Sum of closed convex set and unit ball in normed space

Question: Let $(X, \|.\|)$be a real normed space. Let $A$ be a closed convex suset of $X$ and $\mathbb{B}$ a unit ball in X, i.e.
$$
\mathbb{B}=\{x\in X: \|x\|\leq 1\}.
$$
I would like to ask whether $A+\mathbb{B}$ is still closed.
Answer: Edit: Here is a more complete solution.

Proposition.  Suppose $X$ is a Banach space.  Then $A + \mathbb{B}$ is closed for every closed convex $A$ if and only if $X$ is reflexive.

Proof.  One direction I posted previously.  If $X$ is reflexive then $\mathbb{B}$ is weakly compact.  If $A$ is closed and convex, it is weakly closed.  Then by my answer here, applied to the weak topology, $A+\mathbb{B}$ is weakly closed, and in particular norm closed.
For the converse, James's Theorem asserts that if $X$ is not reflexive, there exists a continuous linear functional $f \in X^*$ which does not attain its norm, i.e. (after rescaling) $\|f\| = 1$ but there is no $x \in \mathbb{B}$ with $f(x) = 1$.  Set $A = \{ x : f(x) \ge 1\}$; $A$ is obviously closed and convex.  Also, there exist $x_n \in \mathbb{B}$ with $f(x_n) \to 1$; let $y_n = \frac{1}{f(x_n)} x_n$, so that $f(y_n) = 1$ and thus $y_n \in A$.  We have $\|y_n + (-x_n)\| = (f(x_n) - \frac{1}{f(x_n)}) \|x_n\| \to 0$, so that $0$ is a limit point of $A + \mathbb{B}$.  Now if $0 \in A + \mathbb{B}$, i.e. there are $x \in \mathbb{B}$ and $y \in A$ with $x+y=0$, then $y=-x$ and so $y \in A \cap \mathbb{B}$.  Since $y \in A$, we have $f(y) \ge 1$.  Since $y \in \mathbb{B}$, $f(y) \le 1$.  Hence $f(y)=1$, but by assumption no such $y$ exists.
For a simple example of a functional which does not attain its norm, consider $X = \ell^1$, $f(x) = \sum_n (1 - \frac{1}{n}) x(n)$.

Here is an example of an incomplete normed space where $A + \mathbb{B}$ need not be closed.
Let $X$ be a dense subspace of $C([0,1])$ which does not contain the constants.  (For example, take $X$ to be the set of all functions $f(x) = p(x) + ce^{x}$, where $p$ is a polynomial with $p(0) = 0$ and $c \in \mathbb{R}$.  $X$ is dense because by the Weierstrass theorem we can approximate $e^x-1$ by polynomials vanishing at 0, so the constants are in the closure of $X$, whence by Weierstrass again, the closure of $X$ is dense.)  $X$ is still equipped with the uniform norm.
Set $A = \{f \in X : f \ge 1\}$.  $A$ is easily seen to be closed and convex in $X$.  Since $X$ is dense in $C([0,1])$, for each $n$ we can choose $f_n, g_n \in X$ with $\|f_n - (1 + 1/n)\| < 1/n$, $\|g_n - (-1 + 1/n)\| < 1/n$.  Then $f_n \in A$ and $g_n \in \mathbb{B}$.  It is easy to see that $f_n + g_n \to 0$ uniformly, so 0 is a limit point of $A+\mathbb{B}$.  On the other hand, if $f \in A$ and $g \in \mathbb{B}$, then $f \ge 1$ and $g(x) \ge -1$, so $f+g \equiv 0$ only if $f \equiv 1$ and $g \equiv -1$, which is impossible.  Hence $0 \notin A+\mathbb{B}$ and so $A+\mathbb{B}$ is not closed.
One question remains: does this property fail in every incomplete normed space?  Another paper of James gives an example of an incomplete normed space where every continuous linear functional attains its norm, so the construction from the non-reflexive case will not carry over.
Answer: Let $(e_n)_{n\in\mathbb{N}}$ be an orthonormal basis in a Hilbert space and let $A = \{(1+\frac{1}{n})e_n : n \in \mathbb{N}\}$.
Comment: Dear Sir. Thank you for your anwser. Here $A$ is not convex.
Answer: In any topological vector space, the sum of a closed set and a compact set is closed. The only book I have handy is "Topological Spaces" by Claude Berge. In that book, this result is theorem 5 in chapter 9. I assume that other books have the same result.
Note: you don't need to require that one of the sets be convex, or that one of them is a unit ball, or that the space has a norm.
Comment: This is true, but doesn't answer the question, as $A$, $\mathbb{B}$ could both be non-compact.
Comment: @bubba: Be careful. $\mathbb{B}$ is not compact in infinite dimensional space $X$.
Comment: @blindman. Oops. It's been about 30 years since I looked at a topology book, and I see that my memory isn't as good as I thought. Apologies.
Answer: I think it's clear that $B$ is closed, because the norm function $X \rightarrow \mathbb{R}$ is continuous, and $B$ is the preimage of the closed unit interval.  Also, the addition function $+: X \times X \rightarrow X$ is continuous.  For any closed $A$ and $B$, $A + B = +[A \times B]$ is the continuous image of a closed set, and is therefore closed.  So the answer is yes.
Comment: The continuous image of a closed set is not in general closed.  Consider $f :\mathbb{R} \to \mathbb{R}$ with $f(x) = \tan^{-1} x$; $\mathbb{R}$ is closed but $f(\mathbb{R}) = (-\pi/2, \pi/2)$ is not.
Comment: I just deleted a completely wrong answer... sorry.
Comment: Very good, thank you @Nate.  I wonder if we can save that argument somehow, though.  If we assume that $A$ is compact, we can say that the image of a compact set is compact, right?  And in a metric space, compact sets are closed.
Comment: @HewWolff: Yes, if $A$ is compact then this is true.  See [my answer here](http://math.stackexchange.com/a/214568/822), which as I mention works for any topological group.
Comment: B is compact, so I don't think we need to require that A is also compact.
Comment: Nate: Oops again. This is harder than I thought, and I'm beginning to wonder if it's true after all. Thanks for pointing out my misreading of the question. It's clear that B is compact, but A is not assumed to be, only closed convex. Back to the drawing board.
Comment: @bubba: Here $\mathbb{B}$ could be noncompact.


Emacs 24.1: How do I restore i-search Ctrl-Y behavior from older versions?

Question: In emacs 24.1, when you do Ctrl-Y in an interactive search, it yanks the kill buffer into the search string ("it pastes the clipboard contents" in any-other-app's language) and tries to
match it.
In the last 20 versions or so, pressing Ctrl-Y matches the rest of the current line.  I
have two very common use cases:

Match this line, revert the buffer, and search for the line
(less often:) Where else is this text in the buffer?

I tried modifying /lisp/isearch.el, switching the bindings for
isearch-yank-line (which I want) and isearch-yank-kill (which I'm fine binding
to the ridiculous \M-s\C-e key sequence). But I don't think this file even gets
picked up. But I don't think this file even gets loaded.  If I explicitly load
it, I still get the 24.1 behavior.
Here's my change:
(add-hook 'isearch-mode-hook
   (lambda ()
     (define-key isearch-mode-map    "\C-y" 'isearch-yank-line)
     (define-key isearch-mode-map "\M-s\C-e" 'isearch-yank-kill)
    ))

No change in the behavior.  I even tried hacking isearch.el, still no change.
This is on Windows btw, but I suspect it doesn't matter.
Could someone tell me how I can restore the old binding?
Answer: what works for me is taking your hook and combining it with my own isearch-mode-hook.
(you could put this in ~/.emacs … i go a bit further and keep separate modes in ~/.emacs.el/.modes.el, then byte-compile that file, then (load ".modes" t t) to keep things a bit less cluttered.)
(setq isearch-mode-hook
      '(lambda nil
     (define-key isearch-mode-map "\C-y"   'isearch-yank-line)
     (define-key isearch-mode-map "\C-f"   'isearch-repeat-forward)
     (define-key isearch-mode-map "\C-t"    'isearch-toggle-regexp)))

works like a charm.  thanks for helping my get my ^Y back


A zero gravity life form that harvests asteroids?

Question: I've got an idea about a creature that lives in a vacuum and uses some faculty to collect elements, integrating them into itself for growth. What would it look like? How would that work? I'm almost thinking like funguses with a collecting mycelium and fruiting bodies. For now, ignoreing what the thing would do in favor of how it would sustain itself and/or grab high-speed objects and eat them, like spaceships. My main characters end up running into one. It wants to eat them. Can this be done?
Comment: Brainstorming is [off-topic](http://worldbuilding.stackexchange.com/help/dont-ask).
Comment: Material is not as much of a concern as how it's going to get its energy.
Comment: Photosynthesis... Maybe? I'm asking for brainstorms,
Comment: Okay. Didn't actually mean brainstorming. Meant "Give me some ways this would work."
Answer: Grabbing things in space is difficult.  Object's velocity vectors with respect to each other tend to be gargantuan.  "Catching" something would probably not be in this creature's repertoire, especially since it doesn't need to catch them to continue to reproduce.
Your fruiting body might be a gossamer net cast out into the black of night.  It might need to stretch for hundreds of kilometers in all directions.  When another body crosses this net, and touches it, the fungus might be able to calculate its ballistic coefficients, and orchistrate a small spore pod to be accelerated into this new mass as a lower insertion velocity... low enough to be able to stick to the mass once it arrives.
From there, now it's just a matter of continuing to reproduce on this object, converting its mass until it is time to produce another fruiting body out of the material it collected from the other object.
Travelers on a space ship likely would not even notice their transit through the gossamer webs of the fruiting body, given how fragile they would be in order to maximize efficiency of material usage.  The distances between asteroids is vast, even in the asteroid belt.  Even with the great patience a fungi can muster, creating a good sized net will be essential.  The traveler would simply continue on their way.
If stellar traffic has been around long enough for evolution to start to play a part, it might even develop a parasitic relationship with spaceships, switching to a different mode of infection if it identifies the materials that make a spaceship different than an asteroid.
Comment: That sounds awesome. May pick that.
Answer: You will have to forgive the lack of sources in this answer, as I am using references from a real book which I own (because I'm really that much of a nerd). Usually I'm much more link heavy in my answers.
The creature that I am using is something like a "cloud" or massive collection of gases, as referenced here. It is made up of small, organic "organs" within a larger, gaseous form. These organs are connected by electrical paths much like our own brain cells are connected to one another. The creature is essentially one giant brain, with the organs acting as cells, communicating. The cloud is made up of the same materials our own body is made up of, but on a much larger scale and in a gaseous form. These allow the brain to travel through the vacuum of space (with some minor handwavium).
This creature feeds on gaseous elements, hydrogen, oxygen, nitrogen, etc, all the gases that are found in abundance in the universe. In the short story it is based on, the creature sucks out needed replacement gases of a planet's atmosphere and leaves behind wastes (the story specifically puts Earth in danger of this creature). It can also eke out pockets of gas by heating up its own body (potentially hotter than a sun) to evaporate gases from asteroids. The creature is even capable of moving through space by thrusting out waste gases to propel it forward, giving it some maneuverability.
Should your spacecraft exude some kind of gaseous waste from its engines, the Black Cloud may be attracted to it, and begin to follow behind it, sucking up the trail of waste gas. It may at first only feed harmlessly on this waste gas. The cloud would then become hungrier, and become aware of an oxygen-rich environment within the craft. While your spacecraft might be fully sealed from gases, perhaps the cloud has some gases which are radioactive, damaging the spacecraft. Perhaps even the cloud can infiltrate the engines to try and get more sweet delicious gases, forcing your spacecraft to a halt. Perhaps the cloud can heat up its body to "smoke out" the gases within your spacecraft, mistaking it for some weird asteroid. And even the solid "organs" of the cloud can perhaps physically attack the ship, seeking to expose the gases within.
Possibilities may or may not be endless with this sort of set up.
Comment: Cool, but I'd gotta be careful not to plagiarize.
Comment: I would consider it taking inspiration from, not plagiarizing. The idea of a gaseous creature could be taken and tweaked as more of an homage to previous authors. This is very common amongst the sci-fi author community. As long as you make it your own idea, no one would accuse you of being anything but an avid sci-fi reader.
Comment: Fair. Good idea, for sure.
Answer: One way that it could spread is with something like a solar sail.
The sail would be very big, and spun from the material harvested from the asteroids; Namely carbon, nickle, iron, etc.
The solar sail would have a tether attached, which would be used to tow the lifeform around, and would look something like a dandelion seed.
It would also collect energy from the sun like a giant leaf or solar cell. This would help it to collect much more energy than it normally would get.
The solar sail would have fruiting bodies around the perimeter, which would act like weights and cause it to act like a weighted net. A little bit like this:

So when the sail encounters an object, the weights would cause it to wrap around the object, entombing it so it can be processed and digested.
The main body of the life form would then use the tether line to pull itself to the new source of materials.
Comment: Or, elaborated, have the sail be the entire thing.
Comment: That would work too. My thought was that this way there would be the possibility of sending sails off by themselves as seeds to create new ones if the life form gets to big. But just growing into a larger sail would work too. Maybe bud off smaller versions as it's able to reproduce.
Comment: Chosen as best because I ended up using this one. Thanks, all!


Why are Turkish people and other Turkik people considered of Mongolic race if their language is not in the Mongolic language family?

Question: I saw that Turkish people are considered of Mongolic race even though Mongolic and Turkic are separate language families? Why are those races considered the same but their languages are so different that they come from different language families ?
Comment: Both Turkish and Mongolic people are considered to be part of the human race.  What is the Mongolic race? how is it defined? by whom? I will also downvote any question that includes an unreferenced citation. If you saw that assertions somewhere, you have to cite that. There is a huge difference between an assertion in a scholarly article and one in the Protocols of the Elders of Zion.
Comment: You and I speak the same language, yet there's a good chance we're not the same 'race'. Why should that be so?
Comment: I never heard about Mongolic race,and racial classification has nothing to do with language. Also, Turkik languages are in the same language family as Mongolian. In short, all your premises are wrong.
Comment: The point of such statements seems to be that the first (recorded) people who called themselves "Turks", i.e. the Göktürks, were centered in what is now Mongolia. That was roughly 1500 years ago. So what is now Mongolia does indeed take an important place in Turkish history. This topic seems to pop up a lot in certain nationaliatic contexts and therefore often accompanied by a certain level of stupidity. But that does not mean that the history behind it is uninteresting.
Answer: There's no scientific definition of "race", so that part of the question is unanswerable.
Linguists do try to classify languages though, since that can be done (mostly) objectively, based on similarity of grammar and words. One popular theory has been Turkic languages and Mongolic languages are part of a larger family of languages, named Altaic.
Today this is no longer a universally accepted theory, with the alternative being that the similarities are more due to long proximity than heritage. But Altaic was the consensus accepted theory until about 15-20 years ago (which is practically yesterday for oldsters like me). So it can be found in many textbooks and references floating around today.
Comment: @DmitryAlexandrov - I'm sorry, but for the most part (the way people like to use it for visual identification of individuals, like the question appears to be shooting for) its just not. For instance, I have "black" friends here in the USA that have genetically tested out (due to their interests in Genealogy) *more* European than a lot of "white" people. Most "black" African-Americans, if they go to Africa, are considered "white" over there. Nothing physically changed about them on the flight over. The popular view of race is an entirely social construct (with a nasty hammer on the end).
Comment: «There's no scientific definition of "race"» — T. E. D. // Untrue. Of course, there are scientific definitions of 'race' – several of them.
Comment: @T.E.D.  Well, the "popular" view on everything is a social construct - that's what "popular" means.  But scientists do discuss race and there are valid reasons to classify human populations according to genetic and physical traits.  Epidemiologists, for example, are keenly interested in questions such as this.
Answer: First, Turkish people are not in general considered of Mongoloid race, neither are Turkic-speaking Azeris. These two peoples are usually classified to belong to Europoid race with maybe only admixture of Mongoloids.
Second, there is a lot of Turkic-speaking peoples that are indeed classified Mongoloid: Kazakhs, Kyrgyz, Uzbek, Turkmen.
The reason is that Mongoloid race was named for Mongols who were a typical representation of the race, but includes also a lot of other peoples with totally unrelated languages: Sami (original), Nentsi, Mansi, Yakuts, Chukchi, Japanese, Chinese, Korean, Thai, Indonesians, Eskimo, Aleuts, Native Americans, etc.
Mongoloid race has multiple defining characteristics, but one typical feature is the existence of epicantus over the eyes.
Comment: @T.E.D. In school we were told it is "Europeoid" (in Russian) but Google search reveals it is called "Europoid" in English. Americans also call it "Caucasian" but it is very confusing term, especially here in Russia where Caucasians are those who lives in the Caucasus.
Comment: Ah, yes, it is probably what we call [Caucasian](https://en.wikipedia.org/wiki/Caucasian_race) (which I totally agree is a really stupid term, since the actual Caucasian languages are their own language families, completely unrelated to Indo-European).
Comment: This is the first time in my life I've seen the word "Europoid". My browser's spell check doesn't even think its a word. I'm wondering where else that is A Thing.
Comment: @T.E.D. Languages are nothing to do with race...
Answer: Your very question has no answer since it is factually wrong — most of population of modern Turkey belongs to Europoid race (more specifically — to Mediterranean, I guess).
However the answer to any question in a form of "Why X belong to Y race, but speak Z language" is because race is biology and language is culture.
I hope you are not very surprised by the fact that both Europoids of Spain and (some) Americanoids of Central America speak Spanish, or that both Europoids of Arabia and Negroids of of modern Sudan speak Arabic.  Reasons to that are only few centuries ago from now so they are well-known: colonization and islamization respectively.
Even though turkization of Lesser Asia (≈ modern Turkey) dates back to IX century — pretty Historic age, the fact that language of Turks is akin to languages of Mongoloids of Central Asia might be surprising for someone.  What to say about events that belongs to Prehistory...
Comment: You probably meant to write XI-th century, not IX-th?
Answer: I am writing this because I believe the Wikipedia article on Turko-Mongol tradition does not really help readers understand the concept, which gave rise to this question (my assumption).
Also, (perhaps) this question stems from a confusion between genetics (biology) and genealogical relationship (linguistics). If that is the case, this article on language family might help clarify: genetic relationship (linguistics).
Having said this, the answer given by T.E.D. is correct insofar that the proposed Altaic language family is now discredited because, if the hypohtesis is true, earlier forms of Turkic and Mongolic language should be more related (linguistically, not biologically) than later forms.
Instead, comparative linguistics has shown that, in fact, "the earliest written records of Mongolic and Turkic languages shows fewer similarities rather than more, which suggests that they do not share a common ancestor, but rather have become more similar through language contact and areal effects. Because of this, most modern linguists do not accept the Altaic family". Source
Again, back to T.E.D.'s answer, on his statement "the similarities are more due to long proximity than heritage" -- this is areal effects.
So, in fact, the present day similarities of Turkic and Mongolic languages is due to a long period of contact and was expedited by Mongolian expansionist policy, which gave rise to Turko-Mongol tradition (14th century).
To end, here's a paragraph from Turko-Mongol Relations (chapter twenty-one of The Mongolic Languages, Routledge, 2003):

A more plausible explanation (for the established Turko-Mongol tradition) is therefore offered by the assumption of a network of linguistic contacts, which have united the 'Altaic' languages since ancient times up to the present day. External contacts with Uralic and Indo-European suggest that Proto-Turkic was once the westernmost member of this network. On the basis of historical information it may be concluded that the period of the most intensive early contact between Turkic and Mongolic coincided with the appearance of the protohistorical ethnopolitical entities of Xiongnu and Donghu in the regions north of China (Mongolia and Manchuria).

Also, see Northeast-Asian sprachbund.
Comment: French has the influences of Frankish (a Germanic language), Latin and some other roots that may or may not have survived from the Celtic and Breton ... :)
Comment: I'd love to see you commentary on the relationship between French, German, and English peoples/languages. (Nice answer, and thank you)
Comment: Thank you. I could do the French and English bit , but Germans ... really?? I'm afraid the Romantic philologists might go on strike. lol.
Comment: I was just having fun about the Germans ... they are a passionate lot when you start talking about their language. No offense intended. Yes, you are right - French is a Romance language (Latin from ancient Romans > Franks > French). Proto-Germanic,  however, is pretty unique and also pervasive in Europe today. A lot of branches, so we're looking at influence into English, Dutch, Icelandic-Norwegian-Danish (Norse) & of course Gothic.


BIOS flash XP, 1 long beep, 2 short beeps, over&over

Question: BIOS issue on HP dv9233cl laptop, wiped drive of Vista, loaded XP, not all the drives loaded. Went to the HP website, downloaded all drivers for this laptop. Started loading them. Loaded WIN Flash HP Network System BIOS Window SP42187. After a minute a low resolution screen appeared stating "It is now safe to turn off the computer" I waited a minute and half. Turned it off. Let it set 10 seconds try to start and No screen images at all and a nasty loud long beep 2 short beeps, 2 seconds of silence and it happens over & over again. I have unplugged/removed battery, still same problem,  Any sugg.... Thx.. Paul
Answer: It sounds like you're getting a beep code which means the motherboard is having problems with some part of the system before it boots into an operating system. Unfortunately I looked around HP's website and i can't seem to find what 1 long, 2 short means for your system.
My suggestion is to check your manual for an explanation of what it means. It should be under troubleshooting if they offer any explanation. If it doesn't have an answer then you should call HP. They should know what the beep codes are for their own systems and will be able to tell you what's wrong with your system.
Answer: I dont know @ hp, but the dell dimension gives the same beep code. I removed the memory and place one in dimm 1 and the second in dimm 3 and the computer booted properly.
Answer: Usually that beep code indicates a memory issue. It could be as simple as re-seating (removing and replacing in the memory slots) or it could be as complicated as the memory controller on the motherboard. If the system is out of warranty, I would try re-seating first, and if that does not work, you can try running the HP on-board diagnostics by pressing F2 i believe on HP's.
If your computer is still under warranty, I would contact HP before you do anything. Simply removing the case incorrectly and causing damage that way can void the warranty. Hope that helps.


Is a Markov chain the same as a finite state machine?

Question: Is a finite state machine just an implementation of a Markov chain? What are the differences between the two?
Comment: You may think a Markov chain as a FSM in which transitions are probability driven
Comment: Please read these papers: Links between Probabilistic Automata and Hidden Markov Models (By Pierre Dupont)
http://www.info.ucl.ac.be/~pdupont/pdupont/pdf/HMM_PA_pres_n4.pdf [The Handbook of Brain Theory and Neural Networks]
Hidden Markov Models and other Finite State Automata for Sequence Processing
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.85.3344&rep=rep1&type=pdf
Answer: Markov chains can be represented by finite state machines. The idea is that a Markov chain describes a process in which the transition to a state at time t+1 depends only on the state at time t. The main thing to keep in mind is that the transitions in a Markov chain are probabilistic rather than deterministic, which means that you can't always say with perfect certainty what will happen at time t+1.
The Wikipedia articles on Finite-state machines has a subsection on Finite Markov-chain processes, I'd recommend reading that for more information. Also, the Wikipedia article on Markov chains has a brief sentence describing the use of finite state machines in representing a Markov chain. That states:

A finite state machine can be used as
  a representation of a Markov chain.
  Assuming a sequence of independent and
  identically distributed input signals
  (for example, symbols from a binary
  alphabet chosen by coin tosses), if
  the machine is in state y at time n,
  then the probability that it moves to
  state x at time n + 1 depends only on
  the current state.
Comment: Unqualified, the term Markov chain means a discrete-time stochastic process with the Markov property, which means that it doesn't depend on past states. The original poster didn't ask about higher-order Markov processes, so they aren't really that relevant. Finite state machine is generally a catch all term for finite automaton, these can be either deterministic or non-deterministic in nature.
Comment: Actually, what you are claiming here about a Markov chain is not 100% correct. What you referred here to is the "First-order Markov process". For a second-order Markov process, the next state will depend on the latest 2 time steps' states, ...... A state machine is a special case of a Markov chain; since a Markov chain is stochastic in nature. A state machine, as far as I know, is deterministic.
Answer: Whilst a Markov chain is a finite state machine, it is distinguished by its transitions being stochastic, i.e. random, and described by probabilities.
Comment: Can I say, stochastic finite state automata?
Answer: The two are similar, but the other explanations here are slightly wrong. Only FINITE Markov chains can be represented by a FSM. Markov chains allow for an infinite state space. As it was pointed out, the transitions of a Markov chain are described by probabilities, but it is also important to mention that the transition probabilities can only depend on the current state. Without this restriction, it would be called a "discrete time stochastic process".
Comment: Actually, I believe it would be called "non-stationary".
Comment: @Michael I might be wrong, because I have been out of the topic a while, but I thought "stationary" was about time dependence. I might be mistaken, but that seems orthogonal.
Comment: "process" is typically used to express continuous time version of the term "chain" (reference: probability theory: a concise course, Rozanov) and a FSM can be represented [infinitely](https://en.wikipedia.org/wiki/Transition_system) or [event-driven](https://en.wikipedia.org/wiki/Event-driven_finite-state_machine) or [non-deterministic](https://en.wikipedia.org/wiki/Nondeterministic_finite_automaton). The only other dependence I can imagine besides state would be time.
Comment: @Michael "process" is a generic term. It can be continuous time or discrete time. An FSM can't be represented infinitely it has the word *finite* in its name. The link you provided even says that is not a finite state machine. You brought up time dependence not me, but in discrete time processes the sequence index is normally considered the time. In that sense, yes a discrete time stochastic process would be non-stationary, but that is not descriptive enough, since it could also potentially be continuous time. I was going for a superset, not the complement in my naming.
Answer: I believe this should answer your question:
https://en.wikipedia.org/wiki/Probabilistic_automaton
And, you are on to the right idea - they are almost the same, subsets, supersets and modifications depending on what adjective describes the chain or the automaton. Automata typically take an input as well, but I am sure there have been papers utilizing 'Markov-chains' with inputs.
Think gaussian distribution vs. normal distribution - same ideas different fields. Automata belong to computer science, Markov belongs to probability and statistics.
Answer: I think most of the answers are not appropriate. A Markov process is generated by a (probablistic) finite state machine, but not every process generated by a probablistic finite state machine is a Markov process. E.g. Hidden Markov Processes are basically the same as processes generated by probabilistic finite state machines, but not every Hidden Markov Process is a Markov Process.
Answer: If leaving the inner working details aside, finite state machine is like a plain value, while markov chain is like a random variable (add probability on top of the plain value). So the answer to the original question is no, they are not the same. In the probabilistic sense, Markov chain is an extension of finite state machine.


How to assess perceptual volume from FFT

Question: So far I could estimate signal volume from FFT using amplitude information, then adding all amplitudes together and divide this number by the number of frequencies. But I think this method does not apply for estimation of subjective perceptual volume.
Answer: If you equate perceptual volume to loudness, there are international standards.
if you look at
https://www.mathworks.com/matlabcentral/fileexchange/46819-a-weighting-filter-with-matlab-implementation
This is an A-weighted Matlab FFT based implementation.
<code>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                  A-weighting Filter                  %
%              with MATLAB Implementation              %
%                                                      %
% Author: M.Sc. Eng. Hristo Zhivomirov        06/01/14 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function xA = filterA(x, fs)

% function: xA = filterA(x, fs)
% x - signal in the time domain
% fs - sampling frequency, Hz
% xA - filtered signal in the time domain

% determine the signal size
sz = size(x);

% represent x as column-vector
x = x(:);

% signal length
xlen = length(x);

% number of unique points
NumUniquePts = ceil((xlen+1)/2);

% FFT
X = fft(x);

% fft is symmetric, throw away second half
X = X(1:NumUniquePts);

% frequency vector with NumUniquePts points
f = (0:NumUniquePts-1)*fs/xlen;

% A-weighting filter coefficients
c1 = 3.5041384e16;
c2 = 20.598997^2;
c3 = 107.65265^2;
c4 = 737.86223^2;
c5 = 12194.217^2;

% evaluate the A-weighting filter in the frequency domain
f = f.^2;
num = c1*f.^4;
den = ((c2+f).^2) .* (c3+f) .* (c4+f) .* ((c5+f).^2);
A = num./den;
A = A(:);

% filtering in the frequency domain
XA = X.*A;

% reconstruct the whole spectrum
if rem(xlen, 2)                     % odd xlen excludes the Nyquist point
    XA = [XA; conj(XA(end:-1:2))];
else                                % even xlen includes the Nyquist point
    XA = [XA; conj(XA(end-1:-1:2))];
end

% IFFT
xA = real(ifft(XA));

% represent the filtered signal in the form of the original one
xA = reshape(xA, sz);

end
</code>
The Mathwork will also sell you their Audio toolbox that has many types of weightings.
I find these standards a bit confusing because you don't know if they correct for the effective noise bandwidth of proportional bandwidth filters and if an FFT implementation should take that into account.
I don't vouch for the Matlab code above.  It seems reasonable.
The Wikipedia article:
https://en.wikipedia.org/wiki/A-weighting
also gives the analog transfer functions, which can be converted to digital filters, but actual digital filters seem harder to find.
If your ultimate purpose is to use a standard where a professional signature is required, or one is exposed to liability, I would be inclined to use the Mathwork's product.
Comment: i think the current ISO standard supports E-weighting over the anachronistic A-weighting.  i have MATLAB code for it.  i think it has something like 64 poles and zeros.
Comment: @robertbristow-johnson so that's a filter followed by a squaring operation?
Comment: yes, filter the audio first, then square that filtered output, then low-pass filter the squared output to get the *"DC"* value (that can change a little, so it's not exactly DC).  then, since this is a squared value, apply $10 \log_{10}(\cdot)$ to that to get dB.
Answer: Your method is bad, because it does
signal -> FFT -> |·|² -> sum
which is, per Parseval's theorem, 100 % identical in information to
signal -> |·|² -> sum
What you can do is apply weights to different frequency bin magnitude squares of the DFT to represent how "important" they'd be for perception.
If you did a weighted thing, you'd be closer to perceptional volume than if you just added up with no (or constant) weighting (which you could do, as said above without the FFT). You'd still not be very exact. The fact that frequency component can mask other frequencies without influence of the overall perceived volume is one of the psychoacoustic reasons audio compressors (such as the well-known MP3) work so well: you simply don't have to take the sound content at some frequencies into account, if specific others are there.
So, psychoacoustic loudness models are rather complex, and have a frequency-crossdependent aspect, as well as probably a strong temporal one.


Ultrium DT3 - Amber warning light and Red 3 on LED

Question: Dell PowerEdge 2900 with IBM Ultrium DTO III installed.
Tape drive ejects and accepts tapes and backup software successfully writes to tape but I have a red 3 on the LED of the tape unit and a flashing amber light.  I have tried the online support at Dell and IBM but cannot find any article - even Google reveals nothing.  Any ideas on how to diagnose the issue - tape drive unit appears in in device manager although in other devices I do have an unknown - this could be something to do with it - or perhaps not?
Answer: Placed LTO unit in maintenance mode (eject tape and press eject button 3 times in two seconds) and then took the LTO unit out of maintenance mode (with unit empty, press eject and hold for 3 seconds).
The display screen reset and the light became green once more.
Comment: See ftp://ftp.software.ibm.com/systems/support/system_x_pdf/39m5625.pdf


Does converting an mp3 format audio file to m4a format makes audio quality better?

Question: Does converting an mp3 format audio file to m4a format makes audio quality better ?
I was just wondering if mp3 is lossy. How it can generate lossless m4a file after conversion.
I know mp3 can be converted to m4a but will this m4a file will give the same audio quality as compared to an originally created m4a file.
Comment: please look into lossless and lossy compression on wikipedia. that will explain more than a straight answer.
http://en.wikipedia.org/wiki/Lossless
http://en.wikipedia.org/wiki/Lossy_data_compression
Comment: You can't "convert to m4a" -- m4a is a _container_ format, and may contain `AAC` (lossy) or `ALAC` (lossless) formats -- or even `mp3`.
Comment: @michael this might help explain to better to people who don't understand what a container is.  I think that is part of the problem https://www.youtube.com/watch?v=WIIKXOrt3bk
Answer: No. Once lossy formats are encoded, any data not saved within the file is lost. You could convert a lossy MP3 to a WAV or an M4A file but the quality of the WAV or M4A would be exactly the same as the original MP3.
Comment: pfarley, are you sure there will not be any loss when transcoding from mp3 to m4a? this would only be the case if transcoding to a lossless format (despite the container (m4a/flac).
Comment: I wanted to stress that you won't get lost data back and was probably a bit misleading, sorry. If you converted to another lossy codec (even if it's 'higher-quality' than what you're converting from) you can still lose data.
Answer: It might be that you loose even more quality due to another file compression algorithm.
Answer: It is mathematically impossible to improve any digital audio stream to a "Better Quality" by a simple conversion to said file type. A poor quality mp3 can be "converted" to any format you like but the poor quality will remain and, as mentioned, you may even lose a bit in the conversion.
There seems to be some misconceptions floating around out there about stepping up quality as many programs allow you to import lossy or low quality audio into a workspace that may be set at a high quality/resolution. That being said the lossy or low quality audio does not get any "better" in doing so. The fundamental problem is that you cant insert samples into a track. you can estimate them (although aliasing can be an issue) but you can't fundamentally insert them.
Answer: Just to add & clarify that m4a is a container format, actually the same spec as mp4, merely a different file extension, and therefore can contain either AAC (lossy) or ALAC (lossless) formats -- or even mp3! -- so the question as stated doesn't make sense (same with many of the answers & comments).
Regardless, the simple answer to the intended question is that converting a lossy format to a non-lossy format inherently can't make audio quality "better" (literally: no new information can be added to the data via this transformation). In theory, the very best you can do is achieve the same quality; in practice, you'll probably lose a little quality, but carefully selecting the right conversion & format options you might not notice the degradation.
Answer: As far as I know, m4a is also considered to be a lossy format. So converting from lossy to lossy would not make any difference, probably worsen the quality depending on the coding standard being used.
Answer: I think it's important to understand: Rakesh, what is your motivation for converting? Also, within M4A, are you specifically referring to http://en.wikipedia.org/wiki/Apple_Lossless ?
Clarifying this will help with useful answers.
Comment: No, i am referring to m4a in general. And, i could not understand what you meant by 'motivation for converting' because in my view it does not matter because it won't change the result anyway.
Comment: I was just asking that 'how can one mp3 file (lossy) can generate an m4a file which is lossless.  But, i think @pfarley has clearified that even when we convert an mp3 fule to an m4a format, it will change the format but the quality will be the same as the source mp3 file.
Answer: It is impossible to undo the losses done to an audio file. Once the audio is lost, it can never be re-obtained. If you want your audio to be lossless, you sadly have to re-record the whole thing and have the recording be initially saved as either wav if you want it to be uncompressed, flac if you want to compress it and are not an apple user, or alac if you want to compress it and you are an apple/mac user. So right back to the studio you go!


What material is the Merlin 1D made from?

Question: I am working on high school presentation about rocket engine materials and I'd like to have a part about Merlin 1D engine as it is supposed to be reusable, but I can't find anything about materials used for this kind of engine. Found a lot of data about single-use engines and solid rockets, but nothing about materials for reusable one.
Could you please provide anything about materials used? I have literally nothing to take off from...
Thanks in advance.
Comment: SpaceX publishes very little detail on their designs. You may have better luck using the Shuttle main engine (RS-25 or SSME) as an example, this was also designed to be reusable.
Answer: The only information I have been able to find only gives what one part of the engine is made of. That is the merlin vacuum variant bell extension.
From wiki

Its combustion chamber is regeneratively cooled, while the 2.7 metres (9 ft)-long niobium alloy expansion nozzle is radiatively cooled.

Specifically, it uses niobium alloy c103 (89-90 Nb, 9-10 Hf, 1Ti), per http://www.alkane.com.au/images/pdf/asx/2017/20170516.pdf.
This backs up Hobbes comment that a lot of this information simply is not public.


Too much lemon in beef stew help!

Question: I have a fruity beef stew with plums, carrots, beef, onion, beef stock and far too much lemon juice and lemon zest.
It tastes too lemony, what can I do to counteract it?
Comment: I've no experience of this so will only comment not answer. I would suggest that anything you try, you try first with a small sample of the gravy/sauce rather than chucking stuff into the whole mix. What I'd suggest is a little sugar to highlight the plum carrot and orange, and possibly an aromatic element like garlic to counter the lemonyness. Elsewhere online I see people recommending a tiny pinch of baking soda to neutralise.
Comment: Generally reducing any flavor in cooking is often done through dilution, though sometimes adding potatoes will absorb the saltiness of a soup/stew. So add more broth and other ingredients to dilute the flavor of lemon that is too strong.
Comment: Does this answer your question? [How do I reduce the lime flavor in my Slow Cooker roast?](https://cooking.stackexchange.com/questions/63576/how-do-i-reduce-the-lime-flavor-in-my-slow-cooker-roast)
Comment: Its it the lemon flavor, the acidity, or both which is a problem? If you could only fix one - which would you choose?
Comment: @brhans  It's not acidic.. Its just lemony
Answer: Try discarding one cup of liquid, and add one cup of water; reduce until desired. Taste the result, and if it is still too lemony, repeat the process until it is to your liking.
Some unsalted butter after the reduction may also help.
Comment: Would this not reduce the overall flavor, however?  From the question, the OP specifically wants to taste less lemon flavor, not less flavor overall.  Dilution here would serve to reduce all of the flavors, rather than just the lemon-y component.
Comment: Even acidity - that can be controled with alkaline ingredients - modify the overall result. When discarting one cup of the liquid, I expect a lot of lemon zest to be discarded too - which would help to remove the lemony flavor more than the overall flavor; in fact, that's why I suggest reducing and fat adding after diluting.. to try to bring back the overall flavor withou the lemony
Comment: If I take a stock that is a bit too strongly flavored with rosemary, and dilute it with water, it loses some of every flavor component, not just the undesired flavor(s).  If I remove some of the resultant liquid, and again dilute it, even more flavor is lost; both the desired flavor(s) making up the stock, as well as the rosemary flavor which I hypothetically want to reduce.  I think that dilution is not, in this instance, the best approach.  Your secondary point about adding fat is good; iAmNoah's answer specifically uses suggestions which do not result in lost overall flavor.
Comment: @SEStrikesAgainUnfortunately To riff on your username, unfortunately this might be the best option. There are very few options to remove a strong, essential oil based flavor. Dilution and then enriching the stock can work.
Answer: options:

generally speaking, mitigate too much citrus zest (bitter) with salt and sweet.  that's not always a better option
bury it with something like BBQ or some other strongly flavored sauce
turn the main dish into an ingredient in some other dish

bitter from citrus is a tough one, since it seems to be strengthened with more cooking
Answer: Let's get that awesome stew fixed and 'souped' up. Get it?
Now, although I've never tried these remedies you could:

Add 1-2 spoonfuls of sugar (depending on the quantity of stew)
Add some fat (yogurt, butter, sour cream, olive oil)

Good luck.

Too much lemon in beef stew help!


Badges that were supposed to be awarded

Question: I have had badges in the past not get awarded to me. For example, the one that won't be awarded to me currently is the curious badge. It has that I have more than 5 positive questions asked but will not award me the badge. What should I do?
Answer: The Curious badge is awarded only when two separate criteria are both met:

Asking a question that is open, not deleted and positively scored on 5 separate days
Having a positive question record, which is defined as:

(total q's - negative q's - closed q's - deleted q's)/total q's >= 0.5

Note in particular that a question that has both a negative score and is closed will count as two penalties, etc.
Source: Asking days badges
Unfortunately, you don't currently have a positive question record. You've asked 19 questions, 4 of which have a negative score, 6 of which have been closed, and 3 of which have been deleted. The relevant figure is thus (19 - 4 - 6 - 3)/19 = 6/19 which is less than 0.5.

In general, if you feel you haven't been awarded a badge you should have been and 24 hours have elapsed (badges can take some time to be awarded), you should post here on meta so that we can look into the issue.
Comment: However, you can work on getting your current questions to positive scores or being reopened by editing them to improve them. This would reduce the number of new good questions you would need to ask.
Comment: waiwai933 How many more questions with positive question records would I have to get?
Comment: Assuming that none of your future questions have a negative score or are closed or deleted, and that none of your current questions change their current state, you would be eligible for the Curious badge with 7 more questions.
Answer: The badges are awarded algorithmically. As you can see, the curious badge is fairly rare, having been awarded less than 1000 times overall. According to this answer, the badge's criteria are:
Curious

bronze; awarded once
Asked a well-received question on 5 separate days, and maintained a positive question record
Any open question that is not deleted and has a score >= 1 is considered well-received
Only days where all questions asked have been well-received, count (source)
A positive question record means you don't have too many closed, downvoted or deleted questions, overall. The formula is <code>(total questions - negative questions - closed - deleted)/total questions >= 0.5.</code> Questions that have been downvoted and closed and deleted count three times in this calculation!

Badges that were supposed to be awarded


Is corrected astigmatism disqualifying for an EASA Class 1 medical?

Question: I realize there are similar questions on the site already, but not one specifically dealt with my problem. I reside and plan to work in Europe so I looked up the EASA regulations, but I couldn't really make sense of them. My question is: I have astigmatism, which is corrected by my glasses. I am also shortsighted, which is also corrected. Does this disqualify me for a Class 1 license?
Answer: I have a registered astigmatism on one eye that is balanced by the other eye. I have a Class 1 medical w.o. problems. In my medical record, the Doc wrote that my astigmatism corresponds to a .75 dpt on one eye.
He also told me that absolute values are not important, important is that the astigmatism is corrected by either the other eye, some glasses or it is so low that the brain can even correct for it.


Which Saves oppose which Conditions?

Question: Is there an official listing of which ability (Str, Dex, Con, Int, Wis, Cha) saves are used to resist which conditions?
Answer: No, because it depends on the effect that is causing the condition. You cannot save against a condition, you save against an effect (a spell, item, monster, maneaver, etc)
The same condition might be opposed by different abilities, when it comes from different sources.
The Cleric Spell Divine Word, for example, can apply Blinded, Deafened, or Stunned if you fail a Charisma save.
But these same conditions can also be applied by Blindness/Deafness or the Monk's Stunning Strike, in which case they are resisted with a Constitution save.
So you'll have to check the source of the condition to see which save is used.
Comment: @Trismegistus I don't think anything is sorted by effect. They are mostly sorted by type (ie; spells go together, monsters go together, classes go together, etc). Any of those things could describe an effect that creates a condition, but the starting point is always the thing in the game that is causing it. You want to know how painful a Dragon's breath is? Look up the Dragon in question, and it'll be shown there. Not in a list of breath weapons.
Comment: I've flipping through the SRD for in formation and was looking by condition, rather than by effect. Are thing sorted by effect inPHB ot DMG?
Answer: In general, you should base the saving throw to be used off of what is causing the effect rather than the effect itself.  There are multiple ways to be stunned, some of them require Constitution saves (Monk's Stunning Strike) while others may require Charisma saves (Divine Word).  The DMG specifies (pg. 238):

Most of the time, a saving throw comes into play when an effect - such as a spell, monster ability, or trap - calls for it, telling you what kind of saving throw is involved and providing a DC for it.
Other times, a situation arises that clearly calls for a saving throw, especially when a character is subjected to a harmful effect that can't be hedged out by armor or a shield. It's up to you to decide which ability score is
  involved. The Saving Throws table offers suggestions.

That said, if you don't want to take the time to look up the specific spell or attack causing the effect, or you're in a scenario where a save should occur but the type isn't specified, there is a general rule of thumb.
From the DMG, pg 238:

Saving Throws

Strength:  Opposing a force that would physically move or bind you
Dexterity:  Dodging out of harm's way
Constitution:  Enduring a disease, poison or other hazard that saps vitality
Intelligence:  Disbelieving certain illusions and resisting mental assaults that can be refuted with logic, sharp memory, or both
Wisdom:  Resisting effects that charm, frighten, or otherwise assault your willpower
Charisma:  Withstanding effects, such as possession, that would subsume your personality or hurl you to another plane of existence

The one part here that can be confusing is when to use intelligence and when to use wisdom.  The DMG (pg 238) has the following to say about how to determine which to use:

INTELLIGENCE CHECK VS. WISDOM CHECK
If you have trouble deciding whether to call for an Intelligence or a Wisdom check to determine whether a character notices something, think of it in terms of what a very high or low score in those two abilities might mean.
A character with a high Wisdom but low Intelligence is aware of the surroundings but is bad at interpreting what things mean. The character might spot that one section of a wall is clean and dusty compared to the others, but he or she wouldn't necessarily make the deduction that a secret
  door is there.
In contrast, a character with high Intelligence and low Wisdom is probably oblivious but clever. The character might not spot the clean section of wall but, if asked about it, could immediately deduce why it's clean.
Wisdom checks allow characters to perceive what is around them (the wall is clean here), while Intelligence checks answer why things are that way (there's probably a secret door).
Answer: There is a passage in the DMG on page 238 (box in the upper right corner) that gives a rule of thumb about when to use what save.
But: All effects that have a save (like spells) require to save according to the effect.
Comment: Please quote the DMG instead of paraphrasing from memory. Your descriptions don't match the DMG text ("integrity" is a very odd way to describe CHA saves) and worse, you've swapped INT and WIS saves.
Comment: Thanks for adding that citation. I'm not a D&D 5e player, but I suggest you refresh your memory of that box to provide something that's not just from the top of your head, but instead a reliable reflection of the actual text which we can have confidence in that it's accurate. The "off the top of my head" bit doesn't necessarily inspire confidence of accuracy. (This isn't a suggestion to copy the text from that box -- doing so might not be fair use -- just a suggestion to communicate what's going on in a  more confidence-inspiring way.)
Comment: Thank you. :-) I have edited a little bit here and there to make my statements more to the point.
Comment: Did not know If quoting this is allowed, so I removed my summary and just pointing to the PHB.
Comment: So I've checked, and [fair use *would* permit](https://fairuse.stanford.edu/overview/fair-use/four-factors/) sharing that list. I'll leave it up to you whether you'd like to roll back and fix the references you had, or quote the text, or whatever else.

Which Saves oppose which Conditions?


Air-conditioning belt is making a loud squealing noise. What should I do?

Question: How long will the air conditioner last if it is making a loud squealing noise. I want to know if I have to replace it right away.
Answer: Usually it will either be the belt is slipping on the AC pulley because the serpentine belt is worn out, the tensioner pulley is no longer providing the amount of tension on the serpentine belt, or the belt needs adjustment. You can try belt replacement first or check the tensioner to see if it is where it should be (a lot of them have a gauge to show where the proper range should be). If it isn't, then you can either change out the tensioner (the springed portion) or the belt depending if you found fault in one of those areas. If that doesn't work, then there may be an issue with the AC itself. More than likely, the AC is not at fault and it will work just fine after the belt/tensioner is replaced.
Answer: Check what Paulster2 said and if that doesn't fix the problem it could be the bearings in the AC clutch..... spray some WD-40 in there and if the problem lessens, then it's a good sign the clutch needs replacement. The WD-40 won't be a fix. Good luck.
Comment: I'm not sure why you'd spray WD-40 onto an A/C clutch? That would only provide a lubricant to make the clutch slip, which is going to wear it out faster. This is definitely something I would advise against.
Comment: @Pᴀᴜʟsᴛᴇʀ2  If the bearing are shot and making the noise, a squirt  of WD-40 would lessen the noise, just for a few minutes. Then you'd know it was the bearings. If you're careful where you spray it you won't get any on the clutch plates.  It's just a test to confirm a problem. We use to do it all the time with fans at a steel heat treating factory.
Comment: Given centripetal force, there's about 0.0% chance you won't get it on the clutches. It really doesn't matter how careful you are with it.


How to advance lab assistants to researchers?

Question: I can't find a list of needs for lab assistants. I gave them everything (they have carbon to upgrade). What else am I missing? I read researched on the internet and couldn't find a solution.
Answer: Their demands consist of energy drinks, fish and Functional Food,
they need to be in a range of a laboratory they have road connection to and finally taxes need to be at the lowest level.
You also must make sure that ascension rights are not disabled at your city center.
Answer: you need to make full all of their needs. comunication food activity ect. and make the tax rate lover
Answer: You must have carbon in your warehouse/depot to advance them!
Comment: he already mentions the assistants having carbon to upgrade.


Does MariaDB-Galera Cluster support LAST_INSERT_ID and mysql_info?

Question: As far as I understand, Galera does not support table locking, but what information can be retrieved about the last query?

LOCK/UNLOCK TABLES cannot be supported in master-master replication. Lock functions (GET_LOCK(), RELEASE_LOCK(),…) are not supported.

What about LAST_INSERT_ID()?  At some point I read, that the nodes use different auto increment values, but it said nothing whether the last insert id will be returned.
And a related question: In PHP I use the mysql_info function to retrieve the "rows matched" on UPDATE.  Is this information expected to be availible in a Galera cluster?
Answer: I know this is a really old question, but yet both are supported just as they are in standard mysql.


Pre-processing (center, scale, impute) among training sets (different forms) and the test set - what is a good approach?

Question: I am currently working on a multi-class classification problem with a large training set. However, it has some specific characteristics, which induced me to experiment with it, resulting in few versions of the training set (as a result of re-sampling, removing observations, etc).
I want to perform pre-processing of the data, that is to scale, center and impute (not much imputation though) values. This is the point where I've started to get confused.
I've been taught that you should always pre-process the test set in the same way you've pre-processed the training set, that is (for scaling and centering) to measure the mean and standard deviation on the training set and apply those values to the test set. This seems reasonably to me.
But what to do in case when you have shrinked/resampled training set? Should one focus on characteristics of the data that is actually feeding the model (that is what would 'train' function in R's caret package suggest, as you can put the pre-processing object in there directly) and apply these to the test set, or maybe one should capture the real characteristics of the data (from the whole untouched training set) and apply these? If the second option is better, maybe it would be worth it to capture the characteristics of the data by merging the training and test data together just for pre-processing step to get as accurate estimates as possible (I've actually never heard of anyone doing that though)?
I know I can simply test some of the approaches specified here, and I surely will, but are there any suggestions based on theory or your intuition/experience on how to tackle this problem?
I also have one additional and optional question. Does it make sense to center but NOT scale the data (or the other way around) in any case? Can anyone present any example where that approach would be reasonable?
Answer: If I understand your question, one of your ideas is to calculate a normalization (center and scale) across all of your data: both test and training.
Imagine that you take all of your data and calculate a centering and a scaling once, then use this on both the training set and test set. Your training set represents the data you have now, your test set represents future data that you don't have when you are training. But you somehow magically calculated centering and scaling values that included this future data. A Leak From The Future (tm), which is bad.


Why can't we reason or logic our way to NIrvana?

Question: I have read at various places that Nirvana can't be described or reached by logic or reason. ONLY meditation is the way. Why is that so? thanks in advance.
Comment: Because all logics included in 62 ditthi already. https://www.accesstoinsight.org/tipitaka/dn/dn.01.0.bodh.html
Comment: You might like to check out the view for which meditation IS enlightenment. For instance -  https://www.huffingtonpost.com/andrew-z-cohen/meditation-is-a-metaphor-for-enlightenment_b_1112021.html
Comment: really good question. i'd be surprised if it never came up in the history of buddhism
Comment: @PeterJ That's a bit like this answer: https://buddhism.stackexchange.com/a/192/254
Comment: @ChrisW - Yes. A useful link.
Comment: Let's take it like this. Process (Sequence of *Citta Veeti*) used for reasoning = bicycle. Process (Sequence of *Citta Veeti*) appear in insight meditation = space shuttle. *Nibbana* = moon. Will you be able to reach the moon by a bicycle? Or do you need a space shuttle? **Note:** Most appropriate simile is *Rocket* not *Space shuttle*. Because the journey is one way.
Answer: I have read at various places that Nirvana can't be described or reached by logic or reason.
I think that's two questions: 1) described, 2) reached.
I think Nirvana is defined as being the end of craving -- not just a temporary pause or lull, but uprooting the "tendencies" and "effluents" which result in the arising of craving -- so changing or undoing habits (if craving is a kind of habit, and results from habits, etc.).
And you can't do something, or accomplish something ("reach" something), just by thinking about it -- you have to do it!
I suppose that's true of everything -- mundane things too not only Nirvana -- e.g. you can't learn to play piano or guitar just by thinking about: you'd have to do it, practice it.
Maybe that's true even of describing something -- I can't describe playing guitar or piano, nor even describe hearing piano or guitar  -- i.e. you'd have to actually do it yourself, play it or hear it, to know it for yourself.
Comment: "I think Nirvana is defined as being the end of craving" --  Sir, In my humble opinion and according to my knowledge and understanding, this is not true. Craving will be uprooted as an effect of attaining Nibbana. Nibbana is an ultimate truth which has been the object for 8 supermundane consciousness. Please correct me if I'm wrong.
Comment: "There's a case when a bhikkhu attains tranquility based on insight, and there's a case when a bhikkhu attains insight based on tranquility" - said in the sutta. Tranquility is end of craving. Insight is seeing the truth. In practice, tranquility and insight develop together step-by-step, I think.
Comment: @Damith Perhaps you're saying that Nibbana is more than the uprooting of craving. I think it's at least the complete uprooting/extinguishment of craving -- and that that doesn't happen only by "logic and reason" and without meditation. I'm not familiar with the [Eight Consciousnesses](https://en.wikipedia.org/wiki/Eight_Consciousnesses) model, which Wikipedia says is "the Yogācāra school of Mahayana Buddhism", only the Pali suttas.
Answer: Great question!
It is possible to use logic to arrive at a conviction of the truth of the dhamma, as Nagarjuna demonstrates and others such as Francis Bradley, Spencer Brown and (ahem) me. But this is map-reading. You can read a thousand books about fire and not know what it feels like to be burnt.
So while logic and reason are useful and trustworthy they are not a carriage that will carry us to Heaven. The Old Testament tale of the Tower of Babel is a teaching story.
Reason and logic applied to metaphysical questions must work by abduction, by the elimination of unworkable views. This means that metaphysical analysis can be a valuable guardian against error, as Aurobindo characterises it, but while it can proscribe truth by ruling out false views it cannot reveal truth or give it meaning for us. Revelation requires burning the maps and undertaking the journey.
It is much the same in physics. Most interpretative theories can be ruled out on the basis of analysis but no theory is provably 'true'. Reason and logic produce theories and having a theory of the existence of a holiday resort is not the same as going on holiday.
Meditation is necessary because truth outruns the intellect and cannot be discovered intellectually. For Mahayana the true nature of reality would be beyond conceptual fabrication and the categories of thought, so no amount of thought is able to take us there. As all the teachers say...
"Man can partake of the Perpetual. He does not do this by thinking he can think about it."
Jan-I-Janan
Sentences of the Khajagan
Answer:
Nirvana can't be described or reached by logic or reason

Logic and reason are functions of the intellect-mind. Nirvana is beyond the intellect-mind.
What is the intellect-mind? The mind that works on and understands mathematics. The mind constructs the equations, then goes on verifying the left and right sides between the "=" are equal; then designs experiments to prove the equations. In brief, intellect-mind is a self-sustaining system, it goes in a loop of generating hypothesis then re-assumed the hypothesis to evidences, that become facts - which condensed and constructed the world. Say, the stone is solid and heavy. But to generate the stone is solid and heavy - the phenomena, it requires the intellect-mind to recognize the concept of stone, then recalls the attributes of the stone; then the physical body, sensory system and brain, etc., of the human will response to the totality of it, by not able to lift it, or not able to walk pass if it is blocking the road...

ONLY meditation is the way

No. Meditation cannot bring one to Nirvana. Those meditation teachers if telling you Nirvana is by reaching certain grade of Jhana, or certain Vipassana, they are just selling you a consumer product with catchy marketing slogan.
Even Vipaśyanā requires getting beyond the intellect-mind. Don't confuse it with the marketed "Vipassana" of Mr. Goenka's or many meditation "teachers", just like a motel with the neon sign "Paradise" doesn't mean it the Paradise. The Buddha's Vipaśyanā is about reaching high level Dhyana, where the sensory inputs are all cut off, the intellect-mind is surpassed, by then insight, the vipaśyanā, can operate.
Therefore intellect-mind is the mind of reason and logic, it is the mind we most familiar with, we use it all the time. No matter how intelligent one owns her/his intellect-mind, how high the IQ score, it doesn't give a slightest edge to this type of person for reaching Nirvana. Though being intelligent is a remarkable gift. Nirvana is removed from reason and logic.

While the less fluid mindset may easily misinterpret the above demoting the unique gift of human intelligence - logic and reason, how it contributes to modern scientific and technological achievements, it is misreading the meaning of this post. Hellenistic civilization after shaped by Aristotle is dominated by seeking analytical/empirical knowledge procured by the intellect. But it is not the totality of the mind. The mind is more mysterious contained much richer facets: such as how a maths genius conceived numbers.

Why Meditation cannot bring one to Nirvana?
Errr... often too advance an answer is not easy to comprehend :)))
I assumed most Buddhists understand that Nirvana cannot be realized by meditation. Apparently it's not the case.
a) The Buddha himself said so and demonstrated it, in the very beginning of his search. Let's go back to Chapter One -
The young Gautama became an ascetic first learnt from Ārāḍa Kālāma, whose specialty was dwelling in the "Sphere of Nothingness" which he regarded was Nirvana - the 7th Dhyana. After acquired the skill and dwelt in it Gautama immediately knew it was not.
He then learnt under Udraka Ramaputra, specialized in dwelling in the "Sphere of neither Perception nor Non-perception" - the 8th Dhyana. He thought that was Nirvana. After training 3 years Gautama skilled in it, but, to his disappointment, it was still not. He found there still subtle and fine "perception/consciousness" remained. And, when the power of Samadhi subsided, the practitioner would still fall back to the cycle of birth-death.1
b) If still not enough to convince, let's look at Buddha's unique discovery - the 9th Dhyana.
The 9th Dhyana is called Nirodha Samapatti (想受滅定), meaning, cessation of thinking and perception. Practitioner entering this Dhyana is virtually dead, read the description of it in the Vinaya (probably not available in Pali text) about Utpalavarṇa and the 500 cow-robbers. Entering this Dhyana one loses her/his autonomy, say, if someone has destroyed her/his body, s/he wouldn't be awaken to stop it. S/he couldn't emerge from this Samadhi without a skillful one "called" her/him. Usually practitioner needs to give her/himself a hint before entering, so that s/he can emerge from it in time. From these characteristics, it hardly can be associated with Nirvana.
c) Nirvana is like someone who removed the headgear and exited from the AR game. Meditation is just the pause in the game, which allows the player to take a break, returns to her/his senses that s/he is just in the game. But to be released from the game, one needs to disengage in it. This analogy also gives better understanding to my two beginning paragraphs.
Or, meditation is like washing a broken dish, it can clean it to see the fracture more clearly, but it can't mend the crack. The Buddha said, the unenlightened's life is with effluence, only an Arhat has ceased the effluence.
footnotes
1. 《佛本行集經》: 「仁者此法不能究竟解脫 (cannot reach ultimate liberation)... 大涅槃 (great Nirvana)。此法還入於生死 (this method still enters back into birth-death;所以者何?既生非想非非想處 (after born in the Sphere of neither Perception nor Non-perception),報盡還入於生死 (when the effect subsides, [one] still enters into birth-death)。」
Comment: Why did you say meditation cannot bring us to nibbana? It is by medition that one results in seeing clearly. Seeing clearly non-self & impermanence, one gets diapassioned. Getting dispassioned, one lets go. This is precisely the reason why one cannot reason out one's way to nibbana because nibbana is not something to acquire, but it is the letting go of all ignorance which doesn't happen by just intellectually understanding certain teachings, but by understanding plus practise. With intellectual knowledge the causes & conditions are still in place for ignorance to arise.
Comment: Yes, I found this an odd remark. Perhaps it needs a little explanation.
Comment: You can't be *"letting go of all ignorance"*, like darkness can't be letting go to make disappear. Ignorance will not arise again if removed, just like if you've learnt calculus, you will not be ignorant to calculus again. The Buddhist doctrines are too subtle and profound I'm afraid too many pretenders ("teachers") giving incorrect interpretations. The Buddha himself said Nirvana cannot be realized by meditation. If it could, Gautama didn't need to search the Path for 6 years. The source you relied (Pali) is too limited. I've tried editing my post to give more info @Val + PeterJ
Comment: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/87729/discussion-on-answer-by-mishu--why-cant-we-reason-or-logic-our-way-to-nirvana).
Comment: @Mishu米殊 - I would be keen to further understand the context of the Vipaśyanā and achieving such as state.
Comment: The simplest way (but really very hard) of vipaśyanā is in practicing [ānāpānasmṛti](https://celestory.com/anpn/) by approx. reaching beyond the 3rd stage (not the Theravadin 16 stages)... @Motivated.
Comment: @Mishu米殊 - I'm aware of breathing meditation however i am unclear how it differs to a constant meditative state.
Comment: Do you read the link @Motivated? What do you mean a constant meditative state? As I understand, normally practitioner cannot even enter the meditative state, not to say "constant". What stage of breathing med. you've arrived at?
Comment: @Mishu米殊 - Could we possibly chat (https://chat.stackexchange.com/rooms/88675/buddhist-enlightenment)?
Answer: In the book chapter entitled "Boiling and the Leidenfrost Effect" (an excerpt is quoted below), physicist Jearl Walker discussed the Leidenfrost Effect and explained how it may protect a firewalker from burns to the feet.
Eventhough logic and the scientific method had led him to have complete conviction in physics, he still had sweaty feet and had to clutch a physics textbook to bolster his faith in physics, while demonstrating the effect himself.
Similarly, logic may give you conviction in Buddhism, but logic may not free you from suffering.

The Leidenfrost effect may also play a role in another foolhardy
  demonstration: walking over hot coals. At times the news media have
  carried reports of a performer striding over red-hot coals with much
  hoopla and mystic nonsense, perhaps claiming that protection from a
  bad burn is afforded by ''mind over matter.'' Actually, physics
  protects the feet when the walk is successful. Particularly important
  is the fact that although the surface of the coals is quite hot, it
  contains surprisingly little energy. If the performer walks at a
  moderate pace, a footfall is so brief that the foot conducts little
  energy from the coals. Of course, a slower walk invites a burn because
  the longer contact allows energy to be conducted to the foot from the
  interior of the coals.
If the feet are wet prior to the walk, the liquid might also help
  protect them. To wet the feet a performer might walk over wet grass
  just before reaching the hot coals. Instead, the feet might just be
  sweaty because of the heat from the coals or the excitement of the
  performance. Once the performer is on the coals, some of the heat
  vaporizes the liquid on the feet, leaving less energy to be conducted
  to the flesh. In addition, there may be points of contact where the
  liquid undergoes film boiling, thereby providing brief protection from
  the coals.
I have walked over hot coals on five occasions. For four of the walks
  I was fearful enough that my feet were sweaty. However, on the fifth
  walk I took my safety so much for granted that my feet were dry. The
  burns I suffered then were extensive and terribly painful. My feet did
  not heal for weeks.
My failure may have been due to a lack of film boiling on the feet,
  but I had also neglected an additional safety factor. On the other
  days I had taken the precaution of clutching an early edition of
  Fundamentals of Physics to my chest during the walks so as to bolster
  my belief in physics. Alas, I forgot the book on the day when I was so
  badly burned.
I have long argued that degree-granting programs should employ
  ''fire-walking'' as a last exam. The chair- person of the program
  should wait on the far side of a bed of red-hot coals while a degree
  candidate is forced to walk over the coals. If the candidate's belief
  in physics is strong enough that the feet are left undamaged, the
  chairperson hands the candidate a graduation certificate. The test
  would be more revealing than traditional final exams.
Answer: Nirvana or enlightenment can't be reached by logic because enlightenment is inside us, within us, and not outside.
Answer: Its simple Nirvana is a state that you mentally realize .You can be convinced by it intellectually but it requires that you go through a transformation ,when that transformation occurs you will mentally realize it.Its like being able to see when you where blind.
A man once came to Buddha and told him I want happiness .Buddha replied first remove the I thats ego then remove want thats desire ,then all what remains is happiness the quality itself :).The quality is in-explainable like the beauty of a flower , the greatness of a mountain or the depth of sadness.
So Nirvana is simply recognizing the quality of your receptions in this moment whatever they are done by desire-less intention and diligence till there is nothing else but the quality......You can be convinced by this statement intellectually but taking it as instruction for your meditation and everyday life can lead you to mentally realize it.
Answer: Well reason, inferences, logic and all that are not knowledge. Only a few puthujjanas claim that there is such a thing as ''intellectual knowledge'' or ''intellectual understanding''.
Those puthujjanas qualify themselves of rationalist. In fact any puthujjana is a rationalist or an intellectual or a philosopher. This is what is natural for a puthujjana.
They claim that truth is reached through debate or truth is reached through inferences of some axioms through some rules of inferences that they themselves invented.
For those people, truth is a quality of a statement: a statement is true, like a banana is ripe or yellow and a true statement means that the statement ''accurately describes'' some event or experience.
All those inferences are fantasies and Those puthujjanas know that they are at sea among all those fantasies that they create.
Those puthujjanas still try to create a way to discriminate among the fantasies that they create: today the most famous discrimination is the one of the scientist where some statement is inferred either form a previous ''proved'' statement or from ''statistical evidence''.
This is for the puhujjana who is a ''secular rationalist''. For the religious puthujjana who is a rationalist, ''reason'' is the way to understand their gods [like the christians] and morality.
Typically, the ''secular rationalists'' claim that the ''inferences'' of the ''religious rationalists'' are fantasies (because ''not grounded in reality'') and that only the ''inferences'' of the ''secular rationalists'' ''make sense''.
Of course those puthujjanas are completely wrong. Truths are not how good a statement describe reality. Truth is at best an event and in terms of event, that's what stops you from ''searching truth'', meaning what appeases you,  which precisely means nibanna.
That's called dhammakaya.
So in terms of knowledge, there is only ''direct knowledge'' (in opposition to ''intellectual knowledge'' whose existence that puthujjanas crave so much, but which really does not exist, no matter what logician, philosophers, intellectuals and other ''pragmatic people'' claim) and the task is to know directly dukkha, the origin of dukkha, the cessation of dukkha.
It turns out that knowing directly anicca, anatta, origin of vedana, cessation of sanna and all that requires a calm citta, which is called ''a citta which has samadhi'' and also sati.
THis is why a non-puthujjana can reach the destination of the path while the citta is in samadhi, since non-puthujjanas know already what to look for.
Puthujjanas must memorize the word of the buddha and get their citta into samadhi. And to get the citta into samadhi, what is required is to judge your thoughts as either thoughts of illwill and lust and thoughts of good will and renuncitation and follow only those latter.
Here are plenty of dualities to contemplate and make you an arhant or once returner.

For the sake of knowing qualities of dualities as they actually are.'
  Which duality are you speaking about? 'This is stress. This is the
  origination of stress': This is one contemplation. 'This is the
  cessation of stress. This is the path of practice leading to the
  cessation of stress': This is a second contemplation. For a monk
  rightly contemplating this duality in this way—heedful, ardent, &
  resolute—one of two fruits can be expected: either gnosis right
  here-&-now, or—if there be any remnant of
  clinging-sustenance—non-return."
That is what the Blessed One said. Having said that, the One
  Well-Gone, the Teacher, said further:
"Those who don't discern stress,
what brings stress into play,
& where it totally stops,
without trace;
who don't know the path,
the way to the stilling of stress:
lowly
in their awareness-release
& discernment-release,
incapable
of making an end,
they're headed
to birth & aging.
But those who discern stress,
what brings stress into play,
& where it totally stops,
without trace;
who discern the path,
the way to the stilling of stress:
consummate
in their awareness-release
& discernment-release,
capable
of making an end,
they aren't headed
to birth & aging.1

here is another one

"Now, if there are any who ask, 'Would there be the right
  contemplation of dualities in yet another way?' they should be told,
  'There would.' How would that be? 'Whatever is considered as "This is
  bliss" by the world with its devas, Māras, & Brahmās, by this
  generation with its contemplatives & brahmans, its royalty &
  commonfolk, is rightly seen as it has come to be with right
  discernment by the noble ones as "This is stressful"': This is one
  contemplation. 'Whatever is considered as "This is stressful" by the
  world with its devas, Māras, & Brahmās, by this generation with its
  contemplatives & brahmans, its royalty & commonfolk, is rightly seen
  as it has come to be with right discernment by the noble ones as "This
  is bliss"': This is a second contemplation. For a monk rightly
  contemplating this duality in this way—heedful, ardent, & resolute—one
  of two fruits can be expected: either gnosis right here-&-now, or—if
  there be any remnant of clinging-sustenance—non-return."

https://www.dhammatalks.org/suttas/KN/StNp/StNp3_12.html
Answer: It is with meditation that results in seeing clearly. Seeing clearly (vipassana) non-self & impermanence, one gets diapassioned. Getting dispassioned, one lets go. This is precisely the reason why one cannot reason out one's way to nibbana because nibbana is not something to acquire, but it is the letting go of all ignorance which doesn't happen by just intellectually understanding certain teachings, but by understanding plus practise. With intellectual knowledge the causes & conditions are still in place for ignorance to arise
Answer: Dr. Dev Pradhan – Intellectually we have wandered too much, The simple question was, Why can't we reason or logic our way to NIrvana?, needs at first instance the same way of answer. When asking by group., as we, its simple answer is that Nirwana is void of any kind self of any group or individual. Hence there you can not use I, you or we.  Its very appearance is possible only with the alignment of understanding of ANATTA. Where you have to drop I you and we with the realization of not only DUKKHA, nor ANICCHA, but  ANATTA, means no self.There you have to drop thinking, mind, and logic also. You remain only in a state of experience of universe. Buddha already said do not reveal para human things to laymen. Scientist are spell bound about universe, and at a loss to know even black holes. Our state of mind is like that. We with out the guided  path try to explore universe. This is what happening with us. When you want to know universe you have to leave earth planet. Without leaving earth if you want to know universe it won't be real experience. Hence if you want to know Nibban you need to learn how to drop the self to view the window of nirwana. After the dives of eight times and fully acquainted, then you will be able to reach the height of NIBBANA. That's why throughout the world people become Bhikkus. It needs practice of nine stages, along with the armor of SILA SAMADHI, PAYYAA. And this only can be explored by individual Buddha, Bodhisatwa, or Arhat.  What Peter J says puthujjanas means laymen, the have to be acquainted and trained of primary knowledge of Sil and Samadhi. Once they acquired foundation they can be taught Pragya, Abhidharama and Parmarthdharmas.
Answer: Why Nibbana can't be described?
This is my simple answer:
How would you explain something that you've already experienced to someone who has never had that experience (not even in his/her dreams)? First you may try to explain its attributes. you describe its shape. But what if that thing has no shape?? Then you try to describe its colors, what it smells like, what it tastes like, what sounds it makes, what it feels like, etc... But what if that thing has none of these attributes?? You may try to explain its location. But what if that thing has no location?? What if that thing only experience through your consciousness? i.e. What if that thing only visible to your mind? How would you describe such a thing?
All the above mentioned statements are also applicable to Nibbana. Words are formed by people to describe worldly things. Shakyamuni Tathagata Lord Buddha preached this Dhamma (which describe ultimate truth) with the help of the words used in conventional truth. One should understand ultimate truth only through the help of conventional truth because we (five aggregates) are in a conventional world. In tipitaka Nibbana is described as much as possible with its features and attributes because Nibbana has no similar dhamma in this entire universe.
For further explanation see this answer which describes Nibbana.
Why Nibbana can't be reached by logic or reasoning?
Every consciousness arise with the help of an object. If there is no object there will be no consciousness. Two things cannot be the object for one consciousness at the same time and only one attribute of one object can be taken as the object of one consciousness. Nibbana is an ultimate dhamma. Nibbana is the object for the eight supermundane consciousness. It cannot be the object of any other consciousness. The supermundane wholesome path consciousness arise in mental processes (citta veeti) when someone enter four stages of enlightenment [Stream-enterer (Sotapanna), Once-returner (Sakadagami), Non-returner (Anāgāmi), Arahant]. Different consciousness arise according to a defined sequence in mental processes. (Note: This is not defined by an almighty god but merely happened due to the citta niyama.) No one has the ability to change this citta niyama. (This also prove the anatta mark of existence in every dhamma) So you cannot suppress some consciousness in a mental process or generate supermundane consciousness in another mental process which is used to reasoning or logic. Meditation is the only way to follow this sequence of mental processes and finally attain Nibbana.
Answer: Nirvana is the "formless". Opinions, words, beliefs are concepts, forms.  All of the opinions, beliefs, judgements, desires are obstacles in the way of reaching Nirvana. Thich Nhat Hanh said that Nirvana is "Freedom from views". So trying to reach Nirvana with views, logic etc.. is the opposite direction. But the concepts can be helpful If you use them as pointers to become free from your attachments to concepts. Just like "I have to meditate for many hours" thought can change your life entirely. So there is also an irony here.
Meditation can be done in many ways. Meditation can be done in sitting in a meditation posture, or during a bus trip etc..The choices are many. So doing "meditation" is absolutely necessary unless the person has a spontaneous enlightenment. But that doesn't mean that a person can only experience Nirvana during a meditation session. The experience of Nirvana comes through seeing impermanence suffering and non-self clearly. Practising mindfulness doesn't lead you to think about the future but still is like making  reservation in the higher realms of existance. Also If a person really does meditation with effort in proper ways, s/he enters to a temporary stream of awareness which makes that mindfulness continous temporarily even when the person isn't doing anything to be mindful. So seeing the meaninglessness of all forms that will cause the experience of Nirvana can come anytime in daily life for the meditator.  But unless the person is very lucky to have a spontaneous enlightenment or unless the person already experienced Nirvana before and attained Stream Entry or other enlightenment stages, it is impossible to experience Nirvana without practising meditation/mindfulness.
Answer: That which is beyond conjecture is such because it is not like anything else and therefore can not be explained or understood in terms of anything else. It is somewhat akin to explaining electro-magnetic forces in terms of rubber bands but worse yet.
It has to be realized by investigating and understanding that which is conditioned, when the theme is well penetrated with understanding an escape from the conditioned is realized and the unconditioned is discerned.
If someone was to say 'come, explain the unconditioned in terms of the conditioned' - that just wouldn't be possible.

"Both formerly and now, monks, I declare only stress and the cessation of stress. MN22

Can we describe not-suffering in terms of suffering?
One can not imagine what the not-made is like descriptively nor explain it in terms of it's color, shape or dimensions.

There is, monks, an unborn[1] — unbecome — unmade — unfabricated. If there were not that unborn — unbecome — unmade — unfabricated, there would not be the case that escape from the born — become — made — fabricated would be discerned. But precisely because there is an unborn — unbecome — unmade — unfabricated, escape from the born — become — made — fabricated is discerned. Ud 8.3

Also an excerpt from the Questions of King Milinda;

"Then, Nagasena, is Nirvana unconditioned?"
"So it is, O King, unconditioned is Nirvana, not made by anything. Of
  Nirvana one cannot say that it is produced, or unproduced, or that it
  should be produced; that it is past, or present, or future; or that
  one can become aware of it by the eye, or the ear, or the nose, or the
  tongue, or the body."
"In that case, Nagasena, you indicate Nirvana as a dharma which is
  not, and Nirvana does not exist."
"Nirvana is something which is recognizable by the mind. A holy
  disciple, who has followed the right road, sees Nirvana with a mind
  which is pure, sublime, straight, unimpeded and disinterested."
"But what then is that Nirvana like? Give me a simile, and convince me
  by arguments. For a dharma which exists can surely be illustrated by a
  simile!"
"Is there, Great King, something called wind?"
"Yes, there is such a thing."
"Please, will Your Majesty show me the wind, its colour and shape, and
  whether it is thin or thick, long or short?"
"One cannot point to the wind like that for the wind does not lend
  itself to being grasped with the hands, or to being untouched. But
  nevertheless there is such a thing called 'wind'."
"If one cannot point to the wind, one might concluded that there is no
  wind at all."
"But I know, Nagasena, that there is wind, I am quite convincted of
  it, in spite of the fact that I cannot point it out."
"Just so, Your Majesty, there is Nirvana, but one cannot point to
  Nirvana, either by its colour or its shape."
Answer: Isn't it a question of purifying the mind sufficiently to see the ever apparent truth of suchness? If someone asks "why can't I reason my way to Nibbana?" isn't it the fault of the questioner's mind and not a shortcoming in Nibbana? If a high school students asks his Physics teacher "why can't I understand Einstein's Theory of Relativity?" Wouldn't the teacher respond "this subject takes a lot of learning and applied thought to understand. If you persist in trying to learn it you might succeed in 10 years upon successful post-doctorate work."
The noble Eightfold path prepares the mind and the heart for not only the experience of Nibbana but also its understanding. But the Buddhadhamma is logical, if the mind is pure enough it can see the truth directly, renounce completely and experience Nibbana immediately. I think there are examples of the Buddha teaching the dhamma to one of pure mind, they going into seclusion to reflect on it (reason it out for oneself) and becoming an arahant in a very short time.
Answer: People actually do try to reason their way into Nirvana. Many think it works, and if they are clever and intelligent, they can defend it quite well. But actually Nirvana is the view taken when subject and object are (subjectively) seen as nothing more than a figure/ground problem. Our ordinary consciousness contains the hand drawing the hand drawing the hand, etc. It's Nirvana that only sees the hand drawing. But we possess a bias ("me") which causes seeing things and not understanding that at the center is our blind spot. Everything about Nirvana is totally logical, but it's a logic that without it, we can't see. Observer bias. Without actual facts, we can't validate anything. We interject a fake "me" into every perception, the result  will always be wrong. The absence of a subjective self has to be experienced before one can understand that is is in no way illogical. Yet, it can't be grasped with the mind that contains the self. Meditation or some other rigorous training is necessary to prevent the mind from by reflex imposing a false projection of the problem in the first place.


How to create a functional document for in-house reference?

Question: I'm the only technical writer in my company with 2 years of experience. I have been assigned with a task of creating a functional document for a web-based (FMCG) product which has been around a long time at least 7 years with no proper documentation.  This is a challenging task for me as I have been only creating GUI based user manuals (with not much technical information). I really want to use this opportunity to create a complete document that is really helpful for the team. The document would only serve as an internal reference document for the product team. How should I gather information and structure the document?
Answer: In many ways you approach this the same way you would approach any other new project:

Review any available high-level descriptions (like functional specifications) and user stories: what is this thing and how are people meant to use it?
Identify your key contact (if you don't have one, ask your manager how to get one) and schedule an overview discussion.  This is a "give Ashvita the lay of the land" discussion, not a "tell Ashvita all the gory details" discussion.
Sit down with your contact and the software and get some hands-on exposure.  Don't try to cover everything; ask the expert to point out the most important and most common paths through the tool.
Start to compile questions (which will surely arise as you work with the product).

Now in addition, this product has been around for years and people have been using it, even without documentation.  Either everything is completely obvious (in which case they probably wouldn't have asked you to document it) or there's a lot of "oral tradition", maybe even informal notes, wiki pages, and so on.  You want to tap into that.
You should ask your key contact for pointers to any such artifacts and, also, who the main in-house users are.  (They might be your own QA department, if you don't have people in-house relying on the product.)  Gather the information you can.
That's all about the research part.  To organize everything you need to have some sense of who your users are and how they'll use the product.  The same techniques that you use for other technical-writing tasks apply here.  A full treatment of user-needs analysis and organizing content would be too much for one Stack Exchange answer, but feel free to ask narrower followup questions.
Answer: I believe that you want to use (structured) FrameMaker, perhaps integrated with RoboHelp if you need a variety of output types. Both products are part of Adobe's Tech Comm Suite product (and you actually need the suite for FM-to-RH integration).
There is a ton of material about how to use FrameMaker. To help you, here's the link for a long list of previously recorded online seminars for FrameMaker (Adobe login required).
Specific concepts that you're interested in are:
-structured FrameMaker (as opposed to unstructured)
-DITA strategies
-ExtendScript
-XSLT and XPath
-Localization strategies (if you're thinking ahead)
There's a lot there, but that's what you want if you're thinking long term. Plus, you'll learn transferable skills that will serve you well in future.
Comment: Isn't choosing a tool or a DTD premature?  It looks to me like the question is more about learning an unfamiliar domain and organizing that.  On the other hand, the OP *did* tag it [tag:tools]; hmm...
Comment: Thanks for the detailed answer. This is what I'm looking for. And yes, the question is about learning the unfamiliar domain and organizing the content. As for the tools part, I use MS Word and Robohelp. I ll have to continue to use MS Word/RH for documenting. The document would serve as an internal functional document for the product team and not for the end users.
Comment: @Ashvita that's important information; internal documentation is different from something you publish broadly.  Could you edit that into your question?  Thanks.