What is the difference between a multiplexed bus and a multi-master bus

Question: The jargon of terms in bus architecture literature is half the difficulty in understanding it. At some places the term 'multiplexed' bus is used while at some other places 'multi-master' bus is used. They both look same to me but maybe they are different in some sense also. How to know what exactly is the meaning of these two terms?
Answer: Any communications channel that is multiplex means it can be accessed by more than one transmitter.  That's pretty general; in your context it means that different transmitters can use it at different times.
A bus master is the piece of hardware that actually controls who has access to the bus.  So a multi-master bus is one that has a mechanism for multiple masters to take over the bus at different times.  Following through on this thought, a multi-master bus has some sort of arbitration scheme so that if more than one master wants control over the bus at one time, only one of them actually gets that control.
Comment: It looks like multiplexed bus has more than one meaning based on context.
Answer: Muli-master is mainly for long serial communications. A bunch of masters on the same bus can simultaneously attempt to initate a transmission. Like a bunch of people trying to yell over each other in a  room until everyone settles down to listen to just one person.
Multi-plexed is only (I think) for parallel processor to memory communications. It is definitely only for parallel since it has no meaning in serial. It is where not every line is dedicated to only a single address or data bit. Some lines might be used/shared for a low and high bit of the same type, or a data and address bit. This lets you reduce the number of lines between processor and memory at expense of speed.
These two things appear in different places. I don't know why they might ever overlap in application.
Answer: According to https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/multiplexed-bus, a multiplexed bus is a type of bus structure in which the number of signal lines comprising the bus is less than the number of bits of data, address, or control information being transferred between elements of the system.
I couldn't find a definition for it in any of the books I have in my personal library.
The definition may depend on the author and the context, but I personnally feed that the definition provided above is appropriate.
"By nature", a bus is shared amongst the "peripherals" connected to it.  Every element will at some time be allowed to "talk" on the bus.  So from that point of view any bus would be "multiplexed".
"Multi-master" already identifies a specific feature on a bus which is not possible in all systems.  But this only indicates that the control over who can talk on the bus is possibly shared by multiple "peripherals" of the bus.  It does not make it more or less multiplexed than other buses.
Therefore, it seems more logical that a multiplexed bus has less signal lines than there are number of bits of data, address or control information.  A current example of a multiplexed bus is the ARM AXI bus at least according to their own documentation: http://infocenter.arm.com/help/index.jsp?topic=/com.arm.doc.dui0362c/Cfhbajif.html .  The data width can be larger than the bus itself, so the data word is multiplexed on the bus.
By these definitions, the I2C bus is both a multiplexed and multimaster bus.  There are only two signal lines: SCL and SDA.  The SCL is the clock, and the SDA line will provide the address, the read/write signal, and the data bits.
To add to the confusion, one can also multiplex buses themselves.  A document by cypress (https://www.cypress.com/file/130941/download ) explains that it is possible to switch between I2C buses - and they call that bus multiplexing.  They do not call it a multiplexed bus though.  I'ld say that bus multiplexing and a multiplexed bus are different definitions, but they can both apply to the same bus in a system.
In conclusion:

The signals of a multiplexed bus are in part used for different purposes.  For example, a signal line can be an address bit at one time, and a data bit at another time.
A multimaster bus indicates that there can be more than one master, but it does not provide any information about the multiplexed nature of a bus.
It is possible to multiplex buses, which is called bus multiplexing.  This can ba applied to multiplexed buses, multimaster buses, or buses with both of these properties.


Can the word "mundane" be used in positive sense

Question: Mundane means ordinary.The word is mostly used in negative sense.Can the word "mundane" be used in positive sense too?
Like"Mr.K is not a wasteful man.He leads a very mundane life."Another example can be"Miss ABC does not show off in front of others.She is a mundane girl."In the examples I am referring mundane to be "ordinary" and in positive sense.Can the examples be used? or is it wrong technically?
Comment: In a word, yes. When the commonplace, everyday or ordinary (but not the banal) is desirable, what's mundane is a positive virtue. You're right that 'mundane' is often used with negative connotations, but it is not exclusively or necessarily so. Whether or not the word is understood negatively will depend on the context (connotations), and it will be up to the writer to make clear what sense is intended.
Comment: Sure: "After the police activity, its nice to return to a mundane commute"
Comment: "Aliens!" "Ghosts!!" "International conspiracy!!!" "No, there is a perfectly mundane explanation." (That sounds like a positive to me, but others may disagree, if they believe in aliens, for example.)
Answer: It isn't technically wrong, but it's almost certain to be misunderstood by the listener.  Consider instead:

frugal (the opposite of wasteful)
unassuming
modest
humble
unpretentious
Comment: so the examples written by me are correct?
Comment: If I read the examples with "mundane", I would not be sure of the writer's intention. @Malvolio's examples are excellent.
Answer: 'Mundane' with the meaning of 'dull and ordinary' (as opposed to 'worldly') is almost always used negatively (or at best neutrally). A positive sense can only be accomplished by a context that somehow makes both dull and ordinary positive qualities.
Replacement by either 'dull' or 'ordinary' might be a good idea.
Comment: You are citing another answer to the same question as your source.  This isn't kosher.
Comment: @ab2 OK. Removed.
Answer: Technically, in the denotative (dictionary) meaning, it is not correct, but it may be misunderstood. It has a bad connotation, as in:  boring, uneventful.
Here are words with better connotations.

Peaceful
Modest
Practical
Answer: Mark Strand's poem, The Continuous Life, introduces mundane as something deeply positive, in that the parents' devotion to the ordinary things of life is what gives freedom to children, both in the immediate and in the future.
The poem begins like this...
<code>What of the neighborhood homes awash
In a silver light, of children hunched in the bushes,
Watching the grown-ups for signs of surrender,
Signs that the irregular pleasures of moving
From day to day, of being adrift on the swell of duty,
Have run their course? O parents, confess
To your little ones the night is a long way off
And your taste for the mundane grows; tell them
Your worship of household chores has barely begun;
</code>


How to disable broadcast messages on my linux session?

Question: I get every 10 min many broadcast messages (maybe by other user). How can I disable those broadcast messages, in order to not see them on my screen?
Comment: I don't know if this is what the OP means, but I'm looking for the answer to a similar question. I'm seeing broadcast messages showing up in a terminal when logged in to a remote server over SSH. Although not exactly the same, similar messages can be created by logging in to the same machine in another terminal and typing "logger -p local3.emerg foobar". That gets me a `Broadcast message from systemd-journald@machine\nbla bla bla` in every terminal. This occurs on our debian servers, but not on my Ubuntu desktop. `mesg n` did not stop them. I'm looking to disable it only in this terminal.
Answer: If they are using wall or write a similar method to write on your terminal or terminals, then mesg n will stop the messages from coming to you.
If you mean something else, explain "broadcast messages" more precisely.
From your comments you seem to be still expecting an answer, so here is the one that you didn't read or didn't understand:

If someone has root on your machine,
  they can do anything they want to
  annoy you. Be glad they aren't killing
  your shells and removing your files.
  The only thing you can do to stop the annoyance
  is log out or ask the irritating person to
  stop. There is no technical solution; you are
  asking where the button is to make
  some kid stop throwing pebbles at you. There
  is no such button.
Answer: I am assuming that you are getting messages sent to your command-line/console window.  If that is the case try this:
$ mesg n

If the messages don't stop they are likely coming from a user/process with root-level permissions, which cannot be stopped.
You mentioned a predictable 10 minute cycle. That could indicate the message is being generated by some daemon process.  Maybe that process is using syslog to record messages.  If so, it is then possible that syslog is configured to send messages that match certain criteria to users' terminals.  Look through /etc/syslog.conf for possible culprits.  The documentation you can see by running man syslog.conf should be able to get you started.   I'd suggest starting with the "EXAMPLES" section.
Answer: Make sure that $ mesg n is applied in your account. If you su to another user and try that command, you will see mesg: cannot change mode.
Comment: I edited your answer, if you are unhappy with the changes feel free to revert them or edit it again.
Answer: Try setting loglevel=3 in your boot parameters.
The loglevel parameter suppresses all messages with a level greater than, or equal to, the number specified.
The levels are:
 0 - Critical, system unusable
 1 - Immediate action required
 2 - Critical event
 3 - Error
 4 - Warning
 5 - Notice
 6 - Informative
 7 - Debugging information


Why is my supervisor ignoring me?

Question: I am an undergraduate student with major aspirations to go to graduate school. I am in my final year. I am currently working on a research project with 2 supervisors (1 of them marks my work and the other just signs off on it). I have meetings with one of them every couple weeks and he always tells me "send me a message whenever you have a question, there are no restrictions". So I had a question last Thursday, yet never received a response. In addition, I have a presentation tomorrow and need his approval before printing out the presentation (it's a poster) to ensure that no private data is shown. He told me to send him my presentation on Monday so I did. However, I have not heard back from him and my presentation is tomorrow. I am not sure if this is a common situation with supervisors? I know the simple solution would be to send him a reminder. However, I really don't want to make anyone angry. I will honestly "kiss up" to anyone to get into my graduate program. So I am treading carefully. If I do send him an email, how should I phrase it?
Comment: There's no harm in you emailing him or visiting his office and asking if he's had a chance to review the poster and reminding him that the presentation is tomorrow. I wouldn't ask why he's "ignoring you", as it's possible he didn't even see your email from last week. Given the amount of emails we get each day, it's not unheard of.
Comment: Follow up, always follow up. And "escalate", if you cannot reach him via email, try going to his office hours or even just come by his office randomly. Or call.
Comment: Part of me wants to point out that your supervisor correctly noted that you can technically *send him a message whenever you have a question*. He did not say that he would answer any of them.
Answer: The blogger UniversityOfLies wrote in a post titled What to do When Your PhD Adviser Ignores You:

Busy [sic] Backson Syndrome (as coined by Winnie the Pooh and Benjamin Hoff)- My first adviser suffered from this.  These people are Too Damn Busy flying around the world, giving lectures anywhere other than their home university, being on TV, and frolicking through the lavender fields of Provence and buying age-inappropriate accessories with Johnny Depp.

You are too late. If I have presentation tomorrow, I will make sure everything is prepared and checked by my supervisor 2 weeks before.

what now you can do since your presentation is tomorrow is:

1. Again, Write him an Email with high priority indication:
2. Meet with the department chair faculty if any available: and ask if it possible to check it with you.
3. If it all fails: print your poster and be prepared to the presentation and make sure your impress the audience
Comment: Thank you, this is helpful. I am always pro-active and never leave things to the "last minute". However, this research project was only 8 weeks and I would not be able to have everything done 2 weeks before. My supervisor knew that so told me to send him the presentation on Monday.
Comment: @aspire94 I see...
Comment: @Krebto the link to the paper by Winnie and Hof appears to be broken, or does seem not link correctly.

Why is my supervisor ignoring me?


How to add new page to a Draw.IO document

Question: I would like to have a single document that contains several diagrams (all the UML diagrams that I need for my project).
How can I add a new page in a Draw.IO document?
Answer: At the bottom of the diagrams.net interface there is a plus "+" symbol that allows you to add a new page:

If you're using the draw.io whiteboard theme, you have to enable pages via the preference menu first:

Once enabled the pages option appears bottom-right of the interface as three vertical dots:

Clicking that brings up the pages actions and details. One of the actions is "insert page":
Comment: ok. Thank you for this information.
Answer: You can add more pages to a draw.io file by placing an object where the new page belongs. The new page will automatically added in order to contain the new object. If you want to have a new page on the right of the current page, place the new object on the right the current page. If you want the new page below the current page, place the new object below the current page.
For more information, check the link below
https://support.draw.io/questions/2949188/how-to-add-pages-to-a-diagram
Comment: This does not actually add a "separate" diagram. It just makes the diagram larger.
Answer: Even though draw.io doesn't support multiple pages, there is a workaround which kind of solves this: Layers (Ctrl+Shift+L).
You can add several layers to a document using the Layers panel, and then tick the layer(s) you want to see, and select the layer you want to add new stuff to and work with. If you have created stuff at one layer you want to move, simply select the elements, and then select the new layer and hit the button to move selected items to current layer.
Usually layers are used for purposes like different detail levels, or adding explanations/comments on a separate layer. Or in a floor plan you could have the base layer showing the rooms, and then extra layers for electricitiy, pipes, furniture, ... In this context you'll show several layers at the same time.
However, opting to only display one level at a time, you'll mimic having pages and the contents can be totally separated from each other.
Answer: Draw.IO Version 13.6.2 (or even earlier) has the option to add new pages (in the lower bar, called "insert page").
Then you can work on different pages, in the same document.
And finnaly you can iterate through the pages with "Ctrl-Shift-Page-Up" and "Ctrl-Shift-Page-Down", which I find very handy!


Can you use TukeyHSD as a post hoc test for a mixed model?

Question: I completed a mixed model with repeated measures.  I did an ANOVA comparing my model to a null model and got a significant value.  Now I need to identify where those significant differences are in my data.  What post hoc test can I use?  Will Tukey HSD work?  Many of the other test suggested such as wald.test and 1-pchisq don't work for me.  If you need more info on the tests I ran let me know. Thanks!
Comment: The answer is yes, provided you have a nice balanced design and you use the appropriate standard error of differences derived from the covariance structure of the mixed model. But if by this you mean to compute the HSD via the formula in Ch 2 or so of your design book, the answer is a definite no. If you're using R, the one-step (default) test in the multcomp package computes the equivalent of Tukey-adjusted p values, even in some messier cases; as does the lsmeans package with `adjust="mvt"`
Comment: Can you elaborate on your situation & your analyses (etc)? What do you mean they didn't "work for you"?
Comment: @rvl, can you elaborate on that & turn it into an official answer? I think that would be a nice contribution.
Comment: I'll try. Won't add the R-specific stuff unless it's needed.
Answer: Consider a balanced design under the simplest assumptions, and let $\bar y_{i\cdot\cdot}$ denote the mean at the $i$th level of one of the fixed factors. With these utopian assumptions, the $\bar y_{i\cdot\cdot}$ are either independent, multivariate normal with a compound-symmetric covariance structure whereby any pair of them has the same correlation $\rho$. It can then be shown that the set of all pairwise pairwise comparisons among the $\bar y_{i\cdot\cdot}$ has the same correlation matrix regardless of the value of $\rho$; and hence that the distribution of the Studentized range holds. Accordingly, the Tukey HSD method is valid as long as the correct standard error estimate is used. The HSD at level $\alpha$ is given by
$$ HSD_{ij} = \frac{q_\alpha(k,\nu)}{\sqrt 2}\cdot SE(\bar y_{i\cdot\cdot} - \bar y_{j\cdot\cdot}) $$
where $q_\alpha(k,\nu)$ is the critical value for the Studentized range, $k$ is the number of different levels $i$, and $\nu$ is the appropriate degrees of freedom for estimating the $SE$. (The tabled value is divided by $\sqrt 2$ because the Studentized range is defined in terms of the SE of one mean rather than the SE of a difference of two of them.) The HSD method protects the overall significance level of the family of comparisons by assuring that in the worst case (comparing the maximum with the minimum), the probability of a type I error is $\alpha$.
In the above formula, the SE is based on a combination of one or more variance components, depending on which ones are involved in the determining the variance of the difference. A between-subjects comparison involves more variances than a within-subjects one. You can't just use the formula shown in a textbook in the context of a one-way ANOVA. Some software can output these standard errors; in other software, it isn't easy to get.
In a more complicated situation such as unbalanced data and fancy covariance structures, the Studentized-range tables no longer apply because the joint distribution of the comparisons is more complicated. However, with appropriate software, an approximate critical value for for $\max(\bar y_{i\cdot\cdot} - \bar y_{j\cdot\cdot})$ can be obtained using the multivariate $t$ distribution with the covariance structure found in the data; then that may be used in place of $\frac{q_\alpha(k,\nu)}{\sqrt 2}$ in the formula.


Ola scripts = log shipping and transaction logs

Question: We use the Ola Hallengren scripts for full/diff/tran log backups.  Ola's site indicates that log shipping is compatible unless we are using transaction logs.  Why is that?
Answer: I believe your answer lies in another answer here on StackExchange.  Transaction log shipping together with backup job = conflict?.

The log shipping process does its work by taking log backups. There
cannot be another job that does the same, it will break the log backup
chain. See Using Log Shipping as Part of a Recovery Plan. Your
recovery strategy should clearly document the location of the log
backups as taken by the log shipping job and detail step-by-step
instructions how to recover the database using these log backups. You
should also test this strategy to validate it.
If you create a maintenance plan (or Ola backup) for a database that is configured as
a log shipping database, do not have the maintenance plan create
transaction log backups. If a maintenance plan and log shipping both
attempt to create transaction log backups of the same database, log
shipping will not function correctly. You can do full and differential
database backups through your maintenance plan (or Ola backup) without any conflict
with log shipping.

According to Ola's Frequently Asked Questions
Does the SQL Server Maintenance Solution support log shipping?

The SQL Server Maintenance Solution supports log shipping. Full and
differential backup, integrity check, and index and statistics
maintenance are performed on the primary database. Transaction log
backups are not performed on databases that are involved in log
shipping.

So, if you implement Log Shipping, just keep in mind that THAT process will be taking your transaction log backups and NOT Ola's process.


A question about aliasing and sampling

Question: Imagine an ADC unit with a sampling rate fs is not used with an anti-aliasing filter and the sampled data is logged. If in FFT of this logged file one sees a suspicious frequency component call it fx, what can we say about the value of the down sampled high frequency component fh which appears as a false fx? Mathematically speaking.
Comment: Welcome to EE.SE! This appears to be a homework question. As such, you need to show us your work so far, and explain which part of the question you're having trouble with. For future reference: Homework questions on EE.SE enjoy/suffer a special treatment. We don't provide complete answers, we only provide hints or Socratic questions, and only when you have demonstrated sufficient effort of your own. Otherwise, we would be doing you a disservice, and getting swamped by homework questions at the same time. See also [here](http://meta.electronics.stackexchange.com/a/5120/7036).
Comment: Has this question been answered to your satisfaction? If not please address this by making a comment under an answer to receive clarification.
Answer: One formula is

fx = |fh - N fs|

or if you prefer

fx = abs(fh - N fs)

where N is whatever integer you need to get a result between 0 and fs.
If fh < fs, then N is 0 and there's no aliasing.  If fs/2 < fh < fs, then N is 1 and you get "folding" of the frequency.
Answer:
If in FFT of this logged file one sees a suspicious frequency
  component call it fx, what can we say about the value of the down
  sampled high frequency component fh which appears as a false fx?

Firstly, if you don't have an adequate anti-alias filter then all you can have are "suspicions".
Secondly, you cannot say it is down-sampled because you have no other reference point. In other words it could be a proper signal in the baseband or it could be an aliased artefact
Thirdly, you cannot say it is a false signal.

The above image shows how two signals at frequencies H1 and H2 are converted into the base band by aliasing (mirror imaging about the nyquist frequency FN). You cannot tell if they are real base band signals or aliased images that were mirrored from above the nyquist frequency.

A question about aliasing and sampling


Selecting secret value in certificateless identity-based encryption

Question: In certificateless identity-based cryptography, selecting secret value $$x_i \in Z_p$$ and declaring public key of individual users such as $$Pub_i=g^{x_i}$$
$g$ is public parameter.
I think there will be some kind of collision in selecting secret value.
In security proof, they make assumption that secret value cannot be allowed to attackers. Is it enough?
Answer:
I think there will be some kind of collision in selecting secret value.

What sort of collision could there be (that has a nontrivial probability of actually happening)?
If $p$ is the order of $g$, then $Pub_i = Pub_j$ only if $x_i = x_j$.  And, if $p$ is large (e.g. at least 256 bits), and we assume that $x_i, x_j$ are selected randomly and independently (that is, no one participant is allowed to peak at any of the other's secret, and they all have good entropy), then the probability of $x_i = x_j$ happening is $< 2^{-256}$, that is, mindboggling unlikely.
In fact, if we have, say 7 billion participants, and each one selects an $x_n$ randomly, the probability of there exists two different participants selecting the same value is $< 2^{-191}$, still mindboggling unlikely.
This does assume that the entropy of each participant is good; something that tends to be ignored in security proofs, but cannot be ignored when implementing the system.

In security proof, they make assumption that secret value cannot be allowed to attackers. Is it enough?

They also assume (and they ought to make it explicit) that the discrete log problem is hard; that is, given the value $g^{x_i}$, it's hard to recover $x_i$.  If the group was small enough that someone would have a nontrivial probability of obtaining $x_i$, by guessing it (and computing $g^{x}$ to verify), well, that'd mean that the discrete log problem would be tractable.
Comment: By $2^{-256}$ you probably mean $2^{-128}$ because of the birthday problem. Also, by *"nontrivial probability"* you probably mean *non-negligible probability*.
Comment: @ArtjomB.: actually, I mean $2^{-256}$; if you have a population of $2^{128}$; then the expected number of internal collisions is approximately 1; however the collision probability for two individuals who each do a single trial is, in fact, $2^{-256}$
Comment: @poncho. How to calculate collision probability in $n$ trials for matching with any one of $m$ user?  Any security weakness for large value of $m$ and $n$?
Comment: @poncho. $\frac{mn}{2^{256}}$?
Comment: @myat: if you have 1 trial with m users, the probability of a collision between any two of those users will be approximately $m^2/2^{257}$ (assuming $m << 2^{128})$.  So, if you have n such trials, then the approximate probability of a collision happening in any of those trials would be about $n m^2 / 2^{257}$.  You can do the math; I believe that for realistic $n, m$ values, this is still negligible.


What is difference apt and snap when I use remove prompt

Question: I have question which is what is the difference apt and snap. I using both of them but there is a small problem between them. I already install chromium-browser software. I want to remove it but when I use "sudo apt remove chromium-browser" it says removed but I can still see chromium software in show application tab and working perfectly. And I already use purge prompt still same. But when I use "sudo snap remove chromium" it says remove and completely removed. Why is this happening?
P.S: I am using Ubuntu 22.04.2
Comment: Not actually. In installition i have no question about it both of them working fine.
Answer: snap and apt ( or deb's) are different packaging systems. Some software is nowadays only availabe as a snap-package but was distributed as deb-package in earlier days. To make the snap installable via apt, so called transitional deb-packages are used.
chromium-browser is such a transitional deb-package, when you install it, it will pull in the snap-package chromium.
When you remove the deb-package chromium-browser it will just remove the transitional deb-package but not the snap-package chromium, thus the application is not uninstalled and still functions properly, if you want to remove the snap you'd have to run snap remove chromium, not snap remove chromium-broser as you wrote in your question, a snap named chromium-broser or even chromium-browser simply does not exist.
~$ snap find chromium
Name                      Version         Publisher        Notes  Summary
chromium                  115.0.5790.102  canonical✓       -      Chromium web browser, open-source version of Chrome
chromium-ffmpeg           0.1             canonical✓       -      FFmpeg codecs (free and proprietary) for use by third-party browser snaps
...
...
...

~$ snap find chromium-broser
No matching snaps for "chromium-broser"

~$ snap find chromium-browser
No matching snaps for "chromium-browser"

~$ apt show chromium-browser | grep Description

WARNING: apt does not have a stable CLI interface. Use with caution in scripts.

Description: Transitional package - chromium-browser -> chromium snap

Comment: I corrected my question as you wrote. Thank you very much for your reply.
Answer: apt is a traditional packet manager. It is meant for all Linux packages. But Snap is meant for Ubuntu at first and other Linux distributions later. Where Snap and apt differ, however, is in how they package software. Snap includes everything required to run an application -- including its dependencies -- in a single package, but apt expects users to deploy dependencies as separate packages alongside the app package.
Comment: So you mean apt promt is remove it some packages (not the critical main software packages) and snap completely?


Why does Moore Finite State Machine need more states than Mealy Finite State Machine?

Question: I was reading about finite state machines. I read about Moore and Mealy machine and also the state representation. I read that in the Moore machine the output depends on the present state only and in the Mealy machine the output depends on input and present state. But I don't understand how this could vary the number of states?
Comment: It's probably best if you set about studying one particular example that has been done up using both methods. But in general, you should be able to see that if you are allowed to combine transitions with states that you can get a higher output-state/machine-state ratio.
Comment: Yes in other words combining the present state with input and transition polarity increases the entropy of information added which both permit more complex but fewer states to realize.
Answer: If you're in state A and input X happens, how do you output Y?
A Moore machine must transition to state B whose sole purpose is to output Y, then back to A.
A Mealy machine can simply transition back to A whilst outputting Y
Thus a Moore machine requires more states. You need at least one state for every combination of outputs your machine requires.
Answer: The more information or Bandwidth there is to determine the next state the fewer states or cycles that are required to complete the entire sequence.
This why DDR2,3,4,5,6,7,8 works faster by using transitions splitting the clock into N phases for parallel operations with N ports combined into 1. Thus the bandwidth is multiplied by the number of inputs added to the present state in this case split into equal phases.
By combining the present state with input you are adding more information and also entropy with the randomness of input states so when added with transitions and polarity of transitions, this extends the bandwidth greatly and allows more complex but fewer Mealy states to realize.
Complexity does not always mean hard to do, it just means more static and dynamic inputs with edge detection logic may be included to reduce the cycle time, latency or registers required.


Human Combustion by Nanites

Question: Nanites would likely generate a lot of heat.  If a large number of nanites infested a human body, multiplied, and began moving / operating what would be the result?  Could the composition of the nanites result in Spontaneous Human Combustion?
Comment: Not really spontaneous if it is caused by reproducing nanites jiggling hotly within the body.  Sort of like spontaneous human combustion caused by many laser beams aimed at the hapless human.  Maybe just "human combustion"?
Comment: The drummer nanites in Stephenson's _The Diamond Age_ did this, from recollection
Comment: @Willke Fair enough.
Comment: What are these nanites doing? Are they designed by humans to perform a task within the human body- if so what?  How do you define "infest"?   Do they hijack DNA to produce copies of themselves or do they have a separate mechanism?  Are they virus-sized, cell-sized? What are their capabilities for movement? What "intelligence" do they have?
Comment: What if each nanite has a sodium molecule inside it's case, could they all just open up and expose all that sodium to water at the same time?
Answer: It is worth remembering that the average human body has something of the order of 1016 energetic, heat-generating intracellular "nanites" in the form of mitochondria.
These can, under the right circumstances, kill the human they're in... one way of doing this is to interfere with various cooling and regulatory mechanisms using suitable pharmaceuticals, causing death by hyperthermia.
This does not actually involve anyone bursting into flames though, as human bodies are pretty soggy and hard to ignite without some pretty weird chemistry being involved. To do it just via heat, without the presence of any other fuels or accelerants or oxidisers or other trickery you must first boil a human to drive off enough water that the stuff left behind is flammable.
If a human weighs 60kg, and they start out at a uniform 36 degrees C (which is obviously inaccurate, but it'll do), and the specific heat capacity of water is 4200 J/kgK, you'd need to impart ~16MJ to raise their body temperature to 100 degrees. You then need to impart another 2260kJ/kg (the latent heat of vapourisation of water) to actually boil the water... that's another 81.4MJ, if you could deliver it only to the water somehow.
So that's about 100MJ, or the energy in 2-3kg of petrol (or gasoline, if you prefer) or more like 10kg of dynamite. A that point you've got to wonder about the energy density of your nanites. How are they getting this much juice? Where do they store it? How do they release enough of it to boil their host without destroying their own pretty delicate structures and chemical processes? Are your nanites actually just antimatter bombs? (they'd need to share about a microgram of the stuff between the entire swarm, FYI)
So, if you want to incinerate a human, either cheating (by releasing chemicals that can cause them to burn whilst wet) or by using external fuels or explosives to do the job. Trying to do it with heat generated inside their body alone seems like a bit too much like implausibly hard work.
On the other hand, generating enough heat to cause serious or fatal hyperthermia seems pretty straightforward, and an entirely reasonable side effect of various kinds of nanomechanism or cybernetic implant.
Comment: Another common chemical that induces a sixth type of hyperthermia - uncoupled phosphorylation - is 2,4-dinitrophenol or DNP, sometimes used for weight loss, with the side effect of death by malignant hyperthermia. Rather than interfering with thermoregulation, uncoupling proteins work by short-circuiting ATP energy into heat rather than any useful cellular work.
Answer: In classical.SciFi and fantasy, nanites are very very small indeed. If there are millions in a body, they need to be. If there are billions, they need to be even smaller (like a lot smaller).  So you're discussing an item of tech probably similar size to a human cell, or a very few of them,or maybe even smaller (they need to be able to interact with individual nerves, cross the blood-brain barrier or whatever).
If they are that small, I don't see a reason why we can't handwave them a power consumption similar to a human cell, in which case they won't make much impact on the body's heat output, beyond what ordinary cells could do. The body will regulate its core temperature exactly as it usually does, and compensate.
It would be a very poorly designed nanite which caused its host to quickly die.
Comment: A nanite would be of the order of a large molecule $10^{-9}$ m, hence the name nanobot
Comment: @nzaman in your dream, less than 1000 atoms is not enough
Comment: The smaller it is, the less energy used. A "large molecule" would only need energy consumption of the order of a large molecule.  And yes, that small is tricky for a functional machine.
Comment: @MolbOrg:Huh? What are you saying?
Comment: @nzaman - from wiki - "More specifically, nanorobotics (as opposed to microrobotics) refers to the nanotechnology engineering discipline of designing and building nanorobots, with devices ranging in size from 0.1 to 10 micrometres and constructed of nanoscale or molecular components." - components are nanoscale, not the thing is nanoscale

Human Combustion by Nanites


Should I continue my classical study (avoiding parallel 5ths and octaves)

Question: I just want to make pop tunes but I do take my hobbie seriously.
Do the Beatles, Led Zeppelin, Rolling Stones, Stevie wonder avoid parallel 5ths/octaves? Have any of you studied their sheet music and actually seen parallel 5ths/octaves or no?
I just don't know if I should continue my classical studies if my favorite musicians don't even follow that.
Comment: You are missing the point of what voice leading is. Music theory doesn't just say avoid parallel 5ths/octaves. Something like power chords is not the same as voice leading. Voice leading comes up when there are multiple melodies. Think the strings in _Yesterday_ by the Beatles and the choir in Bohemian Rhapsody.
Comment: Not an answer, but a side point: Many of these artists explored, experienced, and allowed themselves to be influenced by diverse musical genres outside the ones they worked in. I think you'll agree that "late Beatles" is very different than early Beatles. Nothing against early Beatles, but I'm not sure they'd be legends today if they turned out the same product for decades.
Comment: @Dom are you saying there are no parallel fifths in the Yesterday string quartet or the Bohemian Rhapsody chorus?
Comment: @phoog not none, but they do have parts of independence that would be closer to voice leading than power chords.
Comment: @Dom I'd say that's true of Yesterday.  Bohemian Rhapsody's parallel close harmony strikes me as rather closer to power cords.
Answer: The "classical" voice leading stuff you are thinking of - avoiding parallel fifths and octaves, etc. - is classical music's link to the old Church style and counterpoint. When that historic link to the Church begins to break - like with Liszt, Debussy, and other composers - the parallel fifths/octaves concern is thrown out. Parallel harmony becomes a hallmark of Impressionism and Modernism.
I wanted to make that point so we don't overstate things about "classical" music and voice leading rules.

...Do the Beatles, Led Zeppelin, Rolling Stones, Stevie wonder avoid parallel 5ths/octaves?

I would say: no, not in the sense of the old counterpoint style in classical music.
But, you can get to some of the same voice lead via a different path. Consider that in pop/rock the bass often moves by chord root and root progressions of fourths and fifths, while melodies and upper voices often move step-wise. When you do that, the voice leading will often result in something acceptable by "classical" standards.
Here is an example (Play With Fire by the Rolling Stones, sorry for the poor image quality...)

If you look at the outer voice, the bass and melody, the intervals are P1 P5 M3 P8 P5, or unison, perfect fifth, major third, perfect octave, perfect fifth. Motion to the perfect intervals is by contrary motion. I'd wager Jagger and Richards were not thinking of Fux and counterpoint, but rather playing common guitar chords and singing scale steps, because those are basic materials for guitarists and singers.
But, rock music does something else very, very often: combine common chord progressions with pentatonic melody. Here is an example (Pour Some Sugar on Me by Def Leppard)...

Notice the passage at "sugar on me..." over chords A to B. You could look at the melody E4 moving to F#4 with bass A to B and say "a-ha! parallel perfect fifths", or possibly you might consider the G#4 above bass A as the main melody tone for purposes of voice leading analysis and say G#4 consonant with chord E held as dissonance over chord A resolves down by step to F#4 consonant chord B and moving by contrary motion.
But, all that is very tedious, and not likely how the music was created. The chords E, A, B especially as power chords are just the most elementary I IV V progression in E major that guitarists can play in their sleep. Meanwhile the entire melody of the chorus is derived from the E pentatonic major scale, with a major emphasis on two important segments MI RE DO and alternating between DO and the LA below (those are the solfege syllables.) Those kinds of pentatonic scale segments are very "resonant", easy to sing, the stuff of nursery rhyme songs (but with rock rhythms and quite different lyrics.)
The point is rather than looking at the accompaniment and melody in terms of voice leading, look at it as two different parts that are essentially playing around an E major tonic. When you do that with simple elements like chords I IV V and a melody that moves about MI RE DO it will "work" without a lot of concern for technicalities like voice leading or momentary dissonances. As long as some of the important phrasing points, like the end of lines, have chord and melody match up consonantly things should work.
If you want to look at this in terms of part writing, you should look at pitch and rhythm, and ask to what extent the bass and melody are independent. IMO, the pitch aspect should be reduced to something like this...

...which removes the rhythmic details allowing us to see that in terms of pitch the bass and melody are independent. The fact that there is a momentary parallel perfect fifth movement make no meaningful impact on the basic independence of pitches.
In terms of rhythm the notation doesn't show the bass, but in the recording it's playing roots in repeated eight notes on beats 1 and 3 while resting beats 2 and 4, which is clearly independent of the melody's rhythm.
So, in music like this we may see things that conform to "classical" voice leading, and sometimes not, but that is incidental to the way the parts are really handled. The various parts play in the same tonality, but with a primary concern on rhythmic independence, and a somewhat lesser concern with pitch independence than comes incidentally when bass moves by roots and melodies move in scale steps.

I just don't know if I should continue my classical studies if my favorite musicians don't even follow that.

Music theory is not classical studies. I say study theory and then apply it in ways appropriate for the styles you want to analyze. If you like classical music, keep analyzing it. If you like rock music, analyze it too. But don't treat misapply theory like a Procrustean bed and compare rock music to Church counterpoint. Analyze  it on it's own terms.
Two things to look up are the article Temperley, The Harmonic/Melodic Divorce in Rock Music and the chromatic minor system in Stephenson, What to Listen for in Rock for ideas about how scholars use theory to analyze rock music.
Answer: Yes, keep up your studies. While you may not use some things directly, the principles can be useful. As mentioned in Dom's comments, parallel fifths and octaves are avoided in order to keep musical lines independent. Should such independence not be needed, the "rule" isn't applicable.
A couple of "pop" examples of independent voices would be two singers singing in harmony or the melody of a song and its bass line. Parallels in this case give the appearance of one voice dropping out. Thus one hears close harmony sung in thirds or sixths. Likewise, the bass one doesn't duplicate the singer.
The accompaniment (rhythm guitar, keyboard, etc.) doesn't need such independence in general (though too many parallels in the harmony can sound thin.) I like to think of songs as having three (or four) "logical" parts. There's a melody (or harmonized melody) on top; harmonized melodies do follow theory pretty closely. There's the chord stuff in the middle which provides harmonic support to the melody; between these instruments (even in classical pieces), independence of line isn't that important. There's also the bass line which provides the support for the entire structure; the bass line does avoid parallels with the melody. There's also the rhythm (drums) section which doesn't enter directly into the harmony.
There's also the possibility of doubling a voice that doesn't behave like parallels; it only thickens or enriches the doubled voice.
Answer:
Should I continue my classical study (avoiding parallel 5ths and octaves)

Avoiding parallel 5ths and octaves is useful for keeping the number of apparent independent voices constant. It is a genre-independent, even physical and biological, phenomenon that has nothing to do with pop vs classical.
If you do not CARE about keeping the number of apparent voices the same, then you don't need to avoid parallel 5ths and octaves.
Why would you want to avoid parallel octaves or fifths?
If you have two voices that are stepping up or down by different pitch steps, their sounds are perceived as coming from two different actors, objects, animals, enemies, whatever it is that your ear imagines it's tracking. But if they start moving up or down by exactly locked octaves or 5ths, they appear as one single actor, object, animal, enemy, whatever your ear is tracking. It's a biological phenomenon about how hearing and object-tracking works.
Imagine a hunter on savanna, listening to sounds - is there one, two, three or more animals or enemies? If the voices move so that their sounds are not locked in constant octave/5th relationship (maybe even other intervals apply as long as the frequency ratio is kept constant), your ear tracks them as separate entities. Your ear is answering the question: "how many lions are there". And this phenomenon is why you try to avoid parallel octaves and fifths. That is, IF you want your four-voice piece to make it sound like there are four lions all the time. If you allow parallel octaves or fifths, then during that motion there are only three lions. If ALL voices move locked in perfect unison/octaves/whatever, then there appears to be only ONE, very BIG lion. Do you want that? Sometimes you do want that effect.
The same "how many independent objects are making the sounds" tracking effect applies to all sound regardless of genre. It works in Western pop, classical, jazz, folk, Indian, Japanese, African, ALL sorts of music, and even all sorts of SOUND, even if it's not music at all.
I find it a constant display of the failure of the traditional classical music education culture that this "parallel octaves are magical evil but only in Classical land" superstition keeps being taught as a religious belief without explaining WHY the parallel steps should be avoided. Theory-first music teaching as lists of rules is dumb and it should have stopped a hundred years ago. This thing keeps being asked about on music.stackechange over and over and over again, and nothing helps. The same with minor tonality, scales and keys.
Answer: Pop music does not adhere strictly to the common practice era rules of voice leading. A very clear example is power chords, which are exactly parallel fifths.
Having a solid knowledge of classical theory will certainly illuminate many aspects of pop music, and it is often consistent with "the rules", but pop music is much looser in its approach to voice leading and key relationships.
Comment: Comparing power chords to voice leading is like comparing a jet engine to a bridge. Both have functions, but trying to do the same thing with them doesn't make sense. Pop music follows typical harmonies and cadences and when polyphony does happen, it does typically follow the basic principles of voice leading.
Comment: @Dom Although the prohibition of parallel fifths and octaves emerges from the maintenance of independent voices, it is not restricted to that realm, and is generally present — in classical music, but not pop — in how harmonies progress. The sound of parallel fifths and octaves is jarringly stark when one is accustomed to music in which they are avoided. This is part of the reason power chords have so much power, and why people who like metal also often like early music, when parallels were the norm.
Comment: Ok I'm not interested in power chords. If you gave the Beatles or Stevie wonder the standard chord progression (I IV V I) would they avoid parallel 5ths/octaves? I think dom answered my question
Comment: @GordonO Power chords are just an example of the more general statement: pop does not strictly adhere to the classical rules of harmony and voice leading. Continuing your studies will allow for insights into the Beatles and Stevie Wonder, but it is not essential to it.
Comment: @Aaron that's an oversimplification unless you are only looking at chorals and fugues(even fugues sometimes take breaks from it to in some voices btw) which are polyphonic by default. Classical music tends to have more polyphonic texture, but there are all flavors of textures in classical music. Likewise, while there were not literal chord progression modern harmony is heavily based in classical tonal ideas. There are a lot of differences, but harmony has major overlaps from classical to pop.
Comment: @Dom Your comment sounds like a restatement of exactly what I'm saying. Where do you find the disagreement?
Comment: @GordonO even 19th century piano composers write parallel fifths.  If Brahms would write parallel fifths in a I-IV-V progression, should we think less of Stevie Wonder for doing so?
Answer: My answer is a counter-question: Why do you want avoid parallels?
Make your music sound interesting by using both effects!
Before this rule in western music came up we had only voices in unison and parallels. One main reason for the rule was to be revolutionary opposite to earlier style.
Mind that an overdoses of polyphonic music may become boring too!
Finally: Many 20th century composers applied parallels to get their special effects.


Should we close the question, "I love a girl and I want to marry her, but my family refuses her" (11200)?

Question: Should the question Do I need to obey my family regarding who to marry and who not to marry? be closed for being primarily opinion-based?
Answer: No, it's picked up a useful and interesting answer, and that can be to the benefit of the site if the question is edited to make it primarily about the Islam-related issues in the answer.
I will suggest an edit and maybe others who understand better will improve on what I do.
Comment: [(Discussion in chat.)](http://chat.stackexchange.com/transcript/message/17879802#17879802)
Answer: Should the question be closed, yes.  Should it be closed as primarily opinion-based, no.  The question should instead be closed as Off-Topic (Islam SE: Not an Muslim Peer Support Group).
The question itself is good and very relevant to the subject of Islam, but not everything about the subject of Islam can fit on this site or the SE module.  I do see a good question in it around the subjects of marriage, rights, and family, but as it is now it cannot be salvaged without changing the whole question.
As i see it, the person is unhappy with his family and seeking support, which this site is not for, but should go to local scholars or Imam.  And because this site isn't a support group, the question in my view should be closed as Off-Topic.
Answer: Yes, this question should be closed for being primarily opinion-based. It question is ask nothing in relevant to the subject of Islam.
On a related note I found this answer to have some reasonable and worth having around advices/principles (be it under this question or some other on created in order to accommodate this answer).


Vibration when stopped or on brake

Question: My  car is a 2017 Hyundai Elantra with 49745 miles on it. At times when I brake or slow down to brake at lights it vibrates and rumbles. What does it mean? I bought this car last April 2018 from Enterprise Car Sales.
Comment: Your car should have an OBD port. It would be useful to know what error codes are displayed. Your local auto parts store may well read the codes for free.
Comment: Does the vibration occur while the car is still moving forward, or after it has come to a stop? If while still moving forward, the cause is likely to be found in a worn, damaged, or excessive run-out brake disk or disks.
Comment: What vibrates?  Does the steering wheel feel like it is vibrating?  Does it only happen when you apply the brakes, or also when you let off the gas.  Or does it seem like an engine sound?  And is it in sync with your speed?  Slower vibration at slower speed, etc.
Answer: That just recently happened to my 2014 Chevy Sonic, turned out that it was a faulty O2 sensor that was making the computer add to much gas into the engine. I'd suggest getting it checked soon, I waited too long and had to rebuild my engine.

Vibration when stopped or on brake


In OpenVMS, how can I see where a command is coming from - like "which" in NIX

Question: If I have a command dosomething in OpenVMS, where can I see where it is coming from (Location of script/exe - how it is defined if it is a different kind of animal)
Answer: $SHOW PROCESS/ALL
$SHOW ENTRY
$SHOW ENTRY/FULL
Comment: Don't think that is OpenVMS
Comment: Wow, this is my epic inattention. Correct.
Answer: There exists three DCL "sources" of, as you say, "coming from" something command like.
One warning: syntaxes with visible explicit DCL enforcement, like:
$'dosomething'

are not counted here, only the "visible like command" ones.
Also explicit RUN or MCR commands are commands themselves, then run dosomething are out of interest.
How to check

Symbols
Function: like un*x alias or as "run a program with parameters", nearly like the MCR dosomething.
Do a:
$ show symbol dosomething

Symbols are "first use" (if used, then has priority over next steps)
True DCL command
There no build in utility to check the command table.
However you can setup a freeware VERB utility.
Then do a:
$ verb dosomething

The "image" and "cliroutine" (in VERB output) shows the .EXE or internal DCL routine where runs the command.
Path usage
Do a:
$ directory DCL$PATCH:dosomething

If a .COM or .EXE file exists, the command procedure runs nearly like after @DCL$PATH:dosomething or image of code runs like mcr DCL$PATH:dosomething.
Path usage is a "last chance" one (only if symbol does not exist or not used and true DCL command does not exist also)
"Nearly" in all description above because there are minor syntax interpretation difference, mostly irrelevant.

Some additional explanation

If exists a symbol with name matching your "command", the content of symbol may be translated in two ways:

if the content begins with "$", the use is named "foreign command" and runs image (.EXE file) of rest of content, up to separator (parameter can be applied nearly like in alias); warning: the default directory of specified .EXE is SYS$SYSTEM:, not the default of process!
in all other cases the value may function like un*x alias.

Value of symbol is "inlined" to the command line, and the substituted text is interpreted as ("new") command.
The word "may" applies regarding of the SET SYMBOL setting (check
HELP SET SYMBOL for VERB description).
Be aware, that alias further explains to other real dcl syntax (true command, explicite "@" for procedure or "invisible" DCL$PATH use), but not to next symbol (alias or foreign command).
It it strongly not recommended to substitute any true DCL command with aliases, DO NOT this!
True command are set with the SET COMMAND command (obvious), the executable (.EXE image or internal DCL routine) names are not related in other way to the command name, even if most command has adequate names (the DIRECTORY command runs a SYS$SYSTEM:DIRECTORY.EXE etc, but APPEND runs COPY.EXE and HELP runs VMSHELP.EXE etc)
Path is used like in un*x, but:

Only after the true commands table is checked (of course, also after the alias symbol use, but this is "un*x like")
The images intended for true command usage in most cases can not be used this way (exists somewhere runs with different syntax, example: INSTALL)
Answer: Dont think it works exactly that way in OpenVMS and there's no foolproof way afaik.
For DCL show, most of the qualifiers would end up in SYS$SYSTEM:SHOW.EXE but without the MAP file there would be no way to figure out which source module actually went into this executable. DCL is not like Bash where it will fork-exec another process and load the image of that command.


How can I wrap text around a 2 sided object in Photoshop or Illustrator?

Question: I want to wrap a word around a 2 sided shape (as shown in the image below). Envelope distort, wrap text, perspective tool etc. all not the correct solution (or at least, I can't get the result I'm looking for). How can I do this in Photoshop or Illustrator?
Answer: There is a very simple sttrategy.

Cut your text into 2 pieces:

in illustrator make text, expand, cut via pathfinder or line and divide below.
in Photoshop duplicate text and mask the other half.

Shear and scale across the cut line.

Image 1: Quick and dirty test, could be done better.
Alternate ideas. This can be done with illustrators extrude tool in illustrator just slice your text and assign it as texture to sides of your extrude.
Also this can be done, quite close, with Envelope distort trick is to rotate the text before envelope. Unfortunately envelope distort will not be sharp at the border, but opens up possibilities for images.

Image 2: Similar more carefully done envelope distort.
Comment: In Photoshop you could draw grids in Vanishing point tool and then in the top left corner choose `Render grids to Photoshop`. It could help with the manual tweaking. I would also recommend making the text a Smart Object beforehand. You can copy&paste pictures to the Vanishing point tool and they will conform to the grid, but you'll be better off doing it a bit more manually, so that you can use Smart objects.
Answer: For any shape you can create with Illustrator's limited 3D tools, this is relatively easy. I'll take a cube as an example:

Create and lay-out your text;
Drag your text object into the Symbols palette (Window > Symbols) to make a new symbol out of it;
Draw a square with no stroke;
With the square selected, choose Effect > 3D > Extrude & Bevel;
Switch on 'preview' in the dialogue box and experiment with rotation values and extrusion depth to create the orientation of the cube you need;
Click Map Art...;
Choose your new symbol with your text as the symbol to be used and drag it in place on two adjacent faces. You can choose what face your symbol is mapped to with the 'surface' field;
Click OK in both dialogues to commit your effect.

You might want to Object > Expand Appearance to be able to edit the result and fine-tune placements.


Rav Chaim Volozhiner and Nittelnacht

Question: In discussing the minhagim of Nittelnacht with a few people, I was told that Rav Chaim Volozhin "abolished" Nittelnacht. I don't know why Chaim Volozhiner would have any shaychis to Nittelnacht at all, that he would have to "abolish" it, but does anyone know of any sources that discuss Rav Chaim Volozhiner's dealing with Nittelnacht?
Comment: related http://judaism.stackexchange.com/q/79063/759
Answer: he held that someone must be learning torah 24/7 or else world would cease to be. unless he held that it only goes from shkia until chatzos (in which case the 8.5 hour time difference between the u.s. east coast and iran would take care of it), as opposed to chatzos yom of erev christmas to chatzos layla, advocating that everyone should observe nittelnacht would be advocating that there be a time that the world stop learning. however, perhaps he only held that it should be observed in places with a christian population, which many sefardic lands do/did not.
(or it was no longer dangerous to go to the beis in his time/if he abolished not learning entirely it was probably b/c he felt it was a minhag shdus which possibly gives credence to avoda zara)
Comment: Welcome to MY. Since MY is different from other sites you might be used to, see [here](https://judaism.meta.stackexchange.com/a/3887/11501) for a guide which might help understand the site. Please consider [registering](//judaism.stackexchange.com/users/signup-unregistered) your account, to [enable](//meta.stackexchange.com/questions/44557/why-should-i-register-my-account) more site features, including voting.
Hope to see you around!
Comment: Welcome! This seems more like conjecture about what he may have held. Perhaps a summary of this would make for good comments, but I don't think it makes for the best answer. When you earn 50 rep. You will be able to comment on others'-posts. Hopefully this doesn't discourage you from further contributing to the site in the future.

Rav Chaim Volozhiner and Nittelnacht


How do you find the Lie algebra of a Lie group (in practice)?

Question: Given a Lie group, how are you meant to find its Lie algebra?  The Lie algebra of a Lie group is the set of all the left invariant vector fields, but how would you determine them?  My group is the set of all affine maps $x \rightarrow A.x+v$ from $R^n$ to $R^n$ under function composition.
Comment: Embed your group into GL_n and see if you can figure out what elements of gl_n exponentiate into it.
Comment: @Qiaochu Yuan, you mean in GL_n+1 with each map as {A x, 0 1} where 0 is a row of n zeros?
Comment: Sorry, I didn't intend the two values of n to be the same.
Comment: Please consult the wonderful book on Matrix Lie Groups/Algebra's by [Brian Hall](http://books.google.com/books?id=m1VQi8HmEwcC&printsec=frontcover&dq=brian+c+hall&hl=en&ei=KgtYTdXOGdTHtwfa-_jlDA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC8Q6AEwAA#v=onepage&q&f=false)
Answer: Here a worked out example:
What is the Lie algebra of the group of rotations in 3-dimensional space, $SO(3)$?
Matrices $A\in SO(3)$ are defined by the property that they are invertible and that the scalar product is invariant $\langle A\vec x,A\vec y\rangle = \langle \vec x,\vec y\rangle$ for all vectors $\vec x,\vec y\in \mathbb R^3$. Expanding the latter condition into coordinates, you can see it is equivalent to $A^TA = I$.
To find the Lie algebra, take a smooth path $A(t)$ with $A(0) = I$. In first order, it can be written as
$$A(t) = I + t·H + \mathcal O(t^2) .$$
Plugging this into the condition $A^TA=I$, we get in first order
$$I = (I+t·H)^T(I+t·H) = I + t·(H^T + H) .$$
Hence, the condition on the tanget vector $H$ is that it is antisymmetric
$$ H^T = -H .$$
In other words, the Lie algebra of the rotation group $SO(3)$ consists of antisymmetric 3x3 matrices, which must have the form
$$ H = \begin{pmatrix}0 & -\omega_3 & \omega_2 \\ \omega_3 & 0 & -\omega_1 \\ -\omega_2 & \omega_1 & 0\end{pmatrix} .$$
It is not difficult to show that exponentiating any such matrix will yield an element that preserves the scalar product. Hence, this is the whole Lie algebra.
By the way, the elements of the Lie algebra $so(3)$ are usually represented by the angular velocity $\vec\omega=(\omega_1,\omega_2,\omega_3)$ such that multiplication becomes the cross product
$$ H·\vec x = \vec\omega \times \vec x .$$

A similar method applies to your original problem. For instance, you can embed affine transformations of $\mathbb R^n$ into $GL_{n+1}(\mathbb R)$ by
$$ (x \mapsto Ax + v) \iff \begin{pmatrix} A & v \\ 0 & 1 \end{pmatrix} \in GL_{n+1}(\mathbb R).$$
You can express this as an algebraic condition: a matrix $B\in GL_{n+1}(\mathbb R)$ represents an affine mapping of $\mathbb R^n$ if and only if
$$ (0,0,…,1)·B = (0,0,…,1) .$$
This will induce an equation for the first derivative of a path $B(t)$ and as above, you will obtain the Lie algebra as a set of matrices.
Comment: @HaukeStrasdat: Sure. Basically you just differentiate with respect to $t$ at the point $t=0$. In other words, you calculate $\frac{d}{dt}|_{t=0} A(t)^TA(t) = H^T+H$ where $H=\frac{d}{dt}_{t=0}A(t)$. The expression "first order" refers to "first order in the Taylor expansion". In other words, the formula $A(t) = I + tH + \mathcal O(t^2)$ is just the Taylor expansion of $A(t)$ "up to first order". Admittedly, this kind of language takes a while to get used to, but it's very intuitive once you get the hang of it.
Comment: @HaukeStrasdat: Yes, you set $t=0$ *after* differentiation. In practice, one often keeps the $t$ around *before* differentiation and says that the expression is "to first order in $t$", which means that one silently drops all terms $t^n$ where $n>1$. This has the same effect as differentiating at $t=0$, but this way of thinking is very useful if you are interested in the higher-order terms.
Comment: Okay this makes sense but my example doesn't have the extra condition of A^t.A = I.  So does that mean that all H are acceptable?  That conflicts with Theo's answer.
Comment: @Zeophlite: There's no conflict. You should consider smooth paths $\gamma: (-\varepsilon,\varepsilon) \to \operatorname{Mat}_{n \times n}(\mathbb{R})$ such that $\gamma(t) \in G$ for all $t$, $\gamma(0) = I$ and then take $\dot{\gamma}(0)$. In your example and the notation I use in my answer, you can take $\gamma(t) = \begin{pmatrix} \exp(Xt) & ty \\\ 0 & 1 \end{pmatrix}$.
Comment: I added some information on your particular example, though I am reluctant to present the solution in full.
Comment: @GregGraviton: Could you explain your "first order" argument in more detail. Do you mean by first order the first two terms of the matrix exponential? Why can you ignore the higher-order terms when you differentiate $A^TA$?
Comment: Just to check that I got it right: Is your argument that all higher terms vanishes because of $t=0$? Thus for $A(t)=I +tH+t^2M+{\cal O}(3)$ we have $\frac{\partial}{\partial t}A(t)|_{t=0} = H + 2tM + ... |_{t=0} = H + 0M +... = H$. Or am I on the wrong track?
Comment: How to show $A\in SO(3)\Rightarrow A^TA = I$ , and  exponentiating $H$ will yield an element that preserves the scalar product ?
Answer: To expand Qiaochu's comment: Your $G$ can be seen as the (closed) subgroup of $\operatorname{GL}_{n+1}(\mathbb{R})$ given by the matrices of the form
$$\begin{pmatrix} A & v \\\ 0 & 1 \end{pmatrix}$$ with the usual group multiplication and acting on the affine subspace of vectors of the form $\begin{pmatrix} x \\\ 1 \end{pmatrix}$. If you understand why $\mathfrak{gl}_{n}(\mathbb{R}) = \operatorname{Mat}_{n}(\mathbb{R})$ with the commutator bracket $[X,Y] = XY - YX$ then you should have no difficulty in proving that $\mathfrak{g} = \operatorname{Lie} G$ is given by the matrices of the form $\begin{pmatrix} X & y \\\ 0 & 0 \end{pmatrix}$ with the commutator bracket.
For me, the easiest way to determine the Lie algebra of a matrix group is to think of it as the tangent space at the identity, constructed by tangent vectors of paths through the identity.
Comment: @Zeophlite: Really? Well, $\operatorname{GL}_{n}(\mathbb{R}) = \det^{-1}(\mathbb{R} \smallsetminus \{0\})$ is an open subset of $\operatorname{Mat}_{n}(\mathbb{R})$, hence its tangent space at the identity is all of it. Probably the easiest way to identify the Lie bracket $[X,Y]$ explicitly with the commutator bracket is to use the definition for vector fields applied to the special paths $\exp(tX)$ and $\exp(tY)$, where $\exp$ is the matrix exponential.
Comment: All my text books skip the reason or proof why gln(R)=Matn(R)
Comment: I think I've seen that argument before, but I don't understand it (A open subset of B :. $T_{e}A$ = B).  What do you mean by "special" vector fields?
Comment: @Zeophlite: I meant "special paths", sorry. An open subset $U$ of $\mathbb{R}^{n}$ is a manifold for trivial reasons. The tangent space at a point $p \in U$ is $\mathbb{R}^{n}$ because the paths $p + tx$ where $x \in \mathbb{R}^{n}$ are inside $U$ for $t$ small enough.
Answer: Like Qiaochu says, thinking of this as a matrix group is a good first step. Then you need to find one-parameter smooth paths $A(t)$ through the unit element $I$ corresponding to every tangent direction, where $A(0)=I$. Taking the derivative of these smooth paths at $0$ yields a basis for the Lie algebra.
Comment: Yes, my A is different. Oops for using confusing notation. We are using here the fact that the tangent space at $I$ is in 1-1 correspondence with left-invariant vector fields, and the fact that we are embedded in GL means that the Lie bracket of vector fields will correspond to the associative bracket of matrices: $[X,Y]=XY-YX$.
Comment: Correct me if I'm wrong, but When you say A(t), you aren't refering to my A above (as in A.x+v) but to a map A:t->GL_n+1, right?  The identity of the affine maps is A=I, v=0, which is when embedded in GL_n+1 is I_n+1.  Then a path A(t) = I_n+1 + t*X where X is an element of my embedding.  Assuming that's correct, now what do I do?  The derivative at t=0 is X.  Don't I need to find the left invariant vector fields?


Real world applications of topological & symbolic dynamical systems and ergodic theory?

Question: I have no background in any of these areas and was wondering whether these topics have any significant applications in applied mathematics and/or probability/statistics? From what I've read it seems ergodic theory has some application to statistical mechanics and thermodynamics? Are there other specific concrete examples and areas in applications where these areas in maths are used?
Answer: One key application of topological/symbolic dynamics is to formally analyze the presence of chaos in a dynamical system. The key idea is this:

Describe trajectories in the dynamical system using sequences of symbols.
Determine all the symbol sequences associated with admissible trajectories.
Most of the time, if any symbol sequence is an admissible trajectory, then chaos is present in the system.

This process, and its associated ideas like the  Smale horseshoe, is basically the only way we can formally diagnose chaos in a system. That being said, topological/symbolic dynamics is an extremely powerful and general tool for making statements about qualitative properties of dynamical systems.
Ergodic theory is very closely related, and has key applications in understanding the behavior of many-body systems (i.e. what collective features should we expect given the physics associated with each individual constituent?)
At the risk of self-promotion, I'll mention that these topics don't just have to be applied to abstract mathematical problems—I recently published a paper using symbolic dynamics to discern the behavior of particles in peculiar microfluidic channels.


Hanuman God's birth history

Question: In Shiva Puran according to some sources it is narrated that Parvati and Shiva has had carnal relation through which Hanuman God was born in the form of Vanara and after that, not wishing to carrying his foetus to her womb, Goddess Parvati offered Him to Vayu Wind God.
This one version does not find compatible narrations in some other puranas and spiritual texts related to the life of God Hanuman.
In the Hanuman Chalisa it is understandable - among the qualities of the God in the first 6 shlokas - that He is the son of the Wind God (Vayu) and a partial aavatar of God Shiva.
I am asking if what I have found about the history of the birth of God Hanuman is correct and eventually to receive some more source of knowledge about this topic.
Answer: Sri Shiva Purana 3.20.:

Nandīśvara said:—

O sage, henceforth listen lovingly to the story of Hanūmat, how Śiva performed excellent sports in that form.

Out of love, Lord Śiva rendered great help to Rāma. O brahmin, listen to the whole of that story which is pleasing to all.

Once lord Śiva of wonderful sports saw Viṣṇu in the form of an enchantress (mohinī) with glittering qualities.

As if hit by the arrows of Cupid, Śiva let fall his semen dislodged from its seat, for Rāma's work.

Eagerly urged by him mentally for Rāma's work, the seven celestial sages retained that semen in a leaf.

For Rāma's work that semen was poured through the ears of Añjanī, the daughter of Gautama, by those sages.

In due course Śiva was born of it in the form of a monkey named Hanūmat. He had great strength and exploit.

So, Actually,  Shiva Purana itself not mentioned Hauman's birth between  Shiva-Parvati's union. However, it is mentioned that Lord Hanuman's birth after Bhagawan Shiva saw Lord Vishnu's Mohini incarnation, which was again the form of Mata Tripura Sundari herself.
Sri Brahmanda Purana.: Lalitopakhyana.: 2:04 & 8.:

"Meanwhile, Vishnu began to meditate on Sri Lalita Mahatripurasundari, who was his very own Self."
"By completely identifying himself with Maheshwari, Vishnu manifested himself in her form (as Vishwa Mohini)."

I hope this clarifies all your queries. Prd..

Hanuman God's birth history


Example of a locally trivial semigroup

Question: I was having a look at the block product principle for finite monoids. I wanted to see the derivation of LTT = Acom$*$LI, using an example. But I can't come up with a non-trivial example of a monoid in LI. Any help is appreciated.
Answer: There is no nontrivial monoid in LI. LI is actually a (pseudo)-variety of finite semigroups: it is the class of finite semigroups $S$ such that, for every idempotent $e \in S$, $eSe = e$. If $S$ is a monoid, you can take $e = 1$, the identity of the monoid and get $S = 1S1 = 1$ so the monoid has to be trivial.
Comment: Thanks! I had noticed my mistake. Also, just out of curiosity, is there an extension of block product principle for other classes of semigroups and simultaneously for larger classes of logic?

P.S. I still can't believe I was answered by J.E. Pin!
Comment: Well, if you are satisfied with the answer, don't forget you have the possibility to accept it. About your P.S., you should ask a separate question, but perhaps on math.stackexchange, since it looks like a purely mathematical question.
Comment: Oh I didn't know how to accept the solution. I am fairly new to using stackexchange... And yes, I shall first think about it a bit more before asking it officially.

Example of a locally trivial semigroup


Which outlet box should I use for an unfinished basement?

Question: I want to install a 15-amp AC receptacle in my basement between the ceiling joists.  The basement's not finished so there's plenty of room to play around.  Should I be installing a "new work" new plastic outlet box or a steel one?
Answer: Unless you're using armored (BX, or metal-sheathed) wire, you can use either type box, your preference really. If you use BX, you need to use a metal junction box.
There's a couple different types of boxes. The plastic ones with nails on them, and the metal ones with clips are designed to mount with their face 1/2" farther out than the front, which facilitates having them flush with 1/2" drywall when you finish it.
There's also a type of metal box that's more rounded, with several knock-outs in it (and many types of equivalent plastic boxes) which are not designed for going behind drywall, and look a bit better when you actually do see them (if you care).
Even if it's unfinished, you still need to put a cover plate on. The metal cover plates fit nicely over the rounded metal junction boxes, which makes them much less likely to crack if you hit them accidentally. Regular plastic covers can crack easily because they extend a far ways beyond the edge of the box.
It really comes down to personal preference on metal vs plastic, and then a question of if you will be drywalling, and intend this outlet to be available through the drywall. Also note, it's illegal to cover a junction with drywall: all boxes must be accessible. If you do put drywall up, you either have to remove this box, or have an outlet or blank faceplate on your ceiling.
Comment: BTW, the rounded metal box greg described is commonly called a "handy" box.  Perfect for you application. Don't forget to get some romex connectors to go in the knockouts!
Comment: Thanks, that's very informative.  I had planned to use just regular romex non-metallic wire.  I kind of like the look and feel of the metal boxes so I might go with that.  Tangential question: when would one use armored wire like you describe?  I have some of it in my basement but it seem like only on old stuff.
Comment: One would use armored cable back in 1950!!!
Comment: In a residential situation, you generally don't use BX. It's required in many commercial applications (in particular, you're not allowed to have exposed NM wire: so it must be in conduit or be BX), or if you're running through a wall with metal studs. I would personally use it if I had exposed wiring on a wall in a workshop or garage (though I'm equally likely to use  NM in PVC conduit - depends on the situation, what's already there, and what I have on hand). In your situation, in the ceiling, I'd stick with NM.
Answer: With NM wire, I'd go new-work plastic myself, I find them easier to work with.
The metal boxes must be wired to the ground wire, and they need inserts for the knock-outs to keep the NM cable from possibly being cut by the sharp edges of the knock-out holes. With plastic, neither of these is a concern.
Also, remember that if you plan on finishing the ceiling, mount the box so it will be eventually flush with the drywall, not flush with the joists.
It's not related directly to your query, but don't forget to use a GFCI! It's required by NEC 2008 in an unfinished basement unless the outlet is dedicated to a security or fire alarm system. You may also want to go with a 20A to give you plenty of flexibility with how you're able to use it in the future (larger power tools, sump pump, etc.).
Comment: @Mark Schultheiss - But I like the lights to dim when I run my table saw, it's mood lighting for getting down to business.
Comment: Obviously, only use a 20A outlet if it is on a 20A breaker.
Comment: @Matthew Leingang: it is only protected by the GFCI if it is downstream from it. GFCI receptacles have "line" and "load" terminals, anything on 'load" is protected. Merely being on the same circuit (connected on the "line" side) is not enough.
Comment: IF you DO use a 20A breaker you need wire to match (12 gauge) vs 15A which uses lighter (14 gauge) wire AND 20A fixtures to match - which are labeled as such.  Safety note: do NOT put the lights on the same circut as a power tool.
Comment: Thanks.  This circuit I'm tapping into already has a GFCI receptacle on it.  So I'm OK, right?
Comment: Actually even with plastic boxes, you need to ground them. Typically there is a metal strip or wire in the back that connects the ground to the screw terminals.
Answer: the best way to do any electrical project in your house safely and efficiently is to hire a licensed professional. if you are uncertain on how to do electrical work, no offense you should not do it. the national electrical code is extremely strict and local inspectors are cracking down on do-it yourselfers. please as a licensed electrician do not attempt if you have not the proper training,
thank you
Comment: While this may be accurate, just about every question on a DIY site can be answered "get a professional." If a project is impractical for DIY (such as requiring specialized tools or a license to handle the equipment, e.g. HVAC coolant) then be sure to explain that. Otherwise, the answers we are looking for should educate someone how to do a task and then explain when they cannot do it themselves.
Comment: It's not accurate, either. Home electrical work is something a home owner can learn to do safely and to code.


Riemann integrable function from $\mathbb{R}^n$ is continuous a.e.?

Question: I'm aware of the result in dimension 1 that given $f \in R([a,b])$ ($R$ for Riemann integrable) then $f$ is continuous almost everywhere.
This result is given passing through Lebesgue Measure, that can be given also in $\mathbb{R}^n$. So my question is: The result stated above is true when we pass in $\mathbb{R}^n$, that is: is a function $f: A \subset \mathbb{R}^n \rightarrow\mathbb{R} $ Riemann-integrable necessarly continuous a.e.?
Answer: Just for $A={\bf{R}}^{n}$, if $f$ were improper Riemann integrable, then for any block $I_{(N_{1},...,N_{n})}=[N_{1},N_{1}+1]\times\cdots\times[N_{n},N_{n}+1]$, where $(N_{1},...,N_{n})\in{\bf{Z}}^{n}$, $f$ is Riemann integrable on that block, so it is continuous a.e. on that block. Since the countable union of all such blocks is ${\bf{R}}^{n}$, then $f$ is continuous a.e. on the whole space.
For any other $A$, it is hard to tell because Riemann integral or even improper Riemann integral is defined with certain conditions regarding of $A$.


Are magnetic fields just photon interactions?

Question: Is there a simple explanation to how photons interactions cause the effects of magnetism.
Always wondered what magnetic fields actually are.
I came across the idea when looking at the EM waves of light.
Comment: This may seem like a route to deeper understanding, but it is really kind of a dead end. Photons are defined, roughly, as the fundamental excitations of the electromagnetic field, so this is really asking "are magnetic fields some sort of excitation in the electromagnetic field?" And the answer is yes, but it is almost circular reasoning. I am brushing past some details involving how we keep track of radiating electromagnetic fields versus non-radiating ones (which are sometimes described as due to "virtual photons"), but in my opinion that distinction does not change this fundamental issue.
Comment: I believe [this](https://www.youtube.com/watch?v=1TKSfAkWWN0) may be what you need.
Comment: @CortAmmon wasn't much talk about how photons come in to play but thank you, was a interesting video. Are electric fields also photons then?
Comment: No, there is no _simple_ explanation on electric and magnetic fields or photons.  But electric and magnetic fields are linked. They are part of the same phenomenon we call the electromagnetic field. A specific excitation of this field of a certain energy level that propagates through space at speed c we call a photon.
Answer:
I came across the idea when looking at the EM waves of light.

Light is a classical concept completely described by solutions of the classical Maxwell equations. . There are no photons in classical physics. Just electric and magnetic fields in a sinusoidal time and space dependence .
Photons are elementary particles in the standard model of particlce physics. In the quantum mechanical framework photons are the exchange boson of first order electromagnetic interactions, and there exists a mathematical framework, quantum field theory, where creation and annihilation operators acting on a photon field will describe electromagnetic interactions, including electric and magnetic fields. The mathematics is not simple.
To get an intuition of how classical light waves can emerge from photons have a look at this link.
Answer:
Always wondered what magnetic fields actually are.

There are two possibilities to induce magnetic fields.
The first is the alignment of the magnetic dipoole moments of subatomic particles - mostly electrons - inside a solid. Some materials are permanent magnets and some materials could be magnetized by an external magnetic field. In contrast to an electric field, where charges are separated, for the induction of a magnetic field the magnetic dipole moments of subatomic particles will be aligned.
The second is the emission of photons. However one produce electromagnetic radiation - in a light bulb through chaotic acceleration of the involved electrons or in an antenna rod by the common acceleration of electrons forth and back the rod - in all cases the emission has an electric field component and a magnetic field component. For an antenna rod the magnetic field component is aligned perpendicular to the rod:

The animated sketch see on Wikipedia.

What is the effect of mgnetism?

The effect is simple that an existing magnetic field can induce a magnetic field in materials.
The nature of the constituents of magnetic fields - as well as of electric fields - is not considered. One simply satisfied with the macroscopic effects. This led to the situation that the interaction between magnetic fields and between electric field are explained by virtual photons and this is a useless explanation because beside this claim there is no use or explanation how virtual photons are working.


The root of "okulo"

Question: In my opinion, okulo comes from Kabalalah; in particular, I am talking about the Tree of life. Sefirot (in Esperanto ok) is the sign of Binah; it means understanding (mainly by eyes). Probably okulo could be ok-ul-o. Since The doctor was a Jewish, I guess my opinion is right.
What do you think?
Does anybody know the root of that word?
Comment: Tio ĉi povas esti interesa rimedo. Vian demandon ni ne povas tamen respondi, ĉar Zamenhof mem ne klarigis el kie li ĉerpis radikojn (kvankam ilia origino estas ofte evidenta): https://en.wikipedia.org/wiki/Esperanto_etymology
Comment: Persono, eble esperantisto, de sveda urbo Stokholmo -
estas nulokulo. Telefona numero al Stokholmo komencas per 08
Answer: If we look at existing works on Esperanto etymology, the root "okul/" comes from Latin "oculus".
This idea is shared by Louis Bastien (Naŭlingva etimologia leksikono de la lingvo esperanto, 1907), Ebbe Vilborg (Etimologia Vortaro de Esperanto, v. 4, 1995), André Cherpillod (Konciza Etimologia Vortaro, 2016) and Seikô Yamasaki (Etimologia Vortareto Pragmata de Esperanto, 1991).
Vilborg compares it to English and Spanish "ocular", French "oculaire", Italian "oculare" and Polish "okular". He adds that the root "ocul" is internationally known with all the words that use it.
About the "ul" part of the Esperanto root, Vilborg proposes that Zamenhof, who was an oculist, was inspired by the Latin word and the name of his job.
In its reform project of 1894, Zamenhof proposed to replace the root "okul/" by "okl/". This proposition was rejected, but some later words were influenced: for example, the word "binoklo" (binocular), officialised by the OA3.
Comment: This is supported by https://eo.wiktionary.org/wiki/okulo
Comment: There are no references on Wiktionary's etymology. So don't trust it.
Answer: I do not think your idea is correct. I think it is far more likely that the Esperanto word "okulo" comes from the Latin word "oculus".
Answer: According to dictionaries (e.g. PIV), "okul/" is a root. So the in-Esperanto etymology of "okulo" is trivial: "okul·o", i.e., the root "okul/" with the noun word ending "-o". (Which, as "okul/" is a thing-y root, is in fact the base form of the word.)
As Lepticed's answer layes out, there's consensus among Esperanto etymologists, that "okul/" / "okulo" comes from Latin "okulus", also meaning "eye". But where did "okulus" come from? The entry in Konciza Etimologia Vortaro by André Cherpillod allows us to dig a bit deeper into the exter-Esperanto etymology of the word. It reads

okuloF. L ŏkŭlus ← HE ok. · HE → Sk अक्षि akṣ̂i, Gr ὤψ, Gt augo, Sl око, Li, akis, Arm Աչք aĉk. · L → I òcchio, Ks occhju, F œil, Oc uèlh, H ojo, Kt ull, P olho, Glg ollo, Srd ogu, Rm ochi. Ĝ → G Auge, Jd אויג uyg, Is auga, Nd oog, N øye, Dn øje, Sv öga, Vp Iog. · Sl → R Uk о́ко, Blr Вока, Po Ĉĥ oko, Bg око̀.

So according to Cherpillod, Latin (L) "ŏkŭlus" indeed comes (←) from Indo-European (HE for eo "hindeŭropa") "ok", from which corresponding words (for "eye") in many European and some Asian languages directly or indirectly derive (→). However, he lists no indication of any relation to the Esperanto number word "ok" (8), for which he gives a different etymology also from Indo-European:

okF (8). L octō ← HE okt. HE → Sk aṣ̂ṭan, Gr ὀκτώ, Ga ochto, Ir OĊT, Br eizh, G Nd acht, A eight, Is, átta, Sv åtta, Sl осмь Li aštuoni, Hd आठ āṭh, Pe hǎŝt̀. · L → I òtto, F huit, Oc uèit, Kt vuit, H ocho, P oito, Rm opt.
Kp: He okt «8», ak «pinto»; Gr ὀκτώ, ἄκρα «pinto»; L octō, ăcūtus «akuta»; Sl осмь «8», остръ «akra». Kalkulo sur ok fingropintoj, ne uzante la poleksojn. ☞ naŭ, kvin.

So Cherpillod sees some possible relation (whether causal or not) between the words for 8 and for peak, acute, sharp etc., and probably considers that this might be due to 8 being the maximum one can count on two hands with the fingertips, excluding the thumb (maybe because the thumb was used to touch the "current" finger while counting to keep track).
There's no mention of the Kabbalah, or of Jewish or Israelite languages other than Yiddish (Jd) in either of these entries, though. (If your theory was right, one would probably expect links to ancient or modern Hebrew or similar Semitic languages, which do exist for some other Esperanto words, but aren't known for "okulo" or "ok".) And as "okulo" can be readily explained as being derived from the Latin "okulus", it's very, very unlikely that any such connection would have guided Zamenhof's choice of that word.
Answer: Going with your logic "ok" (to see) + "ul" (person) + "o" (noun) => okulo would rather mean "someone watching, watcher".
There are approaches to reconstruct proto-indo-european language in which the root word is: "oqos" - common in many european languages: oculus (LAT), okulo (EO), ojo (ESP), oko (BOS, BUL, CRO, CZ, POL, SRB, SLK, UKR), øje (DK), вока (BLR), ollo (GAL), окото (MAC), oog (NED), øye (NOR), olho (POR), ochiul (ROM), očesu (SLV), öga (SWE), occhio (ITA), œil (FR), eye (EN). Some of them are quite far away from the original.
Mi pensas, ke "okulo" estas nur prenita el la Latino.

The root of "okulo"


pharygian and harmonic minor scales

Question: I am hearing that the harmonic minor scale has the same notes as the phrygian scale built from the 5th of the harmonic minor scale. But when looking at the A harmonic minor scale I see a G# while the E phrygian (built from the 5th of the A harmonic minor) has no G sharp. Why?
Answer: The 5th mode of Harmonic Minor is called "Phrygian Dominant" but it's different than the "Phrygian" mode of the Major scale. I think that's where you're confused.
So yes Phrygian Dominant has the same notes as Harmonic Minor because it's a mode of it. And it's similar to but slightly different from Phrygian, the 3rd mode of the Major scale. Let's take a look at both scales starting from E and their scale degrees relative to the parallel major scale:
E Phrygian (derived from C Major):

E  F  G  A  B  C  D
1 b2 b3  4  5 b6 b7

E Phrygian Dominant (derived from A Harmonic Minor):

E  F  G# A  B  C  D
1 b2  3  4  5 b6 b7

If you look closely you'll see that the only difference is that Phrygian Dominant has natural 3rd compared to the Phrygian as derived from the Major scale.
So that's where the similar name comes from. The minor modes are often named because of their similarity to major modes. It makes it easier to remember the scale degrees if you already know the major version (Phrygian) because then you only have to remember the degrees that differ (natural 3rd). So "Phrygian" because of that similarity . And "Dominant" because it's the mode associated with the 5th, or dominant, of Harmonic Minor.
By the way it's called other names as well like "Phrygian #3" or "Mixolydian b9b13", which is maybe even a more helpful way of thinking about it as far as practical usage (ex. playing it over a Dominant 7th chord to either match or create the alterations of those chord extensions).
Answer: Phrygian is not a mode of harmonic minor, but of the natural minor scale. The fifth mode of harmonic minor is however called phrygian dominant. Below are both scales, with characteristic tones marked.

The Phrygian scale:
1-b2-b3-4-5-b6-b7
The Phrygian dominant scale:
1-b2-3-4-5-b6-b7

The following resources have more information:

The beginner's guide to (guitar) modes and scales (jazzguitar.be)
Phrygian dominant (wikipedia)
Diatonic scale (wikipedia)
Answer: If you think about it, that is impossible. The steps in the harmonic minor are:
1,  2,  b3,  4,  5,  b6,  7,  8
and there is an augmented 2nd between the b6 and M7 degrees.
It is not possible to start from any other degree and get the same arrangement of notes.
In other words, to be a harmonic minor scale, the augmented 2nd must be between the b6 and M7, but if you start from any other degree, the position of the augmented 2nd is no longer between steps 6 and 7.

pharygian and harmonic minor scales


Importing data from multiple external tables to a single object

Question: I am trying to use a production SQL Server database to send relevant data into Salesforce to generate reports. Some of the data I would like to use however is not consolidated into a single database table and is spread across a few tables. Is it possible to populate fields of a Salesforce object with data from multiple external database tables? Please let me know if there is a better way that I should be going about using my external database to create reports in Salesforce.
Answer: You can write a stored procedure at sql server to retrieve the data from multiple tables and export that dataset into csv format, then put the csv in the network path to import the csv into Salesforce object via CLI.
You can also manually load csv through data loader. By the way, in both the scenarios you need to define proper mapping between csv columns with Salesforce fields of the object to which you are importing.
Comment: Don't you mean a "view"?
Comment: Yes, we can create views, but here creating a dataset and exporting to csv same time better to use stored procedure
Answer: To be honest, it depends on what you feel most comfortable with.
Like @santanuboral said, a Stored procedure could work for you, but you would need to couple it with a script in bash/PowerShell to then pick up the csv and upload it to Salesforce via the Dataloader CLI.
In my case, I would be more comfortable writing a small app in C#, which would pick up the data from the SQL Server and directly pump it through the Bulk API. Also, a script can also do the job just the same, just harder to test, IMO.
The architecture of such an app would be fairly simple, following a normal ETL structure: you would have a set of classes to read from the DB in a paginated way, a small engine with all the different transformations you require which would be applied before loading the data, and lastly another set of classes to connect to Salesforce via OAuth and load the records to the Bulk API.
Once you have that app developed simply schedule it with any standard OS tools in whatever server you want. Schedule it to run every X hours/minutes and that would make sure you have the latest data in Sales Cloud.
Do take into account certain things regarding the transformations:

Date formats don't necessarily match. If you end up using the Bulk API you're going to need to use the yyyy-MM-dd format.
I recommend you to double quote everything and escape quotes, it's usually a headache otherwise.
Take into account that if you need to calculate fields for reporting, it's much easier to do it in any external processes to Salesforce (unless it's a simple sum or similar). Complicated calculations will lead you to Apex/Triggers, and that adds unnecessary complexity to the process.