What is the correct reading order for Stephen King's 'Dark Tower' series (updated)?

Question: There are a considerable number of properties relating to Stephen King's Dark Tower; The original novels as well as various media such as a prequel and sequel-comic series, short stories, mentions in other King novels as well as a PC game.
What is the correct reading order for the Dark Tower series and where do the tie-in products fit into this?
Comment: You have everything you need in the answers. I stopped also for a long time after the same one. Then when restarting the series, I read it again to immerse myself back in the Mid-World and continued up to the last one. I did read tons of books but this one is clearly for me one of the best worked-out world(s) and story. I really urge you to continue your journey with Roland and his ka-tet.
Comment: Here's another list,  alluding to the author's suggestions: http://honkmahfah.blogspot.co.uk/2012/04/dark-tower-suggested-reading-order-for.html?m=1
Comment: I wrote an answer on a similar (possibly duplicate?) question that might also be interesting to you: http://scifi.stackexchange.com/a/153469/23384
Comment: @AncientSwordRage - the corrected link due to the blog's having moved: [the-dark-tower-suggested-reading-order_2128.html](http://thetruthinsidethelie.blogspot.com/2012/04/the-dark-tower-suggested-reading-order_2128.html)
Answer: Per Wikipedia:

The Dark Tower: The Gunslinger
The Dark Tower II: The Drawing of the Three
The Dark Tower III: The Waste Lands
The Dark Tower IV: Wizard and Glass
The Dark Tower V: Wolves of the Calla
The Dark Tower VI: Song of Susannah
The Dark Tower VII: The Dark Tower
(4.5) The Dark Tower: The Wind Through the Keyhole

So to answer the question, you have 2 options.  Wait for the next novel, The Wind Through the Keyhole, to be released (currently scheduled for 2012), or read Wolves of the Calla next.
Comment: Huh, reading more into it, the new book isn't going to take place after "The Dark Tower".  Fixed the chronology.
Comment: And for your edit, I would go reading Wolves of the Calla and finish the story before the release of the 8th book which is quite not there yet... There is no such big hole that it's an issue following the whole plot.
Comment: @LudoMC yeah the Wikipedia page says that King found a sort of small crack in the story where he didn't explicitly have things happen and decided that's where he wanted to write the next novel.
Comment: Yes I've seen this following your link. But I don't know why, I'm not really waiting for the movies... :-/ Hope they won't ruin the whole story.
Comment: I was expecting you to update this with the additional tie-in novels...?
Answer: I would suggest that you read the actual Dark Tower books in the order in which they were published. You can then move on to the comics and the short story about the Little Sisters of Eluria.
It would be incredibly difficult and time consuming to read all of the related secondary works - that list includes the majority of King's books:  It, Insomnia, The Stand, 'Salem's Lot, Hearts in Atlantis, The Mist, The Eyes of the Dragon, Everything's Eventual, Rose Madder, The Talisman, From a Buick 8, Firestarter, Dreamcatcher, Cujo, The Long Walk, Misery, The Dead Zone, and many, many more.
In my own personal opinion, of the secondary books that I have read (It, Insomnia, Misery, The Dead Zone, 'Salem's Lot, Eyes of the Dragon, Firestarter, The Long Walk, The Stand), it seems that the most important ones are as follows:

The Stand
Insomnia
The Eyes of the Dragon
'Salem's Lot

You won't miss many important points if you don't read any of these books, but they do help to provide some background information that enriches the story of the actual Dark Tower series.
The order in which you read the books is ultimately up to you as the reader.  I imagine that many people would recommend reading the secondary stuff first, then starting on the Dark Tower books, comics, etc, but really, it doesn't make much difference.
The books of the Dark Tower series tend to jump back and forth between different timelines and the chronology is not particularly consistent.  For example, most of book IV (Wizard and Glass) takes place in Roland's childhood;  some of the events of book VIII (The Wind Through the Keyhole) take place between the end of book IV and the beginning of book V, but the main story is also set in Roland's youth.  More generally, all of the books include passages in which Roland reminisces about the past and tells stories about what the world was like before it "moved on".
In short, the best advice I can offer you is to read the books in whatever order seems best to you.  There is no right or wrong way to enjoy this epic saga.  The only important thing is to immerse yourself in the story and become part of Roland's world.

Note:  There really isn't a correct answer to this question.  It is all a matter of opinion.  As if to prove this point, here is a list compiled by someone else, showing their own recommended reading list and order in which he/she thinks they should be read.  One of the most interesting features of this list is that it very cleverly suggests reading The Gunslinger (i.e., Book I) again after finishing the series - this suggestion makes a lot of sense to those of us who have read the series.  However, it is very important that I point out that this list contains TWENTY FIVE BOOKS.  This just goes to show you how much secondary material there is to read.
Another list, apparently written before the publication of The Wind Through the Keyhole (Book VIII), is slightly different from the previous one.
Comment: PS:  While the first edition of *The Gunslinger* (book I) contains many inconsistencies relative to the other books, it is far superior to the more consistent second edition.  I would also advise you to try to get the unrevised versions of the other books, because at least some of them were edited to improve the consistency of the speech and minor plot points relative to the later books.
Answer: Dark tower gunslinger. ...dark tower II drawing of the Three... Dark Tower III Wastelands...Salem's lot... Dark Tower IV Wizards and Glass... Wind through the key hole even though it came out after dt7.  Dark Tower V, then VI then VII. Then Insomnia right after DT7.
Comment: Is this based on anything other than your own opinion?
Answer: My two cents:
The Gunslinger
Everything's Eventual (For the purpose of Dark Tower, only read "Little Sisters of Eluria")
The Drawing of the Three
Eyes of the Dragon
The Stand
The Wastelands
The Talisman
Wizard and Glass
The Wind Through the Keyhole
Salem's Lot
Wolves of the Calla
Black House
Song of Susannah
Hearts in Atlantis
Everything's Eventual (Again, for DT, the story "Everything's Eventual")
Insomnia
The Dark Tower


Books or articles on military thought?

Question: I'm looking to find writings on military thought. Not in the sense of tactics or history of war, but in the sense of being in or running a military force in the abstract. Ideally, possible topics would include questions of organization, discipline, military ethics, and so on. In theory, this could also work with something that looked at a particular military institution and examined military life through that, similarly to Absolutely American about West point. Any recommendations?
Comment: I am sorry that I had to downvote. For what reason, would you require some military books only for Absolutely American?? From **philosophical stand point of view**?? I think too and upvoted for Sun Tzu, partly philosophical, and according here http://j.people.com.cn/94475/8071509.html, it says, there more than 10 translated versions of The Art Of War, and it says, it is being used in variety of areas, from literature to politics to even marketing. It says The Art Of War is translated and read in more than 30 countries.
Comment: Sorry, I guess I wasn't as clear as I wanted to be. I've actually read The Art of War, and to me it's a both too specific and too vague, since it reads like a simple list of rules that he felt were the way to go to war, without any explanation, nor any examples. Absolutely American was an example of one particular type of book that would work, a book that is about being in the army and what that's like, just through the lense of a specific institution.
Comment: I think the very difficult point about the Art Of War, is based on the technique of the translation. If you can read Chinese ( the very first language to read it ) or Japanese or Korean ( the probable second options ), the impression or nuance is veeeeeeeeeeerrrrrryyyy different. Even though I quoted English translation below, I have to say, the nuance seems to me a bit different. Btw, for that reason I reset my downvote.
Comment: I am sorry I was not able to upvote. So let me add +1 to the "star". Thank you.
Answer: The most famous philosophical work on military matters is Sun Tzu's The Art of War.  Although thousands of years old, it outlines general principles still applicable today, and although largely about tactics, it also is centrally concerned with "running a military force in the abstract."
Comment: Ha, I was actually considering using The Art of War as an example of what I wasn't quite looking for...
Comment: +1 Chapter 8, 12 : **There are five dangerous faults which may affect a general: (1) Recklessness, which leads to destruction. (2) cowardice, which leads to capture. (3) a hasty temper, which can be provoked by insults. (4) a delicacy of honor which is sensitive to shame. (5) over-solicitude for his men, which exposes him to worry and trouble.** Very suggestive and also (semi)-philosophical to me.
Answer: The classical reference for ground warfare in the European style has been the texts of Clausewitz (q.v. http://www.clausewitz.com/) for a few generations.  He made logical sense of most of Napoleon's actions for the next generation, and since Napoleon was too busy running things to try to explain himself, he is taken as the summary of the military thinking of the European Classical period running from Alexander the Great to Revolutionary France.
Thereafter, the speed of technological change made everyone back off to a higher level of abstraction.  His theory of internal lines does not make metaphorical sense in a modern theater where the lines of combat are not as obvious (e.g. aircraft, tactical explosives, guerilla skirmish, etc.).  But his thinking is thorough and precise, and in certain ways, it does extend to modern life.
Answer: For the psychological/philosophical side of military thought, D. Grossman's book On Killing could be relevant - while it covers a rather narrower topic compared to the whole military life as such, it is probably the main distinction between the mentality of military and other high risk occupations and organizations.

Books or articles on military thought?


I'll read that book in 2 hours

Question: "I'll read that book in 2 hours."
I'm pretty sure this phrase means that after 2 hours from now I will start reading the book, but I can't stop thinking that it could also means that it will take me 2 hours to read (and finish) that book.
My friend says that for the second meaning the following phrase would be more appropriate:
"I'll read that book for 2 hours." Which also makes senso to me, but I get the idea that maybe I won't be able to finish it in just 2 hours.
Could some native speaker elighten me on this problem? Can the first phrase be interpreted in both ways?
Thank you in advance.
Comment: @Jim: I'd say the ***for** 2 hours* strongly implies you don't expect to *finish* the book in that amount of reading time (usually, *starting from now*). OP's first version is, as you say, ambiguous, but I pragmatically I think *It'll take me two hours to read it* would be the far more likely intended sense. And if you *did* intend the *Two hours from now I'll start reading it* sense, you might well say *I'll read it in 2 hours **time*** (you'd *definitely* do something like that if you were at all bothered about any possible ambiguity).
Comment: You are correct that the first is ambiguous.  Your friend is wrong- that sentence means you will read for a length of time of 2 hours, but it says nothing about whether you will finish it in that time.  I'd likely say either, "I can read ***that whole book*** in two hours." or "It'll only take me two hours to read that book."
Comment: I think most people would take it to mean that after two hours time you would have the book completely read.  (Thin book or fast reader.)  "I will *begin* reading the book in two hours" would mean that two hours from now you will start reading.
Comment: The most common interpretation of "I'll read that book in 2 hours"—without any other context—would be that it will take two hours to read the book.
Comment: The alternative meaning of "Two hours from now, I will read that book" is on equal footing. In speech the meanings would be distinguished by intonation.
Comment: @FumbleFingers- Agreed.
Answer: "I'll read that book in two hours" generally means that whenever you start to read the book, it will take you only two hours to finish it; i. e., you are a very fast reader! Otherwise, it would be ambiguous (hard to understand) without additional sentences on either side to give more information about your plans for reading.
"I'll read that book for two hours" means that whenever you start to read the book, after two hours have passed you will stop reading it, without regard to how far along you have gotten in the book.
As you correctly stated, the proper sentence is, "Two hours from now I will start reading the book," if that is what you intend to do, and no implication is made as to how long you will read or whether or not you plan to finish the book in one sitting.

I'll read that book in 2 hours


Distinguishing between quark and gluon jets

Question: How do experimentalists at the LHC differentiate between jets produced by quarks and those produced by gluons. I know that for b quarks there is a b-tagging method, but what do they do for the others in order to separate them from gluon induced jets?
Answer: I found a good paper here titled Distinguishing quark and gluon jets at the LHC from CERN's website that answers your question. The introduction states
"Partons emitted from hard scattering process at the LHC form, due to QCD confinement and
hadronization process, hadronic jets, which can be revealed with tracking and calorimeter systems. As known from theoretical principles and from experimental measurements, reconstructed jets show
different properties depending on flavor of original parton. In general, due to the large color factor
of gluons, gluon-initiated jets have higher particle multiplicity, a softer fragmentation function, and
are less collimated than quark-initiated jets. These differences can be exploited to tag jets, and
such a capability plays a fundamental role in several physics analyses. It results in an increased
ability to discriminate full-hadronic final searches - composed mainly by quark-originated jets, from
QCD background - where the gluon component is predominant".
Comment: In the heavy-ion sector, we've also been experimenting with using the jet's total charge to distinguish quark and gluon jets: https://arxiv.org/abs/2004.00602


How to allow Steam to write into root directory?

Question: I've just installed the latest Linux Mint version and I'm trying to set up some Steam games. I only have 10 GB on my home directory, so I'm willing to create a game library inside the root directory (/usr/games/steamlibrary). I was able to create a folder there, but I have no idea how to let Steam write there. I get the following error: 'New Steam library folder must be writeable'. How can I fix this?
Answer: Instead to think about how make Steam able to write to... you should think about how make that folder writeable to me;
probably you will get the same result but it has a different logic and mostly affect security: I would not be happy if an application can easily write in my root!

Anyway, I would make writable the folder to me:
chown -hR $USER:$GROUP /usr/games/steamlibrary

where $USER is your user and $GROUP your group.
In this way you are able to write to that dir (even if it resides in the root), thus to Steam.
Answer: You should allow steam to write outside of your home partition.
What you should really do is to resize your home partition. The simplest way to do it is to boot linux from a thumbdrive and use gparted to resize the home partition.
An article that explains how to do it on ubuntu
If you still want to save your steam games to your root partition, you need to let steam write to /usr/games/steamlibrary. To do that, you need to change the directory's permission using sudo chmod +rw this command makes it so that you can read and write as the current user without using sudo.
You really should resize your home partition though.
Comment: Did you conversely meant to say `You shouldn't allow steam to write outside of your home partition.`


Is this superficial tire damage or should it be replaced?

Question: enter image description hereThis is my wife's car, not sure how this happened but assuming it was from her hitting a pothole. The tire sidewall was sliced but when I lift the flap I can't see any cords, just black rubber/tire. The car is 1 year old and these are the original tires, they have about 8,000 miles on them and are performance non-runflats. Should I just have this tire replaced to be safe or is it just superficial damage?
[![enter image description here][3]][3]
Comment: I've uploaded new photos with better lighting
Answer: Can't clearly see the damage but if the flap of rubber is more than just say a few sheets of paper thick, then I'd recommend to replace the tyre.. especially if the car does ANY derestricted or motorway speeds etc.
The reason is that sidewall damage isn't always fully visible. It may just show a flap of cut rubber, but the sidewall could be weakened at that point also, as the tyre will have been crushed or pinched somewhat between rim and kerb. This also means possibly damaged carcass fibres which can become a failure point. Its not really worth risking a blowout for the sake of a tyre.
If it was a pothole.. get a picture of the hole with a measuring tape etc showing the depth of the hole, along with a photo of your tyre/wheel damage  (have suspension checked too) and bill the council for the cost of repair.
Comment: Thank you for your reply, I've just added new photos with better lightning. I was going to err on the side of caution and just replace it, actually I was planning to do just that when I brought the car in for service last week at car dealership. They told me the tire was fine and I could superglue the cut as it was cosmetic damage only. I can afford the cost, just wanted to make sure my thought process was justified, better safe than sorry was my thinking. Also, we have a lot of pot holes here, hard to say which one was the culprit as my wife doesn't notice them like I do
Comment: Thanks for updating the photos.. I would definitely replace that tyre.
Answer: That damage looks pretty substantial. The structure of the sidewall is the cords which I can't see in the image, so there is still some (albeit minimal) protection for the cords in the rubber covering it.
However, if that was my tire, I'd replace it. As Orb said, you the event that caused the pretty substantial damage could have damaged the sidewall in a manner that you can't see. If there's only 8000 miles, you probably are safe replacing just one tire if you can find an identical one (unless the "performance" means your wife drives aggressively, which can wear the tires in 8000 miles a lot). Otherwise (if exact identical tire not available) replace both tires on the same axle and use a tire rotation pattern that maintains the property that tires on the same axle won't get put to different axles. However, on some all-wheel drive vehicles you may need to replace all 4.
If going against the advice, I'd monitor the damage area by taking a photograph of it in good lighting (such as using a flash) initially after every single drive, and carefully see whether the damage progresses in either of the two manners: (1) the tire starts to bulge, (2) you can see the cords. In a very tight budget, the monitoring approach could work reasonably, but then you need to be prepared for eventually replacing the tire.
Me? I'd be lazy and just replace the tire. After all, 8000 miles almost surely means you can replace just one.
Comment: Thank you, I agree, I think I'd feel better just replacing it. It's an Audi with all wheel drive, my understanding is that they are super sensitive with regards to tire height differences. However, I've heard that a new tire ordered from Tire Rack can be shaved down to match the tread depth of another tire
Comment: @Zugdud That's a good plan, but be sure to get exact same brand and model of tire. Otherwise you may encounter poor handling of the car. It's not enough to have the same tread depth, the tire needs to be of the same brand and model too.
Answer: Poor photo, can't see enough, but replace it - if it pops on your wife you will never hear the end of it.
Comment: This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - [From Review](/review/low-quality-posts/46667)
Comment: @RoryAlsop title of question says "should it be replaced" & and answer says replace it ....
Comment: Worst case is that he will hear the end of it @SolarMike.
Comment: Thank you for your reply, I've just added new photos with better lightning. I was going to err on the side of caution and just replace it, but wanted to make sure I wasn't just needlessly spending money to correct cosmetic damage.
Answer: Replace it; as others have said.
What is troubling to me is the crack that runs from the "flap" area all the way through the second "O" in GOOD-YEAR".  (Should it be GOØD-YEAR ??)
This suggests a pretty hard hit, and a potential for cord/belt damage in the sidewall - not just limited to the "flap" area which shows no cord.
Check the tread depth on the other tires, but unless you drive very hard, I doubt 8000 miles is enough treadwear variation to disturb your Audi.


Is there an intuitive way to understand why increase in supply decreases value?

Question: "The more of something there is, the less valuable it is" is a common way I hear Supply & Demand explained, but it doesn't make much intuitive sense to me. Why exactly does a unit of something become less valuable just because its overall supply increases? Keep in mind, I'm not asking about marginal utility, which assumes that someone has already obtained at least one unit and measures each subsequent evaluation for an additional unit of that thing (say, for example, bottles of water, in which that first bottle is valued highly, but each additional bottle is valued less). I'm asking why the price of any given unit would be low just because the overall supply is high. For instance, wouldn't it be more profitable if I, as a company, sold the first batch of units for a high price, then slowly lowered the price for each subsequent batch, rather than price ALL units at a low price?
Answer: Consider a market of apples.
There are 5 vendors, each with 10 apples - 50 apples in total = supply for apples.
Then there is 10 buyers, that each want 1 apple - 10 apples in total = demand for apples.
Note that demand < supply, which means that the buyers can pick the vendor with the lowest prices. The vendors knows this and therefore, for example vendor A, will decide to set his price for apples lower than the rest of the vendors, which in turn will make the buyers go to him. In response to this the other vendors will surely lower their prices aswell to be competitve with vendor A. As such the overall prices for apples on the market will fall for the simple reason that there were too many apples.
You could also try to imagine the opposite. Suppose the demand for diamonds are very high, every person in the world wants one - and can afford it (at the current price level). Now if supply is only at a level where 1/10 of people can get one. Then one person might try to guarantee that she will get one by proposing a price higher than everyone else in the world is paying. Obviously everyone else will do the same, which will push the price up until the richest 10% of the world will buy the diamonds. As such the prices of diamonds rose because there was too little supplied.
Does this answer your question? I assumed you was looking for a more intuitive answer or did you need it more technical?
Comment: I understood everything until the diamonds example. Why is the consumer increasing the price of the item/diamond? Doesn't the supplier raise prices?
Comment: Maybe i explained it poorly, obviously the supplier raise prices, but they do it relative to the demand. Assume person 1 has 1 dollar, person 2 has 2 all the way to person 100. Assume there is only 10 diamonds supplied.
If the price of diamonds were 2$ before then person 2-100 will all be able to pay for it and the producers will get a profit of 2*10=20. But why would the producers not just raise prices to 90, then only person 90-100 can afford it, but producers will earn 10*90=900. As such because of the many people demanding, the producers can set prices acordingly so that only the richest


How can I run ALL my Apps "as administrator" in windows 10

Question: I know about the suggestions of http://www.tenforums.com/tutorials/3436-run-administrator-windows-10-a.html. However not one option provides an answer to my question. I want to run as admin all applications without executing an action for each one of them.
Comment: Maybe set UAC to the minimum security level? I know there's a command for it, but it could leave a big security gap in Windows. I'll report back if I find the command...
Comment: This may also help: [204781](http://superuser.com/questions/204781/how-can-i-run-all-my-apps-as-administrator-by-default-in-windows-7).
Comment: why my question is duplicate? where is the reference to double?
Answer: Run Powershell as admin:
run: Set-ItemProperty -Path "HKLM:\Software\Microsoft\Windows\CurrentVersion\Policies\System" -Name "EnableLUA" -Value "0"
restart PC
Comment: This **would not**  elevate a process to an Administrator.  This just disabled the UAC prompt.  Did you try your suggestion before you made it?

How can I run ALL my Apps “as administrator” in windows 10


What information can be publicly read from a signature?

Question: Without knowing anything else than the signature itself, what information if any can be publicly read from the signature?
Answer: Basically the signature doesn't give information. However if you know what has been signed you can retrieve the account of the signer.
Here is a piece of code to show this:
<code>const Web3 = require('web3');
const web3 = new Web3();
async function f() {
    const privateKey = web3.utils.keccak256('Test');
    const address = web3.eth.accounts.privateKeyToAccount(privateKey);
    const toSign="This is a test";
    const signedData = await web3.eth.accounts.sign(toSign, privateKey);
    console.log(`Signing "${toSign}" by account ${address.address} gives signature ${signedData.signature}`);
    const signer=web3.eth.accounts.recover(toSign, signedData.signature);
    console.log(`Knowing the signed text: "${toSign}" we can get the signer: ${signer}`);
}
f();
</code>
Answer: It's one-way hash function, so with only signature you don't have any information.


Building cryptographic primitives using additive maps?

Question: Suppose we have a one-way function F(x) that exhibits the property F(a + b) = F(a) + F(b). Such a function could be used as a cryptographic primitive, no?
Answer: Yes, take an elliptic curve group $E$ with a point $P$ of prime order $p$ such that the discrete logarithm problem is hard. Then we have a cyclic subgroup $\langle P\rangle$ of $E$ generated by $P$ of order $p$.
Define the map $F: \mathbb{Z}_p \rightarrow \langle P\rangle$ as $F(a):=a\cdot P$ (scalar multiplication) which gives you such a linear map (homomorphism and actually it is an isomorphism) as you have that $F(a+b)=F(a)+F(b)$.  Apparently, if the discrete logarithm problem is hard, this map is one-way. The first addition is in $\mathbb{Z}_p$ and the second addition is the "abstract" addition in the elliptic curve group.
This fact is used in various constructions when instantiating DL based crypto with elliptic curves, such as homomorphic commitments, making ElGamal additively homomorphic (aka exponential ElGamal) etc.
Answer: Yes in some sense under the LWE assumption.
For a matrix $A \in \mathbb{Z}_q^{m \times n}$, two vectors $s \in \mathbb{Z}_q^{n}$ and $x \in \mathbb{Z}_q^{m}$, we define
$$
F_A(s,x) = As + x \in \mathbb{Z}_q^{m}.
$$
Under the LWE assumption, the family of functions is one-way, when the function index $A$ is chosen uniformly at random, $s$ is chosen uniformly at random and $x$ is chosen according to an appropriate distribution, say, a folded Gaussian over $\mathbb{Z}_q$ with small variance.
Apparently, this function is additively homomorphic, that is,
$$
F_A(s,x) + F_A(t,y) = F_A(s+t,x+y).
$$


Why does this small corridor look like a huge room on the map?

Question: As you can see on the mini-map this is a large room, but as you can see on the screen it's just a small empty corridor. Any ideas? I can't see any dwarfism entrances.
Comment: I ran into one of these rooms yesterday. I checked all the floors and ceilings for hidden passageways but did not find anything. I think the room is a red herring or a glitch.
Comment: A picture of the room unpaused would be more helpful
Comment: @BlueRaja-DannyPflughoeft: You should be able to see the room on the map, as well as the tiny corridor in the background. The tiny corridor is the entirety of that large room, there is nothing further right.
Comment: I don't think the corridors actually show up on the map.
Answer: Whenever a room occupies a larger space than that which you can see, there is usually something hidden nearby. You may be able to pass through at a certain point in the floor, go through a wall or the roof may have holes in it. Places you can pass through are sometimes painted with a slightly darker color than the surrounding edges. To check the floor, attempt to jump down through it like you would a thin platform by pressing down and jump. Often treasure and fairy chests can be found at the end of a labyrinth of hidden passages.
Sometimes you encounter a room where monsters will be present in unreachable areas but able to attack you. These can sometimes be the objective of a fairy chest and you need to kill them using spells.
Finally that room may be a room whose purpose is to connect other rooms together by passages but in this case no other rooms were placed on the other sides of that room, resulting in a terminated connector room. This could be the case if you can't jump into the walls anywhere and there are no chests or enemies present.
Comment: This is a decent generic answer, but this particular room does not look like it has any monsters or hidden passageways containing chests.
Comment: Then it's probably a connector corridor without any rooms to connect to as a result of the room and layout randomization.
Answer: I've encountered these rooms several times; while I don't know exactly what causes them in the world gen, they seem to be a "corridor" room which can dynamically generate whatever connections it needs.  In this case, the corridor room was generated, but nothing was connected to it except the one side.  You'll often find similar rooms that pass through to the other side, or have passageways up or down, or even a full 4-directional pathway.


Exchange of heat at constant temperature

Question: How could we have an exchange of heat at constant temperature ? Isn't heat related to temperature ?
Answer: First of all i am going to concentrate on an ideal gas system.
Now when we say that during a process, the temperature remains constant, we are essentially talking about isothermal process.
Heat is just a form of energy, hence when we supply heat to a system and if all of that heat energy gets utilized in expansion of gas, that is in doing work for moving the piston by the gas, then no energy is used up in increasing the temperature of the system. Such process turns out to become isothermal.
Generally this is accomplished by providing heat very slowly and allowing the gas to expand such that temperature remains almost const.
Though heat is generally related to temperature, but we should think that heat is just energy and energy can alter any of the system variables of the system and not just temperature. If temperature is by design kept const, then the energy has no other way but to alter other system variables.
Answer: In addition to what @Nisargjoshi says, heat is energy transferred from one object to another due to a temperature difference in the objects. The energy flows from the warmer object to the cooler object.  If the two objects have equal temperatures, there is no heat transfer. Energy would have to be transferred by some other means.


How to open a Taproot channel on c-lightning node?

Question: Will new channels automatically use Taproot now, or is there something to activate in c-lightning to make it use Taproot?
Answer: Channel opening is about communication between two nodes. Therefore it's not a feature C-lightning can unilaterally support. The protocol needs to be specified in the BOLTs.
As of February the 21st, specifications are still being discussed on the mailing list. A concrete protocol for Taproot channel openings has not been publicly proposed yet.
Answer: There are major protocol updates necessary before we can use taproot in lightning and decide how exactly to make use of it in lightning and how to integrate it. Thus I don't think any implementation (that includes c-lightning) as of now or even in this year will add support for it
Comment: "Taproot support" could be split into multiple different things. When Muun say they "added Taproot support" they mean they added the ability to send and receive to a Taproot address. But all the possible upgrades (gossip, MuSig2, PTLCs etc) to the Lightning Network protocol that Taproot offers haven't been implemented yet (as Antoine, Rene say)
Comment: Thanks! As I understood the messages in Muun, they already added Taproot support last year, after it activated.
We had to take some action in the wallet to enable it, if I remember right.
Did i misunderstand that?


How to prove that path of a charged particle in a uniform magnetic field is circular or helical?

Question: I know that Lorentz force acts perpendicularly with the motion of the charged particle and curves the path into a circular one ,but how to show it mathematically?
Answer: I've put down an answer that should help you but doesn't dive deeply into the mathematics, if you're feeling confident I would suggest trying to solve it using equations of motion and coupled differential equations, but if not, I think what's below should lead you in the right direction.
Let's suppose we have a uniform magnetic field in the $z$ direction, $\vec{B}=B_0\hat{z}$ $$\\$$
Now let's give our particle a charge $q$, and an initial velocity vector
$$
\vec{v} = \begin{pmatrix}
v_x \\
v_y \\
v_z \\
\end{pmatrix}
$$
And we have the Lorentz force, $\vec{F} = q\vec{v}\times\vec{B}$
To make things easier, we're going to view things as seen from a frame where we are moving at $\vec{v}_{frame} = v_z\hat{z}$, so the new velocity of our particle is $$
\vec{v}\space' = \begin{pmatrix}
v_x \\
v_y \\
0 \\
\end{pmatrix}
$$
What makes this useful is that is it perpendicular to the magnetic field, so our cross product just becomes the product of the magnitudes of $\vec{B}$ and $\vec{v}\space'$, $F = qv'B$ where $x = \lvert\vec{x}\rvert$
We know, due to the properties of the cross product, that $\vec{F}$ is perpendicular  to the velocity vector $\vec{v}\space'$, and the magnetic field vector $\vec{B}$. This means the force constant, is in the x-y place, and always perpendicular to velocity in that plane, which is sufficient for circular motion. The radius of this motion, you can determine using the formula for centripetal force, $$\vec{F} = \frac{mv^2}{r}$$
Just make sure you use the right velocity! $$$$
So now we know that the motion is circular in the reference where we're travelling at $v_z\hat{z}$, all we have to do is transform back, and now our circle isn't staying in the same place, it's moving, so we have helical motion!
A quick disclaimer: if $v_z$ is near the speed of light, this derivation with the frame transform is a bit shake, since relativity comes into play, but in most cases this is fine.


How to get exchange rates for testnets?

Question: I would like to see what a PETH on Kovan is worth in DAI. How can you look for exchange rates on testnets?
Comment: Note that the testnets could theoretically disappear at any time (and have done in the past).
Answer: There are no exchange rates for test networks as none of the assets are worth anything. They are all valued at zero.
You can get free Ethers from a testnew faucet and use those to exchange to any other tokens. The exchange rate may be basically anything - it makes no difference whether you pay 1 Ether or 1 wei to get your tokens as you can always get more free Ethers. And probably there are free token faucets as well, at least for some tokens.

How to get exchange rates for testnets?


Applications of QFT in theoretical physics

Question: I would like to know which fields in physics have seen growth or benefited by applying QFT? I know that approaches to quantum gravity such as string theory use QFT, HEP and also some branches of condensed matter physics. Where is it applied in condensed matter physics exactly? And in what other areas of theoretical physics, has QFT been applied?
Comment: As DaniH's answer below details, QFT has not merely been applied in *some* branches of condensed matter. It is the only reasonable language we have for many-body physics, which is a cornerstone of all condensed matter theory. Low-energy nuclear theory (though some might consider that a condensed matter problem...) also requires QFT.
Answer: Quantum field theory, the study of fields from the quantum mechanical point of view, is specially useful to treat interacting many-body systems. It has been applied to low dimensional quantum systems [magnetic like Heisenberg or Ising spin chains or non-magnetic like carbon nanotubes or two-dimensional electron gases], strongly correlated conductors, standard BCS-like superconductors, high-Tc superconductors and a large etc.
Feynman diagrams are commonly used by condensed matter theorists. One example of diagrammatic calculation is done in the $3\text{D}$ electron liquid with long-range Coulomb interactions: we can show that the energy at second order in perturbation theory is not divergent but finite due to renormalization of pure Coulomb interaction by the dynamics of the system. Diagrammatic methods coming from quantum field theory also give a microscopic support to more phenomenological theories, like the Fermi liquid theory. They also allow to perform calculations of conductivity in disordered conductors in the presence of interactions between particles in/or scattering with impurities.
Quantum field theory methods are also used to study $1\text{D}$ fermions [Luttinger liquids]. Luttinger liquid physics appears in many systems like carbon nanotubes, semiconducting quasi-$1\text{D}$ wires, anisotropic crystals or edge states in the fractional quantum Hall effect for example.
Finally, quantum field theory has also been applied to statistical mechanics, for example in the study of quantum phase transitions and critical phenomena where renormalization group methods are commonly applied to obtain critical exponents.
The list can go on and on...
Answer: It is also used to model the early universe in cosmology. In the theory of inflation, the vacuum fluctuations, of a scalar field, are expanded to sizes larger than the Hubble horizon where they then form the seeds of structure formation.
Comment: ohh...yeah, ofcourse...i am looking for some non-trivial answers..
Comment: I am not sure that early universe cosmology application is that well known. I have added some more details.


Do HeLa cells prove immortality?

Question: Does modern science, especially HeLa cells, prove that immortality (in the classic sense) is real (for these cells) or possible in the future?
Comment: I don't know, as we are on the philosophy SE, what is correct definition for immortality?
Comment: HeLa cells can be easily killed, indeed it takes a lot of effort to keep them alive, so no. Even life on Earth taken as a whole is not immortal, all it takes is for a strong enough hit to send the Earth into the Sun, or even just alter its orbit into something like Mercury's.
Comment: You can see immortality is real just by looking at bacteria divide, but specifically what kind of immortality do you mean? Imperviousness to death? Or just unlimited replicative lifespan?
Comment: Welcome to SE Philosophy! Thanks for your contribution. Please take a quick moment to take the [tour](https://philosophy.stackexchange.com/tour) or find [help](https://philosophy.stackexchange.com/help). You can perform [searches here](https://philosophy.stackexchange.com/search) or seek additional clarification at the [meta site](https://philosophy.meta.stackexchange.com/).
Comment: Could you expand on your question by adding details and more discussion?
Answer: In regards to HeLa cells, they are already termed immortal by biologists. According to the article:

HeLa (/ˈheɪlɑː/; also Hela or hela) is an immortal cell line used in scientific research.

So, by biological definition, they are immortal, though what that means to biologists philosophically isn't clear by the article. To restructure your assertion and presume that you mean immortality in the sense of biological organisms living without regards to temporal limit, it seems you are asking the question of whether or not a line of cells that can divide with to temporal limit implies that an organism can now live potentially without end. The simple answer is no, and here is why. It is tempting to reason as such:

P1 Cells can live potentially forever
P2 Organisms are made of cells
C Therefore, organisms can live potentially forever.

As stated, it seems persuasive, but unfortunately it is misleadingly so. This argument is an example of a well-known and classic fallacy called the fallacy of composition. Simply put, parts and wholes don't have the same properties necessarily. From the article:

The fallacy of composition arises when one infers that something is true of the whole from the fact that it is true of some part of the whole (or even of every proper part). For example: "This tire is made of rubber, therefore the vehicle to which it is a part is also made of rubber." This is fallacious, because vehicles are made with a variety of parts, many of which may not be made of rubber.

In fact, it is almost certain that the argument above is based on the fact that the verb 'to live' means two very different things for cells and organisms. A complex organism, for instance, a human being is generally recognized as having the property of a mind, and absent this property of mind, one often talks about a person being dead, but their body being alive. This of course wouldn't apply to cells from which you are reasoning. When one uses a word in two different senses, but reasons as if they are the same, one is engaged in the fallacy of equivocation:

In logic, equivocation ('calling two different things by the same name') is an informal fallacy resulting from the use of a particular word/expression in multiple senses throughout an argument leading to a false conclusion.... It is a type of ambiguity that stems from a phrase having two distinct meanings, not from the grammar or structure of the sentence.

It's easy to see why the original argument is misleading! It presumes that the lives of cells and organisms (whatever they mean exactly) essentially are the same thing. You'll be hard-pressed to find an expert in biology who will agree with that literally. As for the possiblity of organismic immortality, I doubt that any biology professional would be willing to argue that the possibility is present because of this one phenomenon. Something as complicated as living forever would require a very strong inductive argument to attain cogency.
So, to reiterate, immortal cells do not imply immortal organisms.
Answer: HeLa cells are "immortal" because their genetic machinery is damaged, causing them to reproduce all the time, and they cannot repair that damage. They are cancer cells and although you can consider them to be "alive" in the sense that they grow and divide, they are not alive in the same sense that noncancerous cells or humans for that matter are.
Answer: Haldane pointed out that when a corpse is buried, most of its cells are still alive. The corpse is not.
Living as a multicellular being involves a delicate between different cell lines, regulated by mechanisms including programmed cell death for defective cells. When these mechanisms fail, this is cancer. Individual cells become "immortal", but the organism become dead.
So if you prize immortality, envy the bacteria.
Comment: I'm not sure that the cells are still alive. They don't have a metabolism anymore. What is "living"?
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Do HeLa cells prove immortality?


Recursive formula for Bernoulli numbers from power series

Question: This is Ch 7, Exercise 62 in Palka's Complex Function Theory. Define
$$ f:B(0,2 \pi) \to \mathbb{C},z \mapsto \frac{z}{e^z-1}\text{ if }z \neq 0, \; f(0):=1$$
Let $f$ have Taylor series
$$f(z)= \sum_{n=0}^\infty \frac{B_n}{n!}z^n$$
where the $B_n$ are Bernoulli numbers (Here I use Wikipedia's notation, not Palka's). The question is to show
$$\sum_{k=1}^{n}\binom{2n+1}{2k}B_{2k}= \frac{2n-1}{2}\tag{1}$$
I am stuck on showing this, but have some initial leads (from earlier in the problem). We have $B_0=f(0)=1$, and from Palka's hint, $z \mapsto z/2+f(z)$ is even:
$$\begin{split}
\frac{z}{2}+f(z)=& \frac{z(e^z-1)+2z}{2(e^z-1)}= \frac{ze^z+z}{2(e^z-1)}\\
\frac{-z}{2}+f(-z)=& \frac{-z}{2}- \frac{ze^z}{1-e^z}= \frac{-z(e^z-1)+2ze^z}{2(e^z-1)}= \frac{ze^z+z}{2(e^z-1)}
\end{split}$$
which reveals $B_1=-1/2$ and $B_n=0$ for $n>2$ odd. I have also tried manipulating $(1)$: since $B_1$ is the only nonzero odd Bernoulli number:
$$\sum_{k=1}^{2n}\binom{2n+1}{k}B_k= \frac{2n-1}{2}+ \binom{2n+1}{1}B_1=-1$$
or starting the sum at $0$:
$$\sum_{k=0}^{2n}\binom{2n+1}{k}B_k=-1+ \binom{2n+1}{0}B_0=0$$
but I didn't get any additional insight on how to show $(1)$. Any help is greatly appreciated.
Answer: Hint:
$$(e^z-1)f(z)=z.$$
Differentiating $n$ times,
$$\sum_{k=0}^n\binom nk(e^z-1)^{(n-k)}f^{(k)}(z)=0.$$
Then with $z=0$,
$$\sum_{k=0}^n\binom nkF_k-F_n=0.$$
Comment: Thx, I see now how binomial coefficients come out by applying the product rule n times.
Answer: Here is a sketch, where I will omit details for you to flesh out. Recall that $\dbinom{n}{k}=\dbinom{n}{n-k}$, and rewrite the sum under consideration as
$$\begin{align*}
\sum_{k=1}^{n}\binom{2n+1}{2k}B_{2k}&=\sum_{k=1}^{n}\binom{2n+1}{2n-2k+1}B_{2k}\\
&=\sum_{k=1}^{n}\frac{(2n+1)!}{(2n-2k+1)!}\frac{B_{2k}}{(2k)!}\\
&=-1+\sum_{k=0}^{n}\frac{(2n+1)!}{(2n-2k+1)!}\frac{B_{2k}}{(2k)!}
\end{align*}$$
where the last sum should be recognizable as a convolution. Recall that multiplying two power series yields a new power series whose coefficients are a convolution of the coefficients of the two original series, and proceed from there.


Vim -- Syntax highlighting depending on whether whole line is commented

Question: Is it possible to have vim highlight folds differently depending on whether every line in a fold is only comments or whitespace? In that case, how?
Answer: You cannot change the fold highlighting, as there's only one highlight group for all folds (:help hl-Folded). What you can do is indicate the "all comments"-nature of a fold via a custom fold-foldtext; for example, you could prepend COMMENTED:. It would then look like this:
+--  3 lines: # some stuff here

COMMENTED: +--  3 lines: # comment

command 2
command 3

The second part of a solution is determining whether all lines inside a fold are actually comments. This could be done by querying the syntax highlighting (via synID()), which would be universal, but also cumbersome and potentially slow. If all you care about is fully commented lines with a comment prefix, you could obtain that from 'comments' for the current filetype and manually match against it. (My ingo-library plugin has a function for that.) If all you care about is a simple, generic comment prefix like # (as used in shell scripts, Perl, etc.), a simple pattern match will do, like this:
function! CommentIndicator()
    for l:lnum in range(v:foldstart, v:foldend)
        if getline(l:lnum) !~# '^\s*#'
            " This fold is not fully commented.
            return ''
        endif
    endfor
    return 'COMMENTED: '
endfunction

let &foldtext = 'CommentIndicator() . foldtext()'

Answer: Yes, it is. Actually, you can use foldmethod=expr.
As an example:
set foldmethod=expr foldexpr=getline(v:lnum)=~'^\s*'.&commentstring[0]
You can see full answer with similiar problem here: [1].
Comment: Thanks for the answer, but as I understand it, this only lets me fold the comments selectively. I'm fine with the method of folding, but I would like to have the folded lines highlighted differently depending on whether they only constitute comments.


Killing a bigger animal causes more bad karma than killing a smaller animal?

Question: I know that killing virtuous beings is a grave bad karma. But when it comes animals, virtue is irrelevant. I have heard from monks that bigger the animal greater the sin it is to kill it. How is that so? Why does physicality matter at all? Isn't it just a matter of your intention when it comes to karma?
Answer: My knowledge in Buddhism is quite poor. IMO it is a greater sin to kill a larger animal than to kill a smaller animal but this cannot be the case always! Let me ask you a question. Which is easier, to kill an ant or to kill an elephant? Generally the effort and planning you have to go through to kill an elephant is much greater than to kill an ant. The greater the effort you are willing to put is because of the greater intensity of cruelness of your mind which makes it a greater sin. True physicality isn't what determines this. Hope this answers the question
Comment: since kamma is intention, i think there's no difference provided in both killings there's intention to kill. in the same way killing an elephant by accident entails bad kamma no greater than unintentional killing of an ant.
Comment: We are not talking about unintentional killing. Your thinking is not exactly accurate. there are instances where in which both karma can be the same. But intense intentions are needed to kill larger animals unlike for smaller animals making it worse than the case of an insect
Comment: Did someone just down vote this??
Answer: The intensity of Karma in killing of a being including an animal can be influenced by these 2 factors:

intensity of volition - more planning or effort the worse (elephant vs ant), more stronger your desire to kill the worst
conciseness of the being - if the being has a higher level of conciseness (elephant vs ant) and virtue (bear vs cow) the worst. Hence virtue of the animal also plays a role. E.g. sakes are to have more wroth than more tame animals.
Answer: In the novel The Dalai Lama's Cat, the Dalai Lama is quoted as teachiing,

I understand what you're saying, but there are some who would say that eating a cow is better, because a single cow can provide more than one thousand meals. A fish, only one meal. Sometimes it takes many prawns, many sentient beings, for only one meal.

And,

It's a very big subject. You will find that some people tell you there is only one way, this way, which happens to be the way they think, and that everyone else should change their views to be like them. But it is really a matter of personal choice. The important thing is to make sure our decisions are guided with compassion and wisdom.

This is a subject on which different people (and, maybe, different schools of Buddhism) differ.
You wrote, "But when it comes animals, virtue is irrelevant" -- I don't know whether there's any Buddhist school/tradition which that's an accurate description of.
The kind of opinion I quoted above is not based on "virtue is irrelevant", instead it's based on "life is dear to all".
Answer: Buddhaghosa, an influential 5th-century Theravada commentator, states:

With regard to animals it is worse to kill large ones than small. Because a more extensive effort is involved. Even where the effort is the same, the difference in substance must be considered. In the case of humans the killing is the more blameworthy the more virtuous they are. Apart from that, the extent of the offence is proportionate to the intensity of the wish to kill.

So it seems to be the additional effort that makes it morally worse to kill bigger animals. Effort is a direct expression of cetana (volition). As Peter Harvey states:

cetana is the motive for which an action is done, its immediate intention (directed at a specific objective, as part of fulfilling a motive), and the immediate mental impulse which sets it going and sustains it.

References:

E. Conze, Buddhist Scriptures, Page 70, Penguin, 1976.
P. Harvey, An Introduction to Buddhist Ethics: Foundations, Values and Issues,
Page 17, Cambridge University Press, 2012.
Answer: According to the Bhikkhu Patimokkha (quoted below), which are rules for monks, killing a human is grounds for immediate and irreversible dismissal from the monastic order (parajika).
However, deliberately killing an animal is an offense that requires only confession (pacittiya) within the monastic order, usually with the intention not to do it again. It's not as severe as killing a human.

Intentionally bringing about the death of a human being, even if it is
still a fetus — whether by killing the person, arranging for an
assassin to kill the person, inciting the person to die, or describing
the advantages of death — is a pārājika offense. (Pr 3)
Pouring water that one knows to contain living beings — or having it
poured — on grass or clay is a pācittiya offense. Pouring anything
that would kill the beings into such water — or having it poured — is
also a pācittiya offense. (Pc 20)
Deliberately killing an animal — or having it killed — is a pācittiya
offense. (Pc 61)
Using water, or getting others to use it, knowing that it contains
living beings that will die from that use, is a pācittiya offense. (Pc
62)

According to AN 6.87, there is actually a list of people a person could kill or injure, and such a person will never be able to have the right mental state or moral capacity to learn the Dhamma:

"Endowed with these six qualities, a person is incapable of alighting
on the lawfulness, the rightness of skillful mental qualities even
when listening to the true Dhamma. Which six?
"He has killed his mother; he has killed his father; he has killed an
arahant; he has, with corrupt intent, caused the blood of a Tathagata
to flow; he has caused a split in the Sangha; or he is a person of
dull discernment, slow & dull-witted.
"Endowed with these six qualities, a person is capable of alighting on
the lawfulness, the rightness of skillful mental qualities even while
listening to the true Dhamma. Which six?
"He has not killed his mother; he has not killed his father; he has
not killed an arahant; he has not, with corrupt intent, caused the
blood of a Tathagata to flow; he has not caused a split in the Sangha;
and he is a discerning person, not slow or dull-witted.

According to MN 86, Angulimala killed many human beings, but he could still change and become an arahant. So, probably, he did not commit the transgressions above (killing father, killing mother, killing arahant, injuring Buddha)
So this shows the value of humans above animals, and the value of the Buddha, the arahant and one's parents above all other humans.
So, the answer is yes, there is a difference in the consequence and effects of killing.
With this, we can extrapolate, that it's worse to kill a dog or cow, than a mosquito or cockroach. It's not the physical size, but it's the mental and emotional capacity of the animal.
That said, it would still be impossible for an arahant to kill any animal, however small, as the arahant is free of all mental defilements. In other words, to do any killing at all, you must have mental defilements.
Answer: Do you think that killing a baby causes less bad karma than killing an adult?
I'm talking about humans here and from my point of view, killing a baby, just for fun, this is pure evil. Maybe even more than killing an adult. Why? Because the baby is not yet able to defend himself.
This is the same thing for the animals. When you kill an animal, you must have a good reason for that. For example, you can kill to survive, to eat and you can kill also to defend yourself when you are being attacked.
If you kill animals just for fun or if you contribute to the extinction of some species, this is evil.
Example, killing hundreds of rhinoceros only to take the horns for sell it to some japanese people who are stupid enough to think it will help them to get better "erections": Evil.
All this to say that you shouldn't feel ashamed if you only have killed a couple of annoying flies in your life. There is way more evil compared to this. Everything is relative...
Comment: I doubt the amount of bad karma is decided on the ability of the victim to defend themselves
Comment: And there is never a good reason to kill. Maybe a least evil reason
Answer: Ants are not animals. Killing should be avoided. The only time to kill an animal, would be in a life threatening situation, or to eat it. The act of killing is the same for a small animal as it is a bigger animal. Both are living creatures. There is no difference. To kill an animal, just to watch it die, is pure evil. Bad Karma would be, is the type of animal that you killed, one day surrounds you in large numbers, and looking for blood.
Comment: Ants are not animals? animals = _Animalia_ → _Arthropoda_ → _Insecta_ → _Hymenoptera_ → _Apocrita_ → _Vespoidea_ → _Formicidae_ = ants.
Answer: It's not about the physical size for a living creature in this universe, it's all about the intention to do so.
For example: A human kill daily billions of living creatures, totally unaware about it. We call them bacteria. But they are living creatures too. The point in this case is: THIS bacteria are only there to do one task and then die cause of thousands reproductions in nearly the same time. So ... it's not your fault ... it's natural intension.
The other site is: To killing an animal / human just for fun is extremely bad and pointed out as a rough negative karma.
But there is a point people are talking very aggressive about, is killing animals for eating. There are many points about this but if it's not 100% necessary to do so (for example as an Eskimo or living in the tundra in Mongolia) there is no way to say "This is normal and the karma doesn't count here".

"To follow the way of a vegetarian is nearly the half way to nirvana."
  - Siddhartha Gautama

.

"In his final teachings before he physically left this earth, the
  Buddha foresaw that a situation would arise in the future where those
  speaking in his name would pervert his Doctrine and encourage meat
  consumption. So here, in this great Nirvana Sutra, he lays down his
  last will and testament on the matter: in no circumstances should one
  eat meat or fish " nor animal corpses, found in the jungle, for
  instance " nor even accept from a donor a meal which contains an
  abundance of flesh-foods. The very contact of other food with meat is
  deemed defiling and requires purification of the food by water. It is
  quite evident from all this that the Buddha in no way condoned the
  eating of meat and was keen for his monastic and lay followers to
  abjure the uncompassionate practice of meat eating and follow the pure
  path of vegetarian Mahayana. In this, we would be wise and benevolent
  to follow him."
Comment: Google suggests that these quotes are from Dr. Tony Page paraphrasing the [Mahāyāna Mahāparinirvāṇa Sūtra](https://en.wikipedia.org/wiki/Mah%C4%81y%C4%81na_Mah%C4%81parinirv%C4%81%E1%B9%87a_S%C5%ABtra).
Answer: IMO it's better to avoid hurting and killing all beings. Despite of how big or small karma will we get. They both aren't do good for us.


jQuery BBQ Plugin Confusion

Question: I am relatively new to JavaScript and jQuery.
I am using the jQuery BBQ plugin to provide back page functionality. I have the following implementation:
<code>// Be sure to bind to the "hashchange" event on document.ready, not
// before, or else it may fail in IE6/7. This limitation may be
// removed in a future revision.
$(function(){

  // Override the default behavior of all `a` elements so that, when
  // clicked, their `href` value is pushed onto the history hash
  // instead of being navigated to directly.
  $(".content a").click(function(){
    var href = $(this).attr( "href" );

    // Push this URL "state" onto the history hash.
    $.bbq.pushState({ url: href });

    // Prevent the default click behavior.
    return false;
  });

  // Bind a callback that executes when document.location.hash changes.
  $(window).bind( "hashchange", function(e) {
    // In jQuery 1.4, use e.getState( "url" );
    var url = $.bbq.getState( "url" );

    // In this example, whenever the event is triggered, iterate over
    // all `a` elements, setting the class to "current" if the
    // href matches (and removing it otherwise).
    $("a").each(function(){
      var href = $(this).attr( "href" );

      if ( href === url ) {
        $(this).addClass( "current" );
      } else {
        $(this).removeClass( "current" );
      }
    });

    console.log(url)
    $.getScript(url)

  });

  // Since the event is only triggered when the hash changes, we need
  // to trigger the event now, to handle the hash the page may have
  // loaded with.
  $(window).trigger( "hashchange" );
});
</code>
Now this works great, if I go direct to mysite.com/brands the URL loads fine, and when I click a tab the URL shows up like this http://localhost:3000/trends#url=/trends/latest which is OK, the back button works when I go through the other tabs on the page.
$.getScript calls the JavaScript that currently loads my partials into the templates.
The problem is that it only seems to work on a one-layer basis. If I click my parent nav item Trends, and click a tab, the plugin doesn't work. Its like it refuses to see it.
I can see the BBQ plugin has advanced features, but I'm not sure if what I want is even advanced.
Can anyone suggest from the jQuery, or previous experience with the plugin what I could do?
Much appreciated.
Thanks,
Geoff
Answer: You probably want 'two layers', as in 'two menus'... The more advanced example on jquery-bbq's website is maybe what you are looking for:
http://benalman.com/code/projects/jquery-bbq/examples/fragment-advanced/

jQuery BBQ Plugin Confusion


Expression for the centripetal acceleration

Question: Is the expression $$\frac{v^2}{r}$$ for centripetal acceleration,only valid for uniform circular motion, or is it also valid even when particle is moving in a non-uniform circular motion?
Comment: It applies to any smooth path. And the specific case of non-uniform circular motion is explicitly discussed [here](https://en.wikipedia.org/wiki/Circular_motion#Non-uniform).
Answer: With little differential geometry, velocity and acceleration can be written as:
\begin{align*}
  \mathbf{v} &= \dot{s} \, \mathbf{T} \\
  &= v \, \mathbf{T} \\
  \mathbf{a} &= \ddot{s} \, \mathbf{T}+ \kappa \, \dot{s}^2\mathbf{N} \\
  &= \frac{d^2s}{dt^2} \mathbf{T} + \frac{v^2}{\rho} \mathbf{N} \\
  &= v\frac{dv}{ds} \mathbf{T} + \frac{v^2}{\rho} \mathbf{N} \\
\end{align*}
where $s$ is the arclength, $\kappa$ is the curvature and $\rho$ is the radius of curvature.
Acceleration will include the tangential component (along $\mathbf{T}$) and normal component (along $\mathbf{N}$) which is the centripetal acceleration but is given by radius of curvature instead.
See also answer 1 and answer 2 of mine.


Nylon or steel strings

Question: I have just bought myself an old acoustic guitar to learn to play. It's a'Kiso Suzuki 9502' It is presently strung with steel strings but is this correct?
  Regards, Marty.
Comment: Yeah, you probably should have passed on this purchase but may work out. That is a nice old guitar. Take the steel strings off immediately and do not ever put on steel strings again. That is a classical and should only have nylon strings.
Answer: Do not put steel strings on a classical guitar.
The construction of a classical guitar is not engineered to withstand the tension required for steel strings.  Steel strings can have two times the tension than nylon, and the additional tension will eventually pull off the bridge and cause warping, and so forth.
Answer: If my google image search is correct, the "Kiso Suzuki 9502" is a classical guitar which means it has to be strung with nylon strings. However, it could be that what you assume to be steel strings is simply nylon wound with metal, in which case your guitar is already strung with nylon strings.

Nylon or steel strings


Gauge anomalies?

Question:
Why are gauge anomalies so important for any model?

Secondly, any model has to respect the gauge anomalies cancellation requirement?
If this isn't true, then why does one check their model to look for gauge anomalies cancellations?
Comment: What do you mean by "so important"? Are you asking why we care about anomalies (gauge or not) to begin with? Related questions that might help you formulate a more precise question: https://physics.stackexchange.com/q/33972/50583, https://physics.stackexchange.com/q/300592/50583
Comment: 1. renormalizability, and its broader implications. 2. Yes.
Answer: Ok I am by no means an expert on the topic but can hopefully give a bit on insight on your question:

It depends on what you mean by so important but I can sketch a few things out for you:

I am not aware where you stumbled across anomalies but there are in essence different types of anomalies:
Purely gauge,
Mixed gauge global &
Purely global, also sometimes known as t'Hooft anomalies.
Now note that in essence, they all work exactly the same calculation wise (up to switching out a few group factors here and there) but their interpretation is widely different.
Let's first sum up what the problem of these anomalies is in general (at least for the non pure global ones):
These anomalies normally tell you that under a symmetry transformation of a certain group the path integral measure will pick up a phase factor depending solely on the group parameters, particle content, and a topological term (in 4-d this term depends on $F\wedge F$ and the manifold you are integrating over, where $F$ is the field strength tensor).
Now what does this tell us? First of all, these anomalies are purely Quantum effects as they come about from the path integral, something which classical physics can not depend upon. Second of all this makes it seem like these anomalies lead to the symmetry not being a symmetry of the
The second point now depends on the type of anomaly we are talking about:
Let us first look at gauge anomalies your mentioned:
The above argument seems to imply that a gauge transformation is no longer a symmetry of our quantum theory if the anomaly does not vanish! But that can never be the case as a gauge symmetry is by definition a redundancy of our theory and as such can never be broken! Therefore we better make sure that this is never broken! i.e that the anomaly of our theory equates to $0$! I think this also answers your second question we do always have to check if the gauge anomaly canceles for our theory to valid as a quantum theory.
Now onto the other types of anomalies:
The mixed gauge, global anomaly has the same problem that it looks like one of the symmetries involved here is no longer valid in the quantum case, but this is no longer a problem, it simply tells us that the global symmetry group we are looking at is no longer valid in the quantum theory! As such these types of anomalies can give us insight on what symmetries survive quantization.
One concrete example of this is the U(1) axial symmetry in QED, which is a symmetry of the classical but not quantum theory.
Now the last type of anomaly is the most subtle but probably also the most powerful one:
t'Hooft anomalies at first just seem to tell us that if we were to gauge one of the symmetry groups that were involved in the calculation, we would either break a global symmetry or just have a sick theory altogether but what happens if you do not plan on doing so? Are they still useful?
The answer is yes and in my opinion they turn out the be the most useful because of the following fact:
Anomalies do not change under RG-flow (up to spontaneous symmetry breaking). Thus the anomalies of the IR- theory have to match those of the UV theory. Why is this useful? Look for example at QCD a theory that flows to strong coupling in the IR. This is a regime where perturbation theory fails completely and it is a major open problem in physics to understand what happens there. We have very few tools to talk about this theory but one of them are anomalies. We know that whatever pyhsics we conjecture to take place, has to have the same t'Hooft anomalies. For example people expect that this theory confines in a certain way and one way to check if that is that that the anomalies have to match! Now this is by no means a proof for this statement but puts a very strong restriction upon the types of allowed models!
If you want to read more about this or see some actual calculations of this stuff I can heavily recommend reading the sections on anomalies in David Tongs notes on Supersymmetry or Gauge theories, both of which can be found here.

Gauge anomalies?


Does "bracing" the core increase the risk of injuries like hernia?

Question: I have had an inguinal hernia surgery about an year ago,and am back to normal lifting,now in case of lifting weights near the PR's we know that we have to brace the core in order to keep the torso stable and both hips and shoulder should rise together(in case of squats) to have a good rep.But bracing the core means keeping air within the diaphragm and contracting the abdominal muscle for a tight torso,now I know that this puts pressure in the abdominal wall,so should I prevent heavy squats or I should keep  just doing it,just keep my progress steady? Also are there any corrective exercises for a person who has suffered from inguinal hernia like strengthening the abdominal walls?
Answer: Abdominals are actually there for our spinal health. We must use our abs and glute muscles to keep our spine under control. However, bracing the abs means contracting them isometrically, it does not mean holding your breath.
If you are afraid, you should not go heavy like 1 rep max. However, even if you are lifting 2 kilos from the ground, you should approach it like it is very heavy. So, try to control your abdominal muscles without "holding" your breath. Holding your breath is not good.
Addition;
No, it does not increase the risk of hernia. Instead it decreases it. It is very possible to get lower-back problems if you don't know how to brace your abs (and also good form).
Comment: Thank you for the advice.Now my training approach is steady progressions instead of trying to hit PRs every week. It's not as exciting but still maybe it's safer comparatively.
Comment: He mentioned he already had inguinal hernia, which is not the same as spinal hernia. Lifting heavy is not without risks and it might increase the risk of hernia.
Comment: @sagnikdas yes, building strength and testing strength is very different. It is actually not useful to check for 1RM unless you are competing. BKE, that is why I specifically mentioned lower-back and spine. Thank you for your insight.


At what point was the Byzantine Empire's decline irreversible?

Question: I've heard various arguments that the Byzantines were dealt the mortal wound at Manzikert in 1071 which allowed the Turks to claim most of Anatolia and set the stage for the later sacking of Constantinople by the Latin Crusaders. I've also heard that the it was the sacking itself that set the Empire on a course to its ultimate end. With the fall of Constantinople in 1453 being generally accepted as the end of the Byzantine Empire proper; when did the slope toward that end begin?
Comment: Bringing the above point back to reality, you _do_ have to want it and you have to make the right societal choices to make it happen. The aristocracy in Byzantium were _extremely_ powerful and plenty of them made separate peaces and side deals in their own interests with the Venetians, the Genoese, the Turks, &c. Sure, there are some people (mostly the poor) who would go to the walls for the Theotokos but there are plenty (including most of a sophisticated cosmopolitan upper class) who are perfectly fine with praying 5 times a day so long as most of their deeds and contracts stay valid.
Comment: I changed the tag [tag:1400s] to [tag:15th-century]. [See here](http://meta.history.stackexchange.com/questions/44/tag-synonyms-and-tagging-to-attract-experts-journalists-students-of-history)
Comment: The decline of Byzantium was not irreversible until quite late, if then.  Had Byzantium made different choices -- in politics, in battle -- or had their enemies made different choices, the outcome could have been very different. Inevitability only happens when *no* choices by either side can affect the final outcome.  Consider, for example, the Turks choosing to move south into Arab lands, or several fortuitous Turkish civil wars, or Enrico Dandolo dying young. This is basically a meaningless question.
Comment: Well according to my thorough and expansive research with the _Europa Universalis_ series, there is __no__ point at which the Byzantine Empire couldn't have rebounded to conquer the world until around 1454.
Answer: I don't think it is possible to idenitify a single point in history as beginning the "slope toward the end". Such thinking results from the simplistic model of an empire's history as consisting of two segements: "growth" and "decline". In reality, the history of the Byzantine empire is a complex sequence of alternating growth and decline.
I'd say that the first high point of the empire was the end of Justinian's rule, when the borders of the Byzantine empire bore some resemblance to the old Roman empire. A large numbers of events weakened the empire from this high point. They include the loss of much of the Italy to the Lombards in the 6th century and the gradual loss of Levant, Mesopotamia and North Africa to Muslim Arabs starting from the rise of the Umayyad Caliphate in the 7th century.
The Emperor Basil II's rule marked a strengthening of the empire, when the First Bulgarian Empire was destroyed in 1014 and Kievan Rus' accepted Byzantine-style Christianity.
In 1054 the Byzantine Church formally split with the Church of Rome, after a long period of growing tensions. The cause of the tensions was a combination of political rivalry between the Byzantine Emperor and the Pope and religious divergence due to movements such as Monophysitism, Monothelitism and Iconoclasm within the Byzantine Empire. This eventually contributed to the demise of the Empire due to its religious and therefore political isolation. Territorial decline continued with the loss of of remaining Italy to the Normans in the 11th and 12th century and the gradual Seljuk takeover of Anatolia starting in the 11th century.
Another high point was the Komnenian restoration in the 12th century, during which much of Anatolia was temporarily recovered. After that, there was return to severe dynastic strife which was another major factor in Byzantine decline.
During the Fourth Crusade, Constantinople was taken by the (Roman Catholic) crusaders in 1203. The key role in this event belonged to the naval–commercial rivalry between the Byzantine Empire the Republic of Venice. The crusaders couldn't pay for the fleet Venice supplied them and agreed to attack Constantinople as a compensation. The fall of Constantinople caused the split of the Empire into three parts: Empire of Nicaea, Empire of Trebizond and the Despotate of Epirus. The crusaders created their own state: the Latin Empire.
The Empire of Nicaea under Michael VIII Palaiologos managed to restore the Byzantine Empire by taking back Constantinople in 1261. This caused the demise of the Latin Empire, in what is probably the last high point in Byzantine history. The rise of the Ottoman Empire in 1299 caused the gradual eclipse of the Byzantine, with Constantinople falling again in 1453 and remaining "mainstream" Byzantine territory in Morea (Peloponnese peninsula) falling in 1460. The Empire of Trebizond fell in 1461 and the Despotate of Epirus lingered on until 1479 when it also was taken over by the Ottoman Turks.
Comment: +1 This is an comprehensive and thoughtful answer that deserves the checkmark, especially for its *Such thinking results from the simplistic model of an empire's history as consisting of two segements: "growth" and "decline".*
Answer: The Fourth Crusade was the turning point.  The crusade was high-jacked by Venice to take revenge on the Byzantines for past deeds: imprisonments, break of contract, etc... The crusade was aimed to land in Egypt originally, as it was seen as the main threat to taking Jerusalem back.  However, since the crusaders could not pay for the large Venetian fleet, it was arranged that they would do a few missions for Venice first.  Not all crusaders agreed, but the majority saw no choice.  Even the Pope was unhappy with this state of affairs.
So, once Venice took control of Constantinople, a series of civil wars and coup happened. This weakened Byzantium to the point where it could not recover.  From there on, it was just a matter of time before another power took control.
As a side note, the Byzantine fleet was in great part responsible for the might of the empire.  Once the Empire gave this to Venice to build and use, it was just a matter of time before the fleet degraded beyond the local ability to rebuild it.  An example of why out-sourcing is bad.
Source: John Julius Norwich: History of Venice, History of Byzantine Empire.
Comment: Well...it recovered a bit. Just not enough. But the Turks still couldn't take the city walls until they brought in newfangled canon, so perhaps gunpowder deserves the credit instead? Within 2 generations these same Turks held all SE Europe up to the gates of Vienna. So perhaps the Turks being badasses had something to do with it too? Again, I personally don't think its quite this simple, but this is the common position, and you put it forth well, so I don't begrudge the checkmark either.
Comment: This is a very common argument (perhaps the most common). I personally have trouble with it because the city didn't fall to the Turks for another 250 years. That's a pretty dang long time. Longer than the USA has existed. But again this is the argument many scholars stand by.
Comment: Opposite point to TED: This is a very common argument and so is his. The go-to for the late turning point—which he doesn't mention—would 1354, the fall of Kallipolis/Gallipoli to the Turks, which surrounded the Romans and made everything basically hopeless. Personally, I'll go with you _both_ being wrong. __It's still Manzikert__, which was the reason the empire got in hock to the Venetians in the first place and was weak enough to strong-arm.
Comment: @T.E.D. That is a fair comment. The justification is that after the fourth crusade, the Byzantine Empire was (more or less) in constant decline. It never really recovered from it despite it taking a long time to finally collapse.
Comment: @Ily Mantzikert was a defeat but how did it lead the Byzantine Empire to fight the Venetians? Still these two forces fought for trade control and sea power?
Answer: A prior article mentions the empire of Justinian (and Leo, by extension), but I would argue that these are 'Roman' empires which are terminated by the eruption of Islam over much of the East Roman Empire.
This was a pretty traumatic event which led to some serious results. Among them, the abandonment of Latin, abandonment (with some exceptions) of universal pretensions in the western Mediterranean, acceptance of defence against the Muslim and recovery of the Holy Places.
And then there was iconoclasm on the cultural front. If you look carefully, there is a discernible shift in Weltanschauing in the 8th century in the lands ruled from Byzantium which may be called the birth of the Byzantine Empire and civilization and civilizing efforts through the Balkans and beyond Now, I am aware that my comments mimic those of Arnold Toynbee, but this is one case where his old thesis does strike true.
Of course, the Byzantine state enjoyed considerable success under generals like Nicephorus Phocas and Johm Tzimisces and others long before the time of Basil II (Bulgaroctes) But was it already becoming a feudal state? Surviving records from the maritime Themes show central control, but what was happening in the 'wild west'? Doesn't the epic poem Digines Akrites portray a feudal society on the frontier?
Anyway, I reckon that a feudal army went to Manzikert in 1079 and the rot set in. The Commneni had a very faint chance a hundred years later. Byzantium was still the strongest regional power at the time of the first crusade. But feudalism, both Byzantine and western, prevented any combined effort. Then the battle of Myriokephalon (various spellings) destroyed forever any Byzantine pretensions to power forever.
The empire limped on a for a few more centuries and the civilization may have a few sparks of life left, but I nominate Myriokefalum as the death knell of Byzantiu
Comment: Not sure about the feudalism angle (too deterministic-sounding for me) but thumbs-up (and an upvote) for the mention of Myriokephalon - an important but often neglected juncture.
Comment: Do you perhaps mean "*Weltanschauin" - German for **worldview** - rather than (the untranslatable) "*Weltanschauing*"?
Comment: @PieterGeerkens Maybe you meant "[Weltanschauung](https://www.merriam-webster.com/dictionary/Weltanschauung)"?
Answer: Personally, for me, the turning point was Manzikert. It wiped out a good portion of the fighting men of the empire, and caused the Seljuks to take the eastern part of Asia Minor, which was a large source of manpower for the emperors under the theme system. So with the threat of a Seljuk invasion, Empire responded with a plea for help to the West, launching the Crusades. The final blow to the Byzantine dominance was the sack of Constantinople by the Fourth Crusade, from which the Empire never really recovered.
Comment: Manzikert is the usual winner in this contest, but I'd suggest rather Myriokephalon - since actually in the 12th century the Byzantines, rather skillfully playing off the Crusader states against the Muslims and each other did manage to retrieve a large part of their losses and even acquire a brief overlordship over the much-diminished Seljuks of Rum. Then came the sordid defeat at Myriokephalon and undid everything; it can also be argued that it paved the way for the iniquity of the 4th crusade.
Comment: This is a fairly good example of a subjective answer to a question. If it included sources/citations, it would be an excellent example. There is an answer, a justification, and sufficient detail for an external observer to evaluate.
Comment: it's kind of funny: my ancestors were Byzantine subjects, and i know a lot about this kind of thing, but i haven't heard of that battle before.
Comment: On your other question, you should have said something like "under the [so-called] theme system, Asia Minor was a large source of manpower for the emperors." You DID know something about this topic, so you should show what you know, so that answerers know what NOT to explain.
Answer: From what I recall from historical texts that I've read in my travels, the event that seems to have started the irreversible decline was the Fourth Crusade, when instead of heading to free Jerusalem, the crusading armies attacked and sacked Constantinople. With large parts of the Empire fragmented into Latin states by the armies that had attacked them, it helped the Seljuk Turks (and later the Ottomans) hold the Anatolia area of Asia Minor and strengthened their position for furthur conquests as those states fell.
References: Wikipedia's article on the Fourth Crusade
Answer: The thing that really started the fatal downward skid for the Byzantine Empire was the arrival of the Turks from central Asia. They were the best warriors in the area, and just as importantly, were dedicated pastoralists. The best land in the area for their purposes was in central Anatolia, which just happened to be smack dab in the middle of the Byzantine Empire.
For the Byzantines the wealthy coastal areas were more important, but whoever held that central anatolian plain could attack any point on the coast at will. Once the Turks showed up, nearly every military effort of theirs (that wasn't spent on internectine warfare) was spent trying to get that good grazing land in the heart of the empire. The Byzantines could slow them down, sometimes even stop them, but they couldn't turn the situation around.
The Crusades started out as a desparate attempt by the Byzantines to get some help kicking the Turks out of anatolia. Some of these worked better than others. As mentioned by others, the Fourth Crusade backfired completely. But it still took a couple of hundred years (and the invention of cannon) before the Turks finally took Constantinople and extinguished the empire for good.
Comment: -1 Do you have any evidence that the "*Crusades started out as desperate attempt by the Byzantines to get some help kicking the Turks out of Anatolia*".?  I have never heard of this in any of my books on Crusades or Byzantium.  The forth crusade did not backfire on Byzantium: they had no control over it whatsoever. The Doge of Venice manipulated the crusade to attack Byzantium instead of its intended target as a repayment for the fleet Venice provided to the crusaders. See [my answer](http://history.stackexchange.com/a/228/103)...
Comment: @Sardathrion -  http://en.wikipedia.org/wiki/Byzantine_Empire#Alexios_I_and_the_First_Crusade, http://en.wikipedia.org/wiki/Council_of_Piacenza, or pretty much any history of the time. Sorry, but I thought this was so well known it didn't need attribution. Bascially at the Council of Piacenza the Byzantine Emperor Alexius' people asked for help from the West. He was most likely just hoping for mercenaries, certianly not what he got.
Comment: My answer is talking about the Turkish people, not their rulers.
Comment: Ironically, the crushing of the Ottoman Turks by Tamurlane gave the Empire a generation or so of breathing space just before the end.
Comment: Okay, I see what you mean now... You are right that the  situation with Byzantium and the Turks did help start the first Crusade. As to whether it was the sole cause (which I read from your post whether or not it was there ^_~) is debatable and certainly it was not a direct cause for the crusades that followed.  Right, edit your post a little and I'll redress that -1...
Comment: @Sardathrion - Yeah, trying to figure out a good way to edit that line. Your comment made me reread it, and I now see it could also be taken to imply the First Crusade was run by Byzantium, which is just way way wrong.
Comment: How about: "*The Byzantines tried to get help from the western parts of Europe against the Turks.  This was a contributing factor to the start of the Crusades which ultimately backfired badly for Byzantium -- see the fourth crusade.  But it still took [...]*".
Comment: But note that we are talking about two different sets of Turks here: Seljuk and later Ottoman!
Comment: @FelixGoldberg: No; that's like saying it's not the *real* Sicilian mafia if it's from Ragusa instead of Enna. The familial line of the rulers changed; but it's all descendants of the same Turks that won at Manzikert.
Answer: i would date the "irreversibility" of Turkish power to the Sack of Constantinople in 1204. This resulted in the division of the former Byzantine Empire into the Latin Empire, the Kingdom of Nicea, and several "splinter" groups (e.g. Epirus and Trebizond), with Constantinople a "football" between the first two. Without access to "Latin" mercentaries, the ultimate "winner," Nicea, could field armies only a fraction of the size of Byzantine armies a century earlier.
It's true, as T.E.D. pointed out that the Turks became a threat to the Byzantine Empire by the mid-11th century. Yet the rise of the Komnenos Dynasty, 1081-1185 involved A "rollback" (or "reversal") of Turkish power out of much of western Turkey during thaT period.
Answer: I would recommend checking this wikipedia article to have a basis on which to elaborate.
If you check the list of sieges of Constantinople that were successful (after of course the beginning of the Byzantine Empire), you'll find very numerous unsuccessful attempts, and only four successful ones:

One Byzantine emperor against another
The Crusaders
One Byzantyne emperor (supported by Italians and Turks) against another
The final success of the Turks

These three successful sieges represent the only forces that were able to shake deeply the Byzantine Empire: The Turks, the Crusaders, Italian republics as a support for both of them, and, last but not least, the Byzantine Empire itself. Considering these elements -and the general history of the Byzantine Empire-, I would not consider any of the Arab offensives as a turning point for the Byzantine Empire. I would not speak like that of the battle of Mantzikert. Not even the 4th Crusade, because even if it deeply shakened the Byzantine Empire and forcedit to destroy the new "Frank" kingdoms in the Balkans, ultimately Byzantine Empire took back control of nearly all contested territories.
No, the turning point for the Byzantine Empire was the battle of Ain Jalut, when the Mamluks were able to repel the Mongols: Through this battle the Mamluks, that otherwise had never fought the Byzantine Empire directly, had changed the face of Middle East and liberate the Turks from their two main competitors: the Mongols and the Crusaders. Those two threats put apart (after a few other campaigns), they could put all their potential against the Byzantine Empire.
Answer: The Papal led Latin Crusader conquest of Constantinople in 1204, initiated the irreversible decline of the Byzantine Empire.
When the Crusaders captured Constantinople, they, (rather unfortunately), destroyed the City's 800 year Library and University and may have also temporarily converted the Saint Sophia Cathedral into a Catholic Church.
While the Latin Christian conquest of Constantinople was only 50 years long, it was enough time for the Ottoman Turkish Muslims in the East to gain greater imperialistic momentum as the Turks conquered country after country-(primarily along The Silk Route). By the 1400's, a beleaguered and increasingly anachronistic Byzantine Empire-(whose Administrative Capital was no longer in Constantinople proper, but was actually relocated to the Southern Peloponnesian town of Mystras), was incapable of unilaterally and independently defending itself from a burgeoning Ottoman Islamic Empire in the East.
By May, 1453, Constantinople and the Byzantine Empire fell to the Ottoman Muslim Turkish Sultanate and with it, the conversion of the centuries old Saint Sophia Greek Eastern rite Cathedral into an Ottoman Turkish Muslim Mosque. (And, the Janissary Corps was established whereby many Christian men from Asia Minor and even Constantinople-(who were mostly Greek), were forcibly and thoroughly Ottomanized when having to serve in the higher ranks of the imperial Turkish military; though it should be noted that were also voluntary members of the Janissary corps, including, the Ottomans' most famous Architect, Mimar Sinan).
While the Ottoman Muslim conquest of Christian Constantinople was a devastating loss for the Byzantines-(and for Greek Eastern rite Christianity at large), there were some other external influences which helped "pave the way" for the Ottoman's success in 1453.
The Latin Christian West and the Byzantine Christian East....hated each other-(for a variety of reasons).  The sectarian infighting between the Christian peoples was bitterly divisive and ultimately led to the Latin Christian West conquest of the Byzantine Christian East-(albeit for a short while, though with devastating long term consequences for the Byzantines).
Even the Northern Italian city-states, such as Genoa and especially, Venice, greatly benefitted from the Latin West's capture of Constantinople. In doing so, the Northern Italian city states were able to conquer many of Byzantium's Greek island territories, such as, Corfu, Crete and the Cyclades, which were all conquered by the Venetians, as well the Eastern Aegean islands which were conquered by the Genoese. And of course the Aegean island of Rhodes, became a major center for Latin Crusaders, as well as for the Venetians-(as evidenced in the island's widespread and very well preserved Late Medieval and Early Modern architecture).
As one can see, the Papacy, as well the Northern Italian city-states, benefitted greatly from Constantinople's demise and may have purposefully encouraged or even welcomed the Ottoman Turkish Muslim conquest of the Empire's Capital city and its Greek Eastern rite Christian territories.  The Latin West's success in conquering Constantinople weakened the power and influence of the Christian East, while simultaneously, maximizing the power and influence of the Latin Christian West which helped to produce major historical and civilizational aftereffects that have survived....well into the Modern Age.
Retrospectively, the Latin Christian West helped turn the legacy of Byzantium...into a historical anecdote reserved for the back pages of World History.
Comment: Please explain the downvote?


Distance vs cost in QGIS network analysis

Question:
I'd like to calculate shortest route and distance in QGIS 3.2. In the past I have used the v.net.iso, v.net.distance and v.net.path tools. However, I've noticed that there is no distance parameter there, but cost. If I want to calculate the distance in meters where do I specify this?
Do cost mean distance on the screenshot? How do I set it to distance?
Answer: [Updated the answer after question was updated]
The default should be distance if you don't input a cost column.
So the field "Cost for isolines" in your screenshot would mean the cost in CRS units if you don't manually select another precomputed cost column.
So your screenshot settings would output a vector file mirroring your input network, but divided into 4 categories (attribute "cat" with values 1,2,3,4).
Since the "Cost for isolines" is set to 1000,2000,3000; "cat" 1 would be 1000 CRS units (meters for example) from your start points, 2 is 2000, 3 is 3000 and 4 is the remaining network.
If you have computed for example the cost to traverse a line segment in seconds in another column (based on a speed limit for example), you can choose that column under Advanced parameters. Then "Cost for isolines" would correspond to 1000 seconds, 2000 seconds and so on.