Is a varied diet necessary while backpacking?

Question: Often when planning food for a backpacking trip, I rely heavily on a very large amount of extremely varied trail-mix, and only throw in some jerky and a scant few "cookable" meals for variety. I haven't had (to my knowledge) any illness from this, but a friend expressed concern that the lack of variety would cause problems given the stress of the hike. Am I doing myself a disservice?
Comment: It might be a good idea to specify - roughly - the amount of time you're going to be backpacking. A few days, or more than a week? A few weeks?
Comment: I would love to hear from someone on real protein needs. A NOLS blog post discusses research showing a loss of muscle mass (and fat) after NOLS courses. Seems like an interesting place to start with nutrition.
Answer: It takes more than 4-5 days to have problems from a limited diet, as long as you get enough of short-term things like salt (which is not normally a problem). Even so, I usually take some Flintstone chewables and dehydrated meals along to be healthy.
Comment: Got a reference for "It takes more than 4-5 days to have problems from a limited diet"?
Answer: I would split your nutritional needs into long, medium, and short term.
Things like Vitamin C and Vitamin A are long term. A week or two of being short on them will not cause you problems during the trip, nor afterwards when you return to your normal eating patterns. You can essentially ignore them, which is kind of a bummer because this would be the easiest shortcoming to fix, by taking a multivitamin or other supplements.
Medium term would be fat and protein. Most people eat lots of protein - beef jerky, nuts in the trail mix, peanut butter - and get enough fat too. If for some reason you were eating meals like "pasta with butter but not cheese" and "white rice with vegetables" then perhaps you would run short of protein. (I say perhaps because grains do have some protein, and we typically need less than we think.) This would manifest itself mostly as feeling hungry too soon given the amount of work you're doing, and maybe not sleeping well. If it kept up long enough you might also be plagued with digestive problems. From reading books about long expeditions it seems to be a month of no fat and very little protein before dysentery sets in.
Short term your big worry is fibre. If you're not eating any fruits or veggies, and you've taken white flour bread and pasta, white rice etc, and no legumes, then you might not be getting any fibre. Depending on your age this can make you feel very uncomnfortable in just a few days. Throw in a little dehydration because you're sweating and drinking water isn't always to hand, and you could be feeling very jammed up.
The solution to fibre may be as close as your trail mix, if it's full of dried fruit. If you ignore the dried fruit, or if your trail mix is full of M&Ms, then you need to make sure you eat some vegetables. A dried soup mix might lead to nice lunches and take care of that for you, or you might try to cook more often. Or you could pay attention to those ads aimed at the 50+ crowd and bring along a fibre supplement - the kind you stir into water would probably be best.
If your concern is "I feel healthy and strong, my body works fine during the trip, but am I setting myself up for a long term health problem with the occasional week of deprivation" I would unequivocally say you are not. A bags-of-chips-on-the-couch habit that lasts for years can do that; a week without enough fibre or Vitamin A will not.
Comment: +1, but leave the white rice at home.  It has almost all the nutrients removed, so it's empty carbs.  Plus, it hits the body too fast since it's too easy to digest.  I use brown rice instead.  It takes longer to absorb and still has nutrients.  Mostly, though, it's about the absorption rate.
Comment: +1 - fiber is something I usually regret if I skip.
Answer: I don't think that a limited diet will cause you health issues.  (caveat, I'm not a doctor...)
But, keep in mind that hiking is typically a strenuous activity.  You need energy, and lots of it.  You need short-term energy, medium-term, and long-term.  A meal of whole-wheat pasta with some tuna or salmon from a pouch and some added olive oil and salt will give you short-term energy from the carbs, medium-term from the protein, and long-term from the fats, plus some salt to replenish what you've lost as you're staying hydrated.  I can last a lot longer and the hills are less imposing when my diet is on-target.  So, you probably won't get sick, but you may be short-changing yourself.
Answer: This would also depend on what your limited diet includes.  You can live quite well on nothing but beans and rice for many months if needed.  Trail mix and jerky, probably not so much.
One of the worst things you can eat on a trail is trail mix.  Nuts take a very long time to digest and much needed calories are burned to digest them.  Meat of any kind is also more difficult to digest and jerky is even worse.  At least the meat or jerky provide you with much needed protein.  Trail mix will fill your belly but it's not particularly nutritious or caloric for it's density.
Find some good beans and rice recipes.  These are much more caloric per density and provide the carbs, sugars, fats, and protein you need.
Comment: I would be interested in a citation for the nuts information.  What do you recommend as a source of fats?
Comment: Interesting with the nuts: I've always been recommended to bring nuts on trips (mountain and sea/river) because they help feel sated. Is that only half the story?
Answer: Some people have great resistance for limited diet.
I've heard a lot of stories from the people I've met during mountaineering about their high mountain trips, where their diet was based mostly on semolina powder mixed with milk powder (something uneatable for me because of lactose intolerance). One of them said he had lost after about 1.5 weeks 10 kg weight... but he still was feeling good...
However, the caloric usage for middle-difficulty backpacking for a male is about 5000-6000 per day, so quite high (I've participated in measurements).


Geological Effects of Nuclear War

Question: Can nuclear war cause geological impact like earthquakes and could it say break the USA into four large quadrants NE, SE, NW, and SW.
Comment: it can cause earthquakes but not break the USA into pieces.
Comment: I can't imagine it being relevant--any event powerful enough to cut two lines down to sea level (the minimum needed to accomplish what you're after) would wipe out the human race.  Maybe bacteria would survive.
Comment: Are you committed to nukes or might any plausible weapon be used? Redirecting asteroids might break up part of the crust, and really highlights why it's not really a viable plan.
Comment: @notstoreboughtdirt The required asteroid would be something like the [Chicxulub crater event](https://en.wikipedia.org/wiki/Chicxulub_crater).  These would be very rare (fortunately) with perhaps millions to tens of millions of years between such events on average.
Comment: Practically, no.  You probably could set off an earthquake with a nuclear explosive, but you would need to set it off in a fairly deep hole on the fault line.  But explosives used as weapons would almost always (except trying to destroy things like https://en.wikipedia.org/wiki/Cheyenne_Mountain_Complex ) be detonated above the surface (airburst) to cause maximum damage.  Of course physically splitting continents would be impossible.
Answer: It all depends on the kind and size of the H-bombs used.
Current versions are way to feeble to do what you ask.
For reference:

$1\times 10^{17}$ J  Energy released on the Earth's surface by the magnitude 9.1–9.3 2004 Indian Ocean earthquake
$2\times 10^{17}$ J  Yield of the Tsar Bomba, the largest nuclear weapon ever tested (50 megatons)
$4\times 10^{22}$ J  Estimated total energy released by the magnitude 9.1–9.3 2004 Indian Ocean earthquake

This means the largest tested H-bomb is more than 5 orders of magnitude less powerful than the largest earthquake registered... which did not split tectonic plates.
Comment: @Nathaniel: You are actually missing one zero. Earthquake beats Tsar by a factor about 200000 (five zeros).
Comment: Note for readers not familiar with scientific notation: 4E22 is a 4 with 22 zeros after it, and 2.1E17 is 21 followed by 16 zeros. The quoted earthquake energy (4E22 J) is 20000 *times* larger than the Tsar Bomba bomb.
Comment: You are correct of course. (I did actually check it with a calculator, but must have then mistyped the answer.)
Answer: Geologically, no.
Physically moving the masses involved to split the USA into essentially four new tectonic plates with oceans between them is far beyond the range of even the strongest nuclear weapons.  Even if nukes could move that much mass in a short time, it would inject enough energy into the biosphere as to wipe earth clean.  Consider that man's larger nuclear weapons leave big holes equivalent to Mount St. Helen's (25 Megatons) which is only a bit of one mountain in one mountain range.  Displacing the Rockies would take absurd numbers of nukes.
Fun note:  If you want to know how big a crater, a given amount of energy will leave behind, have a look at the NASA "Craters are a blast!" PDF.
Further, the earth's crust is not a pane of glass that can be neatly shattered into four pieces.
Geopolitically, though...
Yeah, a few nukes in the right places might fracture the potentially fragile US Federal government.  If the center of the country was turned into a wasteland that you can't even fly over, I could see how the East Coast and West Coast decide to go their different ways.
Comment: energy sufficient to move large continents any distance quickly would just liquify them instead. +1 for finding a solution however.
Answer: Nuclear explosions can indeed trigger earthquakes. But they can only release the energy already stored in Earth's crust, they can not create any new geological faults. Magnitude 8 earthquake is comparable to 15 megaton bomb in the amount of energy released, and magnitude 9 earthquake - to 500 megaton bomb. We need much bigger bombs to split tectonic plates, so US is safe for now.
What is the energy of an earthquake?
Comment: If you created an absurdly powerful device (say a gigaton) and lowered it into the sea bed to a deep ocean fault zone you could trigger massive earthquakes and tsunamis capable of extreme damage to the US west coast. A similar sized device detonated in Yellowstone park might be sufficient to crack the crust enough to unleash the Yellowstone super volcano. XKCD did some calculation with a 100 foot diameter meteor and needed to reach .99 *c* to blast through the crust, which gives you an idea of the energy levels you are dealing with.
Comment: @Thucydides Massive damage - yes, plate fracturing - still no. Yellowstone hotspot had been exploding a number of times during the last several million years, but North American tectonic plate is still intact.
Answer: Geologically impossible.
First of all, landmasses like the US are made of continental crust which is between 30 and 45 km thick. You would have to bomb through that over horizontal distances of thousands of kilometers creating chasms (the amount of energy needed has already been dealt with in another answer). Those chasms would immediatly collapse due to the pressure from the sides.
Every plate the North American Plate moves as one solid object. The movement of the plates is governed by deep mantle convection and can't be influenced from the surface. Changes in mantle convection can of course break continents apart, but that's a process on geological timescales.
So even if you managed to create deep enough fissures through the continent it won't make the separated parts move differently towards each other, it's more likely that after the walls collapsed they will just fuse again and all you end up with is some deep valleys filled with water.

Geological Effects of Nuclear War


Why is it when i go to .onion sites that I'm told that my connection is not secure or encrytped?

Question: Okay so I'm fairly new to actually using Tor, but I have known about it for years. I have read many things on how to stay secure and anonymous while on Tor. I also have the Tor browser security settings on max, so the safest ones yet also the strictest. My question is how come when i visit a .onion address such as the hidden wiki why is it when i click on the information button on the left of the address bar say your connection is not secure or encrypted? Should i be worried and mainly how do i fix this ,or am i just worrying to much and this is just normal? I'm just excited and want to explore the deep web ,but more importantly do it securely and anonymously. So i will delay my exploration until this issue is resolved. Thank you all in advanced if you can help me with this issue have a great day.
Answer: tl;dr
Every connection to a hidden service is anonymous and encrypted. This is just a UX bug.

The absence of a lock (or a "secure connection" message) just means that the site you're connected to doesn't uses TLS. However since your connecting to the site using a hidden service, the connection is encrypted no matter if TLS is used or not.
The UX of this has been improved in the current alpha version of Tor (See Ticket)
Screenshot of new UX


authentication and access control in IoT

Question: I am researching in authentication and access control in IoT. Is there any difference between working in wireless sensor nodes and IoT in the topic authentication and access control as both require lightweight designs?
Comment: Have a look at the analyst community in particular Kuppingercole and their conferences. They have a lot of work on that. Also, Identiverse in Boston next week addresses Identity & Access Mgmt including for IoT
Answer: Not much, my impression is that the problems are more or less the same. People change the term to IoT because it sounds sexier than wireless sensors (and they can sell the same thing again as new). Another similar term is pervasive (ubiquitous) computing. Yet another related term is edge computing or fog computing.
The main underlying research challenges for security in all those are often the following:

resource-limited devices
lack of trust
decentralized
weak physical security
hard to update
often has energy constraints

just to name a few.
Comment: What are the solutions?  2 just means "trust no one" which is good practice anyway.  5 can be solved by an automatic updator that verifies signatures on downloads (this assumes your device can do TFTP). 4 again means "trust no one".  1 just means you get what you pay for.


Can't do outdoor training for 150km and only on trainer. Can anyone give tips and training plan?

Question: I just found out that I cannot train outdoors for the next two months for the 150 km I was planning to attempt in the first week of September. Now I am planning to buy the In'ride 100 trainer from btwin as that's what my budget allows me to buy. Will I still be able to prepare for the 150km on the trainer. What are the advantages and disadvantages?  Can anyone give me a training plan and tips. Thanks.
Comment: How long have you been riding?  How far can you ride *now*?  With a 150km ride only two months away, I'd hope you can at least to 50-60 km with no problems, else you're going to have a very difficult time working up to 150 km in that short of a time.  The more details you can provide for your experience on a bicycle and your current fitness level, the better help you'll get.  And I hope you have a good TV plan of some type - you're going to **need** it given all the time you're going to be riding on that trainer...
Comment: @Andrew Henle I can do 60km but with a little problems. The first 40 km I can ride with an avg pace of 24 kmph but the last 20 km drops to around 15 kmph. I have been riding only for the past two weeks with a total of 8 rides so far.
Comment: For sure you CAN train for it indoor.  Whether you should or not is a different question.  Indoor trainers are best for short hard interval sessions where the changes in intensity and the pain take the mind off the boredom.  Trying to do endurance rides on the indoor trainer (i've done a few) are mentally horrible.
Comment: If you have only been riding for two weeks, and your longest rides are 50-60 km, if you don't already have a really good endurance-activity base of fitness - such as being a long-distance runner or cross-country skier - you are going to have a really, really hard time working up to 150 km in just two months.  If you're staring to fade at 40 km, you have to work up to almost four times as far.  And how hilly will the 150 km ride be?  There's a huge difference between a flat 150 km and 150 km with "just" 3,000 m of climbing.
Answer: Should be possible, but you are going to need a lot of dedication to sitting for hours on the trainer. You'll also need to put a trainer specific or cheap disposable tire on you bike as trainers wear rear tires fast.
The training you need to do depends on what your level of fitness is, the max distance you can currently ride and the nature of the 180km event (flat or lots of hills) and how you want to ride it (target average speed, how long you plan to take overall, number of stops etc.)
It will be easy to search for and build a training plan with 30-60 minute sessions 3-4 times a week that will increase your overall fitness and strength substantially. This should be your initial priority.
The difficulty will replicating the duration and nature of the long ride. I would not try to replicate the distance of the ride on the trainer, but instead the duration and intensity. Estimate the time duration you will take for the event and plan sessions on the trainer working up to about 75% of that, at your planned intensity.
Answer: This is possibly a duplicate of Training for 150 km race in 2 months practicality and plan , so you can still follow the advice in those answers to good effect.
There are some advantages with a trainer because you can control the effort you make on the indoor trainer, and target specific goals with more structure. There are lots of training plans published online. If you use a heart rate (HR) monitor you can set some personalised HR zones and spend time in specific zones to train endurance, power etc. separately as you wish
You can still do shorter, intense rides during the week and longer, steady rides at the weekend, building the distances up week by week like you would have outside.
Tip: using a specific indoor trainer tyre on the trainer because it will not be damaged by the extra heat. Don't then use that indoor tyre outside!
Disadvantages, you need to buy extra stuff and indoor riding can get boring and hot (no airflow). Resistance to pedalling is pretty linear, so estimating speed or distance is not representative of outside, but you can see how well you ride in week one, and build up time, speed, distance week by week.
Comment: +1 GCN suggests fans and lots of them to help simulate riding outside (in that airflow cools you down outside)


EUR/CHF fx rate drop on the 15th of January 2015

Question: I was playing around with some fx rates and what caught my attention was the sudden drop of the fx rate EUR/CHF at the 15th of January 2015 4:00 - 5:00 am EST. What really happened that day? Was there any prior information directed towards traders and market makers in the context of qualitative risk management to avoid heavy looses?
Is there any paper that describes the situation and how biased the volatility forecasts can be from the outliers pollution ?
Answer: What happened was totally unexpected end of peg against the euro @ 1.2CHF regime that Swiss central bank aborted. See some articles about it. As far as I know nobody in the markets knew, there was no indication whatsoever..
In terms of management, I'm afraid lots of people got heavy losses, particularly banks (Austria, Poland, Hungary) - lots of Swiss loans that got shockingly higher instalments overnight (by 20%) caused serious stress to portfolios of banks.
See for instance this good article. or google around this, to get more info - you can set google to look for content only at the beginning of 2015.
Regarding academia, there does not seem to be anything particularly interesting:
https://scholar.google.com/scholar?as_ylo=2015&q=swiss+franc+unpegging&hl=cs&as_sdt=0,5
Regarding volatility forecasting, this would depend on your model, so hard to give a specific answer to that..
Answer: The SNB took away the 1.2000 EURCHF floor it has kept for 2+ years without any prior warning to the market. The floor was initially introduced to keep Swiss Franc from strengthening due to buying demand from a troubled Euro Zone, and being an export economy. The Swiss National Bank had to defend its currency by absorbing Euro and keep on printing Francs. When the ECB, the European Central Bank, was about to announce its own QE programme, the SNB didn't see this as sustainable and threw in the towel and eventually let the market decide where the exchange rate should be. And after that event, the FX Options market has never been the same again...
Comment: What do you mean by "has never been the same again?"


Is my head gasket cracked?

Question: My wife hit a large puddle of water in her 2006 Mazda 5. Until then it was running fine. The check engine light came on and car shut down and would not start again. Mazda says it is a head gasket. Is that possible?
Comment: Possible? Yes, but it would be helpful to know what the CEL code was.
Comment: Any idea how large this large puddle was? How high on the car was the waterline?
Comment: As a rule, heads (and blocks) crack and gaskets are "blown" or breached. Pistons can be "holed".
Comment: How deep was the puddle? A sudden splash of cold water on a hot engine can cause cracks, but if water actually went into the engine, the impact could be much worse. How likely is it that water actually got high enough to be ingested?
Comment: From memory the cold air inlet is right behind the front bumper and in front of the wheel - a ridiculously vulnerable location for an air inlet.  So a puddle over shin height is likely to be ingested.
Answer: It is totally possible. Combustion chambers are quite small and it doesn't take much fluid to fill one up.
As the piston goes down during the intake cycle, a vacuum is created and anything in the intake will be sucked in. During the compression cycle, if fluid has been injected it has to go somewhere since it can't be compressed.
A little bit of it will pass the piston rings, contaminating the oil, but it's a minor amount. After that there are two things that can happen:
The head gasket will either rip allowing the piston to push the fluid out, or the piston rod will bend; often, both.
You can see a bent piston rod:

and a blown head gasket:

An engine with a blown gasket will be able to turn when you crank it; if it can't turn or makes metallic noises, you have a bent piston.
Comment: Nice images to illustrate the answer.
Answer: Yes. If the engine ingests water, you have a big problem: water is incompressible. When water gets into a cylinder, it will be forced out through the path of least resistance: the head gasket. And that's if you're lucky.
If the water isn't squeezed out, you get hydraulic lock and the piston rod will bend or break.
Answer: Depending how fast the engine was running when she hit water and how much was taken in through the inlet manifold and into the cylinders... it's possible that more than one piston rod may fail / the head retaining bolts may fail / the pistons may break / the head or block may fail.
Someone I know of had a bus throw water at her almost new BMW 330d... it destroyed the engine.
Can the engine turn over with the starter motor? Can you turn the engine over with a wrench on the end of the crank shaft? If it turns over at least one revolution it kind of rules out bent rods. If you turn it over by hand you can usually feel the compression on each cylinder because you need to make more effort to compress the air... you can feel if one or more cylinders is leaking air through a blown gasket or holed piston. You might even hear the wheeze of air escaping and be able to hear any cylinders that seem to be leaking badly. If you can get a compression tester you can get a better measure of how much leak there is from the cylinders and if some are way off they indicate a blown gasket or worse.
If you've just got a failed gasket you got off lightly! the fact that the engine won't start makes it unlikely just to be a failed gasket.

Is my head gasket cracked?


Dual monitors and graphic card performance

Question: If we use dual monitors, does it consume more graphic card's power?
In other words: if we use a single monitor, will the graphic processing performance be better than dual one?
Answer: Yes, but if they are not both displaying 3D graphics, the effect on the GPU will be minimal.  The second screen would also use up video memory to render the screen, but this will have a minimal effect as well, unless it was displaying 3D graphics with lots of textures.
Basically, you only have to worry about the available GPU power if you intend to play 3D games with two screens at the same time, or use powerful 3D/CAD software (but I cannot see how you could use both screens at the same time doing that).
You may also have performance issues if you have more than one very high resolution screen connected to very low powered onboard graphics.
Comment: I don't even play a 3D game. I was just curious. By the way. You give me a good answer again. Thanks.
Answer: Depends on the setup in question.  Some setups run twice or three times the resolution and split it to multiple monitors(like the triplehead2go).  Others have multiple GPUs that independently handle multiple ports on the card.  If it's a DVI to DSUB dongle I don't think it has much impact-if any at all.
Answer: Yes, NVidia cards are known to be stuck in 3D high-performance mode when using dual monitors. It is apparently a hardware limitation, which can be worked around by forcing the card into power savings mode. See here http://httputility.com/article/dual-monitor-power-saving-nvidia


Why does $H_2$ form on such a long time scale?

Question: If we were trying to figure out the time scale for a gas-phase reaction between two hydrogen atoms in a molecular cloud (which has density $~10^4/$cm$^3$), apparently the reaction would happen on a time scale proportional to the inverse of the density multiplied by $10^{15}$ years. Aside from the cloud not being dense and the probability that a collision will surpass the activation energy is small, is the time elongated because you need to induce a dipole moment between two hydrogen atoms to actually bind them together?
Answer: The rate of formation is much higher in the presence of dust.  There needs to be a mechanism for the energy of formation of the hydrogen molecule to be dissipated. Dissipating energy via a photon involves a forbidden transition.  Instead, the energy can be transferred to the vibrational lattice of a dust particle.
See The Interstellar Abundance of the Hydrogen Molecule. I. Basic Processes for a detailed explanation.


What are any contemporary, state-of-the-art references defining philosophy, from a meta-philosophical point of view?

Question: What is a comprehensive definition of philosophy? Or is it impossible to define philosophy?
At the risk of being 'too broad' a question, I would like to point out that the question of what philosophy is is a recurrent topic in the history of philosophy. To an extent, maybe it's not any different than the science of linguistics trying to figure out what "language" actually is.
I am not inviting any free general speculation on what philosophy means to you, but curious what robust, theoretical attempts at definition have been offered in contemporary times.
Comment: This question is too vague. It could be a community wiki question collecting historical definitions of philosophy. I am voting to close, but will vote to reopen after an appropriate edit.
Comment: @GeoPapas, agreed, you'd say this kind of question would be particularly on-topic on a site on philosophy (I'm aware that of the fact that meta-philosophy is an existing unanswered branch of philosophy).
Comment: Hmm I dont see why this question is closed as Not Constructive...
Comment: It is etymological fact that philosophy is "love of wisdom". In the sense of initial utterance as philosophy was distinguished from sophistry, "love of wisdom" can be read "respect" or "reverence" for or "virtue of" "obtaining knowledge". Wisdom requires knowledge, not opinion and philosophy contends with *ponderables,* not imponderables, not ways of looking at things nor sentiment. The domain is epistemology and ontology, the purview logic, rhetoric and reason.
Comment: According to [Dictionary.com](http://dictionary.reference.com/browse/philosophy) it is the rational investigation of the truths and principles of being, knowledge or conduct; any of the three branches, namely natural philosophy, moral philosophy, and metaphysical philosophy, that are accepted as composing this study. So it's investigating and studying what makes up the world, and the act of existing.
Answer: I think Wittgenstein is very illuminating in this respect. Some relevant quotations, dealing with some aspects of the question (PI stands for Philosophical Investigations):

PI§109 [...] Philosophy is a battle against the bewitchment of our intelligence by means of our language.
PI§126 [...] One might also give the name "philosophy" to what is possible before all new discoveries and inventions.
PI§127 The work of the philosopher consists in assembling reminders for a particular purpose.

And as far as philosophy speaking of itself posing a problem:

PI§121 One might think: if philosophy speaks of the use of the word "philosophy" there must be a second-order philosophy. But it is not so: it is, rather, like the case of orthography, which deals with the word "orthography" among others without being second-order

In general I highly recommend anyone troubled by the question 'What is philosophy?' to read PI§89-138 - one of the most brilliant self-reflections on the purpose and nature of philosophy in the history of thought. Of course you have to be minimally aware of the context of Wittgenstein's thought, but I feel these passages are elucidatory nonetheless.
Answer: Philosophy is the practice of discovering new ideas and analyzing claims.  The two parts can't themselves claim to be "philosophy" on their own since the very name means lover of wisdom. Can the collector of first editions who never reads them be considered a lover of books? What about the woman who reads every book she finds at the library, but never owns one? What about the man who reads romance novels, but will never look at non-fiction? What about the reviewer who reads books for their job, but never for their own pleasure. Or the reader who never finds fault in what they read? No! The lover of books will not despise them in these ways.  In the same way, the true philosopher will not tire of seeking the truth.
It's been claimed that the work of philosophy can been distilled into the conflict between Plato and Aristotle.  Roughly speaking, the difference between the two can be found in the "discovery" portion of philosophy and thinkers of all sorts may be divided into the Platonic and the Aristotelian camps.  If you think from the abstract to the concrete (top-down) and believe that given a sufficient set of axioms you can deduce all truth, then Plato is your man.  On the other hand, if you start with observations of the world and use inductive reasoning to discover truth (bottom-up), you are a philosophical child of Aristotle.  Both men pioneered new territory in the tools of philosophy (abstract reasoning, logic, preservation of the ideas of previous thinkers, skepticism, and so on), but each remains relevant long after their specific ideas were shown to be wrong.  We remember them because of their unique approaches to how we discover truth.
All ages seem to have their controversies which seem to fall on lines drawn between the two Greek philosophers:  Anselm of Canterbury v. Gaunilo of Marmoutiers, Bertrand Russell v. Kurt Gödel, René Descartes v. Blaise Pascal, Leonhard Euler and Daniel Bernoulli v. Gottfried Leibniz and Christian Wolff,  Bishop Berkeley v. Samuel Johnson,  Immanuel Kant v. David Hume, etc.  That's not to say philosophy hasn't moved on, but rather each bit of new ground has features that resemble the philosophical territory covered by those great Athenians from the 4th-century BC.
Much of the thinking that once fell under the banner of Philosophy has been pushed into more specialized disciplines.  Practically every department at universities can be traced back to philosophy at some point in the distant past.  Even the study of music (studied by Pythagoras and his followers), poetry (Aristotle wrote the book on it), political science (Plato's Republic is standard reading in both departments), and law (the Socratic method plays an important part in many law schools) can be seen as sub-disciplines of philosophy. If Mathematics is "The Queen of the Sciences"1, then Philosophy is her King.

Footnote:
1) It was too much a stretch to use the original Queen: theology.  Thankfully Carl Friedrich Gauss reappropriated the term.
Comment: Last night I realized that I've only covered the Western branch of philosophy here.  I believe my first paragraph covers the Eastern branch as well, but since I know so very little about non-Western thought, I cannot know for sure.  I'm very open to correction there.
Answer: Philosophy is the study, and use, of logic and logical reasoning. Philosophy forms the foundation for the principles of scientific reasoning, deductive reasoning, formal debates, and similar.
Comment: I would say they are also forms of Philosophy.
Comment: What about [alternative logics](http://en.wikipedia.org/wiki/Non-classical_logic)? Where does that fit?
Comment: Philosophy transcends logic and logical reasoning in many respects, however.  Logical reasoning is a subset of natural language, does not philosophy address concerns inherently beyond the expressive capabilities of language?  If something has contradictions it cannot be logical, but it can be a topic of philosophy.
Comment: @Sova I believe what you are referring to are 'Zen Koans', which are largely unrelated to the real field of philosophy.
Answer: I think the study of philosophy can get accurately said to seek for the most comprehensive understanding of things.  Epistemology seeks the most comprehensive understanding of knowledge.  Metaphysics seeks for the most comprehensive understanding of reality.  Ontology seeks for the most comprehensive understanding of being or existence.  Ethics seeks for the most comprehensive understanding of proper conduct.  Aesthetics seeks for the most comprehensive understanding of art.  Logic seeks for the most comprehensive understanding of reasoning (hence the plurality of logics, and symbolic logic as a formal discipline).  And the philosophy of particular disciplines like the philosophy of biology, physics, etc. seeks for the most comprehensive understanding of those disciplines.
Answer: Philosophy is just a word, like many others. As a 'science' it has no scope, and it's entirely based on the difficulties we have in understanding our own language. Look around, there are no genuine philosophical problems. We define words, like "soul" or "God" and then, we talk endlessly about them, that's Philosophy.
Comment: What would constitute genuine philosophical problem? In its root philosophy is a way of critical thinking about us and the world around us and all sciences has emerged from that kind of reflection. Philosophy doctor is a title most commonly awarded to postgraduate students.
Let me ask this, do questions like "why is there  something instead of nothing", "what does it mean to be, to exist" are not genuine problems? What about Kant's 4 basic problems: 1) what can I know, 2) what should I do, 3) what can I expect, 4) what is a man?
Comment: Sorry, but none of the above strikes me as a genuine problem. Let's put it this way, if you would have lived in a perfectly sealed **impossible** to break, huge box all your life, asking what's outside of it (and trying to use words to define what's out there) would have been a great thinking exercise, but not problem solving. In a similar way, Philosophy is a great thinking exercise, but not a science anymore. (it's true that in the past, the lines between Maths, Physics, etc and Philosophy were dim, so it had it's practical uses too).
Answer: Here are some popular definitions of philosophy.
The word "philosophy" comes from the Greek φιλοσοφία (philosophia), which literally means "love of wisdom"
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. It is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational argument.
Webster says,
Philosophy is the love of, or the search for, wisdom or knowledge. It's theory or logical analysis of the principles underlying conduct, thought, knowledge, and the nature of the universe"
Another dictionary says,
Philosophy is the most basic beliefs, concepts, and attitudes of an individual or group
More...
Comment: "love of wisdom" is an awesome way to put it.
Answer: Philosophy is the discipline that undertakes to realize most completely the ideal of consistent answers to all possible questions and a logical interconnection of these answers.


Optical flow equation and real images

Question: We know optical flow equation cannot be calculated without additional constraints. But what I cannot figure out is why it does not hold exactly for real images? This equation has gradient and so, it can be used to estimate the motion vectors by focusing on edges. Is it correct? How we add other constraints like smoothness into account?
Thanks
Comment: Hello, your question is not completely clear about what you're asking. I've tried to answer below, but please do not hesitate to edit your question to make it more explicit.
Answer: Writing the optical flow vector as $(u,v)$, then the optical flow equation only states that light is preserved.
Basically, it states that variations in the observed light patterns (measured by the image derivative with respect to time) are explained by the motion of objects (smaller light patterns inside the image).
Object motion is measured through spatial variations of the said light patterns:
$$\frac{\partial I}{\partial t} + u\cdot\frac{\partial I}{\partial x} + v\cdot\frac{\partial I}{\partial y} = 0$$
This problem is ill-posed for any image, be it synthetic or real.
This is easy to see since 1 pixel provides 1 measurement $\frac{\partial I}{\partial t}$ only, while at the same time there are two unknowns $\left(u(x,y), v(x,y)\right)$.
As you said, since this equation involves image spatial gradients $\nabla I = (\frac{\partial I}{\partial x}, \frac{\partial I}{\partial y})$ it can be solved for edges (by tracking them).
Other ways to overcome this issue:

assuming that the optical flow is constant over a square of several pixels and then solving the resulting system. Typically, using 3x3 squares yields 9 equations and a least squares solution to the optical flow can be computed;
more involved approaches rely on regularized problems. Regularized approaches look for a flow that will fit the observed data while having good properties such as smoothness, exhibiting thin discontinuities...

Optical flow equation and real images


Why this pot is split?

Question:
Beside the flush, the bigger pair doesn`t count here ?
Answer: Repeat after me: poker hands have five cards. EXACTLY five cards. No more, no fewer. In Hold'em, each player plays the best 5-card hand he can out of the seven available.
Vlad's best 5-card hand is A-8-7-4-2 of clubs.
His opponent's best 5-card hand is A-8-7-4-2 of clubs.
Split pot.
If, perchance, our hero had, say, the 6 of clubs in his hand, then his best five-card hand would have been A-8-7-6-4 of clubs, for the win. But such is not the case.
No one can play a flush here without playing exactly the board.
Comment: Repeat after me: poker hands have exactly five cards. Period. No more, no fewer. Stop trying to complicate what is really quite simple. Cards are dealt in various ways to players and to the board, but then each player plays a *hand of five cards* to determine the winner.  Holdem, Omaha, draw, stud, lowball, all have 5-card hands. (Badugi is a popular exception).
Comment: Each player plays 2 cards actually but the minimum combination is always 5. You shouldn't say "poker hands have five cards" sounds like something else than holdem. Omaha have 4 cards. combination is still 5 cards also.
Answer: The winner of a hand is defined by the best combination of 5 cards each user has.
In this case the best combination each player has is a flush. The rest doesn't matter.
If you have a pair 2♠2♣ and the board would be 8♣8♠7♣7♠A♣ you would not have 3 pairs.
Because the best combination with 5 cards you can have in this case would still be the board 8♣8♠7♣7♠A♣.
Your example is the same both players have 7♣4♣2♣8♣A♣ as their best 5 card combination. So the rest of the combinations don't count anymore.

Why this pot is split?


Why do fully homo-morphic constructions use 'ring' or 'lattice' structures?

Question: Is there a significantly advantage to these data structures, or is it simply the status-quo and the easiest to use for describing constructions?
Answer: Lattices are used simply because we do not know how to build homomorphic encryption from any other problems, like factoring or discrete logarithm.  Their mathematical structure was found to simultaneously enable homomorphic addition and multiplication while other bases for encryption could handle at most one of them.  (For the case of ideal lattices/rings, this seems intuitive:  If ciphertexts are elements of a ring then you can naturally add and multiply them, although things are not really that simple.  It was later found that the ring structure could be removed, and that any lattice would suffice.)
Advantages like quantum resistance etc are only incidental.
Comment: Hey David, what exactly is an ideal lattice compared to a regular lattice? I've asked on math SE and other places and haven't been able to get an answer.
Answer: For the second part of question:
Intractability of existing lattice based problems have the following advantages over the existing in number theory as the big prime factorization and the discrete logarithm problem:

Hard to solve in worse case and not in average.
Resilient to quantum attacks yet.
Lattice problems seem to be more easily formulated as they can be draw with paper and pencil.
In the end it is simple, extremely simple operations of linear algebra with noise

but there are still far away to resemble a practical cryptographic efficient scheme compared with the existing ones.


Sync with bitcoin-qt very slow (0,01%)

Question: I have the issue that my node's synchronisation is very slow. I am 14 weeks behind and it estimates to take 12 weeks to get synced. The synchronisation rate per hour is only 0,01%.
I have a fast broadband connection and no other issues with this PC. It should be able to download the whole blockchain in a few hours. However, the average transfer rate is about 0,5 KB/s.
Any idea what the issue might be?
I am running v0.14.2 and the number of outgoing connections is 3.
I have already changed cache memory to 800 MB but that didn't change anything.
Comment: How many incoming connections do you see?  Are you on Windows, Linux, or macOS?  For what it's worth, I have the same problem.  I'm on 0.4.2 on Windows 10 on a 100 Mbit/sec network connection.  The first approx 25% of the blockchain synced quickly, but things got very slow after that.  I receive a new block about every 20 seconds.  Approx 2 incoming, 4 outgoing connections.
Comment: I use it on Windows 8.1. I have 8 outgoing connections now (i needed to delete one blockchain file because a seperate issue after i have asked this question). Currently it takes 3 years to download everything which is nonsense.
Comment: It is probably not the actual downloading of blocks that is making it slow. From personal experience on a 2.5GHz Core i5 notebook running Bitcoin Core v0.15.1, it took more than five days to do the initial sync. Most of the slow seemed to be validating blocks. It was certainly nowhere near as slow initially, so I suspect a BIP has activated somewhere along the blockchain that causes validation to execute slowly after that. I did notice it seemed faster for a while if I safely exited and let Bitcoin Core shut down nicely before starting it up again.
Comment: Hi Willtech, thank you. It turned out that Bitcoin Core does not work very well with network drive. I have mapped the data since with iscsi and this worked fine. Still all the syncing is slow in general by design which is bad, but there seems to be nothing to get around it.
Comment: @michL Thanks. That would do it. If my answer below has helped you I would appreciate it if you would mark it as accepted so that the question does not remain "unanswered".
Comment: My Windows 10 firewall was blocking it
Answer: Bitcoin Core sync very slow
Bitcoin Core is capable of full sync in a relatively short period of time depending mainly on the hardware.
Most of the work done is not actually downloading the blocks, it is validating them and every transaction that they contain. It not only depends on downloading the blocks but also on the quantity and complexity of every transaction. The downloading of the blocks themselves is usually not an issue if you are connected (outbound) to several nodes. I am able to download blocks generally in forty-five seconds each (which includes the request time etc. and validation as well as the transfer) when I have been offline and am catching up on my restricted local 256Kbps link. My upload speed is low, and latency is high. At the rate of one block per forty-five seconds, it would currently take over two-hundred-and-sixty-three days to complete the whole blockchain as there are more than 506822 blocks as of writing.
From my personal experience, the initial sync actually took over five days to complete on a 2.5GHz Core i5 notebook with 4GB of RAM running Fedora with Bitcoin Core v0.15.1. For that, I used ADSL2+ and never perceived the actual downloading of the blocks to be the issue.
Performance of initial sync
Performance of initial sync largely comes down to the individual performance of your computer, provided your internet is fine.
Always use the latest release version of Bitcoin Core (includes bitcoin-qt and bitcoind) downloaded from the official site at www.bitcoin.org. An upgrade is safe and easy, just safely exit Bitcoin Core first and make a new secure backup of your wallet.dat before you upgrade.
Adjusting parameters
There are some parameters that you can look at and consider depending on your system. Always make a backup of your wallet before making any changes. The parameters can be entered at the command line or generally in your bitcoin.conf file, which you would need to exit and restart Bitcoin Core in that case to see the effect. Some things to consider that could make a difference:
I am presuming here that you are running bitcoin-qt which is the GUI version and not bitcoind.
If parameters are used in the bitcoin.conf file, omit the leading -.

-datadir= You could have your datadir on a fast drive. If you move your whole .bitcoin folder you will need to specify this parameter on the command line. Note that if you change your datadir and do not copy the .bitcoin folder over to the new location first, it will create a new wallet and begin downloading the blockchain again from the start.
-dbcache= The default for this is 450. If you have 8GB of RAM, you could easily set this to 4096
par= The default for this setting is auto, but I do not know what the automatic setting does. You could try setting this to -1 which leaves one core free.
-banscore= You could try setting this to 10 to kick off misbehaving nodes sooner.
-listen= You could temporarily set this to 0 to disable incoming connections while you get the initial sync done. Your busy node does not need the additional work.

After the initial sync, you can revert these settings to their defaults but probably leave your datadir wherever you put it.
Some of these parameters are available as options in the bitcoin-qt Settings > Options menu.
TLDR; The short answer if you want it fast is, get a fast computer, loads of RAM, a fast HDD and, fast internet. The same as anytime you want anything fast on a computer.
In the real world, and from personal experience, using an SSD increased sync speed more than 10x on my example system from the performance noted above.
Anecdotes
Real life example of varying system performance: I know someone personally who had to work on a quite large, but not extraordinarily large, Illustrator file. He opened it on his ~12-month-old upper spec Mac which usually performs great and, it was virtually unusable (slow to respond). Just for kicks he thought he would try the same file on a bog standard PC, opened it in Illustrator and it was completely normal. Some hardware/software builds have bottlenecks for some processes. The opposite result is probably true for some operations.
Also note, I have observed that exiting and restarting Bitcoin Core during initial sync seems to speed it up a bit for a while once it connects to nodes again.
Referencing again personal experience, syncing on Windows 10 64-bit seems to be orders of magnitude faster than syncing on Linux on the same hardware - even if Windows is running in Gnome-Boxes, it easily churns through 100 blocks per second during the initial stages of download.
Alternatives
If you are in serious trouble waiting to sync Bitcoin Core (a full node client) and you do not need the additional features that Bitcoin Core provides then, you may consider trying Electrum (not a full node client) which does not need to do the initial sync. On Fedora 27, getting Electrum is as simple as sudo dnf install electrum.
Answer: I had the same problem on a very old machine (with 4 GB RAM and an Intel Core 2 Duo E8400 CPU) running Debian GNU/Linux. I read the very helpful answer of @Willtech and derived the following command:
./bitcoin-qt -banscore=10 -dbcache=1024 -listen=0

This resulted in a sync time of roughly 2 weeks on that PC. Very long indeed but much better than having to buy new hardware...
Answer: Sorry to necro this post, but these problems persist to this day, even on Satoshi:v0.20.x.
Here's a quick fix to alleviate your issues. Manually specify peer IPs to console. If you're using Bitcoin-qt, use ctrl+t to open the console, and type in:
addnode <node IP>:<node port, almost always 8333> onetry

for each IP you want.
You can get node IPs from a public node directory, such as Bitnodes. Pick a bunch of random nodes, and make sure they're not all in the same geographic location and/or from some VPS provider (i.e. Amazon, Google, etc.), and try to diversify them. It should increase your speed a bit since those nodes will assist you with peer discovery.
Answer: I guess your computer is too slow.
Use the latest release (0.15.1 for example) and don't change cache values unless your RAM is less than 8 GB (800 MB is less than the default setting so by setting that you actually made it worse).
Comment: Looking at Bitcoin Core v0.15.1 it says that the default for `dbcache` is 450MB
Answer: For some reason some nodes does not give you any blocks when you are connected to them. To see if this is happening to you, open Peers (Window > Peers) and check to see how much is received for each node. If a node does not give you any data just ban it by right clicking and selecting "Ban for 1 hour" do this until you are connected to a node that actually sends you blocks.
bitcoind connects to 10 nodes as standard but if you are unlucky you will be connected to 10 nodes that does not give you any blocks. Normally just waiting will eventually resolve this issue but banning nodes until you get connected to some fast ones is a much faster way.

Sync with bitcoin-qt very slow (0,01%)


safest apache/mysql/php combo distro?

Question: I'm gonna run a public site on my Win XP and wonder what apache/mysql/php distro I should use. Is it ok to use wamp? or is that just for local developing? would it be safe to have it open for public?
Thanks.
Answer: There are several packages that instal Apache+MySQL+PHP onto Windows, that refer to themselves as WAMP, so you'll have to be specific about which one you mean (I suggest adding a link to it in your question) before you can get a specific answer.
More generally, in terms of "safe" you need to be sure that the package gets timely security updates when they are released by the relevant projects (and that you install said updates when they become available). You can gauge how good a package is at integrating security updates by comparing its history/changelog against those of similar packages and/or of the applications that they install.
If you are unsure about the update policy of the projects that package Windows versions of these utilities, you might be better off running a know-good (in terms of security patch policy) Linux distribution in a VM on your machine and making sure you get updates regularly (i.e. with "aptitude update && aptitude upgrade" under Debian or Ubuntu) - though this requires a little Linux knowledge. You could also maintain the Apache+PHP+MySQL packages yourself - IIRC all three have official Windows binary releases so you'll not need to compile from source unless you want unusual options.
Answer: If you want the safest distribution for this kind of solutions, you should use OpenBSD, but it's an advanced user distribution.
I think Linux (Debian or Ubuntu) could be a good alternative if you don't feel fine with BSD.
Answer: It is as safe as you configure it to. You are responsible for your server, so you must check the settings for Apache, PHP and MySQL anyway.
Do you really want to use Windows XP for a public server? MS bashing aside, it's a desktop OS, not a server OS.
I don't know about WAMP, but since it supports multiple versions of Apache, MySQL and PHP, you should be able to use the latest builds with all security patches.

safest apache/mysql/php combo distro?


If the output from a webapp can't be made accessible, is it worth it to make the rest of the webapp accessible?

Question: If I have a webapp that cannot be fully accessible to visually impaired users because the end goal is for a non-accessible animate bitmap canvas to be output, is it worth it to make the rest of the webapp accessible to them? If so, what should I prioritize adding?
Comment: Accessibility is for your users... if it's not accessible, then who are you designing for?
Comment: I am designing it primarily for sighted users. You are are correct that "accessible" could mean accessible to anyone. I meant to use it in the context of "accessible to users with disabilities"
Comment: It would be a mistake to assume that one accessibility issue covers all of them. Even visual impairments can have different causes from each other with different methods of providing accessibility to someone suffering a different visual degeneration of some sort.

e.g. Colour-blindness is still an accessibility issue that you should consider.
Comment: @Nathanael thank you did that information. It you could write an answer with a list of impairments that would not prevent people from seeing movie-ish content that I should try to accommodate I would mark it as accepted.
Answer: A non-exhaustive list of visual impairments that would not hinder people from being able to consume movie-ish content.

Colour blindness
Low visual acuity;

vision that is somewhere between 20/70 and 20/400 after correction (legal blindness in the USA starts at 20/200 after correction)
or a visual field of 20 degrees of less (this counts as legal blindness in the USA)

Blindness;

vision that is worse than 20/400 after correction
or a visual field of 10 degrees or less

Glaucoma; The vision loss is typically tunnel-like, with intact vision in the center, which decreases as the vision loss in the peripheries expands.
Macular Degeneration; A level of increasing opacity forms in the center of the vision. It blurs the sharp, central vision, but does not necessarily result in total vision loss, so may not stop consumption of movie-ish content to begin with.
Cataracts; does not stop the consumption of movie-ish content, even if seeing/reading the content is harder. In fact, movie-ish content may be easier for many sufferers than reading.

Obviously the level of impairment is a major factor; e.g. Cataracts can get bad enough that they cannot see.
Design considerations for these users would allow many of them to continue to use your service. They would also improve the usability for non-impaired users.
Accessibility considerations should also be given to those with motor impairments; they may not be able to easily tap or click on small target areas.
There are also cognitive impairments that should be considered
A former colleague of mine has created a tool that helps to understand many of the accessibility considerations that will affect your product.
http://www.antigravity-systems.com/labs/accsim/index.php
Answer: Here are some reasons you would want to make the site accessible to visually impaired users:
1) A user with poor vision might be able to see well enough to use the animated bitmap, but still need accessibility features such as labeling for form elements and standards-compliant zooming for text and buttons.
2) Are there cases where a user who can't see the output could still generate output to share with someone who can see it?
3) A visually impaired user might encounter one of your images, and visit your site to learn about how it was generated. This information might be important to them, or they might share your website with other potential users.
If you don't think that a visually impaired user would be able to make use of your images, or interact with the tool for creating them, you should at least follow standard accessibility guidelines for the informational areas of your site.


Maven Jetty plugin with endorsed external directory

Question: I have a project with more than an hundred external library dependencies, here we use tomcat with this endorsed jar libs configured on a directory in the server (now is under $CATALINA_HOME/lib/endorsed), so the webapp can access those resources on runtime start.
I wanted to try jetty instead, because tomcat takes too much memory and crashes frequently. Now I'm wondering if there is a parameter to pass on maven-jetty-plugin to specify this jar's folder so as the webapp class loader find them in its classpath.
I've tried extraClasspath in configuration tag, but it seems to load only classes and ignore all jars in the directory I set into (if I pass the full name path of the jar, it is loaded, but I don't want to set every library that I need there).
Thanks in advance for the help
update:I know it's not a standard maven operation, i'm searching for an emergency workaround since this project is very huge and I can't refactor as I want.
But also I expected this feature was not as tricky as it seemed to me at first glance.
Answer: You need to pass them as absolute paths, or, alternatively, have them as dependencies of the plugin itself.
What you want to have done goes against Maven's portability principles, so don't expect it to support it.


Is there a minimal implementation of Stellar Consensus Protocol besides stellar-core?

Question: I'm learning about consensus and I'd like to explore SCP in depth. However, the stellar-core implementation is difficult for a newcomer to grok. Is there a minimal SCP implementation elsewhere I can learn from, ideally in Rust or another high-level language?
Answer: I believe there are implementations either complete or in progress, but am not sure if any have been publicly released.  If you want to implement SCP, I strongly recommend starting with the protocol specification draft rather than the whitepaper.  Many of the people following the draft hang out on the IRTF Decentralized Internet Infrastructure list, so that would be a good place to hear about or discuss implementations as well as to provide any feedback might have on the draft.
Answer: I am not aware of an alternate implementation of the SCP code. I'd recommend using the white paper as a starting point to take advantage of whatever language you'd pick to do it.


How can electric field be defined as force per charge, if the charge makes its own, singular electric field?

Question: The electric field $\bf{E}$ represents how much force would act on a particle at a certain position per unit charge.
However, if we actually place a particle in that position, the electric field will have a singularity there (because of the $\frac{1}{r^2}$ in Coulomb's law). Isn't this kind of a paradox? In my eyes, this makes the concept of electric field useless, because it cannot be used to calculate the force on a particle.
Comment: general comment: physical laws doesn't have to be useful everywhere. They are just  models that work in some circumstances. Part of physics education is to learn these details
Comment: More on [singularity in Coulomb's law](https://physics.stackexchange.com/questions/tagged/singularities+coulombs-law).
Comment: It is no more a singularity than an impact between two objects. Easily handled by using diracs delta function. Even if the impulse, or the value of the electric field,, is infinite at some time or point, it is finite over a time signature or area. It all is moot since in the end, elections aren't point charges and objects aren't rigid - but the models consider them so. The models work very well, so no point complicating them over this.
Comment: Try calculating the speed when two point-particles collide due to gravitational or electromagnetic attraction.  The answer you'll get is "infinite speed", because point-particles are just a convenient abstraction, which fails in that case.
Comment: What is "that position" in "if we actually place a particle in that position"? Why will there be a singularity?
Answer: It's true that a point particle with finite charge is problematic in electromagnetism because of the infinite field and associated energy near such a particle. However, we don't need that concept in order to make a defining statement about the electric field. Rather, we can use
$$
{\bf E} = \lim_{r \rightarrow 0} \frac{\bf f}{q}
$$
where $\bf f$ is the force on a charged sphere of radius $r$ with a finite charge density $\rho$ independent of $r$, and $q = (4/3) \pi r^3 \rho$ is the charge on the sphere. This charge $q$ will tend to zero as the radius does, and it does so sufficiently quickly that no infinities arise and everything is ok.
Comment: For further info, see: https://physics.stackexchange.com/questions/491532/difference-between-coulomb-law-and-qed/492275#492275
Answer: You're forgetting one thing: a particle cannot feel its own electric field, so a point charge that generates a $1/r^2$ field doesn't do anything unless acted upon by an external field. You also can't place a particle at $r=0$ of another particle's $1/r^2$ electric field, because, well, there's already a particle there. (Also, how are you going to get it there, even if you could? It takes so much energy to even get close that you're leaving the realm of classical electromagnetism when you try.)
Comment: "It takes so much energy to even get close" - unless the two particles have opposite charges and the interaction is attractive. (still, +1 from me.)
Comment: Exactly. The singularity at the position even hints that it's useless to discuss force on another particle at that point, as the position is already taken.
Comment: @Emilio Pisanty: But electric fields aren't the only forces involved.  Get two particles of opposite charge close enough, and they probably start to feel the strong nuclear force. or whatever it is that underlies the Pauli Exclusion Principle...  And of course if your particles happen to be say an electron and a positron, they annihilate each other, thus neatly avoiding the singularity :-)
Answer:
Isn't this kind of a paradox?

Consider two point charges, $q_1$ and $q_2$, in the vacuum with separation vector $\mathbf{r}_{12}$.  Coulomb's Law for the force on charge $q_2$:
$$\mathbf{F}_2=q_2\frac{q_1}{4\pi\epsilon_0}\frac{\hat{\mathbf{r}_{12}}}{|\mathbf{r}_{12}|^2}=q_2\mathbf{E}_1$$
Thus, the force on charge $q_2$ is due to the electric field of charge $q_1$ only. Similarly,
$$\mathbf{F}_1=q_1\frac{q_2}{4\pi\epsilon_0}\frac{\hat{\mathbf{r}_{21}}}{|\mathbf{r}_{21}|^2}=q_1\mathbf{E}_2$$
the force on charge $q_1$ is due to the electric field of charge $q_2$ only. This easily generalizes to $N$ point charges; the force on charge $q_n$ is the vector sum of the forces due to electric field of each of the other $N-1$ charges.
You may (or may not) be familiar with the notion of a test charge which 'feels' the electric field due to other charges but has no significant electric field.  Armed with this abstraction, one can say that the (total) electric field at a point is the force per unit charge at that point. Indeed, from the Wikipedia article Electric field

The electric field is defined mathematically as a vector field that
  associates to each point in space the (electrostatic or Coulomb) force
  per unit of charge exerted on an infinitesimal positive test charge at
  rest at that point.

(emphasis mine)
Comment: It is not correct to say that a test charge has no associated electric field. Rather, its field vanishes in proportion to the charge and in the limit is negligible in its effects. Also, the Wikipedia article is not showing awareness of all the issues.
Answer: You should distinguish the interaction if a charge with another charge from its self-interaction. For the first case there is no issue. For the second case there are issues. For a classical point particle the self-interaction energy diverges, so you will have to assume a finite radius. If you assume a homogeneus spherical distribution and equate the self energy to the rest energy you find about 2.8 femtometer for an electron. See https://en.m.wikipedia.org/wiki/Classical_electron_radius. However there is no experimental evidence for a finite value of the electron radius. As far as high energy physicists know it is a point particle.
Answer: The basic reason here is that "electric field", like all theories in physics and science, is a model for reality, not "reality" itself, to which we have no direct access, and thus what one should really be asking here is what it is intended to model and how best to conceptualize that model. A poster here named @Cort Ammon likes to emphasize points along this line. Science doesn't tell us what things "really" are - insofar as its "pictures" are concerned, it actually really is a social construct, sorry, but those "useless" degrees aren't useless. What isn't a construct, is what it tells us we can and can't do, or what will happen if we do something, when those actually happen. Photons may be a social construct and if you want you can imagine little green gnomes instead, but it is not a construct that if you put your hand under a magnifier focusing the Sun (DON'T), you'll get a nasty lil' mark. The former is a framework we have in our heads to think about the latter, why and what happens during it, perh. also why that such burn may have a slightly greater chance of cancer in the future (and that works a bit better than green gnomes do :g:).
An electric field is such a construct whose initial purpose is to model one kind of phenomenon: how an electrically-charged object moves when placed in a region of space that didn't before have one, by (simplifiedly) putting little arrows at each place in space that point in the direction in which it seems compelled to move, and making the contours of such mathematically precise with the tools originally developed by Rene Descartes and Pierre de Fermat known as analytic geometry.
Because of that, it is an answer to a kind of "counterfactual" question, and hence what the arrows of the electric field you are describing in your post, then, where you've added the second object as producing field, do is to describe how a hypothetical third object not already present there would move. If we want to talk of the motion of the second object, we thus need to consider the field from the first alone, without adding its "own" field in as you just did.
You might also compare Cort Ammon's answer at the top of here:
Why doesn't a particle exert force on itself?
as this touches on the philosophical blurb at the beginning.


Fetwa about pieces of the relegion

Question: Hello what is the judgment for people who accept religion of God partially? For example : Declare that there is only one God and Muhammad is his Messenger and than say : No need to pray, or fasting is stupid and things like that .
Comment: We are not a fatwa site. Maybe my answer on [Conditions to do fatiha for marriage](https://islam.stackexchange.com/questions/48262/conditions-to-do-fatiha-for-mariage/48290#48290) is relevant.
Answer: If someone believes Allah, the he should believe the source of his belief too(It must be Qura'n and Hadith. Nothing else describes Allah directly). Then if he believes in Qura'n, in it's verse 42 and 43 Allah has said,

"What put you into Saqar(Jahannam/Hell)?" They will say, "We were not of those who prayed,"

So I think the person who says there's no need to pray, it may be right if he wanna enter the Jahannam or Hell(as he wants he has no need to pray). Or if he wanna go to Jannat, not to pray Salah is nothing but stupidity.
Then go to the subject of fasting,
From Quran:

"The month of Ramadan (is the month) in which the Qur'an has been sent down as guidance for mankind containing clear signs which lead (to the straight road) and distinguishing (the truth from falsehood).." (Q 2:185)

Also if a man can't be able to fast he has to feed the same quality and amount of food to someone else. Or if he breaks his fast willingly then he has to take 3 days of fasting for each days he had broken the fast.
Suppose he also believes in Muhammad and only 3 prophets(Who asked the Question wanted to know in the comment box). But he is not right. Because there are existence of name of 25 prophets(some of them are Rasul too). Muhammad(Peace of Allah and Rahmat Allah be upon him) has said,

"There were 1,24,000(2,24,000 in some books) prophets including me"

In Quran:

We certainly sent into every nation a messenger (16:36)

And believing Allah and his Messenger without believing it is foolish work. Isn't it? So this type of Fetwa(eg. No need to pray) should not be given.
Comment: Good answer although I was actually not talking only for fasting or salah . Lets say a person who accepts only 3 prophets of islam instead of all of them ... Is this an ignorant , kafir , or stupid?
Comment: I edited the answer for your additional question. See it again. And you shouldn't also say anyone kafir who believes in Allah. It may be dangerous for you. He may be stupid. Make him understood

Fetwa about pieces of the relegion


Switch to default keyboard in password fields

Question: I primarily use SwiftKey keyboard on my Samsung Galaxy 10.1 tablet. I want to find a way to automatically switch to the default Samsung keyboard when I enter a password. Currently I have to pull down the notification tray and choose "Select input method". I want to have this automated. If it is not possible to detect whether you are entering a password then maybe I can do it on a per app basis.
Comment: I can think of two approaches right now. One is very easy, which is to use a Firewall to restrict SwiftKey from getting connected to Internet, so that you don't have to worry about logged passwords getting uploaded somewhere.  Second is, the table `secure` of `settings.db` (Settings Storage) has keys like default input method (Samsung/Swiftkey) and some related keys. Change their values using Tasker when your specific app is launched and you're good to go. I don't have a Samsung device, otherwise, I would've attempted to answer. //Is the device rooted, and which Android version are you using?
Comment: I like the firewall approach. I am rooted and running Kit Kat 4.4.2. Can you recommend an application I should look at to control firewall settings?
Comment: Since the device is rooted, look no further than [AFWall+](https://play.google.com/store/apps/details?id=dev.ukanth.ufirewall). It's easy as well as effective.  // There is a third method I forgot to write last time: you can on-the-fly disable the SwiftKey when your specific app is launched, because when Swiftkey is disabled (i.e. not available), Android will tend to fall back to what's available keyboard which would be the Samsung one. This technique can be achieved by Tasker, and while it's theoretical I believe it would also work.
Comment: Yes I have tried it. I can verify it is blocking SwiftKey from sending packets to the web. The app is a little annoying since at first it blocked all web traffic. However by using the firewall logs Im starting to 1 by 1 re-enable applications to access web. If you want to write formal answer. I can accept it as solved.
Answer: The goal may seem to be switching the keyboard app when the password is to be entered, but the real issue is to protect the password from being logged by third-party keyboard apps, or at least be restricted from being uploaded somewhere. In that case, I suggest using a firewall so that you can restrict any app from connecting to Internet, let alone it can send the passwords among other things.
Be it a rooted device or not, there are firewall apps available to suit your needs. Some of them are mentioned here:

Closing internet access for some apps (see my answer here)
Block apps from accessing the Internet on Android device

I've tested two firewall apps: AFWall+ (needs root access), and NoRoot Firewall, former tested on Android 4.2.1, 4.4.2 and 5.0.2, while the latter is tested on Android 4.2.1, and 4.4.2.
Since your device is rooted, I suggest using AFWall+ to be in control of the device. It runs default in White list mode i.e. all the apps including System apps and Kernel are denied root access. You can change that mode however.
Things to do

Install the app
Tap the three dots vertical line next to lens icon → Preferences, and check the options suitable to you. I prefer:

Show notification icon
Show filter option -- it will break the app list into "All", "Core", System", and "User".
Active Rules
Confirm box on AFWall+ disable
Enable Firewall logs
Turn on log service
Device Admin; and others you won't need

Choose Blacklist mode over White list mode if you intend to block specific apps while allowing Internet access to everything apps
 (Click image to enlarge)

Find your app in the list (under "All" or "User") and check the boxes at its left if you're in Blacklist mode, or have it unchecked for White list mode.
Choose Apply by tapping that three dots vertical line, and you're good to go. You can check Firewall logs after sometime for assurance.

As for NoRoot Firewall, it's very intuitive, straightforward, runs in Blacklist mode, so you would know what to do.

However, if you're still adamant to use the idea of switching the keyboard app, then I suggest you take a look at my comments:
Delve into settings.db

The table secure of settings.db (Settings Storage) has keys like default_input_method (Samsung/Swiftkey) and some related keys. Change their values using Tasker when your specific app is launched and you're good to go.

Enable/Disable the app on-the-fly

You can on-the-fly disable the SwiftKey when your specific app is launched, because when SwiftKey is disabled (i.e. not available), Android will tend to fall back to the available keyboard which would be the Samsung one. This technique can be achieved by Tasker, and while it's theoretical, I believe it would also work.
Comment: I'd like people to know that any app with Accessibility Service enabled can record what's being shown (including what is being typed) on the screen. This answer doesn't address that.


Soloing over major and minor mixed chords

Question: if you have a progression like I vi IV V, ( which include a minor chord) is ok to use the major pentatonic for soloing,or do I have to stay with the minor pentatonic because of the minor chord?
Answer: Those four chords are all diatonic in the same key, so your major pentatonic scales will work over all of them, as will the key's full major scale.
Answer: The major pentatonic will cover the 'correct' notes. The only quirk will be the dominant chord (V) where the c is 'considered' an avoid note. See also here https://en.wikipedia.org/wiki/Avoid_note
Answer: The minor (or major) pent will reflect notes from the KEY, rather than any other minor chord in that key. So, put another way, in, say, C major, use C major pent notes and it'll all work fairly well. If you want to use minor pent notes, well, serendipity, use A minor pent because the notes happen to be EXACTLY THE SAME!
If you wanted to put an edge to what you play, then use C minor pent, which will work in a bluesy way over the same chord sequence. Strange how it works, but it's been used millions of times with great success. It does help, though, on the root chord (C here) to  bend up the minor third to a sweeter major third.
Answer: Let's translate this into specific triads C, Am, F G. All these triads are in C Major, so
1) Play C Major (CDEFGAB) or C Major Pentatonic (CDEGA) over all of them. Those are the "key scales".
(A general principle of soloing is don't "SIT" on the fourth or minor sixth of any chord. "Avoiding" notes is a silly idea. Of course you can play note C over chord G if you resolve it elegantly.)
2) For variation, each triad has its own Pentatonic scale, and all of these scale are subsets of C Major:
Am --> Am Pentatonic (ACDEG)
F  --> F Major Pentatonic (FGACD)
G  --> G Major Pentatonic (GABDE)
If you want to be a real musician I suggest you learn this in all 12 keys.
Comment: @JohnMercer as someone "new to all this theory stuff" I just want to give some friendly advice, that your ears ALWAYS come first. Theory is a powerful tool that lets you understand why what sounds good to you sounds good, and then apply the tool in new and interesting ways and discover new sounds. It can NEVER tell you whether something that sounds good to you is right or wrong. If you like the sound of a C major pentatonic in that context, the right question is less "can I play a C major pentatonic here" and more "why does it sound good when I play a C major pentatonic over an F chord here?".
Comment: Sorry to be a pest about it, but I'm fairly new in this theory stuff. You said that I can use major pentatonic over all of them, but the IV chord is F. There is no F in the C maj. pent. scale. That 's still ok to use?
Comment: @JohnMercer yes.


GNUStep Getting Started

Question: I downloaded GNUStep and installed it, however I am not sure where I can find an IDE. does anyone know what programs serve as a GNUStep IDE/where to get them? Failing that, does anyone know of a tutorial on how to create and compile a basic GNUStep program?
Answer: Well my experiences with that are devastating. ProjectCenter the IDE distributed for GNUstep does not work here at all the debugger intergration is well not existant. But that's what you get with GNUstep. There is Gorm as interface builder and ProjectCenter. Not more. That's very discouraging. The best you can do with Objective-C is currently having a Mac in some form and use XCode. That's the best you can get currently, and I expect that won't change in any forseeable future.
Now you should step back and just use the "plain" old Makefile route. There is a somewhat very rough tutorial about GNUStep makefile starting somewhere below
http://wiki.gnustep.org/index.php/User_Guides
Regards
Friedrich
Answer: As Friedrich already mentions in his post above there is Gorm for creating interfaces and ProjectCenter as IDE (gdb integration is worked on as far as I know).
For compiling GNUstep programs you are best of using GNUstep-make. You can find some recently updated tutorials here:
Basic GNUstep-make tutorial
More advanced GNUstep-make tutorial
And there is always the whole bunch of newsgroups, irc and mailinglists where you can usually get quick answers to your questions. Maybe not on IRC currently.
Answer: You can try to make eclipse
work with gnustep/msys/mingw:
http://wirecode.blogspot.com/2007/11/objective-c-and-eclipse.html
http://djsilenceboy.wordpress.com/2012/02/13/install-minggw-and-gnustep-for-ccobj-c-for-windows/

GNUStep Getting Started


Is 5 hours too long of a drive for single parent with 2 year-old?

Question: I'd like to take my 2yo son on a 5h road trip - but the mother is against this idea. I have to admit - it does seem daunting - but would like to try.
Comment: Are you planning on driving without stopping, or take reasonable breaks throughout? (Considering diaper changes, there will be some mandatory breaks!)
Comment: Some other relevant questions (not necessarily duplicates) -- [Road trip with a 3-year-old](http://parenting.stackexchange.com/q/11909/4054) and [How can we make a long road trip pleasant for a toddler and the parents?](http://parenting.stackexchange.com/q/2347/4054)
Comment: Can you break the trip in half? Anywhere at the half way point to play and get out some energy?
Answer: 5 hours doesn't seem that long - double that is definitely doable.
The important thing is how you plan it-

regular stops, whether for fuel, feed, snacks for you, nappy change, or just a walk around in fresh air
have everything you may need close to hand: wipes, cloths, maybe a bottle
a car seat that is safe and legal, and that allows your baby to see you
make sure you aren't tired, and be focused on the road. Don't panic if your baby decides to suddenly be loudly upset with something - just plan to pull over at the next safe spot and then deal with it.
Comment: I agree on everything but perhaps on the 'see you' - that may be infeasible with a 2 year old.  A 2 year old should be in a rear facing seat, and while mirrors are useful for infants I never found them practical for 2 year olds.
Comment: Yep! Plan out stopping points every little while to get out. Will make the trip **MUCH** more enjoyable. See some sights along the way. Teach him to pee in the woods. Kiddos always like that :)
Comment: In the UK a rearward facing seat is fine in the front passenger seat - just disable the air bag if you have one.
Comment: In the US state I live in, it is illegal to have kids in the front seat before they turn 13, unless the car has no back seat (or back seats without seatbelts for old cars). So check your laws :). btw Mirrors worked fine for us at older ages.
Answer: Does your 2-year old nap in the car? In that case, I think 5 hours is not too bad.
Even if not, just including rest stops it should be fine.
Think of something like (if he naps after lunch):

leave in the AM, an hour or 2 before lunch. Have some entertainment your son can play with, such as matchbox cars or a book.
have a nice lunch and a break, run around a little.
After driving a little he should nap again, about 1.5 hours maybe?
Take a break about 15-30 min after he wakes. Maybe you can find a park or playground. get some snacks, maybe even something special like ice cream.
Now you have 1.5 hours left to drive.

Add more stops if necessary!
We have done road trips with our kids at various ages, and some of them were long. Not really a big deal, but you do need to be flexible with breaks.
Answer: Depends what you mean by a "five hour road trip". Do you mean five hours one way to a destination? Or a five hour trip, both directions, with stops etc.
Expecting a 2-year-old not to be bored (and act it!) having to amuse themselves for five hours while strapped into a car seat may be a bit much to ask.
That said, we used to rent a cottage that was about a four hour drive from home, and our solution was to start the trip about an hour before the kids bedtimes. The kids would get bored and drop off to sleep and the road trip was then easy to manage.
But if you have to stay engaged with the munchkin to keep them amused, then I'd argue that maybe you might consider how that could have the potential to distract you from your main task - driving safely.
You know your kid best. If they are able to amuse themselves for long periods, then a five hour drive with a couple of "get out, run around, snack, bathroom" breaks might make it work. If they are needier, then it might be a disaster.
Answer: I would not recommend doing that much driving in a single day with a 2 year old. Even if the child was able to tolerate it. It's really not fair.
Your son will most likely not enjoy it. He'll get frustrated and stressed and uncomfortable being in his seat for that length of time.
With breaks, that could easily end up being 7 or 8 hours total traveling time.
We recently did a road trip with a 4 year old and a 6 year old. The longest stretch we did in a single day was about 5 hours driving time, 7 hours door-to-door. It was about the limit of what they could reasonably cope with, without becoming very stressed and upset, and that was with regular stops.
With a 2 year old I would not advise doing any more than 3 hours driving in a single day.
The problem with the idea of giving it a try. What happens if it doesn't work out so well? Will you have a backup plan? What happens if you're 2 hours into your drive, with 3 hours still to go and your little boy gets very upset and doesn't want to get back into his seat after a break? Sure you could simply force him, but would you really want to do that?
Road trips are supposed to be fun for everyone. I just can't imagine a child that young having fun being in a car for that long.
Perhaps you could split it over 2 days instead.
Comment: I disagree with the majority of this answer. My children coped quite cheerfully with extended car trips more or less from birth onwards. Indeed, a younger child is almost easier because they are likely to have an extended nap at some point during the day -- ideal to get in a long stretch of driving without worrying about stops and breaks.
Comment: I disagree too. My kids are fine with extended driving, and having a 4 and 6 year unable to do more than 5 hours is puzzling to me. My 3 and 5 year old does 5 hours just fine, and have done more. Just add stops!
Comment: We try not to drive more than 2 to 2.5 hours with kids at that age, even with sleep time. Certainly 5 hours in one go is way too long.
Answer: No 5 hours isn't too long. But you should do a lot of planning ahead of time. Make it an enjoyable experience, plan on stoping at a playground, a store, a quick service restaurant, and a library. Have activities and snacks. Hopefully your child naps, but if not you can talk to them about your next stop and how much fun it will be.


Backend user view own articles

Question: I need to provide access through joomla 3.6 backoffice to different groups of users: they must be able to SEE, create and edit only their categories and their articles.
How can I do? With the ACL system I can only avoid that they can modify the items but can still see them.
Thank you in advance
Answer: With ACL Manager (paid extension), you can use its enhanced ACL feature (from its options), to show only editable articles and modules to your users.
From the features description of the component:

Enhanced Joomla ACL
A selection of powerful additional ACL features on top of the Joomla
  ACL system like: Permissions per Module, Show Editable Modules only,
  Show Editable Articles only and Permissions for the Category Manager.
Comment: I love ACL Manager and install it on every site I build.  Definitely worth the money.

Backend user view own articles


Old malt extract (liquid) for a yeast starter

Question: So by old I'm talking maybe ten years! I was cleaning and found quite a bit of LME gifted to me with all my original homebrew equipment. I was mid-swing into the trash can when I wondered if maybe I could use this old stuff for yeast starters? A good boil should clean up any nasties in there right? It's been sealed in a plastic screw-top jar that was taped and some in a can. It sure would be a penny saver if I could use it, what do you think?
Answer: Doing some searching around, LME can go bad, but I don't know how much it would effect your beer if it's just a yeast starter.  You apparently get what people have dubbed "Extract Twang" if the LME is shelved for too long, as well as the color of the extract darkens, but I'd imagine a yeast starter is insignificant enough in quantity that you probably don't have to worry much.
If I had to choose between the two, I'd say the canned is probably your best bet, as it sounds as though the plastic jar may be permeable to oxygen, therefor making it the least preserved over time between the two.  I'd say use up the canned LME in your starters before using the plastic container, and if you don't notice any off smell/flavors with the canned starter/beer, you probably won't notice any issues with the plastic jar.  That is of course, assuming the plastic jar isn't being re-opened and rotting from previous exposure to the elements.
Just bear in mind, I assume you won't use all of the extract in one starter, as soon as you open it, you're already at a disadvantage, so make sure the remaining extract is refrigerated, and used before very long after opening the old can/jar.  While I'm guessing at this, I wouldn't hold onto it for more than 2 months after opening it, and even that seems to be a bit long.
Referencing:
Liquid malt extract storage
Can liquid malt extract go rancid
Answer: Sure, dilute it, boil it to get about 1.040 SG and use it in the starter. All of the sugar content is still there. It may have staled and developed soapy compounds but the yeast don't care about those - they just want the sugar!
After making the starter, put it in the fridge to flocculate the yeast and pour off the liquid so none of it makes it into the beer.
If you have access to canning equipment, can the rest so that it's ready for starters for subsequent brews.


May I ask this question?

Question: I wonder how I should evaluate different features for my website. The features are mockups at best, and some features are only ideas. I also have good basic functionality deployed, but now I want to evaluate which non-implemented feature that I should work on. Is that a good fit for your site, or is the question too subjective?
Answer: This question is really up to your team and your customer. Not really a good fit for UX.SE, since we can't guess what your customer wants. So head over to your project lead and ask what you should do with the features...
Answer: I understand you need to test some ideas because it is a problem for each functionality that prevents it from becoming a feature.
I think if you can describe your problem or what you want to know, here, even you add a specific example with a mockup, the users will help you.
It will be ok if the example is the base of a question that can be generalised and can help other people in the future, but if you want just help for testing your website, that will be not useful for other users.

May I ask this question?


Android: Action bar vs. Toolbar, Spinner vs. Dropdown

Question: Is there any distinction between the key functionality of Android controls: Action bar vs. Toolbar, Spinner vs. Dropdown. To me they seem to be the same and I wonder if there is a reason of introducing new terminology for the controls that already existed.
Answer: Spinners and Pickers are effectively attractive drop-down lists, but they both have a slightly different form.
A spinner is more streamlined, and can be found within the action bar to quickly change data sets or views(email account, calendar view, etc).

A picker takes up more space, and is more like an analog radio dial, in my mind.  It's great for step-wise data like Times, Dates, or other gradually increasing/decreasing numbers.

I do admit to being a little confused about the names, since you pick from a spinner and spin a picker, but I try not to ponder that too much.
I'm not sure if anything in Android is called a toolbar, but the action bar tends to serve this purpose in most apps.  The main functions sit on the action bar, with the rest overflowing when needed.  The action bar can change its buttons depending on context, which makes it behave like a toolbar that only shows up when you need it.  For instance, when you select an email, you get options to Archive, Delete, Label, Mark as unread, Star, etc.
Comment: Thank you Karen :) I was mostly wondering why Android doesn't call a "spinner" a "dropdown" and and "actionbar" a "toolbar". Dropdown and a toolbar are established terms that everyone knows so I was curious if there was a specific reason to invent new names specifically for the android.
Comment: My assumption was always that they wanted the new terms so that specific details and functionality would be recognizable.  Everyone knows what a "toolbar" is: a bunch of buttons in a row.  But a "context sensitive action bar" is a distinct subset of that category with clear, defining characteristics.  Same with spinner and picker.  Perhaps a case of a square being a rectangle, but a rectangle not being a square...
Comment: Anna, could you please mark Karen's answer as the answer to your question.
Comment: Your assessment of the Toolbar/ActionBar isn't quite correct. There is a Toolbar class (now; didn't use to be). Both ActionBars and Toolbars can have have context aware items on them, though it is easier to pull off with the newer Toolbar class. Either way, it's not a one vs the other thing between the two, it's kinda' weird. See my answer below for details. You also describe toolbar as "showing up when you need it" which sounds more like a context menu, which also exists but is a different system in Android.
Answer: @Karen covers the Spinner vs Picker question. Regarding the ActionBar vs Toolbar question:
Definition of Toolbar

A Toolbar is a generalization of action bars for use within
application layouts.

History
ActionBar was the first design introduced in Android v3.0 (Honeycomb). It was liked, but difficult to extend beyond the specific use cases Google initially planned for. Later on, Google accepted that the implementation of the ActionBar was a little rigid for what developers wanted to do with it. Especially when the Material guidelines were released.
That brings us to the Material design that was released with Android v5.0 (Lollipop). Due to the increasingly robust uses they wanted the ActionBar to perform, they needed to make something more flexible. But backwards compatibility forced the following workaround: Keep the ActionBar concept and related Activity methods, but copy most of its functionality into another class called Toolbar that is implemented more like a regular View. Now you create a Toolbar and assign it to the ActionBar's spot, replacing the old, limited ActionBar implementation.
The benefit is that this new Toolbar class behaves more like a regular View while still including many of the built-in behaviors of the ActionBar. The new Toolbar can be placed anywhere in an activity/fragment layout, can contain other custom views and layouts, interact with parent views that contain the Toolbar, and more. The ActionBar wasn't nearly as flexible.
tl;dr
Nowadays, everyone uses the Toolbar class then assigns it to the ActionBar of the Activity. (The details of how are easily found in the Android Developer guides.)
In fact, the Material design guidelines pretty much require this since the Toolbar is required to interact with scrolling content and other features that the ActionBar can not offer by itself.
For further reading, see the Android Toolbar developer documentation


Pages: Formula/Equation Editor

Question: Does Pages have an in-built formula editor? If yes how do I access it? If no, are there any third party software I can use?
Answer: You can use Grapher.app (in /Applications/Utilities or via Spotlight), enter the formula there and then just copy&paste the formatted formula into Pages.
Answer: Pages does not have an equation editor by default. Apple does say, however, that if you have MathType 6 installed, you can use that from within Pages, and equations are then treated as graphics.
Answer: One option is to install a Latex distribution like MacTex and then use a small software called LatexIt.
It allows you to type equation with the full power of Latex without having to care about anything else of latex, you just type the equation and it generates a display of it that you can drag'n drop to your Page document, save in a standalone pdf or other format.

Pages: Formula/Equation Editor