Question: Can someone please explain Fermat's Little Theorem? No, I don't mean his Last Theorem. I'm really confused. I understand what the mod function does, but I don't understand how it's used here or what the theorem as a whole is saying. Please explain the different parts of it, and its proof.

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 Can someone please explain Fermat's Little Theorem? No, I don't mean his Last Theorem. I'm really confused. I understand what the mod function does, but I don't understand how it's used here or what the theorem as a whole is saying. Please explain the different parts of it, and its proof.

First, what is (mod n). Modulus is an operator that can be thought of as the remainder--well, sort of, I won't go into the more rigorous definition. So 7 (mod 3) = 4. FLT says a^(p - 1) = 1 (mod p). So if you take a number a, raise it to power of a prime minus 1, you'll get 1 (mod p). This is incredibly important; almost everything you do on the internet is secure because of this property. The proof is a little subtle. And honestly it's not really somethinga 5 year could understand. But here it is: Consider a the galois field x ~gp(n) where n is a prime, which is the set {1, 2, ... n - 1} You an create a bijection x - > x by simply multiplying it by a number a. So create bijection f(x) - > ax (mod n). Since this is essentially just reordering the set, multiplying the elements of both sets should equal the the same number so n! = n!*a^(n -1) (mod n) which means 1 = a^(n - 1) (mod n) Edit: realized this was a bit too brief if there's anything particularly confusing feel free to reply with it


Question: Why does pouring water on grease fire increase the amount of flames?

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 Why does pouring water on grease fire increase the amount of flames?

Grease is an oil, it's a liquid at burning temperatures. Oil and water don't mix, so when you squirt water on grease you get balls of water in oil and vice versa. The balls of water in oil are a big problem. The oil is over 212˚F (100˚C) so the water boils into steam. The steam expands, spreading the oil into a big, thin sheet, before it pops. Now you have a big, thin sheet of burning oil and the pop sends it flying through the air. Super-bad.


Question: Why does food look so nasty when extremely over-sized?

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 Why does food look so nasty when extremely over-sized?

I think you might be referring to buzzfeed videos such as the 30lb burger or the mile long pizza. I think part of it is that the materials making up the food, like pepperoni, have ratios of size to the pizza as a whole. We expect it to be 1” in diameter on a 14” pizza but when you have a giant pizza the pepperoni won’t be the right size. The same thing is true for the burger, where the cheese slices won’t look the right ratio or the burger bits are the wrong size. There’s also something to be said about gravity and strength of the materials. So with the burger, you are stacking ingredients vertically and like the pure weight of the buns or burger will push down more on the whole stack(compressing the stack) to make it look weird


Question: Why does shaking a bottle of carbonated liquid before opening the cap cause such a huge release of carbon dioxide compared to not shaking it?

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 Why does shaking a bottle of carbonated liquid before opening the cap cause such a huge release of carbon dioxide compared to not shaking it?

Soda in a can/bottle is highly pressurised. This pressure forces the carbon dioxide to dissolve into the liquid. When you open the can/bottle, this pressure is released, so the carbon dioxide no longer has a 'reason' to stay dissolved, and it starts to come out of solution (the fancy way of saying 'un-dissolve'). Gas in a liquid, of course, forms bubbles. And, as these bubbles make their way to the surface and release the carbon dioxide into the air, you end up with a flat soda after a while. What if you don't want it to take a while? What if you want it to happen faster? It's actually pretty difficult for bubbles to form initially, but they can form more easily at locations called *nucleation sites*. The factors that cause this are probably beyond the scope of an ELI5 answer, but suffice to say these sites are spots that happen to provide ideal conditions for gas to come out of solution. If you boil some water in a pot, you may notice that bubbles tend to stream from certain specific locations on the inside of the pot - those specific spots are nucleation sites. So now we know how carbon dioxide escapes (via bubbles) and how we can speed that up (via nucleation sites). Well, it so happens that bubbles themselves can act like nucleation sites. It may be difficult for a bubble to form initially, but once one has formed (at a nucleation site), it's progressively easier for more gas to come out of solution and expand that bubble. This is also why bubbles in boiling water get bigger as they rise. And when you shake soda, you mix air into it, which creates bubbles, kickstarting this whole process. **tl;dr: when you shake soda, you create lots of bubbles, each of which makes it easier for the dissolved carbon dioxide to come out of solution. The result is a chain reaction that leads to a huge release of CO2.**


Question: - 25 degrees (C) is a nice warm day, yet 25 degrees is a horribly cold bath by comparison, why does water at the same temperature as air feel so significantly colder?

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 - 25 degrees (C) is a nice warm day, yet 25 degrees is a horribly cold bath by comparison, why does water at the same temperature as air feel so significantly colder?

We don't feel a specific temperature, but rather, how quickly heat is moving out of us. Humans produce a certain amount of heat in a certain amount of time, as do all warm blooded mammals. At about 25 degrees Celsius, air pulls away heat at just the right rate that we don't get any warmer ourselves. Water has the capacity to hold much more heat than air, so at 25 degrees Celsius, it pulls away significantly more heat in the same amount of time. This means our core temperature is actually getting lower in the water.


Question: — when it comes to the last letter of the alphabet, why does the US say "ZEE" and the UK say "ZED?"

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 — when it comes to the last letter of the alphabet, why does the US say "ZEE" and the UK say "ZED?"

For the same reason you hear “chips” vs. “French fries” or the way you hear “brilliant” vs. “awesome.” They’re just dialectical differences in words. Letter names fall into that category of “words” too, though it feels weird to think about it that way. Letter names are just names for written symbols. An easier example to think about is this: we call this thing, this symbol here — > ? a “question mark.” “Question mark” is that symbol’s name. We can also name the kind of symbols we refer to as “letters.” We call this thing here — > S an “ess.” “Ess” is its name (though we don’t denote it when writing - we just write “S”). Since these are just words/names, the reason is pretty simple...Names for anything — letters, objects, characteristics, actions — often have dialectical differences by virtue of different groups of people residing in different regions. These geographically separated groups each come to an agreement on different names among themselves, without much influence from those who aren’t in their region. Sometimes, by chance, the same word is chosen (e.g. we all say “want”) and sometimes not (“carriage” vs. “pram”). And that’s okay! It adds color to language. Source: speech-language pathologist/linguist


Question: How does the physical film from cinema cameras get transferred to computers for editing?

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 How does the physical film from cinema cameras get transferred to computers for editing?

Very few movies these days are actually shot on film, they're mostly digital from the start. But for the few that are shot on traditional reel, the film is fed through a digital scanner which itself is a projector with a lens kit that focuses the image onto a CMOS or CCD sensor so that the film can be recorded digitally frame by frame.


Question: How does organ transplant from an adult to a young child work?

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 How does organ transplant from an adult to a young child work?

It short, it doesn't. Children can be donors as well, though. Size is one of the major factors used to determine organ compatibility. From the [UNOS website]( URL_0 ): "Proper organ size is critical to a successful transplant, which means that children often respond better to child-sized organs. Although pediatric candidates have their own unique scoring system, children essentially are first in line for other children’s organs."


Question: What's the difference between steam and water vapor?

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 What's the difference between steam and water vapor?

Other answers are not correct: steam is NOT visible. What you are seeing as "steam" is droplets of *liquid* water as the steam (which is an invisible gas) condenses as it cools in the air. That is the same as fog and clouds: droplets of liquid water suspended in the air. As for the right answer, your guess is correct. Steam is just water vapor that is hotter than the boiling point, where liquid water can no longer exist. Water vapor is the more general term.


Question: Why does the water in the pool feel so cold at first, but after a while, it's room temperature or even warm?

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 Why does the water in the pool feel so cold at first, but after a while, it's room temperature or even warm?

Water conducts much better than air so when you go in your skin will cool quickly, so it feels cold. But after that your skin will be settle in an equilibrium with the water and the heat in your body, at a lower temperature than in air (depends on water temperature of course) so you don’t feel cold.


Question: the presence of all colours makes white, how come the paint combination of all primary colours makes brown?

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 the presence of all colours makes white, how come the paint combination of all primary colours makes brown?

The presence of *all colors of light* makes white. Paint removes colors from white light that hits it. The result is that red paint *removes* the cyan (and cyan-near) light. A green paint removes pink and pink-near light. Blue paint removes orange/yellow light. All three together remove more or less all light; black.


Question: why is it most top 40 radio stations only play ~5 songs on repeat?

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 why is it most top 40 radio stations only play ~5 songs on repeat?

The answer is that one company owns almost all those stations, and has broadcast licenses for a limited set of music. They used to be called Clear Channel and rebranded themselves as iHeart Media, Inc. a number of years back. They buy up all the independent stations and turn them into part of the borg.


Question: Why does the greenhouse effect doesn't work both ways?

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 Why does the greenhouse effect doesn't work both ways?

It’s different wavelengths of light. The sun sends us a broad spectrum of light which warms the earth. The earth radiates back to space light primarily at longer wavelength infrared spectrum. Greenhouse gasses only block infrared light. It’s similar in concept to blue blockers sunglasses which also only filter out a narrow range of light


Question: How can people have a different laughter from each other/ one person have multiple laughs?

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 How can people have a different laughter from each other/ one person have multiple laughs?

1) tubas and flutes don't sound alike, why sound the same with different anatomy and neurology? Even twins' speaking voices sound a little different if you know them long enough. 2) Like breathing, it is semi-autonomous. Sometimes you can't help from laughing. Others times you do it deliberately, In the latter you each more control of the rhythm of what's going on in the chest. In any case, you have the whole vocal apparatus to channel it through. There are like 5000 entire languages that can produce, messing a laugh around different ways is a task toddlers can do. 3) Most vitally, the control of laughter elevates us above all other animals. It is impossible to be a Mad Scientist without precise laugh control. All other animals are stuck with normal scientist and so still haven't figured out changing rocks into tool form.


Question: How does Imre Lakatos mean we should separate between science and pseudoscience?

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 How does Imre Lakatos mean we should separate between science and pseudoscience?

Lakatos considered many different means of distinguishing science from pseudoscience and found them lacking. In particular, he found the popular idea that scientific theories are falsifiable while pseudoscientific theories aren't to be not quite right. Many established scientific theories resist falsification in much the same way as pseudoscientific theories. Faced with evidence that appears to falsify the theory, people invested in it being correct come up with explanations for how that evidence is actually consistent with the theory or can be driven by some heretofore overlooked consideration. In science, this can be a productive avenue towards additional discoveries. In pseudoscience, it simply piles misconceptions on top of each other. Instead, Lakatos proposes that science should be distinguished from pseudoscience because it produces novel facts. He uses the example of Halley's comet. Halley used Newtonian principles to predict when and where a comet would reappear. 72 years later, it did exactly that. Without Halley's prediction, nobody would have thought to look at that particular patch of sky at that particular time. But science predicted it would be interesting, and it was. Rather than trying to explain the evidence after the fact, Halley told us where we could find additional evidence. These moments, where a scientific program tells us a new place to look and correctly anticipates what we find when we look there, help us to distinguish between lines of thinking that illuminate the world and those that obscure it. Thus, according to Lakatos, we should treat something like Flat Earth as pseudoscience not because there's copious evidence against its hypotheses, but because Flat Earth theorists have never used their system to produce a novel prediction that turned out to be true.


Question: can anyone explain what the difference is between oxo degradable plastics and oxoBIOdegradable plastics?

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 can anyone explain what the difference is between oxo degradable plastics and oxoBIOdegradable plastics?

Bioengineer here. Oxo-degradable plastics contain a catalyst to speed up the oxidative degradation process. (Usually Titanium Dioxide). What this means is the plastic will begin to break itself down, as long as there is oxygen. However, while the plastic is broken down into smaller pieces, those smaller pieces themselves may or may not be degradable. The worry is about the small fragments causing micro plastic pollution. The term oxo-degradable plastics is so large, it contains plastics may or may not need heat, UV light, acids and/or time to degrade. There are literally thousands of formulations with different properties. Some might create micro plastics, some might not. Oxo-BIOdegradable plastics means that the small fragments produced are biodegradable, or at least broken down till the point where microbes can absorb them. This paper suggests that oxo-biodegradable plastics are completely broken down, then release an acid to finish the job. URL_1 This paper suggests that microbes in the soil can degrade the small chains left after he catalyst breaks the big plastic into smaller fragments. URL_0 A paper was published by 150 companies to ban these plastics, claiming that the previous results were false, and microplastic pollution still occurs in oxo-biodegradable plastics. I personally think this is 80% true. While some oxo-biodegradable plastics do break themselves down until microbes absorb them in the lab, we have no field tests, and the formulation for such plastics is so varied that you cannot generalise them. But the plastic companies could disprove this with field data, if such data exists. By the way, there are many more biodegrade plastics which are known to be completely safe, instead of these oxo-biodegradable plastics. You can use PLA, PGA, PLGA or PVA plastics, these will safely degrade after a few months to a year (not as fast as oxo-biodegradable, but known to be safe).


Question: How were there surrenders in such large numbers during WW2?

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 How were there surrenders in such large numbers during WW2?

People don't like dying, and obedience is enforced harshly in the military. If you have a bunch of people encircled and out of options the question is either them surrendering or killing them all. When the order from leadership comes down to surrender then soldiers are expected to obey, as if they don't either the enemy will kill them or their own side will.


Question: How did Roman technology get lost and how did it stay lost for so long?

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 How did Roman technology get lost and how did it stay lost for so long?

It’s a bit of a false history that Roman technology was collectively lost for centuries. Facing internal divisions and external pressure, the Roman Empire split in half in the 4th century and the western half collapsed soon after. The Eastern half survived for another 1000 years before falling to the Ottomans in the 1400s. The collapse of the western half split the empire into innumerable feudal states with local leaders. This badly disrupted trade routes and severely decreased the availability of money, materials, and manpower to complete large infrastructure projects. Technology and architecture continued to advance, but there were few places in the west capable of financing major architectural projects.


Question: How do food scientists/Nutritionists/Dieticians determine how many calories are in a certain food or food product?

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 How do food scientists/Nutritionists/Dieticians determine how many calories are in a certain food or food product?

Setting shit on fire is the technical way I would suppose. Based on the meaning of calories and kilo calories, anyway. Heating up an amount of water by a measured degree is the amount of calories. So like.. technically gasoline has some amount of calories. Probably a lot of them. In my high school chemistry class we would set items on fire and measure the temperature of like 100 milliliter of water and see how much the burned item raised the temp. After some math you get the calorie content of what was burned.


Question: how does the laser thermometer measure how hot/cold something is, by just shining on it with a few rays of laserlight?

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 how does the laser thermometer measure how hot/cold something is, by just shining on it with a few rays of laserlight?

It has nothing to do with the laser, that is just an indicator to see where it is pointed. Instead the temperature is measured by gauging the frequency of infrared light the object emits, as that directly relates to the temperature of the object. If it gets hot enough the frequency actually raises into the visible spectrum which is why very hot things will start to glow.


Question: If an electronic device or machine is hit by an EMP powerful enough to knock it out, what will you have to do to get it running again?

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 If an electronic device or machine is hit by an EMP powerful enough to knock it out, what will you have to do to get it running again?

When electricity pass through a wire it creates an electric field around the wire. Similarly when an electric field is close to a wire, it makes a small amount of electricity pass through the wire. EMPs generate massive electric fields so they can make large amounts of electricity pass through wires over a large range. For most wires this is fine and they can handle the amount of electricity. But for computer circuits, they have tiny wires that will get overwhelmed by the amount of electricity. The wires will burn out and physical damage will occur. Any circuit with tiny wires that is in the range of the EMP will be effected regardless of whether it's powered up or not. It will be physically damaged and will no longer function. **NOTE** I'm describing the way an IDEAL EMP would work. I'm not discussing whether there currently are any that can achieve any real world damage. Maybe there are, maybe there aren't, I don't know. Just describing what, in theory, would happen in an ideal circumstance.


Question: What determines what color a scar will be?

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 What determines what color a scar will be?

Simply, you have cells in your skin that create melanin. Those cells are called Melanocytes. They can be excited by damage causing your scar to heal dark. They can also be killed by damage causing your scar to heal light. A little more complicated: Melanocytes in your skin and the degree of damage cause the difference. The Melanocytes are cells that create melanin. Melanin is what colors your skin. The more active your melanocytes are, the darker it will scar. Unless the injury has destroyed the tissue entirely in which case it will heal without pigment. The darker your skin, the more likely you are to hyper-pigment or hypo-pigment. Now, if you get a particularly bad burn, sun or otherwise, you can cause the melanocytes to die off. In that case, it will heal without pigment. You cannot grow more melanocytes. If they are dead, they are dead. That area will never have pigment again. If they become hyperactive, they will likely settle down eventually. Hydroquinone and Broadband Light are treatments that can help lighten a scar. & #x200B; & #x200B;


Question: How does the government actually take in and spend money?

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 How does the government actually take in and spend money?

> Is there just some big bank account, and do they just write a check/ is there some sort of government wire transfer system? The Federal Reserve (AKA The Fed) is the closest thing to a "big bank account" for the government. It's super complicated, but that is one of the Federal Reserves many functions. It's a pretty big organization and its general role is to maintain oversight of the country's economy and make sure that it stays as healthy as possible. > Every time I hear something like "US approves $55 million in spending" how do they actually spend it? Generally congress will approve spending on certain things. For example, they will allocate a certain amount of money to be spent on the military, Social Security, Etc. So this funding is what literally funds federal and (some portions of) state organizations. > Where does that money come from and who gets it? That's a complicated question. Actual money comes from the Treasury Department (who prints it) and collecting taxes. Since the Federal Reserve is where all the money is reserved, it functions somewhat similarly to a bank, in that other parts of the governement (and other organizations in general) will take out money to fund themselves. Where does the money in the Federal Reserve come from? Well, the main way is by selling debt (known as bonds or treasuries) to other organizations. Basically, they will offer these bonds to investors with pretty low interest rates (~2% is pretty normal), so if you buy a $1000 dollar bond, in 10 years you can redeem it with 2% accumulated interest. The Fed will tweak these rates in general to regulate the economy and maintain a target inflation rate.


Question: Why are 3D glasses red/blue and not complementary colors like red/green or orange/blue?

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 Why are 3D glasses red/blue and not complementary colors like red/green or orange/blue?

To build a filter you the important part is not a circular spectrum like how we humans interpret the colors but the linear spectrum that that describe them in physical way. Red have a wavelength of 700nm and blue is at 450nm. Green is at 550 nm and yellow at 600 nm so red and blue is more separated. Color physical films is also build up up multiple colored ink so you need to choose the color as one that exist as a single color. The other part is that film and TV is made up a few colors. TV and move in digital from is red green and blue. Yellow is made buy using both the red and green color. So it is a lot simple if you only filter one color at the time. If I am not mistaken human eye is more sensitive to green the other colors so nog using it and instead used red and blur that the sensitivity is more similar makt is simpler to get a balance between the two colors in precised brightness..


Question: Why is it that a wet tissue or piece of cardboard or paper tear more easily? How does water affect the structural integrity of paper products?

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 Why is it that a wet tissue or piece of cardboard or paper tear more easily? How does water affect the structural integrity of paper products?

Paper products are made from wood fibers that are basically matted together in random orientations like felt. As the paper dries, little hairs and random kinks in the fibers cause them to link up like tangled hair. Pressing/rolling operations enhance this effect. Paper fiber is very hydrophilic, meaning it can soak up water easily and will soak up far more than its own weight in water. As the water wets the paper, capillary action pulls the water into the spaces between fibers and forces them apart. At the same same time, the fibers themselves absorb water, swelling up. Between the swelling and the capillary action, the fibers are simply not as able to cling together.


Question: How did people reset their clocks when the power went out, 50 years ago?

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 How did people reset their clocks when the power went out, 50 years ago?

Well son, back in my day we had these time pieces we wore on our arms and they called them watches. If you didn't have one or your battery dies, you could just ask the fella next to you: "Hey bud, you got the time?" And he would be happy to oblige and tell you.


Question: what actually happens when a molecule activates a receptor vs when an inhibitor molecule just blocks it?

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 what actually happens when a molecule activates a receptor vs when an inhibitor molecule just blocks it?

Think of the molecule as a key and the receptor as a lock. The "real" key will always be able to open the lock as intended. However, there are some keys that coincidentally have a similar shape to the "real" key, but not similar enough to open the lock. So when you try to open the lock with the similar key, instead of opening the lock, it gets jammed and it gets stuck. The lock is still locked while the key is stuck, which is a metaphor for how the inhibitor just gets stuck in the receptor without causing a biological effect.


Question: why do experts say to grab vertical ropes when climbing nets?

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 why do experts say to grab vertical ropes when climbing nets?

Stability. The horizontal ropes will bend and cause a lot more sway in the net if you grab them. You can picture how a horizontal rope will bend to make a "smile" shape when you put your weight on it. The vertical rope will be put under tension and won't deform like this.


Question: Why is it that when someone suffers from amnesia, they forget specific things or completely who they are but not how to act as a human and complete basic tasks like eating and talking?

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 Why is it that when someone suffers from amnesia, they forget specific things or completely who they are but not how to act as a human and complete basic tasks like eating and talking?

Different memories are stored in differing parts of the brain, with differing degrees of permanence. If the amnesia affects only one part of the brain, then memories stored elsewhere are unaffected. In fact, when trauma happens to the language centers of the brain, a person can "forget" how to speak and understand speech properly, yet be fully cognizant of how to cook meals or what house they live in. For obvious reasons, the brain stores its most essential memories - like how to eat, what is edible, what causes pain - in the most protected sections of the brain. Both short-term memory (what card did you just pick?) and medium-term memory (What year is it?) are more volatile.


Question: Why do bananas remain sweet and get creamy when they freeze while other fruits seize up into flavorless ice orbs?

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 Why do bananas remain sweet and get creamy when they freeze while other fruits seize up into flavorless ice orbs?

Think of a popsicle they get that frosty texture/look when you bite into it, that's all the sugar in between water molecules, if there was less sugar it would freeze more like ice and solid. Bananas have a lot of substrates in it compared to water content to prevent the water molecules from sticking to each other and freezing hard which is what happens in those other fruits like strawberry, blueberrys, etc. Also the more ripe it gets the more sugar and less fibers it has to help it from freezing solid. But that being said you can still freeze a banana solid, it just takes longer, I've definitely had bananas that have gone all black that I've frozen to save for banana bread


Question: Why does pills (eg. painkillers) have an expiration date? Aren’t they usable after that date?

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 Why does pills (eg. painkillers) have an expiration date? Aren’t they usable after that date?

The FDA requires that all medications have an expiration date of no more than 2 years following the date of manufacture. Medications are guaranteed to remain effective until that date, assuming that you properly stored them. Medications do lose potency over time, eventually they will stop working altogether. The US military did a study on this and found that, properly stored, most medications retained their effectiveness for at least 5 years. You can safely use painkillers after their expiration date but you shouldn't try to guess at how much of the effectiveness has been lost - getting your guess wrong could cause you to OD on some medications. But if the painkiller is working then there's no reason not to continue to take it. Antibiotics shouldn't be taken past the expiration date because you don't know how much of the effectiveness has been lost and the loss of even a small amount may render them ineffective. Medications *cannot* become unsafe to use over time. If you take a medication 10, 20, of infinity years after its expiration date it will not harm you. If the medication would harm you after a certain period of time then the FDA will not approve it. The worst thing that will happen is it just won't work or may have turned to vinegar if its suspended in alcohol (such as something like Nyquil).


Question: Many insects appear to move extremely fast relative to their size (like ants, moths, flies, etc). If I could somehow magically enlarge an ant to, say, human size - would its speed and agility increase proportionally as well?

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 Many insects appear to move extremely fast relative to their size (like ants, moths, flies, etc). If I could somehow magically enlarge an ant to, say, human size - would its speed and agility increase proportionally as well?

The problem arises with "magic shrink ray". How would that work, in theory? Growing or shrinking animals wouldn't really work well in any case, since their anatomy is optimized for their current size. I can't say for sure, but I would doubt an ant the size of a human would be able to move at all, let along run. As you increase size, mass increases exponentially, so it would likely be too heavy for its limbs


Question: What makes a liquid thick?

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 What makes a liquid thick?

The property is called viscosity. It tells you how much force you would need to move two "layers" of liquid against eachother. It is essentially the equivalent to friction. There is not simply one source to viscosity. It is not easy to "guess" the viscosity of a liquid just from its atomic structure. In "thin" liquids, the main contributor are collisions and forces between molecules. Very thick liquids often consist of very long molecule-chains, which form multiple weak bonds with each other and can become tangled (and are thus very difficult to move against each other).


Question: Why does a beer overlow when someone hits the top of a beer with the bottom of theirs?

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 Why does a beer overlow when someone hits the top of a beer with the bottom of theirs?

Because it causes the bottle to almost intantly move down, but the beer tends to stay where it was. This causes a considerable decompression between the beer and the bottom of the bottle, favoring the formation (and expansion) of bubbles, which will rise and form the foam that you see. Basically umit's the sped up version of shaking the bottle P.s. sorry for my english


Question: In regards to alcohol, what does proof and percent by volume really mean? Is one more important than the other?

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 In regards to alcohol, what does proof and percent by volume really mean? Is one more important than the other?

The term "Proof" is a holdover from less scientific days, where unscrupulous people might try to sell you watered down booze. You'd mix a bit of the liquid with some gun powder and drop a match. If it burned, that was "proof" that the beverage was not watered down. In modern times "proof" is quantified properly, and 2 "proof" points equals 1% ABV (so 100 proof whiskey would be 50% ABV). So ultimately we're talking about 2 terms with slightly different scales measuring the exact same thing.


Question: how/why do pot holes randomly form in the middle of straight flat roads where weight from vechiles would be evenly distributed?

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 how/why do pot holes randomly form in the middle of straight flat roads where weight from vechiles would be evenly distributed?

Weight isn't necessarily what causes potholes. Expansion and contraction from heat causes cracks, and from there the break-up of material is inevitable. Different places will have different causes. I recently heard a guest speaker on NPR talking about how there were so many kinds of potholes. I'll see if I can find what I was listening to and link it. Edit - found it! [All Things Considered, March 14, 2019]( URL_0 ) > There's all kinds of modes of failure for pavement. What's likely the most common one in many parts of the nation where you have a street that's got multiple layers on it - we have this in Des Moines, where it's an older concrete street that's been overlaid with two inches of asphalt. What happens is, over time, the concrete and the asphalt shrink and grow at different rates as we experience temperature extremes. And then water will get in those cracks that are formed by that movement, and then it freezes and can pop out the top two inches of that asphalt. And > The most common ones are slab breaks, corner, you know, de-cracking, pop-outs, frost heaving. There's a whole menu of different ways that a street will fail.


Question: If light can't escape black holes, where does it go? Do chemical reactions still happen on/inside them? Can heat escape?

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 If light can't escape black holes, where does it go? Do chemical reactions still happen on/inside them? Can heat escape?

this raises a lot of questions in a lot of people, so good work, you share something in common with leading physicists. we don't entirely know what happens in a black hole, it is impossible for us to observe it, but the current belief is that there is a "singularity" in the center that is infinitely small, infinitely dense, and infinitely hot. there's also a predicted phenomenon called hawking radiation that is generated by the black hole near the event horizon, that could be the answer to what will eventually happen to black holes, that eventually they will slowly radiate energy away and evaporate, but i dont believe this has been proven yet.


Question: How/why is 'Jewish' a religion AND a race?

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 How/why is 'Jewish' a religion AND a race?

Unlike other religions, perticularly Christianity but also Islam, Jews do not actively recruit new members. It is also much tougher requirement to be considered a Jew then other religions. This means that most Jews today is the decendents of only twelve tribes. This makes them a seperate race as marriges between Jews and non-jews have been rare.


Question: Why do companies/government always consider interest whenever they are lending you money but when an individual is "lending" to them no interest is ever accounted for?

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 Why do companies/government always consider interest whenever they are lending you money but when an individual is "lending" to them no interest is ever accounted for?

It’s about risks. When you deposit your money with the bank there are several channels to invest the money. For example if you’re opening a savings account, you’re getting a small interest. But your money is guaranteed over a long period. They can take this money and invest it in the stock market - sometimes trading high risk shares. If that brings high profit, you don’t see that but neither the potential loses. That being said, you can always skip the regular savings account and opt for higher risk investments. You have many investing channels today. But you are right - as an individual, you do not have leverage over the bank and your negotiation options are insignificant. They set the rules. In most cases you can either take it or not. And it goes even further: banks are coordinated with one another and its not likely to get a much better deal elsewhere. There is no real competition between them. The feds sets the rules and these are (almost) equal for all banks. The government decided long ago that stability of the banks is on a higher priority than the individual customer.


Question: How does a calculator work?

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 How does a calculator work?

Do you mean on hardware or "software" level? The field of [numerical analysis]( URL_0 ) is how one approximates functions, which is to say arrives at a "close enough" solution to problems which are either hard to solve, or don't even have a "simple" exact solution. Most of the time this involves solving some kind of [system of linear equations]( URL_4 ), which is a collection of simple calculations. This is the "software" level. On a theoretical level, we can write some functions as simpler functions. [For instance, the sine function can be expressed as a polynomial]( URL_1 ). Computers calculate sine by taking enough parts of that series that we get close enough approximation for our needs. If you mean on hardware level, they are basically just miniature computers. /u/speculative_goat gave you a link the Adder wikipedia article, which are one of the building blocks for computers. The basic idea is like thus: * The final result is an electric component with multiple outputs. Each output can either have electricity coming out, or not. You can imagine the output as a collection of little lamps. We then agree that the way the lights are lighted corresponds to a [(binary) number]( URL_3 ). * Two of our inputs are the numbers we operate on. Maybe we want to do something with the numbers 5 and 2. * An additional input tells us what kind of operation we want. Let's say we want to sum aforementioned 5 and 2. * There is an electric circuit which manipulates the flow of electricity such that we get 5+2 to the final output (as in, the lamps light to show number 7). The details of this would be a bit cumbersome to explain because there are multiple levels of detail to it, but it is always about using simple components to build more complex components. If you want to learn more about how calculators and computers work, I recommend [nand2tetris]( URL_2 ). It's a collection of exercises through which you first build electric components, out of which you build a small calculator, out of which you build a computer, to which you implement an ~~compiler~~ assembler, etc.


Question: Why do helicopters crash so much more often than other aircraft?

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 Why do helicopters crash so much more often than other aircraft?

Helicopters have extremely poor glide characteristics. Your best case scenario for a malfunction resulting in loss of lift is a controlled crash. There are a lot of flight regimes in which you're basically just 100% screwed in a helicopter because you simply don't have enough velocity or altitude to make any real recovery. Planes have a lot more options because they are much simpler machines, and most are pretty decent gliders. A small private plane that loses power at altitude can get a pretty good distance before he hits the ground. That allows for the pilot to have some time to consider the situation, attempt to recover the aircraft, or pick a good spot to land/crash. Helicopters also tend to operate near the ground a lot more often than planes.


Question: Why does the moon in the SpaceX spaceman video appear smaller than the moon appears from earth?

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 Why does the moon in the SpaceX spaceman video appear smaller than the moon appears from earth?

How large something looks in a image taken with a camera will depend on the magnification of the lens. Try to take a picture of the moon with your cellphone and you will notice that is looks smaller then if you look at it with your own eyes. The cameras that was in the Space X video was choose to show a car large in the frame. So a camera that produced a framing with the car from the distance they could mount them on fixed metal arms that stretched out from the car had to be choose. They had short enough to be inside the payload faring. The result is that the lenses are quite wide and that result it that the moon looks small. Look at this image: URL_1 It show the same subject with different lenses. She is the same size on each image but the background change. The photographer has to move farther away the higher the magnification for het to remain the same size. So it is obvious that different lenses and camera placement changes composition of the image and the size of object in the background. A image like URL_0 is taken with high magnification with the photographer far away from the man with the telescope. So a image from earth with a prominent moon is deliberate created to look that way.


Question: Why are places like the Caspian and Dead seas considered seas, but all the Great Lakes are lakes? What about the Great Salt Lake?

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 Why are places like the Caspian and Dead seas considered seas, but all the Great Lakes are lakes? What about the Great Salt Lake?

Many of these were given names soon after their discovery. And finding out if something is connected to the ocean or not was not that simple. They often used criteria like "Can you see the other side?" and "Does it taste salty?". In the case of the Caspian sea the answer to both of these is "yes" but in thacase of the Great Salt Lake you can see across it and even go around it in a reasonable time. And in the case of the Great Lakes they contain fresh water.


Question: How does Supply and Demand work together in Economics?

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 How does Supply and Demand work together in Economics?

Low demand high supply: You sell ice cream. You spent money to buy it and want to make more money. It's cold outside and no one wants to buy ice cream. You lower the price and say "hey. Ice cream is cheaper now. Come get it." I buy ice cream from you and you make a small profit. Low supply, high demand: Now its summer. Everyone wants ice cream. You don't have much left. You say "I have the only ice cream around. If you want it, you have to pay triple the normal price" I buy ice cream because I'm desperate and you make lots of money High supply, high demand: your neighbor opens an ice cream shop. You lower your prices so people buy from you and not him Low supply, low demand: there is no ice cream shop. You live in Alaska. No one wants ice cream anyway.


Question: Can someone explain confidence interval in simple words? Also, what is the difference between confidence level and confidence interval?

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 Can someone explain confidence interval in simple words? Also, what is the difference between confidence level and confidence interval?

The general framework here is usually that you know a little bit about the distribution of something, but not the specifics. For example, a coin comes up either heads or tails, but you don't know how likely each one is (it might not be a fair coin). Or you know a distribution is normal, but don't know what the mean of the distribution is. Your goal is to take a sample of data, and from that give some sort of estimation of the parameter you care about. But not all estimations are equally precise. For example, consider the following two situations. * I flipped a coin twice, and it came up heads once. * I flipped a coin *2000* times, and it came up heads *1000* times. In both cases the coin came up heads half the time, but the second case in some sense provides a lot more evidence than the first that the actual probability of heads is close to *1/2*. Just saying something like "I estimate the probability of heads is *1/2*" doesn't make that difference clear. So instead, you want to give an estimate that includes some amount of margin of error. This is where confidence intervals come into play. What confidence intervals really are are methods for converting your sample to an estimate for a parameter. You give it your data set, it'll output some interval that "usually" (more on this in a moment) contains the actual value of the parameter. The differing uncertainties in examples like the one above are captured by this: Usually the more data you have, the better estimate you can get, which shows up in a narrower confidence interval. The difficult part about understanding confidence intervals is nailing down what exactly this "usually" is. Suppose I'm trying to estimate a parameter *a*. Formally a "*95%* confidence interval for *a*" means that no matter what my value of *a* is, *95%* of the time my method will give me an interval that contains *a*. For example, say I actually have a fair coin (but don't know it), and I ask *100* people to come in, perform an experiment, and give me a confidence interval for the probability of heads based on their own data. Because each person is using different data, they'll get different confidence intervals. But if they're using a method that constructs *95%* confidence intervals, then on average *95* of the *100* intervals they construct will contain *1/2*. If I then asked them to repeat the experiment, but this time with a biased coin that came up heads *68%* of the time, they'll get new confidence intervals. But, on average, *95* of the *100* confidence intervals they construct will contain *0.68*. (Continued in next comment, this is getting long).