command into a script and run the script, there is no problem:  $ cat myscript echo "Hello!Tim" $ bash myscript  Hello!Tim   Why is that? Does the bash manual mention the reason? This is my first question in /photography. I'm a very amateur photographer, doing things wrong and by eye with lots of trial-and-error all the time.  I currently own a reflex Nikon D70 my uncle gave us after he bought a better one. It has some nice settings, and he bought a a Nikkor 28-80mm F/3.5-5.6 zoom lens for it. It behaves nicely, but it's getting old (it has those old cartridges before SD cards existed) and every new charge takes longer than the last.  I'm planning to upgrade to a better camera, and there are some neat offers on a nearby superstore (MediaMarkt), this one catching my eye:  Sony DSC-H400 63x, Sensor Super HAD 1/2/3 CCD 20.1MP -> for less than 300€ taxes included  I don't have any type of extra information aside from that, all I can get from the official site is clinical data from other cameras that I suspect it's not 100% accurate, and there's no photography expert on the store to ask.  The common things I use my D70 for are: taking pictures of scenery (castles, towns, forests, waves hitting rocks, etc...), nearby (&lt;5m) persons and objects, and well, things where I want to save a memory in digital format, not for professional purposes at all.  Being that my objective is to have a decent, good-zooming (superzoom looks awesome), amateur (but with manual settings) camera, is this Sony a good replacement? Will I miss any features? Is there any better, similarly-priced alternative you know of?  Basically, I want to know whether I will get better quality photos than I currently do, given the examples, with any averagely-priced bridge camera similar to that Sony, and if it's worth it.  examples of current camera results  Full zoom-out of town at night, bad quality I know; notice the pink blur at the left.    Maximum zoom on that pink blur from almost the same spot:    Daylight, cloudy, modified with Adobe Lightroom, scenery:    Same day, same beach, different settings:    Same day, same beach, rocks: Prove: If a sequence converges, then every subsequence converges to the same limit. Full Disk Encryption using Ubuntu Core\Snappy I'm not sure if this is the right place to ask , but anyway :   I'm running ubuntu-core (snappy) on Raspberry Pi 3 and I'm willing  to perform partition\full disk encryption using cli\code. is it possible?  thanks Cannot remove a repository that complains it has no public key Meaning of 'const' last in a function declaration of a class? Are proofs by contradiction really logical? What is Stack Overflow's deployment process? I'm looking for some insight into how Stack Overflow releases are deployed and managed.   What software/tooling is used? What time are releases generally performed? How many and what steps are involved?   I'm assuming it's not too stringent given the light team working on the codebase. But considering the high rate of change, I could see some kind of tooling and automation becoming increasingly relevant, so I'm curious to learn what kind of decisions are being made to deal with the changes in scale and feature set over time.  Is this information available somewhere? I am trying to understand capitalization rules with Mom and Dad. I believe I have it correct below, but please let me know if I do not.     The one thing I learned from my dad was that it was good to earn the trust of one's children. Dad has shown me how good that a dad can be. One day when I went to his house, and Dad wasn't there, I ran outside....   The above passage is just made-up just so that you would see what I mean about capitalization. Let's put numbers by each one, like so:     The one thing I learned from my dad(1) was that it was good to earn the trust of one's children. Dad(2) has shown me how good that a dad(3) can be. One day when I went to his house, and Dad(4) wasn't there, I ran outside....    This is one where I'm not certain. I believe in this sense I'm showing possession here with "my", and it just didn't seem right saying "my Dad". I don't know what the grammar rule is here, or if I even have it right. This one is obvious—it starts the sentence. In this case, I'm using Dad like a name instead of saying "Larry". Therefore, it should be capitalized. Again, just like 3. Title of a book telling about people teleported to a hostile planet while in deep meditation I read it sometime in the 90's but it seemed at least 15 years old at that time. The title might be containing something with 'wolves' or 'wilderness'.  Alert - Spoilers below      The book tells of some (I think) earth cult that dictates the practice of meditation. This cult is somewhat of a scam as When reaching the top level of meditation the meditator is either teleported or his consciousness abducted (I can't remember..) to be used as a calculation machine by the abductors.   Any references would be greatly appreciated. Is there any way to solve this problem using the diagonalization method? I know there's the proof that uses $\mathcal{P}(\mathbb{N})$ = set of all finite subsets $\cup$ set of all infinite subsets, but I'm trying to solve it using the diagonalization method specifically. I was thinking that we can assume the two have the same cardinality and arrive at a contradiction, but I don't know how to get there. How can we show there has to be some infinite set in the set of all infinite subsets that cannot match 1-1 with a natural number? I inherited a project using SQL Server 2005.  Recently there were some performance problems and I started looking at the indexes, and found  _dta_index_survey_25_135059617__K1_K10_K19:     id ASC, sent_date ASC, group_id ASC   and  _dta_index_survey_21_364632442__K18_K1_K2_K9:     group_id ASC, id ASC, campaign_id ASC, sent_date ASC   which appears to be generated by some kind of automatic performance tuning tool.  I think SQL Server comes with something like that but I'm not familiar with it.  Anyway, id is the primary key, and what I'm trying to understand here is how it could possibly be beneficial to include the primary key within a secondary index... because you have to have the leftmost pieces of information to use an index and if you know id then you've got the row anyway.  Can someone explain why a tool would have generated these indexes and if there's any point in keeping them?  Just because the indexes are getting used doesn't mean they're a good design.  SQL Server is using the wrong indexes lately, and I'm trying to determine why. More specifically, queries against this table that ran in milliseconds a month ago are now taking multiple seconds.  The table is huge (4M rows), and growing steadily, but at the same pace it's been going at for years.  Almost every query joins across group_id or campaign_id.  Often both.  The application almost never specifically selects or sorts by the PK, but I could see how ID could be useful when comparing or merging lists of IDs within the database engine.  ... But id is also an identity column, and an index holds lists of row ids, so it still seems redundant to have the ID in the key when it's also in the index "buckets".  And the additional fields could still be covered by the index without being part of the key.  I discovered that (id, sent_date, group_id) hardly ever gets read.  Meanwhile (group_id, id, campaign_id, sent_date) is one of the hottest indexes.  Next I found that an index which I thought was pretty reasonable (campaign_id, sent_date, group_id, id) also has a index_columns_include of every other column in the table, and occupies more space than the primary clustered index on id!  (but it's also pretty hot...)  Surely I can replace it with a simple (campaign_id, sent_date, group_id)? Cannot change backlight brightness Ubuntu 14.04 This morning I found that I cannot change the brightness of my Dell XPs 13 laptop's display anymore. I tried the following to change the brightness   Use keyboard brightness keys Run the commands shown below Boot with kernel option acpi_backlight=vendor. This resulted in a dell_something folder being present in the /sys/class/backlight folder. Changing the brightness file in that folder does not help. Add 'intel_backlight' to xorg.conf Set "load legacy option ROM" BIOS option to enabled and "secure boot" to disabled Boot with kernel option i915.disable-pch_pwm=0 Boot from a fresh Ubuntu 12.04 USB stick installation. I can still not control the brightness. This is strange as the laptop came preinstalled with 12.04. Maybe this a hardware problem? Install latest intel video driver   Any ideas why this broke suddendly? I've upgraded from 12.04 to 14.04 in April and till yesterday the brightness keys were working fine.  Thanks!  echo 100 &gt; /sys/class/backlight/intel_backlight/brightness echo 100 &gt; /sys/class/backlight/acpi_video0/brightness join comma delimited data column I use HD Tune to measure performance of the hard drive.  The tests typically take 2-3 minutes and the transfer rate of a regular hard drive decreases dramatically as the test comes to a close.    However, the SSD drive performance stays the same over (pic below) the life of the test.  This happens on all my computers.  Why is that? How to troubleshoot booting to a black screen on VirtualBox I was using 13.04 as a guest OS on my VirtualBox 14.2.18. Host is Windows 8. After upgrade to 13.10 Ubuntu does not start. I can see a black screen and blinking cursor. I am pretty new to Ubuntu. I suspect a problem with graphics drivers. I can access tty and all files (/home) are there.