When is a list too long to not be numbered?

Question: I want to know if I can get away without numbering a list of items. My hypothesis is that when the # of list items is < X that a user will not need numbering to indicate the order in which that item is in the list. If this is can be true then what is the max X?
Answer: It depends less on the number of items on the list as the nature of the list.
If order matters, then you should use a numbered list regardless of its length. If order doesn't matter, then a bullet list works just fine.
e.g. you have a recipe
The list of ingredients may contain 10 items, but is given as a regular bullet list. But the 3 steps in the recipe should be numbered.
Comment: The problem is I don't know if "order matters". The use case is logging sets in a workout. They all happened in a set order, chronologically, but it is often more contextually appropriate to refer to the set relatively i.e. 'B happened before C'. To be honest, I did end up using a numbered list, but am still hesitant on my decision.
Comment: @occur ah if most of the time people do think of sets relatively, then yes using a numbered list makes a lot of sense.
Answer: If i understand, you want your user to be able to numerate items "at glance". If your list has no spatial clues the maximum number should be 5. This is just my opinion, not cognitive science.
Otherwise, you can perform some simple test simply asking "how many they are?" and showing a list of items for 1 sec. Starting from 2 or 3 items and adding items each test. You should probably note a decrease of correct answers percentage after 5 or 6 items.
Answer: It does not depend on list length, but on two others factors:

if the order matters;
if single items' length is really long to refer to them easily.

For example, if you have to refer to an article of a law.


Asteroids turning out to be Meteorites

Question: What causes an asteroid to loose control over it's orbit and enter in to another objects atmosphere?
Comment: This question appears to be off-topic because it appears to presume intention as capability of celestial bodies.
Comment: @Gerald Whether or not a question is technically correct is not necessarily grounds for it to be dismissed as off-topic. The question, however, could possibly be too broad or unclear.
Comment: @called2voyage Tried to consider possible misconception in the answer.
Answer: Asteroids don't have control of their orbit. They are influenced by gravity; they obey the laws of physics.
There aren't any traffic lights for them in space to obey so they know to slow down and stop to avoid a collision with a planet. They'll just carry right on going like someone driving through a red light. If it goes right in front of a planet at the wrong moment then it gets t-boned.
Or it might miss. But here is where the analogy falls apart. Because if someone drives through a red light and misses everyone, they carry on without any subsequent repercussions (except maybe a ticket). An asteroid passing close by a planet will be influenced by gravity between the planet and the asteroid, and it's path will change. That might mean it is flung far away, or it may mean it is captured, putting it on a looping path that eventually draws it in to crash onto the planet.
Answer: Asteroids don't have control over their orbit. The orbits are a consequence of the laws of physics.
This way asteroids can just happen to cross the orbit of an other celestial body. Products of such a collision take new orbits, which may or may not result in new collisions.
Orbits, which had been free of intersections with orbits of other bodies, may get moved away from Kepler ellipses over time by the gravitational pull of other celestial objects, e.g. planets like Jupiter or even by stars lightyears away. An orbit can also leave its ellipsis within a short time due to a close encounter with a planet.
Orbits around a planet can decay e.g. due to uneven mass distribution on the planet.

Asteroids turning out to be Meteorites


Which type of Machine Learning is used in robots?

Question: Which type of Machine Learning is used in robots?
Is it supervised learning or unsupervised learning or Reinforcement learning? Especially the robots that were sent in space?
Comment: Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer.
Comment: There are lots of types of robots. Many don't use machine learning at all (it's actually quite dangerous to use black-box learners on machines that could cause damage if incorrectly operated), and I'm pretty sure you will also find plenty that use each type of ML depending on purpose. Many will use multiple types of ML, for different sub-tasks withinn the robot. One way to narrow this question down would be to ask about a specific type of robot
Comment: The general question asks for a general answer. There's the risk that this will lead to many different answers, though, which we want to prevent. I think a good answer to this question would be general and maybe provide 1-2 specific examples. Anyway, yes, some robots use ML, in labs, at least. I am pretty of this because I know people that did research on this. Now, I don't really know about the robots for space. So, what I'd suggest is that you at least narrow down the type of robot, although you're already saying "especially the robots that were sent in space", which might still be too broad
Comment: So, please, if you're interested only in robots that were sent into space, edit your question, including the title, to be specific. Otherwise you will get answers for all types of robots and this might be too broad. If you always aks multiple questions, one for each type of robot you have in mind.
Comment: Are you interested only in ML applications in robotics or also want to known about the "engineering way" (pretty much non-ML) of doing robotics?
Comment: I'll just vote to close this because I think this will generate a lot of different answers.
Answer: Robotics primarily uses RL and supervised learning. To give examples:
Supervised Learning is used for vision and perception
Reinforcement Learning is used for control
Unsupervised Learning for robotics is less commmon, but I am sure exists.
Source: I work in a robotics lab and use these daily.
Comment: Nice reply. Voted


Is there an SBL citation style?

Question: Does anyone know if there exists a .bst file for the Society of Biblical Literature citation format? Or a biblatex style?
Answer: I'm the author of the original SBL LaTeX BibTeX styles. This is no longer supported.
But for those who find this thread in google, you might be interested in a completely new implementation covering SBLHS 2nd ed. done in BibLaTeX.
See https://github.com/dcpurton/biblatex-sbl for source and issue tracker.
It's also available in CTAN and in TeXLive and MiKTeX.
It's much more flexible and robust than the BibTeX implementation, and much easier to maintain.
Answer: Have a look at this page: http://wiki.marshwiggle.net/doku.php?id=sbllatex:main There are many examples including some classes and packages dedicated to this kind of style.
You can find the corresponding .bst file here: http://svn.marshwiggle.net/sbllatex/trunk/bst/sbl.bst
Comment: Unfortunately I couldn't even get their example files to compile without errors. I am using MikTeX on Windows and I think these files might assume TeXLive. In any case, right now the site has completely disappeared.
Answer: The SBL style described here is basically an author-year style; in the bibliography, however, the year is not displayed right after the author name(s), but at or near the end of the respective entry. In case you want to use biblatex, you should load the package like this:
\usepackage[citestyle=authoryear,bibstyle=authortitle]{biblatex}

For minor modifications that might be necessary to create a "true" SBL biblatex style, have a look at Guidelines for customizing biblatex styles. To remove the "In:" for @article entries, use Herbert's answer to Suppress "In:" biblatex.
Comment: Thanks. I found that the historian style is almost identical and close enough for my purposes. The following command gives what I need   \usepackage[bibstyle=historian,citestyle=authoryear-comp,natbib,sorting=nty,babel=hyphen,printseries]{biblatex}
Answer: The same people who used to publish the MarshWiggle website have started another with a more robust SBL Latex style. I have been using this for quite a while with very good results. I made a few changes to the essay style to suit my needs, but the BST is very good.
https://launchpad.net/sbllatex
Comment: The link is about a 'traditional' BibTeX style, not one for `biblatex`.
Comment: You know, I never new there was a difference...
Answer: If anyone's interest I have maintained Robet Fischer's SBL-paper and am porting biblatex-chicago which I hope to have on CTAN soon. Contact me for more info.
Note: I just found https://github.com/dcpurton/biblatex-sbl/blob/master/README.md
I couldn't tell you just yet how different or similar this is to mine.

Is there an SBL citation style?


LINQ query getting runtime error

Question: I have this linq query and am using EF edmx.
        forms = (from f in db.Forms
                 join ffl in db.FormFirstLetters on f.FormID equals ffl.FormID
                 where f.IsActive
                 where criteria.CategoryNames == null || criteria.CategoryNames.Contains(f.Category)
                 where startsWith == null || startsWith.Contains(ffl.FirstLetter)
                 orderby f.FormName
                 select new FormSummary
                 {
                     FormID = f.FormID,
                     Category = f.Category,
                     FormName = f.FormName,
                     AcceptSubmissions = f.AcceptSubmissions,
                     TodaysEntries = f.FormSubmissions.Count(tbl => tbl.SubmissionDate >= todaysDate),
                     TotalEntries = f.FormSubmissions.Count(),
                     LatestEntry = f.FormSubmissions.OrderByDescending(x => x.SubmissionDate).Select(x => x.SubmissionDate).FirstOrDefault()
                 }).ToArray();

I am getting this error

Unable to create a constant value of type
  'System.Collections.Generic.IEnumerable`1'. Only primitive types
  ('such as Int32, String, and Guid') are supported in this context.

I thought using Contains was acceptable and have used it many times before in these types of linq queries but for some reason it is not working. Both criteria.CategoryNames and startsWith are IEnumerable<string> and the field being searched for are strings. Why is this not working?
Comment: Note: There is no reason to use multiple `where` clauses. Just use `&&` and parantheses.
Answer: Had a value in one of the lists that was an empty string. Apparently EF doesn't know how to translate that to sql? Wow.

LINQ query getting runtime error


Pre-populating new Page creation with shortcodes

Question: I would like to have my authors to be able to create new pages on my site, but I would like a couple of shortcodes to automatically be included when they create each page. The shortcodes independently work with pages already with no adjustments or editing. How can I have this done automatically?
Answer: You can add any default content you like, but I don't know of a way of doing it just for Pages (the following will apply to both Pages and Posts):
add_filter( 'default_content', 'my_default_post_content' );

function my_default_post_content( $content ) {
    $content = "Hello World!";
    return $content;
}

(place this in your functions.php file)


Allow authenticated user to create an article

Question: hey im fairly new to D7 and ive noticed that there isn't really a way to create an article without the admin toolbar, but i would like users of my websites to be able to create articles. How would i do this without giving them access to the toolbar?
Answer: Go to admin/people/permissions and check the permission "Article: create content"
and maybe on a block create a link for them called create content.
Answer: Go to Admin->People->Permissions, check the permission Article: Create new content for the Authenticated user.  Scroll down to the bottom and click Save permissions.  Now, there will appaear a link "Add content" in the navigation menu for the Authenticated user.
(There should be no need for you to create this link explicitly.)
Answer: I had the same problem. The permissions were turned on but I still couldn't see the toolbar.
Solution:
The "Add content" link for authenticated users was in the sidebar, not at the top, as it is for administrators. I had to scroll down to see the link.


Stop PostgreSQL from starting on Windows?

Question: I have a local postgresql database for development purposes that I dont want to start up every time Windows does - how do I stop it from starting!
Answer: If it is running as a Windows service:  Start -> Run -> (then type in:) services.msc.
Scroll to PostgresSQL services, double click and set them to manual instead of automatic.

If you do need them again, just fire up services.msc again and click the Start icon/button once you have reselected the PostgresSQL service.
Comment: @Piotrek When a service's Startup type set to Manual Windows doesn't start it after reboot. Automatic services are all [attempted to be] started after reboot.
Comment: will it somehow affect how postgresSQL works? I don't want to have Postgres running in background when I don't need it, but I also need it to work properly when I'm working with it. What will change if I set that service to `manual`?
Answer: You can check this out
Type services.msc as previously mentioned and read the path-to-executable as follows;

Path to executable: "C:\Program Files\PostgreSQL\9.3\bin\pg_ctl.exe" runservice -N "postgresql-x64-9.3" -D "C:/Program Files/PostgreSQL/9.3/data" -w
Net service name is defined as postgresql-x64-9.3
So simply, whenever I want to shut down postgresql, I just type the following on a command line instance (to create a cmd instance, type windows+r and enter cmd);
net stop postgresql-x64-9.3

If you run another version of postgresql, you can just check the service name as explained and use this as a shortcut. Hope that it helps.
Comment: Some comments:  1. for Windows 7 services run `msconfig`  2. cmd run as Admin
Answer: The accepted answer didn't work for me because everything is greyed out and I can't disable anything.
If you have the same issue, it could be due to privileges.
You will need to launch CMD as an admin user:

Open Start, type: CMD
Right click CMD
Click Run as administrator

Then you can disable PostgreSQL by running the following commands:
sc stop postgresql-x64-13
sc config postgresql-x64-13 start=disabled

Replace 13 with your PostgreSQL version number. You can find the service name by running:
sc query

Of course the better solution is to install Linux ;)
Answer: This question is old and already answered, but this might help someone.
From Windows Command line
Start:
NET START postgresql-x64-9.2
Stop:
NET STOP postgresql-x64-9.2
Change your version and windows. This is for 64-bit windows, version 9.2.
Comment: How does this prevent postgresql from starting when Windows does?


Difference between Lebesgue theorem on Differentiability of functions of bounded variation and Rademacher theorem on 1D functions

Question: I am currently trying to understand Rademachers theorem for $\mathbb{R}^N$ functions, and stumbled upon the following problem:
On $\mathbb{R}$, to my knowledge, locally Lipschitz continuous functions are absolutely continuous and thus of bounded variation. From Lebesgue's Theorem then follows differentiability almost everywhere.
Now Rademacher on one dimensional functions states the locally Lipschitz continuous functions are differentiable almost everywhere. Isn't that the same? Or did I mix something up?
Any help would be greatly appreciated! :)
Answer: The point is that, like always $\mathbb{R}$ is a very small place to be. How can you define a.c. functions on $\mathbb{R}^n$? You may answer functions in $W^{1,1}$ and I would kind of agree. However the point is that on the line ac functions happen to be difference of increasing functions, which are themseves functions differentiable almost everywhere. Moreover I shold remark how a $metric$ derivative, which is given by Rademacher is deeply different from the $measure $ $theoretical$ one given by the theory of ac functions. While Rademacher theorem holds true even if you change the measure with something like $\delta_0$ nothing would change. On the other hand, if you change the measure with respect to which you are integrating, the set of ac functions should change. Indeed it is a non trivial result that $W^{1,\infty}$ is made of Lipschitz functions. I hope these short discussion is clear enogh.


Error in Eclipse: An internal error occurred during: "Contacting Software Sites",org/eclipse/ecf/core/identity/ID

Question: Please remove the Java JDK 8 Early Access from your system or change the system default from the JDK 8. The system default can normally be removed by using the Java Control Panel in Windows 7. However, with the JDK 8, for some reason, this default could not be changed. The only way was to uninstall. Hopefully Oracle will change this behavior soon . Can someone help me how to change the default JDK in the Java Control panel.
Comment: Could you rephrase this question and give additional details on what exactly is your issue?
Answer: I don't know much about using the Java Control Panel but I found that after installing JDK8 copies of java.exe, javaws.exe and javaw.exe are placed inside your system32 folder and override what is set on your PATH environment variable which causes the error message you describe in the title.
The solutions I tried were:
To back up these files and remove them from the system32 folder ensuring my PATH environment was set correctly to my desired JDK and then reopen Eclipse and it worked fine.
And to change my PATH enviroment variable so that the JDK was before:
%SystemRoot%\system32;
I've written a blog post on this that I will edit in later today when I have published it but that's essentially all I did.
The first answer to this question is related to the java.exe being placed in system32: How to prevent that java.exe is installed in Windows' system32?
Edit: Here it is http://blog.idrsolutions.com/2013/03/why-installing-java-8-may-break-your-system/


Insert Link to Audio versus Embed Audio Player

Question: I've run into a very odd problem. One of my authors will upload an audio file in the Media Manager, and instead of giving the option to embed a media player, it just inserts a link to the audio file. If he deletes the link and reopens Media Manager, the Embed Media Player option reappears. I have not been able to replicate this in any other user account, and I've had him log out, clear his cache and cookies, and log back in to no avail. Any ideas?
Comment: Try e.g. to see if it's browser or audio type related? Any console errors? Otherwise I vote to close, as this error sounds too localized. Best of luck.
Answer: Haven't been able to figure this one out, so I'm going to go ahead and close it. Seems to be localized to a specific computer/user account.


Constant ADC sampling rate on ESP8266 or ESP32

Question: I want to sample Sound input with either an ESP8266 (preferred) or ESP32. As I'm using a low pass filter anyway, a sample rate of 1000-2000hz would be totally ok. What is more important, is that it is constant. Can I use DMA for that? If so: how? Or should i go via Timer interrupts?
I know about the wifi issue on the ESP8266, but I intend to just turn Wifi off as I don't need it for this project.
Answer: You have several options for controlling the sampling rate.
Software only
This is the simplest, and the previous answer got it almost right. Here
is my take:
const SAMPLE_INTERVAL = 500;  // 500 microseconds

void loop() {
    static unsigned long last_sample_time;
    if (micros() - last_sample_time >= SAMPLE_INTERVAL) {  // note 1
         last_sample_time += SAMPLE_INTERVAL;  // note 2
         // Take your sample here.
    }
}

Note 1: On the AVR-based boards, millis() is not accurate to the
millisecond. It tends to get late, then compensate for this by jumping
by two milliseconds at once. For controlling a process that should
happen every 1 ms exactly, millis() is very clearly not
suitable. I do not know how good is the ESP8266's millis(). It may
well be better than the AVR version. However, even a perfect millis()
will not be good for anything faster than 1 kHz.
The solution to this problem is pretty trivial: just count the time in
microseconds instead of milliseconds. The only drawback of using
micros() is that you cannot measure durations longer than about
71.6 minutes, which in turn means you cannot use it for sampling at
any rate slower than 233 µHz. Obviously this is not something you
should be concerned about. Note that the micros() rollover is not an
issue as long as you are sampling faster than the rollover period.
Note 2: It is impossible to have a steady sampling rate if it is
controlled by software. The best you can hope for is a tight control on
the average sampling period. This is accomplished by updating
last_sample_time as
last_sample_time += SAMPLE_INTERVAL;

Note that this variable holds the time when the last sample was supposed
to be taken, not the time it was actually taken. The sample was probably
taken a little bit behind schedule, as anything the CPU does takes time.
Updating last_sample_time this way means that these timing errors are
not cumulative. They would be cumulative if you did it in the "Blink
without delay" style, namely
previousMillis = currentMillis;

The drawback of this software method is that it inherently has a
significant amount of jitter. The program tests the current time only
once per loop iteration, and it may have other things to do within that
loop that adds to its execution time.
Software triggered by interrupts
I have never programmer an ESP timer but, if you can, it should provide
you better timings than the software-only version. Have the timer
deliver an interrupt at the desired sampling period, and use the ISR for
triggering the ADC. You may wait for the result inside the ISR, store it
in RAM, and set a flag to tell the main loop that a new sample is
available, as in
volatile int analog_sample;
volatile bool analog_sample_valid;

ISR(whatever_timer_interrupt)
{
    analog_sample = analogRead(ANALOG_PIN);
    analog_sample_valid = true;
}

void loop()
{
    if (analog_sample_valid) {
        int analog_sample_copy = analog_sample;  // note 1
        analog_sample_valid = false;
        // handle analog_sample_copy here
    }
}

Note 1: On an 8 bit Arduino, you would have to do this with
interrupts disabled. You shouldn't need to disable interrupts on a
32 bit platform.
This method should significantly reduce the jitter compared to the
software-only version. Now the sampling doesn't have to wait for the
program to run through the loop and reach the point when the time is
tested. Instead, whatever the program is doing, it will be immediately
interrupted for doing the sampling. Well... almost. From time to time it
will happen that the interrupt fires when the program is running with
interrupts disabled. This may be the case if it is already servicing
another interrupt. When this happens, the sampling will have to wait
until interrupts are enabled again. You end up with a jitter that is
most of the time a small fraction of a microsecond, and then
occasionally a sample is late by several microseconds.
Hardware only
On an AVR, you can configure the ADC to be automatically triggered by a
timer, or even to automatically trigger itself in the so called "free
running mode". I do not know the specifics of the ADC in the ESP8266.
You may want to read the datasheet and see if it offer similar
functionality. If you can enable ADC auto-triggering, then you will have
cycle-accurate timings. The steadiness of your sampling will be just
as good as the quartz crystal clocking your MCU. No software solution
can ever come close to this level of perfection. The only drawback of
this method is that you will have to study the datasheet of your ESP in
order to implement it.
Answer: Have you looked "BlinkWithoutDelay" sample on Arduino? The most valuable part of it is the following:
void loop() {

    unsigned long currentMillis = millis();   // NOTE: 1

    if (currentMillis - previousMillis >= interval) {  // NOTE: 2
         // save the last time you blinked the LED
         previousMillis = currentMillis;  //NOTE: 3
         .. do your thing here ..
    }
}

Take into account the places from NOTE 1 to NOTE 3 I have marked in comments:
NOTE 1:
First thing in the loop where you mainly go is taking current time in millis. Should not take a lot of effort from Arduino to achieve.
NOTE 2:
Second thing is a comparison: is there enough time gone to make your thing ( = to take the sample) or not? If it is false, you make another round. If true, make it! Again, no big effort from computer.
NOTE 3:
Here you reset the timer, BEFORE doing anything else. So, your "sample interval clock" is quite precise, it consists of three little steps inside the computer and it should work in fractions of seconds accuracy (time estimate = (1 / Arduino clock speed) * some machine commands).
The other commands: taking sample, storing or sending it, should happen inside the one millisecond left from these commands. Do make a note, 1000 samples gives you 1ms time and 2000 samples 0.5ms time. This example fits perfectly to the 1000 samples case, as the accuracy of your clock is 1ms. I would go with that, if possible.
The time left, 1ms is quite long as a machine's executing time, but you have to make sure that some other components like a WiFi connection you mentioned, may be harmful for this approach. The other part of code inside the loop cannot take more than 1ms, otherwise it affects to the constant rate. Anything less than 1ms is ok, this algorithm makes no difference between 0.1ms or 0.9ms hard work inside the if, the accuracy of 1-10 machine words always holds.
(I don't know exactly how long command if is, nor how long is function millis(). If you want to be very precise, you may take these in account, but IMHO you can omit their importance in calculations: whether they take some time or not, anyways the execution of these may be quite well taking the same on every round - in constant time!)
SOURCE:
https://www.arduino.cc/en/Tutorial/BlinkWithoutDelay
Comment: and how exactly do you want to get above 1000hz with "millis"? :P this is a highly imprecise solution.
Comment: This is accurate only for 1000hz, you are right.


working directory in gnuplot

Question: How do I specify the working directory for gnuplot in interactive mode?
If I want to call a script with "call 'label_loop.gnu'" and do not want to put the script file in the gnuplot installation folder, do I need to specify the full path each time? I think the following would be the case with normal usage. "I put the data or script I want to load in any directory"-> "I plot it in interactive mode"-> "I want to adjust the position of the label (preferably) with the mouse action"- > "I copy and paste the previous commands and I create a batch file"-> "GnuPlot converts the output to PDF"
Answer: If I understand you clearly, look for GNUPLOT_LIB in man gnuplot:

GNUPLOT_LIB
Additional  search  directories for data and command files. The variable may contain a single directory name, or a list of
directories separated by ':'. The contents of GNUPLOT_LIB are appended to the "loadpath" variable, but not saved with the "save" and
"save
set" commands.

So, just call gnuplot with the environment variable you want:
GNUPLOT_LIB=my/chosen/path gnuplot

For example, this plots a curve for the points (0,0), (1,1) and (2,3):
$ cat Test/data.dat
0 0
1 1
2 3
$ GNUPLOT_LIB=Test gnuplot
gnuplot> plot 'data.dat' with lines

working directory in gnuplot


Is torque important when drilling hole in ceramic tile?

Question: I want to drill a 2-3cm diameter hole in a ceramic tile. There are diamond-coated hole saw bits, and I read that a cordless drill is recommended if water is used for cooling. I own a 10.8V 30Nm torque drill, but there are more powerful 45 and 85Nm versions too. Is my drill OK for this, or should I invest in a more powerful one?
Comment: Torque should be maxed, the drill should not be yielding to the material. It's ceramic so you don't need to worry about it work hardening.  Other than that, drilling through any material is about feeds and speeds - feed being insertion rate and speed being drill RPM. When you get it right, *you know it*.
Answer: I'm not a professional, but have drilled a lot of holes in masonry.  For a tile, I don't think that the torque will matter much, just chuck it, set it to high speed and drill.  Drill a test hole in a piece of scrap first, so you will know what to expect.  I think your toughest problem will be trying to get the hole started on your center accurately. Nicking the tile with a punch may help.
Drilling an 8" x 3/4 inch hole into 10 year old concrete will require a bit more torque.
Answer: You don't have to push hard in fact high torque can crack tile, I use high speed and water as a lubricant with ceramic and clay once you punch through the glaze back off on the pressure, porcilin I maintain a constant force until almost completely through.


Is it unlawful for a minor to own shares of a company?

Question: I was wondering if it was unlawful for a minor to own shares of a company in Massachusetts if the company bylaws allow for it.
Comment: how did he obtain them?
Comment: Gifted by business owner.
Answer: It is lawful, but not as straightforward as for an adult
As Dale points out, minor children can own stock (or other property) in Massachusetts. However, because unemancipated minors cannot buy or sell property on their own, managing their stocks can be a hassle. For example, children need a guardian if they want to sell the stock.
To avoid these hassles, in many (most?) cases, the stock is owned through some legal entity that gives an adult control over that stock. These range from custodial IRAs to living trusts. In all of these, the stock belongs to the minor, but is managed by an adult. These entities differ in all sorts of ways, including when (if ever) the minor gets control of the stock, how the stock is taxed, what the stock can be used for, and so on.
One of the most popular entities is a UTMA Account. These are named after the Universal Transfer to Minors Act, found at Chap. 201A of the General Laws of Massachusetts. These are custodial accounts designed specifically to allow minors to hold property, including stock. These accounts simplify the management of the minor's stock, and offer some tax breaks. In Massachusetts, the custodianship generally terminates when the minor turns 21. At that point, she gets complete control of her stock.
To find out more about the advantages and disadvantages of the UTMA compared to other ways of holding property for children, see here, here and here.
Comment: Why do you think children cannot buy or sell property?
Comment: @DaleM I do not know about Australia, but in the US, with a few exceptions (such as contracts for "necessities") *any contract* signed by a minor is considered "voidable". As a practical matter, this means *minors cannot be legally bound by contracts they agree to.* Thus, anyone who buys or sells property from/to a minor, runs the risk the minor will renounce the contract, and demand return of his property or money. Courts have consistently upheld these renunciations (although in a few cases, housing has been considered a "necessity.")
Comment: that's not quite true - they are also not voidable if they are of benefit to the minor. A contract for a chocolate bar that the minor eats, or of shares (at fair value) for which the minor receives dividends are not voidable.
Comment: @DaleM Again, I don't know about Australia, but that's not how it works in the US. In the US, this is called the *retained* benefits doctrine because it requires the minor to return any *retained* benefits as a condition of voiding the contract. Many courts do not require the returned "benefit" to have the same value as the original. For example, courts have held that a minor who wrecks a car only has to return the wrecked car to get his money back. (In some states, the seller may also deduct the benefit the minor got from driving the car from the sales price.)
Comment: @DaleM Since chocolate is food, the chocolate bar would probably be covered as a "necessity."
Answer: No
Minors can possess personal property like shares. Further, s21 explicitly contemplates guardians (among others) exercising the rights of their wards. Now, not only children have guardians but all children do.


Problem with login feature

Question: I am making an Training and Placement cell application which would be useful for our institutions but i am having problem with login feature.There are two user in my application admin and student and i have to make login with two different restrictions so how can i make?
Comment: What is the UX question? It sounds like an implementation question.
Comment: Once the user logs in, you'll know what role they have, right (i.e. you'll know if it's an admin or a student account)? Do you need to know this before they log in?
Answer: There should not be two different types of login. Any user should login normally. Once a user logs in, the rights of the users if assigned as an Admin should be displayed preferably with a tag called 'Admin' somewhere near the username on the profile.
Answer: It depends on who the primary audience is:
The login for the primary audience would take the center stage and be shown on the login page when the application is accessed.
You can create Tabbed Login box to facilitate both Student and Admin login and possibly add another functionality to save login information such that if the same user logs in using their device they would see the credentials entry view which pertains to them.

Problem with login feature


IRF540 power Mosfet 12 volt motor gate resistance

Question: I have a IRF540 power Mosfet driving a 12 volt motor. Currently I am using a 100 ohm gate input resistor, It is working fine. What I want is the maximum gate resistor value that I can use and still drive it properly with 8 Volts DC, This does not need to be an exact value just some approximation will do.
In most case this is a steady state voltage so timing is not a real consideration.
The only reason for this is if the IRF540 shorts out, I do not want it to take out the driver IC as well. I know about heat sinking and current protection circuits but sometimes this still happens.
Comment: Can you increase your gate voltage to 10V minimum?  Datasheet says that 8V is at the bare edge of the FET being fully-enhanced.
Answer: The IRF540's maximum specified Gate leakage is 100nA at 25°c, so theoretically you could use up to 1 Meg (for voltage drop of 0.1V or less). However leakage current increases with temperature, and such a high resistance could make the Gate quite sensitive to noise.
Use the lowest value that meets your safety requirements. Anything up to 10k should be fine.
Comment: Thank you for your answer I was thinking of 470 ohms so I am way under the maximum you have given me. Just wanted to be sure I was driving it well. I have done experiments increasing the gate voltage until the drain voltage changed no more and found 8 volts met this requirement.


Weird Qt SSL issue -- error "No Error" shows up, nothing else, and if I ignore it, everything works

Question: The issue is as follows : in my Qt app, I have a QWebView, which I use to load a HTTPS page.
Everything worked fine on my development machine, so I'm now trying to get it to run on a test machine. I ran the app, but the page didn't load (the QWebView was blank). After much debugging, I found the problem is that an SSL error shows up, and the sslErrors() signal is fired.
Here is my sslErrors() handling code:
void blah::sslErrors(QNetworkReply *reply, const QList<QSslError> &errors) {
  foreach(QSslError error, errors) {
    qDebug() << error.errorString() << endl;
  }
  reply->ignoreSslErrors();
}

The only thing the above code prints is:
"No error"

So there's no error, but unless I call reply->ignoreSslErrors(), the page doesn't load (on the test machine, on my developer computer no error is reported). Huh? Is this a bug?
Is it safe to ignore the error, if I make sure it's of the type "No error"?
Answer: You may be hitting QTBUG-28343 which is due to a binary incompatibility in openssl between the version your Qt was compiled against and the one you are running. This will be fixed in Qt 4.8.5.
http://lists.qt-project.org/pipermail/announce/2013-January/000020.html
https://bugreports.qt-project.org/browse/QTBUG-28343
Answer: QSslSocket builds a NoError SslError only when translating an OpenSSL X509_V_OK error.
The OpenSSL documentation reports:

If no peer certificate was presented, the returned result code is
  X509_V_OK. This is because no verification error occurred, it does
  however not indicate success.

You should use tcpdump or a similar tool to check that certificates are correctly exchanged between peers.


How can I pass display exposed filter in views-view-unformatted.html.twig?

Question: I would like to display an exposed filter inside views-view-unformatted.html.twig rather than views-view.html.twig due to specific UI design?
Comment: I've provided an answer, but more of an explanation of your use case and where you got stuck would be really helpful.
Comment: Thanks, @Beau! Used Twig Tweak, displayed it using drupal_block, and solved my problem!
Answer: Try using Views Exposed Filter Blocks.

Use the Twig Tweak module and embed the exposed filter block in your template with code like this: <code>{{ drupal_block('views_exposed_filter_block:my_view_id-my_views_block_id', wrapper=false) }}</code>.
You can also just place the exposed filter block in any region.


How can Skarner increase the distance he can pull an Impaled champion?

Question: Besides Movement Speed effects, I would like to know a list of any ways Skarner can move/be moved (using the help of his allies, not enemies) while his ultimate, Impale is active.
Answer: Thresh is the only champion that can relocate his allies at the moment, so I scoured Youtube for Dark Passage/Impale combination. Here is the result.

So I think I can safely say that this combination does work. Have fun dragging your enemies under tower from a great distance!
(There are also a large number of champions that can grant movement speed buffs, but that doesn't sound like what you're looking for.)
Edit: With the release of Kalista, another method has arisen, and it works!

Edit 2: Electric Boogaloo: Neither Bard's Magical Journey, nor Tahm Kench's Abyssal Journey work. I think that Kench's Devour does work, but I'm having difficulty finding proof.
Comment: Ey mate, Im going through some of my past answers and questions, and - for the giggles - would you be arsed to add Bard to the list if you find any proof? Im curious if you can drag people through his tunnel thing.
Comment: @user1337 Skarner can't drag enemies through a bard portal, from the digging I've done this morning.
Comment: Much appreciated.


Finding the amplidude of a single frequency in signal

Question: I'm not experienced whatsoever in signal processing. I want to isolate a single frequency (83 Hz) out of a noisy signal. Goertzel works just fine but was wondering if there was any other, maybe even (computationally) simpler technique to do that. I only want the amplitude of that single frequency.
Comment: If you want a single frequency, I think Goertzel is pretty much unbeatable. It's linear in the number of samples (only $2N$ additions and $N$ multiplications). Can't really go much lower than that.
Answer: Goertzel in fact is the matched filter for a single frequency – so, it's, in the presence of uncorrelated noise, the estimator that gives the best estimation variance under fixed observation.
But: for Goertzel to work, you need to use a number of samples that is

an integer and
a multiple of $f_\text{sample}/83\,\text{Hz}$.

Unless your sampling rate hence is a small multiple of 83 Hz, that's usually a bad deal.
You can remedy that with a number of things: often, a narrowband (often: even resonant) filter can filter out a frequency range, but you'll need to deal with the skirt of that filter. That skirting will be different than that of Goertzel's algorithm (unless you happen to have also windowed the signal before applying the Goertzel, and now use the same Window as filter design prototype; sounds unlikely).
If you know more about the signal than you're telling us (it's result of AR processes, so you can apply Yule-Walker to get an appropriate model of what's happening, for example. Or, you know the signal is the sum of white noise and a known number of oscillations – then, autocorrelation subspace methods such as MUSIC are very efficient), then you might have methods that are very exact, but use even fewer samples than minimal Goertzel.
Anyway, the beauty of Goertzel really lies in the fact that it's pretty efficient to begin with. Honestly, if your frequency of interest is 83 Hz, and you still can't detect it in realtime even on the weakest of microcontrollers, then you're doing something wrong, with 99.5% probability¹. You really might want to ask a different question on here, describing what you overall want to do (where does your signal come from? What's at 83 Hz? Why do you want to determine the amplitue of that? How exactly do you know that frequency? What's the amplitude estimate reliability that you really need? So many things to talk about...).

¹ This number, like 22.36% of all study results, is totally made up.
Comment: The signal acutally is the sum of white noise and the 83 Hz (rectangular) oscillation. I want to know how strong the 83 Hz signal is. I know that it's always at 83 Hz and rectangular.
I am able to detect in realtime, I was just wondering if there was an even more efficient way.
Comment: again, what to recommend here isn't answerable with the amount of info you're giving. I recommend you heed the advice from the last paragraph of my answer: Ask a separate question where you explain what you're doing overall. What you're asking here sounds a lot like you're posing an [XY Problem](http://xyproblem.info).


Do you have to declare a function's type?

Question: One thing I do not fully understand about Haskell is declaring functions and their types: is it something you have to do or is it just something you should do for clarity? Or are there certain scenarios where you need to do it, just not all?
Comment: If by "declare a function" you mean explicitly providing the type-signature of the function before its definition, then in general this is optional because GHC can often infer the types automatically. In practice, it's always a good idea to write an explicit type signature for top-level functions, both as documentation and as confirmation that GHC has inferred what you expected it to.
Comment: If you don't provide the type, GHC will often infer one. If, however, you also make a mistake in your code, there's a chance that your code still makes sense, and just makes GHC infer a type which was not what you intended. In practice, this causes type errors to show up in other parts of the code, causing confusion. It's a good, recommended practice to provide type annotations at least for the top-level identifiers.
Comment: As long as it is not a duplicate, this question is actually good
Comment: Yeah, this is what I thought. Thank you for clearing it up.
Answer: You don't need to declare the type of any function that uses only standard Haskell type system features. Haskell 98 is specified with global type inference, meaning that the types of all top-level bindings are guaranteed to be inferable.
However, it's good practice to include type annotations for top-level definitions, for a few reasons:

Verifying that the inferred type matches your expectations

Helping the compiler producing better diagnostic messages when there are type mismatches

Most importantly, documenting your intent and making the code more readable for humans!

As for definitions in where clauses, it's a matter of style. The conventional style is to omit them, partly because in some cases, their types could not be written explicitly before the ScopedTypeVariables extension. I consider the omission of scoped type variables a bit of a bug in the 1998 and 2010 standards, and GHC is the de facto standard compiler today, but it's still a nonstandard extension. Regardless, it's good practice to include annotations where possible for nontrivial code, and helpful for you as a programmer.
In practice, it's common to use some language extensions that complicate type inference or make it "undecidable", meaning that, at least for arbitrary programs, it's impossible to always infer a type, or at least a unique "best" type. But for the sake of usability, extensions are usually designed very carefully to only require annotations at the point where you actually use them.
For example, GHC (and standard Haskell) will only infer polymorphic types with top-level foralls, which are normally left entirely implicit. (They can be written explicitly using ExplicitForAll.) If you need to pass a polymorphic function as an argument to another function like (forall t. …) -> … using RankNTypes, this requires an annotation to override the compiler's assumption that you meant something like forall t. (… -> …), or that you mistakenly applied the function on different types.
If an extension requires annotations, the rules for when and where you must include them are typically documented in places like the GHC User's Guide, and formally specified in the papers specifying the feature.
Answer: Short answer:  Functions are defined in "bindings" and have their types declared in "type signatures".  Type signatures for bindings are always syntactically optional, as the language doesn't require their use in any particular case.  (There are some places type signatures are required for things other than bindings, like in class definitions or in declarations of data types, but I don't think there's any case where a binding requires an accompanying type signature according to the syntax of the language, though I might be forgetting some weird situation.)  The reason they aren't required is that the compiler can usually, though not always, figure out the types of functions itself as part of its type-checking operation.
However, some programs may not compile unless a type signature is added to a binding, and some programs may not compile unless a type signature is removed, so sometimes you need to use them, and sometimes you can't use them (at least not without a language extension and some changes to the syntax of other, nearby type signatures to use the extension).
It is considered best practice to include type signatures for every top-level binding, and the GHC -Wall flag will warn you if any top-level bindings lack an associated type signature.  The rationale for this is that top-level signatures (1) provide documentation for the "interface" of your code, (2) aren't so numerous that they overburden the programmer, and (3) usually provide sufficient guidance to the compiler that you get better error messages than if you omit type signatures entirely.
If you look at almost any real-world Haskell source code (e.g., browse the source of any decent library on Hackage), you'll see this convention being used -- all top-level bindings have type signatures, and type signatures are used sparingly in other contexts (in expressions or where or let clauses).  I'd encourage any beginner to use this same convention in the code they write as they're learning Haskell.  It's a good habit and will avoid many frustrating error messages.
Long answer:
In Haskell, a binding assigns a name to a chunk of code, like the following binding for the function hypo:
 hypo a b = sqrt (a*a + b*b)

When compiling a binding (or collection of related bindings), the compiler performs a type-checking operation on the expressions and subexpressions that are involved.
It is this type-checking operation that allows the compiler to determine that the variable a in the above expression must be of some type t that has a Num t constraint (in order to support the * operation), that the result of a*a will be the same type t, and that this implies that b*b and so b are also of this same type t (since only two values of the same type can be added together with +), and that a*a + b*b is therefore of type t, and so the result of the sqrt must also be of this same type t which must incidentally have a Floating t constraint to support the sqrt operation.  The information collected and type relationships deduced during this type checking allow the compiler to infer a general type signature for the hypo function automatically, namely:
hypo :: (Floating t) => t -> t -> t

(The Num t constraint doesn't appear because it's implied by Floating t).
Because the compiler can learn the type signatures of (most) bound names, like hypo, automatically as a side-effect of the type-checking operation, there's no fundamental need for the programmer to explicitly supply this information, and that's the motivation for the language making type signatures optional.  The only requirements the language places on type signatures is that if they are supplied, they must appear in the same declaration list as the associated binding (e.g., both must appear in the same module, or in the same where clause or whatever, and you can't have a type signature without a binding), there must be at most one type signature for a binding (no duplicate type signatures, even if they are identical, unlike in C, say), and the type supplied in the type signature must not be in conflict with the results of type checking.
The language allows the type signature and binding to appear anywhere in the same declaration list, in any order, and with no requirement they be next to each other, so the following is valid Haskell code:
double :: (Num a) => a -> a
half x = x / 2
double x = x + x
half :: (Fractional a) => a -> a

Such silliness is not recommended, however, and the convention is to place the type signature immediately before the corresponding binding, though one exception is to have a type signature shared across multiple bindings of the same type, whose definitions follow:
ex1, ex2, ex3 :: Tree Int
ex1 = Leaf 1
ex2 = Node (Leaf 2) (Leaf 3)
ex3 = Node (Node (Leaf 4) (Leaf 5)) (Leaf 5)

In some situations, the compiler cannot automatically infer the correct type for a binding, and a type signature may be required.  The following binding requires a type signature and won't compile without it.  (The technical problem is that toList is written using polymorphic recursion.)
data Binary a = Leaf a | Pair (Binary (a,a)) deriving (Show)

-- following type signature is required...
toList :: Binary a -> [a]
toList (Leaf x) = [x]
toList (Pair b) = concatMap (\(x,y) -> [x,y]) (toList b)

In other situations, the compiler can automatically infer the correct type for a binding, but the type can't be expressed in a type signature (at least, not without some GHC extensions to the standard language).  This happens most often in where clauses.  (The technical problem is that type variables aren't scoped, and go's type involves the type variable a from the type signature of myLookup.)
myLookup :: Eq a => a -> [(a,b)] -> Maybe b
myLookup k = go
  where -- go :: [(a,b)] -> Maybe b
        go ((k',v):rest) | k == k'   = Just v
                         | otherwise = go rest
        go [] = Nothing

There's no type signature in standard Haskell for go that would work here.  However, if you enable an extension, you can write one if you also modify the type signature for myLookup itself to scope the type variables.
myLookup :: forall a b. Eq a => a -> [(a,b)] -> Maybe b
myLookup k = go
  where go :: [(a,b)] -> Maybe b
        go ((k',v):rest) | k == k'   = Just v
                         | otherwise = go rest
        go [] = Nothing

It's considered best practice to put type signatures on all top-level bindings and use them sparingly elsewhere.  The -Wall compiler flag turns on the -Wmissing-signatures warning which warns about any missing top-level signatures.
The main motivation, I think, is that top-level bindings are the ones that are most likely to be used in multiple places throughout the code at some distance from where they are defined, and the type signature usually provides concise documentation for what a function does and how it's intended to be used.  Consider the following type signatures from a Sudoku solver I wrote many years ago.  Is there much doubt what these functions do?
possibleSymbols :: Index -> Board -> [Symbol]
possibleBoards :: Index -> Board -> [Board]
setSymbol :: Index -> Board -> Symbol -> Board

While the type signatures auto-generated by the compiler also serve as decent documentation and can be inspected in GHCi, it's convenient to have the type signatures in the source code, as a form of compiler-checked comment documenting the binding's purpose.
Any Haskell programmer who's spent a moment trying to use an unfamiliar library, read someone else's code, or read their own past code knows how helpful top-level signatures are as documentation.  (Admittedly, a frequently levelled criticism of Haskell is that sometimes the type signatures are the only documentation for a library.)
A secondary motivation is that in developing and refactoring code, type signatures make it easier to "control" the types and localize errors.  Without any signatures, the compiler can infer some really crazy types for code, and the error messages that get generated can be baffling, often identifying parts of the code that have nothing to do with the underlying error.
For example, consider this program:
data Tree a = Leaf a | Node (Tree a) (Tree a)

leaves (Leaf x) = x
leaves (Node l r) = leaves l ++ leaves r
hasLeaf x t = elem x (leaves t)

main = do
  -- some tests
  print $ hasLeaf 1 (Leaf 1)
  print $ hasLeaf 1 (Node (Leaf 2) (Leaf 3))

The functions leaves and hasLeaf compile fine, but main barfs out the following cascade of errors (abbreviated for this posting):

Leaves.hs:12:11-28: error:
    • Ambiguous type variable 'a0' arising from a use of 'hasLeaf'
      prevents the constraint '(Eq a0)' from being solved.
      Probable fix: use a type annotation to specify what 'a0' should be.
Leaves.hs:12:19: error:
    • Ambiguous type variable 'a0' arising from the literal '1'
      prevents the constraint '(Num a0)' from being solved.
      Probable fix: use a type annotation to specify what 'a0' should be.
Leaves.hs:12:27: error:
    • No instance for (Num [a0]) arising from the literal '1'
Leaves.hs:13:11-44: error:
    • Ambiguous type variable 'a1' arising from a use of 'hasLeaf'
      prevents the constraint '(Eq a1)' from being solved.
      Probable fix: use a type annotation to specify what 'a1' should be.
Leaves.hs:13:19: error:
    • Ambiguous type variable 'a1' arising from the literal '1'
      prevents the constraint '(Num a1)' from being solved.
      Probable fix: use a type annotation to specify what 'a1' should be.
Leaves.hs:13:33: error:
    • No instance for (Num [a1]) arising from the literal '2'

With programmer-supplied top-level type signatures:
leaves :: Tree a -> [a]
leaves (Leaf x) = x
leaves (Node l r) = leaves l ++ leaves r

hasLeaf :: (Eq a) => a -> Tree a -> Bool
hasLeaf x t = elem x (leaves t)

a single error is immediately localized to the offending line:
leaves (Leaf x) = x
                  ^
Leaves.hs:4:19: error:
    • Occurs check: cannot construct the infinite type: a ~ [a]

Beginners might not understand the "occurs check" but are at least looking at the right place to make the simple fix:
leaves (Leaf x) = [x]

So, why not add type signatures everywhere, not just at top-level?  Well, if you literally tried to add type signatures everywhere they were syntactically valid, you'd be writing code like:
{-# LANGUAGE ScopedTypeVariables #-}
hypo :: forall t. (Floating t) => t -> t -> t
hypo (a :: t) (b :: t) = sqrt (((a :: t) * (a :: t) :: t) + ((b :: t) * (b :: t) :: t) :: t) :: t

so you want to draw the line somewhere.  The main argument against adding them for all bindings in let and where clauses is that those bindings are often short bindings easily understood at a glance, and they're localized to the code that you're trying to understand "all at once" anyway.  The signatures are also potentially less useful as documentation because bindings in these clauses are more likely to refer to and use other nearby bindings of arguments or intermediate results, so they aren't "self-contained" like a top-level binding.  The signature only documents a small portion of what the binding is doing.  For example, in:
qsort :: (Ord a) => [a] -> [a]
qsort (x:xs) = qsort l ++ [x] ++ qsort r
      where -- l, r :: [a]
            l = filter (<=x) xs
            r = filter (>x)  xs
qsort [] = []

having type signatures l, r :: [a] in the where clause wouldn't add very much.  There's also the additional complication that you'd need the ScopedTypeVariables extension to write it, as above, so that's maybe another reason to omit it.
As I say, I think any Haskell beginner should be encouraged to adopt a similar convention of writing top-level type signatures, ideally writing the top-level signature before starting to write the accompanying bindings.  It's one of the easiest ways to leverage the type system to guide the design process and write good Haskell code.


Why did a subdomain from a trusted website download a file?

Question: I clicked on a link for the subdomain of a trusted website (the subdomain slackin.brilliant.org of the website brilliant.org), and instead of being directed to another page, a file called "download" simply downloaded onto my computer. I deleted the file right away, so I don't know its contents, but I  was worried that maybe the file had malicious contents (could Brilliant.org maybe own a domain and not have control of this subdomain, therefore allowing perpetrators of malware to capitalize on this?).
Answer: Nothing malicious is going on. The file is empty.
This happens when there is a misconfiguration of the webserver and instead of serving a page to display, it transfers the target as a file. In this case, there was nothing to transfer.
This sort of thing was a lot more common in the early days of the web, but I'm shocked to see it these days.
Comment: What was the MIME type?
Comment: no MIME type - empty - 0 bytes
Comment: (@Daisetsu) for me, Content-Type is application/octet-stream which admittedly is often used to mean 'I haven't got a clue'. (And yes Content-Length 0.)


what I should do in this situation?

Question: After creating a project using npm rect-native init command, when I try to run the project I got some errors
npm ERR! code E404

npm ERR! 404 Not Found - GET http://registry.npmjs.org/run-android - Not found

npm ERR! 404

npm ERR! 404  'run-android@latest' is not in the npm registry.

npm ERR! 404 You should bug the author to publish it (or use the name yourself!)

npm ERR! 404

npm ERR! 404 Note that you can also install from a

npm ERR! 404 tarball, folder, http url, or git url.

npm ERR! A complete log of this run can be found in:
npm ERR!     C:\Users\<Username>\AppData\Roaming\npm-cache\_logs\2020-09-14T05_04_23_787Z-debug.log
Install for [ 'run-android@latest' ] failed with code 1

I tried so many things like reinstalling react native or create new user but still have same problem. Please help.
Comment: Please share more details
Answer: First, make sure you are inside project directory.
I think the command you're looking for is if react-native-cli is installed
react-native run-android

cd into your project and run this command.
OR
you can run this command without react-native-cli installation:
npx react-native run-android

what I should do in this situation?


From whom or what did Arius learn his theology?

Question: Where did Arius learn his theology? Did he rely on specific theologians that wrote before him? Origen? Clement of Alexandria? Lucian of Antioch? Were his ideas based on the Bible or on Greek philosophy? Was he part of a specific school of thought or did he develop an entirely new system?
Answer: Early life and personality

Reconstructing the life and doctrine of Arius has proven to be a difficult task, as none of his original writings survive. Emperor Constantine ordered their burning while Arius was still living, and any that survived this purge were later destroyed by his orthodox opponents. Those works which have survived are quoted in the works of churchmen who denounced him as a heretic. This leads some—but not all—scholars to question their reliability.[7]

Origen and Arius

Like many third-century Christian scholars, Arius was influenced by the writings of Origen, widely regarded as the first great theologian of Christianity.[16] However, while both agreed on the subordination of the Son to the Father, and Arius drew support from Origen's theories on the Logos, the two did not agree on everything. Arius clearly argued that the Logos had a beginning and that the Son, therefore, was not eternal, the Logos being the highest of the Created Order. This idea is summarized in the statement "there was a time when the Son was not." By way of contrast, Origen believed the relation of the Son to the Father had no beginning, and that the Son was "eternally generated".[17]

Arius objected to Origen's doctrine, complaining about it in his letter to the Nicomedian Eusebius, who had also studied under Lucian. Nevertheless, despite disagreeing with Origen on this point, Arius found solace in his writings, which used expressions that favored Arius's contention that the Logos was of a different substance than the Father, and owed his existence to his Father's will. However, because Origen's theological speculations were often proffered to stimulate further inquiry rather than to put an end to any given dispute, both Arius and his opponents were able to invoke the authority of this revered (at the time) theologian during their debate.[18]

Both of the above are from Wikipedia - Arius
Comment: Some quick comments: (1) Arius' letters to Alexander and Eusebius of Nicomedia survived until today. (2) I do not think the his orthodox opponents destroyed his writings. As Rowan Williams stated, the so-called "Arians" did not have a high regard for Arius. They did not bother to keep copies of his writings. (3) Arius never said 'there was a TIME when He was not'. That is what Athanasius said he said. Arius said 'the was when he was not'. (See the Greek of the Nicene Creed.) The significance is that Arius stated that the Son was begotten BEFORE TIME even existed.
Comment: @Andries It's pretty clear Athanasius is recognizing that unless you're speaking of eternity (God alone), you're speaking of a temporal (time) existence. So time is not a misrepresentation. There can't be an intermediate between 'eternal' and 'time.' You are either atemporal/eternal, or you exist somewhere along the axis of 'eternal' to 'the end of time.'
Comment: @Andries [Richard Bauckman's review](https://www.thegospelcoalition.org/themelios/review/arius-heresy-and-tradition/) of Rowan Williams 2002 book on Arius made the case that the primary influence is Alexandrian tradition.  Rowan's book seems the best, most recent, scholarly assessment of Arius's true position.  You may want to check out the 2021 book [Arianism: Past Imperfect](https://www.arc-humanities.org/9781641891004/arianism/) as well.
Comment: @SolaGratia Arius lived in a different world, culture, and philosophical context. To understand him, we must understand his context. Certain concepts were accepted by all theologians at his time, for example, the world is the centre of the universe, things existed before time existed, the Son is subordinate to the Father, and that the Son was generated by the Father's will. In our context, time began with the big bang. Beyond this universe and beyond the big band exists the infinity that produced this universe. Arius might have said the Son was begotten before the big bang.
Comment: @GratefulDisciple Alexandrian tradition - I assume that is Alexandrian church tradition. Certain bishops of Alexandria made very Arian-like statements. E.g. Bishop Dionysius of Alexandria (247 to 264), similar to Arius, described the Son as a created being who "did not exist before he came into existence" (Hanson, page 73).
Answer: From whom or what did Arius learn his theology?
To answer this question clearly, one has to admit that it's complicated!
To answer it even remotely accurately it would seem plausible that Arius (250 or 256 – 336) was influenced by Paul of Samosata, Lucian of Antioch and Origen.

The Arian controversy
Beginnings
The Trinitarian historian Socrates of Constantinople reports that Arius sparked the controversy that bears his name when Alexander of Alexandria, who had succeeded Achillas as the Bishop of Alexandria, gave a sermon stating the similarity of the Son to the Father. Arius interpreted Alexander's speech as being a revival of Sabellianism, condemned it, and then argued that "if the Father begat the Son, he that was begotten had a beginning of existence: and from this it is evident, that there was a time when the Son was not. It therefore necessarily follows, that he [the Son] had his substance from nothing." This quote describes the essence of Arius's doctrine.
Socrates of Constantinople believed that Arius was influenced in his thinking by the teachings of Lucian of Antioch, a celebrated Christian teacher and martyr. In a letter to Patriarch Alexander of Constantinople Arius's bishop, Alexander of Alexandria, wrote that Arius derived his theology from Lucian. The express purpose of the letter was to complain about the doctrines that Arius was spreading, but his charge of heresy against Arius is vague and unsupported by other authorities. Furthermore, Alexander's language, like that of most controversialists in those days, is quite bitter and abusive. Moreover, even Alexander never accused Lucian of having taught Arianism; rather, he accused Lucian ad invidiam of heretical tendencies—which apparently, according to him, were transferred to his pupil, Arius. The noted Russian historian Alexander Vasiliev refers to Lucian as "the Arius before Arius".

Paul of Samosata (200 to 275) was the Bishop of Antioch from 260 to 268 and the originator of the Paulianist heresy named after him. He was a believer in monarchianism, a nontrinitarian doctrine; his teachings reflect adoptionism. Paul of Samosata Paul rejected the term homoousios; but naturally only in a false sense used by Paul; not, it seems because he meant by it an unity of Hypostasis in the Trinity.

History of Arianism
Paul of Samosata, who was contemporary with Dionysius, and Bishop of Antioch, may be judged the true ancestor of those heresies which relegated Christ beyond the Divine sphere, whatever epithets of deity they allowed Him. The man Jesus, said Paul, was distinct from the Logos, and, in Milton's later language, by merit was made the Son of God. The Supreme is one in Person as in Essence. Three councils held at Antioch (264-268, or 269) condemned and excommunicated the Samosatene. But these Fathers would not accept the Homoousian formula, dreading lest it be taken to signify one material or abstract substance, according to the usage of the heathen philosophies. Associated with Paul, and for years cut off from the Catholic communion, we find the well-known Lucian, who edited the Septuagint and became at last a martyr. From this learned man the school of Antioch drew its inspiration. Eusebius the historian, Eusebius of Nicomedia, and Arius himself, all came under Lucian's influence. Not, therefore, to Egypt and its mystical teaching, but to Syria, where Aristotle flourished with his logic and its tendency to Rationalism, should we look for the home of an aberration which had it finally triumphed, would have anticipated Islam, reducing the Eternal Son to the rank of a prophet, and thus undoing the Christian revelation.

Lucian of Antioch (240 – January 7, 312) at one time fell under suspicion for heresy, and was excommunicated, but was later reconciled to the Church and is now venerated as a martyr. Arius is believed to have been a student at the exegetical school in Antioch, where he once studied under Lucian.

Lucian of Antioch (c. 240 – January 7, 312), known as Lucian the Martyr, was a Christian presbyter, theologian and martyr. He was noted for both his scholarship and ascetic piety.
According to Suidas, Lucian was born at Samosata, Kommagene, Syria, to Christian parents, and was educated in the neighbouring city of Edessa, Mesopotamia, at the school of Macarius. However, this tradition might be due to a conflation with his famous namesake, Lucian of Samosata, the pagan satirist of the second century.
At Antioch, Lucian was ordained presbyter. Eusebius of Caesarea notes his theological learning and Lucian's vita (composed after 327) reports that he founded a Didaskaleion, a school. Scholars following Adolf von Harnack see him as the first head of the School of Antioch, with links to later theologians Diodorus of Tarsus and Theodore of Mopsuestia, but that contention is unrecorded in the extant sources.
After the deposition of Antioch's bishop Paul of Samosata, he fell under suspicion for heresy, and was excommunicated. According to Alexander of Alexandria, he remained in schism during the episcopates of three bishops, Domnus, Timaeus and Cyril, whose administration extended from 268 to 303. Lucian was reconciled with the Church either early in the episcopate of Cyril (perhaps about 285), which seems more likely, or under Cyril's successor Tyrannus.
During the persecution of Maximinus Daia, Lucian was arrested at Antioch and sent to Nicomedia, where he endured many tortures over nine years of imprisonment. He was twice brought up for examination, and both times defended himself ably and refused to renounce his Christian faith.
His death is uncertain. He might have been starved to death. Another, more likely, possibility is that he was beheaded. The traditional date ascribed to his execution is January 7, 312, in Nicomedia.
He was buried at Drepanum on the Gulf of Nicomedia, which was later renamed Helenopolis to honour Helena, mother of Constantine the Great.
He is also commemorated as a saint, with a feast day of January 7 in the Roman Catholic Church and October 15 in the Orthodox Church.

Wikipedia tries to link Arius to the exegetical school in Antioch, where he studied under Saint Lucian.

Arius
Early life and personality
His father's name is given as Ammonius. Arius is believed to have been a student at the exegetical school in Antioch, where he studied under Saint Lucian. Having returned to Alexandria, Arius, according to a single source, sided with Meletius of Lycopolis in his dispute over the re-admission of those who had denied Christianity under fear of Roman torture, and was ordained a deacon under the latter's auspices. He was excommunicated by Bishop Peter of Alexandria in 311 for supporting Meletius, but under Peter's successor Achillas, Arius was re-admitted to Christian communion and in 313 made presbyter of the Baucalis district in Alexandria.

And last, but not least Arius was influenced by Origen of Alexandria (185 – 253).

Arius
The Arian controversy
Origen and Arius
Like many third-century Christian scholars, Arius was influenced by the writings of Origen, widely regarded as the first great theologian of Christianity. However, while both agreed on the subordination of the Son to the Father, and Arius drew support from Origen's theories on the Logos, the two did not agree on everything. Arius clearly argued that the Logos had a beginning and that the Son, therefore, was not eternal, the Logos being the highest of the Created Order. This idea is summarized in the statement "there was a time when the Son was not." By way of contrast, Origen believed the relation of the Son to the Father had no beginning, and that the Son was "eternally generated".
Arius objected to Origen's doctrine, complaining about it in his letter to the Nicomedian Eusebius, who had also studied under Lucian. Nevertheless, despite disagreeing with Origen on this point, Arius found solace in his writings, which used expressions that favored Arius's contention that the Logos was of a different substance than the Father, and owed his existence to his Father's will. However, because Origen's theological speculations were often proffered to stimulate further inquiry rather than to put an end to any given dispute, both Arius and his opponents were able to invoke the authority of this revered (at the time) theologian during their debate.
Arius emphasized the supremacy and uniqueness of God the Father, meaning that the Father alone is infinite and eternal and almighty, and that therefore the Father's divinity must be greater than the Son's. Arius taught that the Son had a beginning, contrary to Origen, who taught that the Son was less than the Father only in power, but not in time. Arius maintained that the Son possessed neither the eternity nor the true divinity of the Father, but was rather made "God" only by the Father's permission and power, and that the Logos was rather the very first and the most perfect of God's productions, before ages.

Origen significantly contributed to the development of the concept of the Trinity and was among the first to name the Holy Spirit as a member of the Godhead, but he was also a subordinationist, who taught that the Father was superior to the Son and the Son was superior to the Holy Spirit.
Comment: Some very interesting and useful articles. +1 for that final diagram showing what the Trinity is not, and what it is.
Answer: Arius was a conservative. He did not say anything new.
Introduction
Arius was a presbyter in the city of Alexandria, Egypt. In the year 318, he confronted his bishop Alexander for 'erroneous' teachings concerning the nature of the Son of God. Their disagreement escalated and even became a threat to the unity of the empire. So, Emperor Constantine called a council at Nicaea in the year 325 where Arius' theology was presented, discussed, and soon rejected.
Purpose
This article discusses Arius' antecedents: From whom did Arius receive his theology? Or did he develop his theology himself? In the traditional account of the Arian Controversy, Arius' theology was an innovation opposing established orthodoxy. But this article shows that Arius did not say anything new.
Was Arius important?
Only a few pages of what Arius wrote survived until today. The reason is that, as discussed in a previous article, Arius was not regarded by his peers as a particularly significant writer.
Still another article concluded that, while Athanasius' enemies labeled him as a Sabellian, Athanasius invented the terms 'Arian' and 'Arianism' to label his opponents with Arius' theology, with all the incoherence and inadequacy that teaching displayed. But his opponents were not 'Arians', meaning that they were not followers of Arius. They were the anti-Nicenes of a different place and time. In fact, they also opposed Arius' theology.
Nevertheless, Arius was significant in the first 7 of the 62 years of the 'Arian' Controversy. (See - The Arian Controversy had two phases.) To understand the Nicene Creed, we need to understand him.
Authors
This article is mainly based on the following books:

RH = Bishop R.P.C. Hanson, The Search for the Christian Doctrine of God - The Arian Controversy 318-381 (1981), particularly chapter 3.
RW = Archbishop Rowan Williams, Arius, Heresy & Tradition (2001)

These are world-class scholars and Trinitarians.
Specific Predecessors
"A very large number of names have been suggested as predecessors of Arius" (RH, 60).
"His enemies first associated him with Paul of Samosata and with Judaizing tendences in Christology; later on, after the reputation of Origen had been virtually ruined in the Church, Arius was regarded by some as an Origen redivivus (a reborn Origen). Some more modern scholars have been much preoccupied with the question of whether Antioch or Alexandria should be seen as his spiritual and intellectual home." (RW, 116)
This section summarizes Hanson's and Williams' conclusions concerning Arius' dependence on specific predecessors:
Plato
Plato's philosophy of time and the origin of the universe still dominated in the fourth century and shaped what most influential writers of that time said about creation:

"Plato's Timaeus served as the central text upon which discussions of
the world's origins focused, not only in late antiquity, but right up
to the revival of Christian Aristotelianism in the thirteenth century.
…
There can be no doubt that for many of the most influential writers of
the age, from Origen to Eusebius Pamphilus, the contemporary
discussion of time and the universe shaped their conceptions of what
could intelligibly be said of creation." (RW, 181)

"Plato distinguishes between:

What exists without cause and, therefore always exists and never comes into being, and
The universe as we perceive it, which had a beginning, is not eternal, and never exists stably." (RW, 181)

Furthermore, Plato argues that, since the cosmos is beautiful; it must therefore be modeled upon what is higher and better. The Creator made something like himself; reflecting order and beauty. To establish this order, God created time. The heavenly bodies are made in order to measure and regulate time. In other words, so to speak, time did not always exist. (RW, 181-2) (Similar to the modern big bang theory)
So, yes, Arius was influenced by Plato, but so was every other theologian of his time.
Philo of Alexandria
Philo (20 BC – 50 AD) was a Hellenistic Jewish philosopher who interpreted Jewish scripture in terms of Greek philosophy. That is significant because the Christian theologians of the second and third centuries did the same with the New Testament (See - the Apologists).

Wolfson concluded, "Arius was responsible for 'a reversion to the
original view of Philo' on the Logos, after the aberrations of a
modalism which deprived the Logos of real subsistence" (RW, 117).
"Wolfson … suggested that Philo may have been a former of Arius'
thought because he too taught two Logoi, and the creation of one of
them ex nihilo, and the incomparability of God.
But then, Wolfson was obsessed to an excessive degree with the
influence of Philo on the fathers; Philo's Logos-doctrine is confused
and obscure; he does not make the same division between the Logos and
God as did the Arians. We cannot claim Philo as an ancestor of Arius'
thought." (RH, 60)

After discussing the evidence, Rowan Williams comes to a similar conclusion. He says that the similarities between Philo and Arius "should not … mislead us into hastily concluding that Arius was an assiduous student of Philo. What all this shows is, rather, that Philo mapped out the ground for the Alexandrian theological tradition to build on, and that Arius' theological problematic is firmly within that tradition." (RW, 122-123)
So, to the same extent that Arius was influenced by Philo, Alexandrian theologians, in general, were also influenced by him. Philo was not the origin of Arius' idiosyncrasies.
Gnosticism
Arius also did not receive his theology from the Gnostics:

"There are some resemblances to Gnostic doctrines in Arius' thought. …
But these resemblances are either too general or refer to terms used
for different things in the two authors. Furthermore, Arius several
times rejects the favourite Gnostic concept of the 'issue' … of
beings, from God." (RH, 60)

Clement of Alexandria
Clement (150-215) was the bishop of Alexandria in the early third century in the same city where Arius and his bishop lived.
Clément's theology included one of the peculiar aspects of Arius' theology, namely, "two Logoi." (See the explanation below.) However, Clement's "two Logoi are quite different from those of Arius." (RH, 60)
Furthermore, while Arius taught 'there was when He (the Son) was not, Clement taught "the eternity of the Son." (RH, 60)
Clement describes the Logos as:

"The primary image of God … the 'second cause' in heaven, 'life
itself'." (RW, 125-126)

After showing that Clement's theology is significantly different from that of Arius, Williams concludes:

"However, this is not to deny that Clement also passes on a positive
legacy to Arius and his generation. … There are the numerous parallels
in vocabulary between Arius' Thalia and the language of Clement." (RW,
126)
"It is less a question of a direct influence on Arius than of a common
ethos ... Arius begins from the apophatic tradition shared by Philo,
Clement and heterodox Gnosticism … but his importance lies in his
refusal to … (admit) into the divine substance … a second principle."
(RW, 131)

So, Arius inherited many things from Clement, just like he received many things from many other theologians, but the peculiar aspects of Arius' theology cannot be blamed on Clement (RH, 60).
Origen
Origen (185-253) was the most influential theologian of the first three centuries. "From very early on, there were those who saw Origen as the ultimate source of Arius' heresy" (RW, 131). The similarities and differences between Origen and Arius are discussed in a separate article. Hanson concluded:

"Arius probably inherited some terms and even some ideas from Origen,
… he certainly did not adopt any large or significant part of Origen's
theology." (RH, 70)
"He was not without influence from Origen, but cannot seriously be
called an Origenist" (RH, 98).

Dionysius of Alexandria
"Dionysius was bishop of Alexandria from 247 to 264." (RH, 72) "The Arians … were adducing (offering) Dionysius of Alexandria as a great authority in the past who supported their doctrine." (RH, 73) For example, Dionysius wrote:

"The Son of God is a creature and generate, and he is not by nature
belonging to but is alien in ousia from the Father, just as the
planter of the vine is to the vine, and the shipbuilder to the ship;
Further, because he is a creature he did not exist before he came into
existence" (RH, 73).
"Dionysius ... rejected homoousios because it did not occur in the
Bible." (RH, 75)

"Athanasius defends Dionysius, though he admits that he wrote these words, on the grounds that the circumstances, since he was combating Sabellianism, justified such expressions" (RH, 73).
"Basil … says that Dionysius unwittingly sowed the first seeds of the Anhomoian error, by leaning too far in the opposite direction in his anxiety to correct wrong Sabellian views" (RH, 74).
Hanson concludes as follows:

"However Dionysius may have refined his later theology, it is
impossible to avoid seeing some influence from his work in the
theology of Arius. The later Arians and Basil were right. The damning
passage quoted from his letter … is altogether too like the doctrine
of Arius for us to regard it as insignificant." (RH, 75-76)
"If, as seems likely, Arius put together an eclectic pattern of
theology ... Dionysius of Alexandria certainly contributed to that
pattern" (RH, 76).

So, of all the writers referred to above, Dionysius is the first one who really could have been the source of Arius' theology. And Dionysius was the bishop of the city when Arius was born there.
Paul of Samosata
Paul was Bishop of Antioch from 260 to 268. At the time, Antioch was the headquarters of the church. "Many scholars have conjectured that the views of Paul of Samosata, or at least of his school, must have influenced Arius" (RH, 70). However:

"Apparently for Paul the Son was Jesus Christ the historical figure
without any preexistent history at all.
And the stock accusation made against Paul by all ancient writers who
mention him from the ivth century onward was that he declared Jesus to
be no more than a mere man." (RH, 71)
"Apart from his (moral?) superiority to us in all things because of
his miraculous generation, he is 'equal to us'. Wisdom dwells in Jesus
'as in a temple': the prophets and Moses and "many lords' (kings?)
were indwelt by Wisdom, but Jesus has the fullest degree of
participation in it." (RW, 159-160)

"This is an idea which all Arian writers after Arius (and, in my view, probably Arius himself) regularly rejected." "Arius believed firmly in a pre-existent Son." (RH, 71) "Arius … ranges himself with those who most strongly opposed Paul. (RW, 161)
To conclude:

"We know very little with certainty about Paul of Samosata."
Therefore, "any attribution of influence from Paul of Samosata upon
Arius must rest almost wholly upon speculation." (RH, 72)

Theognostus of Alexandria
Theognostus wrote between 247 and 280. His views "echoes Arian concerns in insisting that the Father is not divided" but he also had some quite un-Arian views, such as that:

The Son is an issue of the Father (RH, 78).
"The ousia of the Son … was (not) introduced from non-existence, but
it was of the Father's ousia." (RH, 77) "Theognostus explicitly
disowned the doctrine, which Arius certainly held, that the Son was
created out of non-existence" (RH, 78).

While Arius taught "that there are two Logoi (one immanent in the Father and one a name given somewhat inaccurately to the Son)," ... Theognostus insisted that there was only one Logos (RH, 79). Therefore:

"We cannot glean any satisfactory evidence that Theognostus was a
predecessor of Arius." (RH, 79)

Methodius of Olympia
Methodius of Olympia (died c. 311) was a bishop, ecclesiastical author, and martyr.
He was "the most vocal critic of Origen in the pre-Arian period" (RW, 168). He "seems to assume that Origen's doctrine of the eternity of creation implies the eternity of matter as a rival self-subsistent reality alongside God" (RW, 168).
He "produces some views which interestingly resemble those of Arius. For example:

"The Son ... is wholly dependent on the Father." (RH, 83).
The Son is "the first of all created things" (RH, 83).
"God alone … is ingenerate [meaning, exists without a cause]; nothing
else in the universe is so, certainly not, he implies, the Son." (RH,
83)
"God the Father is the 'unoriginated origin', God the Son the
beginning after the beginning, the origin of everything else created."
(RH, 83)
"God the Father creates by his will alone. God the Son is the 'hand'
of the Father, orders and adorns what the Father has created out of
nothing." (RH, 83)

Lucian of Antioch
The authorities above are discussed in chronological sequence. Lucian was the last of them. He died as a martyr in 312, only 6 years before Arius and his bishop clashed.
"Jerome ... describes Lucian thus: 'A very learned man, a presbyter of the church of Antioch" (RH, 81). He was "well versed in sacred learning" (RH, 79).
Evidence that Arius was a follower of Lucian
"A figure to whom many scholars have looked in order to explain the origins of Arius' thought is Lucian of Antioch:"

"Arius describes Eusebius of Nicomedia, to whom he is writing, as 'a
genuine fellow-disciple of Lucian'" (RH, 80), implying that Arius
himself was a "disciple of Lucian."
Philostorgius also described Eusebius of Nicomedia, who was one of
Arius' close friends, as "the _ disciple of Lucian the martyr'" (RH,
81).
Epiphanius identifies "the Arians" with "the Lucianists" (RH, 80).
"'Lucian and all the Lucianists', he says, 'deny that the Son of God
took a soul [i.e. a human soul), 'in order that, of course, they may
attach human experiences directly to the Logos." (RH, 80) This was a
standard teaching of the Arians.

Lucian's theology

"According to Sozomen, the second creed of the Dedication Council on
Antioch in 341 was said to be a confession of faith stemming from
Lucian." (RW, 163-4; cf. RH, 80-81)
"There is one fact, and one fact only, which we can with any
confidence accept as authentic about Lucian's doctrine. … Lucian
taught that the Saviour at the Incarnation assumed a body without a
soul" (RH, 83).

But Arius deviated from Lucian.

"Philostorgius knew of a tradition that Arius and the Lucianists
disagreed about the Son's knowledge of the Father, (RW, 165)
While Arius maintained "that God was incomprehensible … also to the
only-begotten Son of God' (RW, 165), "the Lucianists … were remembered
to have held that God was fully known by the Son … Eusebius of
Caesarea says much the same." (RW, 165)

If these are true, then Arius differed from Lucian on this key aspect of his teachings.
Conclusions re Lucian

"We can be sure that Arius drew on the teachings of Lucian, but … we
do not know what Lucian taught" (RH, 82, cf. 83). "Our witnesses to
Lucian's theology are fragmentary and uncertain in the extreme." (RW,
163)
"It is wholly unlikely that Arius was a vox clamantis in deserto (a
lone voice calling in the desert). He represents a school, probably
the school of Lucian of Antioch, and the school was to some extent
independent of him. Arianism did not look back on him later with
respect and awe as its founder." (RH, 97)

Antioch or Alexandria?

"Some … modern scholars have been much preoccupied with the question
of whether Antioch or Alexandria should be seen as his spiritual and
intellectual home." (RW, 116).
However, "the stark distinctions once drawn between Antiochene and
Alexandrian exegesis or theology have come increasingly to look
exaggerated. (RW, 158)
"Arius is an unmistakable Alexandrian in his apophaticism (knowledge
of God). … We have no real justification even for regarding him as a
rebel in the matter of exegesis." (RW, 156) "Arius inherits a dual
concern that is very typically Alexandrian." (RW, 176)

CONCLUSIONS
Arius did not cause the Controversy.
The analysis above shows that the authors preceding Arius had very conflicting views of the Son. Sabellian and his supporters are not even mentioned above because Arius was on the opposite end of the spectrum. Consequently:

"Many of the issues raised by the controversy were under lively
discussion before Arius and Alexander publicly clashed" (RH, 52).
"The views of Arius were such as … to bring into unavoidable
prominence a doctrinal crisis which had gradually been gathering. … He
was (only) the spark that started the explosion." (RH, xvii)

Arius was particularly influenced by two authors.
Arius rejected Gnosticism and the theology of Paul of Samosata.
Arius is unmistakably Alexandrian in his theology and the general heritage of the church in Alexandria was shaped by Plato, Philo, Clement, Origen, and Lucian:

Arius' theology was "clearly the result of a very large number of
theological views." (RW, 171)

The two authors whom Arius could rightly claim as his theological predecessors are Dionysius, bishop of Alexandria, and Methodius, bishop of Olympia:

It is likely that Bishop Dionysius of Alexandria contributed to Arius'
theology (RH, 76).
Bishop Methodius of Olympia regarded the Father alone as ingenerate;
the 'unoriginated origin' and the Son as the first of all created
things and wholly dependent on the Father (RH, 83).

While Hanson said that "Arius ... represents a school, probably the school of Lucian of Antioch" (RH, 97), Williams proposed that "it is perhaps a mistake to look for one self-contained and exclusive 'theological school' to which to assign him" (RW, 115).
Arius did not say anything new.

Arius' book (The Thalia) "is conservative in the sense that there is
almost nothing in it that could not be found in earlier writers; it is
radical and individual in the way it combines and reorganizes
traditional ideas and presses them to their logical conclusions." (RW,
177).
"Arius … can no longer be regarded as the strange monster of heresy
which Gwatkin, and even Harnack, depicted him to be" (RH, 84-85).

SPECIFIC DOCTRINES
This second section discusses specific doctrines which Arius might have received from his predecessors. Almost everything that Arius wrote can be found in the writings of his predecessors. This section relies on both the discussion above and the article - Was Origen the ultimate source of Arius' heresy?
A Creature
Both Origen and bishop Dionysius of Alexandria (247 to 264), described the Son as a 'creature' (RH, 63):

"Origen did … describe the Son both as 'having come into existence'
and as a 'creature'. … But at the same time, he declares his belief in
the eternity of the Son as a distinct entity from the Father" (RH,
63-64). He used the term 'creature' in the general sense of a being
whose existence was caused by another. That would include 'begotten'
beings.
Dionysius described the Son of God as "a creature," "alien in ousia
from the Father" (RH, 73).

Originated
Methodius emphasized that the Father alone exists without a cause and, therefore, without a beginning. Origen, similarly, described the Son as "the originated God" (RH 62).
Subordinate
"Origen, with Arius, can be said to have subordinated the Son to the Father" (RH, 64). Hanson also explains that, for Origen, the Son was less subordinate than for Arius (RH, 64). Nevertheless, Hanson goes on to say that all theologians in the Eastern or the Western Church before the outbreak of the Arian Controversy regarded the Son as subordinate to the Father.

"Subordinationism might indeed, until the denouement (end) of the
controversy, have been described as accepted orthodoxy" (RH, xix).

For example, Bishop Methodius of Olympia (died c. 311) regards the Son as the first of all created things and wholly dependent on the Father (RH, 83).
Not fully understand
Origen taught that the Son does not fully understand the Father.
Produced by the Father's will
In contrast to Nicene theology, in which God never made a decision to generate the Son; the Son simply always exists, "Ignatius, Justin, Hippolytus, Clement of Alexandria and Origen" taught "the Son was produced by the Father's will" (RH, 90).
Not homoousios
Dionysius of Alexandria "rejected homoousios" (RH, 75) and said that "the Son of God … is alien in ousia from the Father" (RH, 73).
There was when He was not
Dionysius of Alexandria said that the Son did not always exist:

"Because he is a creature he did not exist before he came into
existence" (RH, 73).

From non-existence
As indicated by the anathemas attached to the Nicene Creed, this was one of the main aspects of Arius' theology to which the Council objected. In opposition to the view that the Son is from non-existence, the Nicene Creed interprets "begotten" as that He is from the substance of the Father.
Hanson says that "Arius' view, that "the Son was created from non-existent things, has never been supplied with a convincing antecedent." (RH, 88)
But I would like to differ a bit from Hanson in this regard. I cannot find a place where Arius adds the word "things" to this statement. Arius simply said, "God made him 'out of non-existence'" (RH, 20, 24). To me, this simply means that the Son did not exist before He was begotten. If that is the meaning, bishop Dionysius of Alexandria said the same thing about 50 years earlier when he said, "Because he is a creature he did not exist before he came into existence" (RH, 73).
Two Logoi
One of the unique aspects of Arius' teaching was 'two logoi'. Clement of Alexandria also taught "two Logoi" (RH, 60) but Theognostus of Alexandria "insisted that there was only one Logos" (RH, 79). This aspect requires more detail because the modern reader would not off-hand understand the significance:
Logos-theology had only one Logos.
The church became Gentile (non-Jewish) dominated in the second century but was still persecuted by the Roman Empire. These 'Gentile' theologians developed the Logos-theology and this became generally accepted in the church.
Logos-theology was an interpretation of the New Testament on the basis of Greek philosophy, which still dominated the intellectual world of the Roman Empire (see - The Apologists).
In Greek philosophy, God's Logos (Word, Wisdomhas always existed as part of God but became a separate reality (hypostasis) when God decided to create. So, in Greek philosophy, there was only one Logos.
These church fathers explained the pre-existent Jesus Christ as the Logos of Greek philosophy. Consequently, the pre-existent Jesus Christ was explained as God's only Logos. In this theology, God does not have another Logos. In other words, God does not have his own 'mind' or 'Wisdom' apart from His Son.
This view was challenged by Sabellianism in the third century but Sabellianism was rejected. Consequently, Logos-theology was the general explanation of the Son with which the church entered the fourth century. For example, Theognostus of Alexandria (247 to 280) "insisted that there was only one Logos" (RH, 79).
Since Hanson mentions only one theologian who taught "two Logoi" (Clement of Alexandria - RH, 60), presumably all other theologians taught one single Logos - as per the traditional Logos theology. For a further discussion, see - Logos-Theology.
Arius deviated from Logos-theology.
Both Alexander and Athanasius noted that Arius taught two Logoi (two Wisdoms): The Son is Logos and God has His own Logos (mind). For example, Athanasius, in his paraphrasing of Arius' teaching, wrote:

"There are … two Wisdoms, one God's own who has existed eternally with
God, the other the Son who was brought into existence. … There is
another Word in God besides the Son" (RH, 13, cf. 16).

The fact that they mentioned this shows that they regarded this as noteworthy and even a deviation. Arius is very often accused of bringing philosophy into the church. However, his two Logoi seem to be a protest against the influence of Greek philosophy on church doctrine.