Question: I'm allergic to penicillin/amoxicillin. Could there be a point where giving it to me anyways and dealing with the symptoms is a better option than not?

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 I'm allergic to penicillin/amoxicillin. Could there be a point where giving it to me anyways and dealing with the symptoms is a better option than not?

Possibly. A common headache in medicine is seeing "penicillin allergy" on a chart. Research has found that only a small fraction of people who say they're allergic actually are. While we have lots of antibiotics, there are times when a penicillin or related antibiotic is crucial. Drugs with the beta-lactam structure (including penicillins, cephalosporins, and carbapenems) are just plain better at killing bacteria than other types. For run-of-the-mill infections, an antibiotic that simply stops bacteria from growing is fine. If you're critically ill from a bacterial infection, you need a drug that kills. (Historically, it's been said that ten percent of people with penicillin allergy will also react to its beta-lactam cousins, but that's likely an exaggeration.) Mostly, you can get by with alternatives to penicillin. For syphilis in pregnancy, you carefully desensitize the mother with increasing doses. In general, if you really have to give a drug someone is allergic to, you can pretreat them with steroids and antihistamines to blunt the effect.


Question: What do people mean when they say "50% of American money is in circulation outside the US"?

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 What do people mean when they say "50% of American money is in circulation outside the US"?

It means that of all the physical US currency (ie, bills and coins) in the world, more than half of it by value is outside the US. Demand for physical currency isn't huge in developed countries like the US, since things like credit cards and debit cards allow transactions to happen without it. In other countries, physical currency is more necessary, but the local currency is sometimes unstable or unreliable in various ways. Importing and using US dollars allows people in those places to get a stable currency without giving up the advantages of physical currency.


Question: What are complex numbers and why are they useful?

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 What are complex numbers and why are they useful?

The original impetus for complex numbers was the Fundamental Theorem of Algebra. While the phrasing has undergone some modification over the years, the basic premise is that a single variable polynomial has a number of roots (places where it evaluates to zero) equal to the highest power of the polynomial. So if you've got f(x) = x + 2, you've got a polynomial of power 1 that crosses the x-axis at a single point (x = -2). However, the problem with this is that it's not actually true with real numbers. Consider the parabola: f(x) = x^2 + x + 1 If you plot this parabola, you'll notice it's entirely in the top half of the plane. It never crosses the x-axis and thus has no roots. From the standpoint of mathematics, this posed a dilemma. Without the Fundamental Theorem of Algebra being true, algebra wasn't 'closed' - you could follow all the rules and end up with results that lay outside the system. The solution they came up with was to come up with complex numbers - a way to create non-real roots that would make the FToA true. However, the consequences of this were far reaching. One of the most important is with regards to periodicity/rotation. If you multiply two real numbers, you just end up with a larger or smaller real number. If you continue to perform such multiplications, you just proceed linearly off to the infinite/infinitesmals. However, if you multiply complex numbers, you can create a cycle of numbers. If you keep multiplying i by itself, you get the sequence: i, -1, -i, 1, i, ... This is how periodicity/rotation work. They return to the previous value at some point and repeat. As a result, complex numbers proved to be an excellent way to model anything that rotates or repeats. All of the trigonometry you learned in high school can be replaced by complex representations. Since complex numbers tend to be easier to manipulate than trigonometric ones, it meant you work much more easily with all the real world periodic/rotational issues.


Question: How does the Options market work and can you use a lifelike example of a put / call position which is relatable?

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 How does the Options market work and can you use a lifelike example of a put / call position which is relatable?

You can see Options as a "price guarantee" for something you want to buy / sell in the future, but you want to agree on the price in advance. **Put Option Example**: You are an American company and get a contract from an EU company. You'll get the payment of one million EUR for your work in one year. Today, 1 EUR is roughly 1.10 USD, but you don't know what the exchange rate will be in a year. If you want to "insure" that exchange rate, i.e. make sure you really get 1.1 million USD in a year, you can buy a put option on the EUR/USD exchange rate. A put option on EUR/USD with a strike of 1.10, expiring in one year and a total contract of 1 million EUR will guarantee that you at least get the 1.1 million USD in one year. This put option gives you the right, but not the duty, to sell 1 million EUR and receive 1.1 million USD in return. If the exchange rate were to rise, then you just let the option expire (i.e. you don't exercise your right), and do the exchange at the current rate. **Call Option Example**: For this job above, you'll need a part from a Canadian company which costs 100k Canadian Dollars (CAD). Today, that's 75k USD. You'll need that part in 6 month, which is also when you'll pay the Canadian company. Again, if you don't want to gamble with the exchange rate, you'll get a call option on the USD/CAD at strike 1.33 (current rate), expiry in 6 months, total contract of 100k CAD. The Call Option gives you the right, but not the duty, to buy 100k CAD for 75k USD in 6 months.


Question: What’s the ‘need’ for the stock prices to change every minute?

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 What’s the ‘need’ for the stock prices to change every minute?

The stock market is a haggle market. Buyers want to pay some low price. Sellers want some high price. Each individual is willing to pay a different price. One buyer wants to buy for $5.00. another one wants it more for $5.10. another wants it less for $4.80. etc. Each buyer has a different tolerance for the price of the stock. Same for seller side. If a buyer price meets a seller's price, then a sale is made. The price at which that sale occurred is now the new price of the stock.


Question: what happens to the flooded cars after a major flood?

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 what happens to the flooded cars after a major flood?

From what I remember after hurricane Sandy, the cars that were floating around tunnels and underground parking garages are indeed written off by their insurers. However they are also scooped up, cleaned, and somehow find their way to ethically questionable used car lots that attempt to resell them. Usually along with a predatory car loan to people who can't afford it. The cars from Sandy have probably been repossessed and resold several times by now.


Question: Given the brutality of World War 2, how have relations between the major Allied and Axis powers continued to be so positive? Why are the alliances between the U.S. and Japan/Germany, in particular, so strong? What was different about WW2 from other wars that prevented ongoing tension/conflict?

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 Given the brutality of World War 2, how have relations between the major Allied and Axis powers continued to be so positive? Why are the alliances between the U.S. and Japan/Germany, in particular, so strong? What was different about WW2 from other wars that prevented ongoing tension/conflict?

It wasn't the war, it was the recovery. The Allied powers knew that the harsh reparations leveled on Germany after WW1 had *directly* lead to WW2. They were much softer with reparations and lead a significant rebuilding effort in the Axis countries after the war to ensure they got back on their feet with fewer hard feelings than last time around. Japan was also pretty well stripped of their military and told they had to focus economically and were given a ton of help to do so. This meant that any resentment that there may be wouldn't materialize as war again, though Japan's stance on the events of WW2 is still a bit ... *odd*


Question: Why do some foods (especially sweet ones) taste fine when cold, but others (especially savoury/salty ones) taste best when hot?

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 Why do some foods (especially sweet ones) taste fine when cold, but others (especially savoury/salty ones) taste best when hot?

Many, many reasons, I'll just mention a few common ones: - Lipid viscosity. That is to say - how solid the fats are. Animal fats are typically solid at room temperature and colder, but liquid or partially liquid when hot. Therefore, the temperature of fat has a huge impact on the texture of it. You can try this at home: cook some bacon, then poor the fat into a bowl and wait for it to cool. Then, take a spoon and eat some of it. Pretty disgusting, right? Even though hot bacon grease on bread is fucking delicious. - Nerve cell activity. Every biological process is simply a chemical reaction, and chemical reactions happen faster at higher temperatures. The hotter the food is, the more the taste-causing particles in the food will react with the taste-particle-detecting-molecules on your tongue. - Nose tasting. We actually have more taste buds in our nose than in our mouth. Well, not exactly, but they're very similar. A big part of tasting food is the *smell* of food. And the spell of food relies on taste-causing particles vaporising - separating from the solid food and distributing themselves through the air and up into your nose. This happens more readily when the temperature of the food is higher, because hot molecules have more movement in them than cold molecules. - Expectations. If you expect food to be hot and it's not, that's surprising and unpleasant. You more often expect savoury food to be hot. - Condensation. Water is, as you may be aware, wet. However, when water gets very hot, water stops being wet - it becomes a gas instead. As the temperature decreases though, the water stops being a gas and becomes a wet liquid again. This wet liquid, commonly known as "water", soaks itself through many foodstuffs and makes those foodstuffs wet. Thus, food that is supposed to be crispy tends to become soggy when it's cold, especially if that food has quite a lot of water in it already, such as deep-fried chicken. Savoury foods tend to rely on combinations of many different tastes. If any one of these things changes at cold temperatures, the food becomes kinda awful when it gets cold. Sweet food however relies on only one dominant chemical: Sugar. As it happens, sugar behaves pretty similarly when hot as it does when cold. This is because it is dissolves in water, which means that the only "taste" aspect of sugar is how it reacts chemically with your taste buds. There's no texture involved. And if it gets wet? Well then, big deal. Your taste buds only care about the chemicals present, so hot and cold sugar are all the same to them. All temperature is doing is stimulating your temperature-sensing nerves. It's not having a significant effect on the taste of the sugars themselves.


Question: Why does getting paper wet make it so much weaker?

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 Why does getting paper wet make it so much weaker?

Paper is mostly made of fibres (specifically cellulose fibres), and cellulose fibres have a bunch of hydroxyl (OH)-groups (look at [this image]( URL_0 )). These groups form hydrogen bonds to each other, giving the fibres strong bonds and allowing the individual fibres to be "stiff", as well as holding the fibres together. When you add water, the OH-part of the water will hydrogen bond to the OH-part of the fibres, tearing the fibre OH-group away, causing each individual fibre to become less stiff, as well as allowing them to seperate easier.


Question: Why are there so many different kinds of soap?

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 Why are there so many different kinds of soap?

My economics professor insisted that soap is soap and the only thing that sets different ones apart is marketing. That is largely true, but some soaps are a bit different, so be careful. The best example is dishwasher soap. NEVER use anything else in your dishwasher unless you want to clean up a huge mess. You have been warned. For the rest, most of the difference s fragrance, and of course convenience is a consideration. At one time people actally shredded up bar soap to wash clothes, so powder was a convenience. now we have liquids and pods and all sorts. I am old enough to have used bar soap in the shower and at the sink to wash my body and hands and I still do. It seems a lot more cost-effective. When you get into liquid soaps, a lot of times the cheap ones just have a lot more water and less soap, so it can be a mistake to buy the cheapest one. And yes, I actually use liquid hand soap as dish soap when I wash dishes by hand. It workd fine. Last but not least, never try to convince a woman to give up her special soap. Just don't.


Question: can someone please explain mixed radix number systems and maybe give an example of counting in one?

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 can someone please explain mixed radix number systems and maybe give an example of counting in one?

Mixed radix number system is a system in which the "base" of each position in a quantity is different, hence mixed Simplest example is when we measure time. I.e. 1 year 2 months 3 weeks 4 days 5 hours and 6 minutes. The year has no base since it is the largest, month has base 12 (there is 12 months in a year), week has base 4 (there is 4 weeks in a month), days has base 7 (7 days in a week), hours base 24 (24 hours in a day) and minutes base 60 (60 minutes in a day)


Question: If someone was found not guilty of killing several people but later came out and admitted to the murders, why couldn’t he/she be recharged and retried?

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 If someone was found not guilty of killing several people but later came out and admitted to the murders, why couldn’t he/she be recharged and retried?

The fifth amendment says that you can't be retried for a crime again after being punished or acquitted (the legal term is "double jeopardy"). That said if they had decided to drop any of the original cases due to lack of evidence, there was a mistrial, or your admission involved other crimes that you weren't necessarily being tried for the first time around they could still nail you for those even if they couldn't get you for the original crimes you were found innocent of. As for "why" a big reason is to prevent the government from bringing you to court again and again until you either run out of money or they manage to convict you.


Question: Why does multiplying two negative numbers equal a positive?

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 Why does multiplying two negative numbers equal a positive?

Multiplication is just adding something many times. 6 * X just means 6+6+...+6 with X 6s. So 6 * 3 is 6+6+6 or 18. It's the same for negative numbers. -6 * X just means (-6)+(-6)+...+(-6) with X 6s. So (-6) x 3 is (-6)+(-6)+(-6) or 18. Now let's lower the multiplication factor 1 by 1... With + 6 we get: 6 * 3 = 18 6*2 = 12 6*1 = 6 It LOWERS by 6 every time because we have one less 6 so logically 6*0 becomes 6, 6*(-1) becomes -6, 6*(-2) becomes -12 etc. So in the same way with negative numbers it goes: -6 * 3 = -18 -6 * 2 = -12 -6 * 1 = -6 It keeps going up and continues! -6 * 0 = 0 -6 * -1 = 6 -6 * -2 = 12 And voila.


Question: how does dungeons and dragons work?

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 how does dungeons and dragons work?

Dungeons and Dragons is a tabletop roleplaying game. Basically, a group of people gather together to tell a story and play a game at the same time. It's sort of like mixing a board game with improvisational theatre. D & D generally is about telling stories of fantasy adventure, where a group of heroes, like elf wizards, dwarf fighters, or human thieves, fight monsters, solve puzzles, get in trouble, locate treasure. Each player has a character they are portraying in the game, except for one player who is the Dungeon Master, who portrays all the villains, side characters, does narration and arbitrates rules. There's a series of rules that determines things like "how much damage does a fireball spell do against an Owlbear" or "Can I climb to the top of the ceiling to get the cursed ruby out of it?" The game uses dice rolls to add excitement and chance to the adventure. In general, your character has stats and skills that determine what they are good and bad at, and you use those plus the result of a dice rolls to figure out if you succeed or fail. At the end, it's a game about stories. Your group's characters may start off defending their small town from bandits, then learn about a lost treasure the bandits were trying to get, go into a dungeon to recover that lost treasure for the townsfolk, discover an evil wizard's plan to conquer the kingdom, and go on a quest to stop him. You generally play for about 4 to 6 hours a time, about once per week.


Question: How does tax havens work?

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 How does tax havens work?

From Hong Kong here. It’s not as simple as packing your luggage and getting on a plane. There are mainly two ways to do it: 1) Moving headquarters. This requires a lot of man power and resource so you can’t do it willy nilly. You need to move the majority of your operations overseas, rehire a lot of people, and make sure they’re competent. Obviously apart from the cost there’s a lot of time and risk involved. 2) Simply move your company’s registration to a tax haven. A lot of company already does this, but by doing so still keep a lot of local offices and you don’t avoid as much tax as the first option. So no, even if you raise taxes people can’t just up and move to another country and not pay them at all. And even if you do so it’ll cost some and more. Companies within US are protected by US laws and regulations which their tax paid for and it’s not always wise to throw away these advantages. Remember the US once had a 90% tax rate and business did not leave the country en mass.


Question: Why is the tech market crashing and how does it relate to bonds and inflation etc?

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 Why is the tech market crashing and how does it relate to bonds and inflation etc?

When interest rates are low, many investors would rather invest their money in the stock market, where they can get higher returns, than buy treasury notes or bonds. Because COVID has shifted a lot of activity (work, school, and entertainment) online, tech stocks have generally performed well during the pandemic, and have been the focus of a lot of investing. However, as interest rates rise, some investors are selling their shares in tech stocks in order to buy treasury notes or bonds instead, causing the prices of those tech stocks to fall as supply exceeds demand at the current price. Other tech investors are seeing the stock prices fall, and are concerned more investors will pull out as interest rates continue to rise, and they sell as well.


Question: Shoemaker Levy left burn marks the size of the Earth on Jupiter's surface for months. How is this possible if Jupiter has no surface?

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 Shoemaker Levy left burn marks the size of the Earth on Jupiter's surface for months. How is this possible if Jupiter has no surface?

It left huge marks on the clouds that make up the atmosphere of Jupiter not the surface. A impact is a collision with a object and it might only be the atmosphere. The [Chelyabinsk meteor]( URL_0 ) that exploded over Russia in 2013 and was captured on a log of camera is a meteor impact on earth but not a impact on the surface on earth. The high pressure generated when a high speed object hit the atmosphere can have the result they blow up before they hit anything solid. So the same way as clouds and storm in out atmosphere can exist and keep the general shape the same can happen on Jupiter. The [Great\_Red\_Spot]( URL_1 ) is a persistent high pressure system in Jupiter that have existed for certainly since 1830 and even observation since the first back in 1665 have some observation but with long gaps in time so it have existed for more then 189 years or even more then 350 years. It might have existed even for longer but the telescope was not invented so there is not observation. So large disturbances like meteor impact can leave changes in the atmosphere that is visible for months.


Question: How is it that some drugs find whole other purposes when used in human trials? Does this show a major lack of understanding on our part?

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 How is it that some drugs find whole other purposes when used in human trials? Does this show a major lack of understanding on our part?

Biological interactions at the organism level tend to be extremely complex and, while we may be able to model individual biological systems, there's no current way to model an entire organism without direct testing. It's helpful to illustrate this with the particular example of Gleevac: 1. Scientists found that the Philadelphia chromosome mutation is responsible for a type of cancer (leukemia) 2. They tested thousands of chemicals, and found that Gleevac can inhibit this mutation at the molecular level 3. Then they tested Gleevac against cancer cells, and it was able to inhibit the cancer cells 4. Then they tested Gleevac in mice that were made to have leukemia (a mouse model of the disease), and it helped improve mice survival 5. Finally Gleevac was tested in patients with leukemia, and after been shown to be both safe and effective, was approved to be marketed for the treatment of leukemia 6. It just so happens that a type of cells that are involved in leukemia, called mast cells, are also suspected to be involved in severe, treatment-resistant asthma, but this line of treatment has never been proven 7. Now that Gleevac has been approved and is much easier to obtain, some scientists decided to test out the drug in asthma patients, and in early studies it's shown to have good results Drug development is very costly, and as you can see, there is a strong line of rational decisions that led to the development of Gleevac as a cancer drug. On the other hand, there wasn't nearly as much evidence to suggest it could be a good asthma drug. Therefore, only after it's already been developed and approved can doctors then go and test drugs for these suspected indications at much lower cost. Another very famous example is Viagra. Viagra was initially developed to treat cardiovascular disease, but was found to be ineffective. However, many patients reported getting an erection as a side effect, and Pfizer quickly pivoted the program towards that instead.


Question: Why do colleges care about legacies? How does having parents or grandparents who are alumni of a certain university make the student a more qualified candidate?

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 Why do colleges care about legacies? How does having parents or grandparents who are alumni of a certain university make the student a more qualified candidate?

Colleges thrive on gifts from alumni. If they can establish a family as loyal alumni, they can ensure a steady stream of donations. This is the cynical view. A more optimistic view is that colleges love passing down traditions, and having multiple generations of a family go to the same college further embeds that sense of identity and tradition. In reality, both explanations probably play a role.


Question: What causes an oasis to grow in the middle of deserts?

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 What causes an oasis to grow in the middle of deserts?

Essentially the surface of the ground erodes to the level of the water table (there is water beneath a desert!) at some point in history, plants take hold, draw the water table down a bit, the ground surface follows it down, and you end up with a permanently vegetated depression in the sand containing some surface water.


Question: What makes cyanides so extremely poisonous when Carbon and Nitrogen are found everywhere in non-toxic states?

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 What makes cyanides so extremely poisonous when Carbon and Nitrogen are found everywhere in non-toxic states?

Cyanide is different from other Carbon and Nitrogen containing compounds. It is made of a single Carbon and single Nitrogen atom, which make up the anion CN- This ion binds to and inhibits the function of an enzyme in the body that is vital to aerobic respiration, which your heart and central nervous system heavily depend on


Question: What is the "Pattern Day Trader Rule" and why does it exist?

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 What is the "Pattern Day Trader Rule" and why does it exist?

Pattern day trading is trading stocks back and forth multiple times a day. The trader typically never looks at the firm's financials, or even what the company does. All the pattern day trader sees is that Alphabet has gone up 5% and if they could make a lot of money if it goes up 6%. This is gambling. A lot of people can do this and function perfectly fine and exercise a great deal of responsibility. Others can't. Pattern day trading is like betting on horses. The winners typically win, the losers lose, but sometimes the winners break their legs and the losers become winners. Except that you have to pay a fee on top of every bet you make, win or lose. And you have to pay again the change your bet. That's all fine and good, but why won't Robinhood let me do this? Aside from not wanting to expose themselves to legal liability ("it's not my fault I lost my retirement because pumpkin futures bottom out in January, the app lets me gamble from my phone!"). Pattern day trading also introduces a level of volatility in the markets, which is downright irresponsible. Some platforms have heat maps showing what stocks are hot (being traded frequently), and the hottest stocks attract more day traders making them hotter, and then suddenly the horse in last looks like it's winning when really it finished 6th. Trading bonds is like betting on a horse after the race has started.


Question: How does hashing work for single value like the letter "a"?

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 How does hashing work for single value like the letter "a"?

You didn't specify what hashing algorithm, but in general, if the input wasn't long enough you would pad it by adding "zero bits" to it. Technically, even long strings often need padding as well. This is because to be able to work with the bit string properly it needs to be a certain length (or divisible by a certain length). Each algorithm has its own rules for such things. Sort of like if you had a number 42, but you actually needed a 10-digit number you would change it to 0000000042, but instead of using digits, you would use bits.


Question: What happens to non-perishable or preserved food after it has been stored for over 200 years?

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 What happens to non-perishable or preserved food after it has been stored for over 200 years?

Honey pretty much never goes bad. Bacteria and stuff cant survive in or on it, so honey left sitting in a tomb 6,000 years ago is just as safe to eat as honey harvested today. Although the dust wont be great for you and any toxic substances on the surface still fuck you up pretty good.


Question: Why does the burn of alcohol on a small cut go away temporally when blowing on it?

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 Why does the burn of alcohol on a small cut go away temporally when blowing on it?

By blowing on it, you evaporate the alcohol faster. This reduces the contact time on the wound, and therefore reduces the pain. Most of the time, alcohol needs very little contact time to disinfect. However, by blowing on it, you could be limiting the scope of the alcohol's disinfecting power, but you also are blowing more germs right onto the open wound from your mouth. Remember, the human mouth is one of the dirtiest places in the world. It is even worse than a dog or a cat mouth.


Question: How can captcha know I am not a robot from just a click?

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 How can captcha know I am not a robot from just a click?

When you click the button, it sends information about your browser and about how you were using the web page. How long you were on the web page before you clicked the captcha button, information about how you scrolled through the page, how your mouse moved and other 'odd' information. You are very different from a computer, so the data you generate will be very different from a computer bot. The CAPTCHA programmers showed a program what 'human' data looks like, and what computer data looks like, and taught it to spot the difference.


Question: How do some math problems become so massive they take up full massive chalk boards?

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 How do some math problems become so massive they take up full massive chalk boards?

Some math problems are so massive, they involve more than just a chalk board, but rather entire books with hundreds, even thousands of pages. Most of it is establishing the problem in a formal, concrete way, and then creating a mathematical framework which you can use to solve the problem. For example, suppose your problem is trying to determine the number of prime numbers in the range 1 to 100. Well, first you have to define what a prime number is. Now you have to show some way to find prime numbers. Now you have to actually calculate the solution. Even for something trivial like this, we could probably fill a chalk board.


Question: How does the Troxler Effect work?

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 How does the Troxler Effect work?

First you must understand our vision. Our eyes move in short sharp movements called saccades. Our vision works like a flip book it takes images of what it sees and sends that to the brain for processing. Just like how a camera focuses on something and makes the bakground blurry that’s also how our eyes work when fixating on something. The troxler effect happens when you are fixated at something small, in a dim ligt, or movement. Your brain keeps getting those images with the same background and eventually your brain starts to blur away what’s unimportant (outside of what you’re fixated on) and it will disappear or in dim light it can even change shape.


Question: What would happen to you if you jump into a deep pool of boiling hot metal like this guy? [NSFW]

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 What would happen to you if you jump into a deep pool of boiling hot metal like this guy? [NSFW]

Yes he felt it. Your skin would burn just from the heat radiation, your muscles and internal organs which contain more water would instantly turn from water to steam and burst ( causing that large flash) . Nothing would be left, the water in his body exploded in to steam and the remainder burnt till it was only carbon. Nothing left. No there would be no statue, the metal would have what ever was left of you as carbon content and anything like your shoes or zipper or teeth fillings would be dipped off as slag.


Question: Why are so many types of toothpaste advertised as “whitening” toothpastes? Shouldn’t every type of toothpaste be cleaning and whitening your teeth regardless of the type?

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 Why are so many types of toothpaste advertised as “whitening” toothpastes? Shouldn’t every type of toothpaste be cleaning and whitening your teeth regardless of the type?

"Whitening' toothpastes typically contain stronger abrasives and substances with the specific aim of attacking hard-to-break-down stains and changing color through chemical action. This is in addition to the contents of usual tooth paste, which is mostly concerned with breaking down plaque, minimizing decay, and freshening breath. This can certainly lead to an improvement of appearance, but not necessarily to the same scale if you've got significant coloring.


Question: How did Isaac Newton just invent Calculus?

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 How did Isaac Newton just invent Calculus?

Short answer... Pretty much on a dare. He wanted to explain why the moon orbits earth. (And other physical phenomena) There is some controversy about it since Leibniz claimed to have invented it first. I'm fact crude version of specific calculus applications were already in use. Newton applied calculus to generic physics problems, Leibniz to more abstract concepts. Calculus is the next logical step in mathematics once you understand algebra. It is a huge step nonetheless. If you study something simple such as a parabolic shot you can understand how to calculate the distance the projectile will land. but some calculations become a little difficult with simple algebra but trivial with calculus. For instance calculate the highest point the projectile will reach and the exact time when this will happen.


Question: why is math (statistics, calculus, etc) so important for a strong programmer?

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 why is math (statistics, calculus, etc) so important for a strong programmer?

There are lots of areas of programming that require only basic math. If you're doing development for a moderate-sized web site or app, it's quite possible you'll almost never use any math, and never anything beyond things taught in high-school algebra. More generally, some programmers use a lot of math all the time, some hardly use math at all. There are many more specialized areas of programming that require a lot of math. Computer graphics uses a lot of trigonometry and calculus, so pretty much any game that requires physics or 3-d rendering uses a lot of math. Video and audio compression uses Fourier analysis. Cryptography uses number theory. Those are just a few examples - there are lots of specialties. Good programmers often need to have at least some familiarity with those areas, even if that isn't their area of expertise. Quite often large-scale software engineering requires more math - for example web sites that need to scale to millions of users. It's hard to properly optimize sites to handle a lot of traffic without a good foundation in probability and statistics. A degree in Computer Science typically covers many of those things, which is why there's a math requirement. In addition, Computer Science involves a lot of mathematical analysis of programs, including determining what's possible to compute, determining asymptotic runtime and memory usage, and mathematical proofs of bounds and of correctness.


Question: In math, what exactly is a Manifold?

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 In math, what exactly is a Manifold?

A manifold is a space that "looks like" regular old Euclidean space (like a line, a plane, 3d space, and so on) if you zoom in enough. More formally, every point in a manifold has a neighborhood that is homeomorphic to ("the same as") a neighborhood in some Euclidean space. Easy examples include circles and spheres. A circle is curved in a global sense, but if you're realllllllly close to a circle, it looks like a line. Similarly, a sphere is curved in a global sense, but if you're really close, it looks like a plane (which is why the Earth looks flat when you live on it). If you cut off a little chunk of circle, it's essentially just a line (that is, it's the same as 1D Euclidean space). If you cut off a little chunk of sphere, it's essentially just a plane (that is, it's the same as 2D Euclidean space).


Question: How are people who move around a lot in their sleep able to keep themselves from falling off of the bed?

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 How are people who move around a lot in their sleep able to keep themselves from falling off of the bed?

Short answer: I didn't always. When I was a kid I did manage to roll out of bed a few times. Now that I'm an adult, my body can feel where the edge is and usually moves me back towards the center of the mattress. My skin feels where the bed "stops" and tells my brain it shouldn't go further.


Question: what are and what causes those colors and patterns you see when you close your eyes or when you are in complete darkness?

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 what are and what causes those colors and patterns you see when you close your eyes or when you are in complete darkness?

Phosphenes is the term. It is caused by mechanical stimulations like rubbing or touching your eyes while closed. The patterns are pretty much the response of the brain when your eye sense something other than light. It seems that when you touch(pressure) your closed eyes, it activates the retinal cells in a similar way as light does. And that reaction will eventually reach your brain and it makes images based on that reaction. If you didn't touch your eyes and a pattern still develops, what you see is a CEV or hallucination, a type of phosphenes. It might also resemble fractals.


Question: What causes the economy to go into a depression?

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 What causes the economy to go into a depression?

Sorry if my english is bad. & #x200B; Economy is basically a game of supply and demand. The more products are demanded, the more people you need to produce them. & #x200B; For example you live in a small town and have a bookstore with 3 employees. You pay these 3 employees their wage. With the wage they go to the shop next door to buy groceries. The employees of this store go to the bakery and buy bread and cake and the baker comes to you and buys books. Over the years you established a balance between shops and employees. & #x200B; Next is a shock, something radically changing to distrub your balance. For example Amazon. The baker and the grocery shop employees don't come to your book store anymore, because they buy their books online. (The shock is a sudden drop of demand for any reason, i just choose the Amazon example to illustrate. During the housing crises a decade ago it was a combination of multiple factors, but this would be a too compley topic to fit it in this reply.) They don't need consultation or going out anymore. So there isn't a need for 3 employees at the book store anymore. So you fire 2 of them, since you don't earn the money to pay them their wages (less need for consultation, less supply of empoyees needed). So now the grocery shop has two customers less, that would buy groceries, so one of them got fired too, because with two customers less, you need one person less in the grocery store. So now the bakery got less money, because they lost 3 customers. So they go less to the book store. The employees of the grocery stores, that still got their jobs now think it is a good idea to prepare if they got fired and safe their money, they would spend on books and keep it to have a little saving if times get rought. Which means, you have to also fire the last employee and do all the work by yourself. If that happens on a bigger scale, like a whole country, you see the downwards spiral this is leading to. & #x200B; This is a very basic idea of what is happening.


Question: What are the requirements for a scar to form instead of a full recovery?

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 What are the requirements for a scar to form instead of a full recovery?

Your skin can only regenerate from the bottom up (the deepest layer) so if the wound is deep enough that you lose the bottom layer it can’t regenerate. If that happens, the connective tissue that lives underneath the skin has to grow into that space to heal up the area. That tissue, what we call a scar, is made up of entirely different cells than your skin so it doesn’t look the same or function the same as the skin it’s replacing.


Question: Serotonin is the hormone what makes us happy, so why aren't we just injecting it into our body/taking it as tablets to get out of misery on command?

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 Serotonin is the hormone what makes us happy, so why aren't we just injecting it into our body/taking it as tablets to get out of misery on command?

Hormones like serotonin are like ingredients in a recipe. You need them to be in the right balance for a dish to work. Imagine serotonin as sugar, if used sparingly, you would enjoy it as a glaze or sauce in your entrees and finish your meal with a sweeter dessert. If you dumped a container of sugar on every dish of your meal, none of it would be enjoyable. People's bodies, like their tastes, differ as well. Some people like their dishes sweeter while others do not. Therefore a set sweetness for one person would not be enjoyable for others. This is why it is difficult to find the right medicine to treat neurological diseases like depression because every person is different. The body also has limited tools to communicate with other organs. Serotonin affects mood in the brain but also appetite and digestion in your digestive system. Some of the side effects from drugs increasing or decreasing one hormone is due to the body reusing the hormone for many functions. Lastly, the body is naturally ~~lazy~~ efficient. If it's getting a hormone from an injection or pill, it is less likely to make it. Therefore, when a person stops taking the injections or pills the body goes into withdrawal because it stopped making that hormone, causing other symptoms. This can cause a dependence on the substance, otherwise known as an addiction.


Question: By default our voice is meant to be clear, but how do some voice actors make their voice become raspy or coarse on the fly?

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 By default our voice is meant to be clear, but how do some voice actors make their voice become raspy or coarse on the fly?

Not an expert, but as a 5th year linguistics student (focus on phonetics and phonology) I can tell you that manipulating your voice in many ways can be done with training and you can turn it on or off. Basically, your voice is a combination of your actual vocal chords vibrating and then your physical mouth and tongue shaping the sound as it comes out. Each consonant and vowel has a mouth shape (throat muscle tension is also a factor) so changing these positions slightly is how we get can achieve voice affects and accents! If you train your mouth, lips, jaw, and tongue to have muscle memory in different shapes, then you will be able to produce any variation of your voice on command. Hope this helps!


Question: The solution to Fermat’s Last Theorem (unsolved problem in math for 358 years until Wiles in 1995)?

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 The solution to Fermat’s Last Theorem (unsolved problem in math for 358 years until Wiles in 1995)?

I’ll give it a try, but it’s going to be very basic since most mathematicians don’t even understand it. Someone will have to correct me if I’m wrong. The idea is this: there are these 2 areas in math, modular forms and elliptic curves. An elliptic curve is just a graph that fits a certain parameter (like, linear functions are any function of the form ax+b, elliptic curves are a bit more complicated). Modular forms are just some functions satisfying another, different set of parameters (which are more complicated to understand). It turns out that there’s a connection between them though, and this connection is the key and the hard part. There was another conjecture (a guess, basically) that there is some sort of correspondence between modular forms and these elliptic curves. That’s what wiles actually proved to be true. Why is that helpful? It had been seen before that integers solutions to a^n + b^n = c^n existed if and only if a certain type of modular form existed. But, we didn’t know if that type of modular form actually existed or not. Now that Wiles proved that elliptic curves and modular forms have this correspondence, he showed that *if* that certain type of modular form existed, *then* something would be true about elliptic curves. BUT, we knew that that thing about elliptic curves was false, so that tells us that the modular curve couldn’t exist. But, that’s the same as Fermats last theorem. *Edit*: I got things backwards. See the comment below to get things the right way around.


Question: Why are people trying to find the biggest prime number?

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 Why are people trying to find the biggest prime number?

It's an exercise in computation, mostly. There are a few large prime number searches that are trying to settle old mathematical conjectures (e.g. the Prime Sierpinski Problem), but for the most part it's just people who are fans of mathematics and who have computers letting them run to see if they can find a large prime number. These prime numbers may have slight interest to mathematicians who could study their distribution and may come up with interesting mathematics as a result, but that's not too likely. It's long been known that there are infinitely many prime numbers. Note that there have been various awards offered over the years for finding especially large prime numbers. Most notable are some przes [offered by the EFF]( URL_0 ). Since these only judge the size of the primes it's most logical to search through numbers that are both 1: likely to be prime, and 2: easy to test. That best describes Mersenne primes, in the form of 2^P - 1 (where P is itself a prime number). The Great Internet Mersenne Prime Search, or GIMPS, is the most notable collaboration looking for such large prime numbers. Their client, Prime95, is notable for being brutal to CPUs and is sometimes used in the overclocking community to demonstrate that a CPU is stable--if Prime95 can't break it then hopefully nothing can. The EFF awards are all about encouraging the development of technology for collaborative computing. It's not so important that the search is for prime numbers. It's all about building the technology.


Question: If some of the elements on the periodic table can only be produced in a lab, why are they considered elements?

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 If some of the elements on the periodic table can only be produced in a lab, why are they considered elements?

Because they still exist? The periodic table isn't a list of things you'll find in your yard - it is a list of the nuclear elements which we have observed. As for why studying things that don't naturally exist is *useful*, the elements which only exist for brief periods often play a crucial role in nuclear chemistry. Nuclear reactors, for instance, would not be practically possible without 'delayed neutrons' from these elements.


Question: Why is it OK to compare and draw conclusions from data where there are two samples of very different size?

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 Why is it OK to compare and draw conclusions from data where there are two samples of very different size?

Sample size is important on its own as it relates to the statistical “power” of a study. Power is about how large of a sample size you need to detect a statistical difference between variables with a given amount of certainty. For example, let’s say we have a two-sided coin, and we don’t know whether it’s a fair coin (i.e. 50/50 odds). If we flip it twice and we get the same side both times, does that mean that it’s not a fair coin? Maybe. But what if we flip it 5000 times and it comes up heads 4750 of those times? Would we be suspicious? We’d be more certain that it wasn’t a fair coin, and we’d have a fairly good idea of the odds. That’s statistical power as it relates to sample size. The other concept in some studies is generalizability and it relates somewhat to power. If we look at a population of 100 people and we find that 80 of them like cold weather, could we then say that 80% of people like cold weather? Again, maybe. But what if I told you that those 100 people all live in Maine and are between the ages of 18-24. We might not be so certain that we could apply the data from those 100 people and make conclusions about people in general. But, if we have a large enough sample, we might be able to find that we have a diverse group of people different locations and different ages and other demographics, and we might be able to generalize our findings. That’s generalizability. Combining these ideas gives you a sense of how we can use smaller sample sizes to imply information about larger sample sizes.


Question: How, at 93 million miles away, does the sun feel so warm, yet when a simple cloud passes over it the warmth is incredibly dampened?

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 How, at 93 million miles away, does the sun feel so warm, yet when a simple cloud passes over it the warmth is incredibly dampened?

So when you feel the sun's warmth, you're not feeling heat coming from the sun. You're instead feeling heat created *on your skin* by the sun's light. Light carries energy. Things with colour, like your skin, absorb light. When they do, the atoms that make them up get 'excited'. Depending on the atom, and what state its in, a few things can happen. If the atom is part of a molecule that energy can go to work breaking it out of the molecule. If the atom or molecule is on the surface of a solid or liquid, the energy can go towards flinging it off, into the air, turning into a gas. If there's not enough energy to do either of those things, then the atom will just release the energy to its surroundings. Most of the time, most of the energy is released as heat. This is what you feel when the sun feels warm. Sometimes the energy can be released as light. This is how glow-in-the-dark things work. A cloud doesn't block all the light from the sun, but it does ~~absorb~~ *scatter* a lot of it. *Think of water droplets in a cloud like a million tiny disco balls*. The light that gets through is either too sparce to be noticeable, or high-enough energy that it causes damage instead (ie. UV light).