Why do some rich countries have no skyscrapers (like Sweden)?



Skyscrapers are first and foremost a space saving measure in places where you have to cram plenty of office space into a downtown location in order to accommodate all the people who are going to work there.



The notion that a skyscraper is a sign of development and affluence comes from places that have no space.



Sweden doesn’t need skyscrapers for two reasons:




  • we actually have space in our cities.

  • many operations are shifted to small towns because in this day and age, there is no need to confine everyone physically to a big city location, and then pay crazy rents.



When you live in Sweden, you notice that all your bills come from obscure little towns, not from Stockholm.



Why put a skyscraper in there?



There are some high buildings here, but if you’ve been to Shanghai or Hong Kong, they look pretty quaint. 



 



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Why don’t airport runways have a ramp at the end to help the plane get off the ground?



On some aircraft carriers, a ski-jump is used at the end of the runway to help aircraft take off. The jump reduces the space required to take off (which is rather limited on a ship) and allows a higher take-off weight, which means more fuel and more ammunition can be carried.



However, there are downsides too. First off, the jump puts more stress on the airframe, requiring a beefier aircraft structure. Secondly, the take-off must be a success or it will be a major failure. If the aircraft doesn’t get enough speed to take off, it will fall in the sea, or if on land, will crash into the ground. Thirdly, it forces the runway to be unidirectional. You can only land from the non-ski-jump end. Not a big problem for a ship which can turn round, but an issue for a ground-based airport that wants to land planes into the wind and has to cope with changeable weather.



For military aircraft, some of the above downsides are worth it for the additional payload and shorter take-off run. They can accept the risks. For commercial and private aircraft, the risk/return ratio is rather different. Commercial airlines give high priority to safety. They can’t accept the risk of an aborted take-off but no runway space to brake and stop on. They can’t accept not landing in the best direction for the current weather. They need runways to operate both ways as required. They can’t accept the extra maintenance and construction costs for the stronger aircraft required by a jump.



Ultimately, the airlines just don’t need ski-jumps. The world is full of long land-based airports that have more than enough length to allow even the largest jets to land. For smaller airports, there is usually less demand, so airlines can operate smaller aircraft, with shorter take-off runs, to serve those locations.



 



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In mathematics, how do you know when you have proven a theorem?



Two things: You learn that you don’t know, and you learn that deep inside, you do.



When you find, or compose, or are moonstruck by a good proof, there’s a sense of inevitability, of innate truth. You understand that the thing is true, and you understand why, and you see that it can’t be any other way. It’s like falling in love. How do you know that you’ve fallen in love? You just do.



Such proofs may be incomplete, or even downright wrong. It doesn’t matter. They have a true core, and you know it, you see it, and from there it’s only a matter of filling the gaps, cleaning things up, eliminating redundancy, finding shortcuts, rearranging arguments, organizing lemmas, generalizing, generalizing more, realizing that you’ve overgeneralized and backtracking, writing it all neatly in a paper, showing it around, and having someone show you that your brilliant proof is simply wrong.



And this is where you either realize that you’ve completely fooled yourself because you so wanted to be in love, which happens more often when you’re young and inexperienced, or you realize that it’s merely technically wrong and the core is still there, pulsing with beauty. You fix it, and everything is good with the world again.



Experience, discipline, intuition, trust and the passage of time are the things that make the latter more likely than the former. When do you know for sure? You never know for sure. I have papers I wrote in 1995 that I’m still afraid to look at because I don’t know what I’ll find there, and there’s a girl I thought I loved in 7th grade and I don’t know if that was really love or just teenage folly. You never know.



Fortunately, with mathematical proofs, you can have people peer into your soul and tell you if it’s real or not, something that’s harder to arrange with crushes. That’s the only way, of course. The best mathematicians need that process in order to know for sure. Someone mentioned Andrew Wiles; his was one of the most famous instances of public failure, but it’s far from unique. I don’t think any mathematician never had a colleague demolish their wonderful creation.



Breaking proofs into steps (called lemmas) can help immensely, because the truth of the lemmas can be verified independently. If you’re disciplined, you work hard to disprove your lemmas, to find counterexamples, to encourage others to find counterexamples, to critique your own lemmas as though they belonged to someone else. This is the very old and very useful idea of modularization: split up your Scala code, or your engineering project, or your proof, or what have you, into meaningful pieces and wrestle with each one independently. This way, even if your proof is broken, it’s perhaps just one lemma that’s broken, and if the lemma is actually true and it’s just your proof that’s wrong, you can still salvage everything by re-proving the lemma.



Or not. Maybe the lemma is harder than your theorem. Maybe it’s unprovable. Maybe it’s wrong and you’re not seeing it. Harsh mistress she is, math, and this is a long battle. It may takes weeks, or months, or years, and in the end it may not feel at all like having created a masterpiece; it may feel more like a house of sand and fog, with rooms and walls that you only vaguely believe are standing firm. So you send it for publication and await the responses.



Peer reviewers sometimes write: this step is wrong, but I don’t think it’s a big deal, you can fix it. They themselves may not even know how to fix it, but they have the experience and the intuition to know that it’s fine, and fixing it is just work. They ask you politely to do the work, and they may even accept the paper for publication pending the clean up of such details.



There are, sometimes, errors in published papers. It happens. We’re all human. Proofs that are central have been redone so many times that they are more infallible than anything of value, and we can be as certain of them as we are certain of anything. Proofs that are marginal and minor are more likely to be occasionally wrong.



So when do you know for sure? When reviewers reviewed, and time passes, and people redo your work and build on it and expand it, and over time it becomes absolutely clear that the underlying truth is unassailable. Then you know. It doesn’t happen overnight, but eventually you know.



And if you’re good, it just reaffirms what you knew, deep inside, from the very beginning.



Mathematical proofs can be formalized, using various logical frameworks (syntactic languages, axiom systems, inference rules). In that they are different from various other human endeavors.



It's important to realize, however, that actual working mathematicians almost never write down formal versions of their proofs. Open any paper in any math journal and you'll invariably find prose, a story told in some human language (usually English, sometimes French or German). There are certainly lots of math symbols and nomenclature, but the arguments are still communicated in English.



In recent decades, tremendous progress has been made on practical formalizations of real proofs. With systems like Coq, HOL, Flyspeck and others, it has become possible to write down a completely formal list of steps for proving a theorem, and have a computer verify those steps and issue a formal certificate that the proof is, indeed, correct.



The motivation for setting up those systems is, at least in part, precisely the desire to remove the human, personal aspects I described and make it unambiguously clear if a proof is correct or not.



One of the key proponents of those systems is Thomas Hales, who developed an immensely complex proof of the Kepler Conjecture and was driven by a strong desire to know whether it's correct or not. I'm fairly certain he wanted, first and foremost, to know the answer to that question himself. Hales couldn't tell, by himself, if his own proof is correct.



It is possible that in the coming decades the process will become entirely mechanized, although it won't happen overnight. As of 2016, the vast majority of proofs are still developed, communicated and verified in a very social, human way, as they were for hundreds of years, with all the hope, faith, imprecision, failure and joy that human endeavors entail.



 



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Why can't you take Coca-Cola into space?



We have tested Coca-Cola (and Pepsi) in space. In 1985, we flew special dispensers from the manufacturers as an experiment aboard the Space Shuttle.



Soda in space is a bit problematic. In micro-gravity, the light gas bubbles won't rush to the top of the liquid and escape. They will stay within the liquid. This means the astronaut will consume significantly more gas drinking a soda in space than one would drinking a soda on the ground. Drinking a carbonated beverage could be like drinking a foamy slurp.



That means there will be more of a need to burp, to release that gas. That would be okay, except burping in space is unpleasant, for the same reason mentioned above for the soda. On the ground, gases and liquids naturally separate in the digestive system because the lighter gases rise above the heavier liquids. But, in micro-gravity, that doesn't happen. When one burps in space, it is often a "wet burp" which means some liquid is expelled. It's kind of like acid reflux.



 



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Why does a calendar have 12 months? Why does a clock have 12 digits? What is the logic behind the number 12?



12 is a very practical number. Unlike 10, which you can only divide by 2 and 5, you can divide 12 by 2, 3, 4 and 6. When you have not yet invented the decimal system and are doing fractions instead, being able to divide something by a lot of other numbers is very very practical.



24 is also pretty practical, much more practical than 25 or 20. 25 can only be divided by 5, and 20 can only be divided by 2, 4, 5 and 10. 24, on the other hand, can be divided by 2, 3, 4, 6, 8 and 12.



60 is another such practical number. Unlike 50 (divisible only by 2, 5, 10, and 25), 60 can be divided by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30.



360, well, the same thing again: you can divide it by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 20, 24, 30, 45, 60, 90, 120, and 180.



So if you live in a society which not yet have invented the decimal system, and had to be using fractions, these numbers were very practical.



As you have noticed, at least 12 is associated with circles, the numbers of a clock face. Well, so are the others, specifically 24 (hours from mid-day to mid-day) and 360 (degrees of a circle).



It is no accident. Nature is full of circles, including the sky, and these numbers are very well suited for circular things. So when the Babylonians and Sumerians started to describe things that move in the sky, they used these numbers to do it.



They rounded a bit, for instance about the year which they realised was not perfectly 360 days, but 365. A common way for ancient civilisations was to have a five day party when you reached the end of the year. The Moon’s cycle was not perfectly 30 days. Depending on if you thought that the constellations and sun were more important than the Moon, you rounded by just declaring months to be 30 days, or you inserted a “leap month” every other year or so.



So that’s where you have the zodiac from as well: people associated patterns of stars to gods and monsters in their legends, and constructed belt of 12 of them across the cosmic equator. They are not perfectly aligned or evenly spread out, but close enough to still squeeze them into the number 12. These could then be used to tell which month you were in (if you thought that the sun and constellations were more important than the Moon cycle).



 



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What will happen if an astronaut fires a gun from the Moon aiming at Earth?



The .220 Swift remains the fastest commercial cartridge in the world, with a published velocity of 4,665 ft/s (1,422 m/s) and the escape velocity of the MOON is 2,400 m/s so the bullet will not leave the vicinity of the Moon and will eventually return to the surface.



And to respond to the dozen’s of people who have commented below that a rifle bullet will not work in space or on the Moon , yes it will , and actually , like a rocket it will work marginally better . A bullet carries it’s own oxygen in it’s propellant powder and does not need air to ignite !



The only ballistic (Non missile) round that would leave the moon would be one coming from a rail gun which can reach a velocity of upwards 5–6000 m/s (21,600 km hr).



If aimed very accurately which would be very difficult to do it could enter the earth’s atmosphere at a speed in excess of 40,000 km/h or 11,100 m/s .



As the projectile enters the Earth’s atmosphere it will compress the air ahead of it to a temperature of 8000–10,000ºC and melt and burn up , not striking the ground but vaporizing 15 -20 kilometers above ground maybe terminating in a loud explosion.



 



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How do space telescopes keep their lenses clean?



They don’t get dirty.



There is nothing in the vacuum of space to collect on the mirror.



Orbital debris is a potential problem, but experience with Hubble shows that it’s not too serious. But if the mirror does get hit, it’s not something you’ll be able to clean off…it’ll be a hole the size of a quarter.



Hubble’s biggest problems with debris has been impacts to its solar panels:



But Hubble is in a moderately low orbit - because that’s as high as the crappy Space Shuttle could get it.



These days, we’d put it MUCH farther from the Earth—far from the places where debris is common.



The James Webb Space telescope isn’t even going to be orbiting the Earth—it’s going to be parked in a Sun-centered orbit at the Earth/Sun L2 point.



 



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If an astronaut fell over a 300 ft cliff on The Moon, would the low gravity save him, and would he bounce?



It’s not the fall that kills you, it’s the sudden stop at the bottom.



Bouncing doesn’t come into it. The question is, how fast are you going when you hit something. The faster you are going, the more energy you contain when you hit the ground—energy that now tries to break bones and crush organs like tomatoes on the windscreen of a passing car.



On Earth, the general rule of thumb is that you risk serious injury from any fall higher than you are. On the moon that would have to be adjusted; lunar gravity is only 1/6th as strong, but there is no air—so you will never reach a “terminal velocity” beyond which you don’t speed up any further.



If an astronaut fell 300 feet on the moon, that’s a 91.44 meter drop at 1.633 meters per second per second acceleration (we’ll do this in metric because metric isn’t a stupid, byzantine measuring system). With no air resistance at all, our hapless astronaut will hit the ground after 10.6 seconds, at a velocity of 17.2 meters per second.



How dangerous is that? Well on Earth, to hit the ground at 17.2 meters per second (ignoring air resistance), you’d have to fall from a height of 15.2 meters, or 49.8 feet, or the roof of a five story building. Onto rock or dry sand. Does that sound like a good idea?



No. Such a drop would likely break the spacesuit and would certainly break the occupant.



 



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Why is gold expensive? Why can't we consider gold as other metals like iron, aluminum, and silver?



Iron mining in Western Australia produced 826 million tons of iron ore in 2018, which will convert to roughly several hundred million tons of iron metal. (Note that ratio of ore to metal.) The scale of Australian extraction of iron ore is quite impressive. Those piles in the first picture? That’s iron ore, a mountain of it.



Iron ores are easily accessible, easily converted to iron metal, and can be found in vast quantities. Iron ore is so plentiful that Australia makes a profit selling the ore at $100 to $170 (Australian dollars) per ton. That’s pennies per pound of iron ore, never mind the cost per troy ounce.



Aluminum is also produced in huge quantities, with tens of millions of tons of metal made per year. Aluminum is found in a number of rich deposits of bauxite (available by the tens of billions of tons around the world) that converts from 2 tons of bauxite to 1 ton of aluminum metal.



But gold?



Gold’s yield from rock is measured in ounces per ton of ore. Gold mines may have to extract up to 100 tons of rock to get an ounce of gold.



If those 826 million tons of Australian iron ore were gold-bearing rock instead then you might get as little as 230 tons of gold from them. (Current global gold production is about 3,100 tons per year.)



Further, gold deposits are not as common as iron ores or aluminum ores.



That’s why gold isn’t going to be treated as an inexpensive metal like iron or aluminum. It just isn’t as common or easily found. Iron and aluminum actually make up a significant percentage of Earth’s mass; gold does not.



Gold is subject to some odd consumer demand that drives up its price unnecessarily at times, but one reason for its high cost is that it’s hard to extract and isn’t nearly as common as iron or aluminum.



 



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How do they keep the International Space Station’s inside temperature warm?



The outside of the ISS can reach temperatures as high as 250 degrees F (121°C) on the sunny side and as low as -250 degrees F (-157°C) on the shady side. Inside the ISS are plenty of things that generate heat – such as human bodies, laptop computers, pumps, and other electrical devices. It takes a lot of work and complicated thermal control systems to remove that heat from its sources and transport it outside where it can be radiated to space.



For the parts of the ISS that do need active effort to keep warm, that is accomplished using simple electrical resistance heater pads, like the one shown in the below picture. They work on a simple premise – the thin pad has a wire running back and forth and back and forth many times within it. That wire is attached to an electrical source and electricity flows through the wire. The circuit has resistance and resistance results in heat. The wire gets warm, so the pad gets warm, and so whatever surface it is adhered to will also get warm. A thermostat will measure the temperature in that vicinity and the value of that temperature will be used to turn the electrical circuit for the heater pad on and off. There are hundreds of these pads throughout the vehicle.



It is important to use these heater pads to keep the shell of the vehicle warm, because if the temperature drops below the dew point, condensation will form on that surface. Accumulations of water can cause problems with electrical equipment and can promote the growth of microorganisms.



 



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Is it true that travel to Mars can occur only once in every two years? If so, why is that so?



It isn't true that travel can only occur every two years, but the conditions are far more optimal at those times, essentially making other times unconsidered.



There are different types of Earth-Mars mission trajectories. They don't all start when Mars and Earth are close. There are multiple factors involved, including whether or not the spacecraft is to come home, whether a gravity assist from Venus is available, and the capabilities of the launch vehicle. However, for the typical one-way mission to get a probe or rover to Mars, we do indeed launch when Mars and Earth are fairly close.



Mars and Earth are at their closest to each other when they are at opposition. However, we don't actually want to launch at this point. We want to launch before this point.



We want to use a minimum energy transfer orbit in order to use the least amount of fuel. A Hohmann transfer orbit does this. Our spacecraft starts at Earth's orbit. A Hohmann transfer orbit uses a burn at the starting point (periapsis) that increases the aphelion of the orbit such that it occurs at the orbit of Mars. This will be 180-degrees later in the orbit.



So, our goal is to time the launch such that Mars will be at that same location when the spacecraft gets there. Since Mars is in a larger orbit, it takes longer to move the same angular distance as the Earth. That means we need Mars to be ahead of Earth when we launch our spacecraft.



We calculate the period of the orbit that our spacecraft will be in. That turns out to be about 520 days. Our spacecraft is traveling half of an orbit, so our trip will be about 260 days. Mars has an orbital period of 687 days. In 260 days, Mars will travel an angular distance of 136 degrees. That means the optimal time to launch the spacecraft is when Mars is 44 degrees (180-136) ahead of Earth in its orbit, as shown below. That means we launch the spacecraft about three months before Mars and Earth are at their closest.



 



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Why do astronauts in space sleep while standing?



On Earth, gravity pulls down on us. In the standing position, that means our head is pressing on our neck, our neck is pressing on our torso, our torso is pressing on our legs, and our legs are pressing on our feet. We lie down, partly, because in doing so we spread the load across our body, taking a lot of stress off of the lower parts of our body.



We also lie down because it leaves us in a stable position, so we don't have to worry about losing our balance and falling, once we are asleep and no longer actively maintaining our balance.



In an orbiting spacecraft, we are in free fall, so we experience weightlessness. All of those red arrows (loads from gravity) disappear. The body now experiences no change in loading from the vertical to the horizontal position. Both are equally stable and both feel the same.



So, sleeping is done in whatever position best fits the available room.



 



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Solar probe reveals sun’s tiny ‘campfires’



A solar probe built by the European Space Agency and NASA has delivered the closest photos ever taken of the sun's surface, revealing a landscape rife with thousands of tiny solar flares that scientists dubbed "campfires" and offering clues about the extreme heat of the outermost part of its atmosphere.



The Solar Orbiter snapped the images using the probe's Extreme Ultraviolet Imager as it orbited nearly 77 million km from the sun's surface or roughly halfway between the sun and earth,



The "campfires" are believed to be tiny explosions, called nanoflares, and could explain why the sun's outer shield, the corona, is 300 times hotter than the star's surface.



Scientists typically have relied upon Earth-based telescopes for close-ups of the sun's surface. But Earth's atmosphere limits the amount of visible light needed to glean views as intimate as those obtained by the Solar Orbiter.



 



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Rare plant species discovered from Sikkim Himalayas



Researchers from Pune and Kerala have rediscovered a rare and critically endangered plant species called Globba andersonii from the Sikkim Himalayas after a gap of 135 years. The plant, commonly known as 'dancing ladies' or 'swan flowers' was thought to have been extinct until its "re-collection for the first time since 1875 when the British botanist, Sir George King, collected it from the Sikkim Himalayas. Globba andersonii are characterised by white flowers and a "yellowish lip". The species is restricted mainly to the Teesta River Valley region which includes the Sikkim Himalayas and Darjeeling hill ranges. The plant usually grows in a dense colony as a lithophyte (plant growing on a bare rock or stone) on rocky slopes in the outskirts of evergreen forests.



Globba andersonii are characterised by white ?owers, non-appendaged anthers (the part of a stamen that contains the pollen) and a “yellowish lip”. Classified as “critically endangered” and “narrowly endemic”, the species is restricted mainly to Teesta River Valley region which includes the Sikkim Himalays and Darjeeling hill ranges.



“As no live collections were made for the last 136 years, it was considered as presumably extinct in the wild. E?orts made by us for the rediscovery of the taxon for the past several years were in vain. However, Dr. Punekar could locate some specimens during his visit to Sevoke in July 2011, which was used to make a detailed description,” said Mr. Thachat.



 



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Blind people can 'see' letters traced directly onto their brains



Scientists have developed a new way to create "sight" for blind people. The approach bypasses the eyes and delivers a sequence of electrical signals to the brain, creating the perception of a glowing light that traces a shape. The method might one day restore aspects of vision to people with damaged eyes or optic nerves.



The team "drew" letters of the alphabet on blind people's brains by giving them specific patterns of electrical stimulation. Tiny jolts of electricity to the visual cortex, a span of neural tissue at the back of the brain, can make a person "see" small bursts of light called phosphenes. When electrical stimulation was used to dynamically trace letters directly on patients' brains, they were able to see the intended letter shapes and could correctly identify different letters. They described seeing glowing spots or lines forming the letters. Researchers said their inspiration for this was the idea of tracing a letter in the palm of someone's hand.



So far, only simple shapes, such as the letters C, W and U, have been tested. But outlines of common objects, such as faces, houses or cars, could be traced using the same idea, they said.



 



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