21st century, known as the Age Of [Shit](shit.md) or Dark Ages, is already one of the worst centuries in history, despite only being around for a short time. How unlucky it is to have been born in such a shitty time. In this century there exists no more [good](good.md), there is just [evil](right.md) opposed by [another evil](pseudoleft.md) and people no longer even know what good means, they only support one of the two evils, thinking it's the good; there are rare few who support some kind of third evil that's not one of the two major evils, but all in all there is nothing but evil.
21st century, known as the Age Of [Shit](shit.md) or Dark Ages, is already one of the worst centuries in history, despite only being around for a short time. How unlucky it is to have been born in such a shitty time. Abominations walk in the streets. In this century there exists no more [good](good.md), there is just [evil](right.md) opposed by [another evil](pseudoleft.md) and people no longer even know what good means, they only support one of the two evils, thinking it's the good; there are rare few who support some kind of third evil that's not one of the two major evils, but all in all there is nothing but evil.
ASCII art is the [art](art.md) of (mostly manually) creating graphics and images only out of [fixed-width](fixed_width.md) (monospace) [ASCII](ascii.md) characters. Strictly speaking this means no [Unicode](unicode.md) or extended ASCII characters are allowed -- these would rather be called Unicode art, [ANSI art](ansi_art.md) etc., though the term ASCII art is quite often used loosely for any art of this kind. If we keep being pedantic, ASCII art might also be seen as separate from mere [ASCII rendering](ascii_rendering.md), i.e. automatically rendering a bitmap image with ASCII characters in place of [pixels](pixel.md), and ASCII graphics that utilizes the same techniques as ASCII art but can't really be called art (e.g. computer generated diagrams); though in practice this distinction is also rarely made. Pure ASCII art is [plain text](plain_text.md), i.e. it can't make use of [color](color.md), text decoration and other [rich text](rich_text.md) formatting.
This kind of art used to be a great part of the [culture](culture.md) of earliest [Internet](internet.md) and near-Internet (e.g. [BBS](bbs.md)) communities for a number of reasons imposed largely by the limitations of old computers -- it could be created easily with a text editor and saved in pure text format, it didn't take much space to store or send over a network and it could be displayed on text-only displays and [terminals](terminal.md). The idea itself even predates computers, people were already making this kind of images with type writers, e.g. some poets were formatting their poems with typewriters to picture-shapes. Despite the technical limitations of displays having been overpassed, ASCII art survives even to present day and lives on in the [hacker culture](hacking.md), among [programmers](programming.md), in [Unix](unix.md) and "retro" game communities as well as on the [Smol Internet](smol_internet.md), among people who just want to [keep it simple](kiss.md) and so on. ASCII diagram may very well be embedded in a comment on a text-only forum or in source code to explain some spatial concept. We, [LRS](lrs.md), highly advocate use of ASCII art whenever it's [good enough](good_enough.md).
This kind of art used to be a great part of the [culture](culture.md) of earliest [Internet](internet.md) and near-Internet (e.g. [BBS](bbs.md)) communities for a number of reasons imposed largely by the limitations of old computers -- it could be created easily with a text editor and saved in pure text format, it didn't take much space to store or send over a network and it could be displayed on text-only displays and [terminals](terminal.md). The idea itself even predates computers, people were already making this kind of images with type writers, e.g. some poets were formatting their poems with typewriters to picture-shapes. Despite the technical limitations of displays having been overpassed, ASCII art survives even to present day and lives on in the [hacker culture](hacking.md), among [programmers](programming.md), in [Unix](unix.md) and "retro" game communities as well as on the [Smol Internet](smol_internet.md), among people who just want to [keep it simple](kiss.md) and so on. ASCII diagram may very well be embedded in a comment on a text-only forum or in source code to explain some spatial concept. ASCII art may even be superior for making certain types of drawings from purely user perspective exactly by being simplified, it can be performed merely with keyboard with little distraction (not caring about colors, not having to focus on right angles, to care about line thicknesses, switching tools, deleting imprecise strokes, ...), similarly to how for example it may be easier to create a rough model of a house in [Minetest](minetest.md) than to model it in [Blender](blender.md). { I found that for making quick diagrams I prefer ASCII art to graphic tools. ~drummyfish } We, [LRS](lrs.md), highly advocate use of ASCII art whenever it's [good enough](good_enough.md).
Here is a simple 16-shade ASCII [palette](palette.md) (but watch out, whether it works will depend on your font): `#OVaxsflc/!;,.- `. Another one can be e.g.: `WM0KXkxocl;:,'. `.
@ -8,4 +8,9 @@ So if you tell someone "You shouldn't do this because it's bad" and he replies "
The effect is of course abused by politicians: once you get a certain number of people moving in a certain shared direction, others will follow just by the need to mimic others. Note that just creating an illusion (using the tricks of [marketing](marketing.md)) of "everyone doing something" is enough -- that's why you see 150 year old grandmas in ads using modern smartphones -- it's to force old people into thinking that other old people are using smartphones so they have to do it as well.
Another potentially valid use of the argument is in the meaning of "everyone does it so I am FORCED to do it as well". For example an employer could argue "I have to abuse my employees otherwise I'll lose the edge on the market and will be defeated by those who continue to abuse their employees". This is very true but it seems like many people don't see or intend this meaning.
Another potentially valid use of the argument is in the meaning of "everyone does it so I am FORCED to do it as well". For example an employer could argue "I have to abuse my employees otherwise I'll lose the edge on the market and will be defeated by those who continue to abuse their employees". This is very true but it seems like many people don't see or intend this meaning.
Here are some questions to test your LRS related knowledge :D
1. What's the difference between *[free software](free_software.md)* and *[open source](open_source.md)*?
2. Name at least 10 different [programming languages](programming_language.md).
3. Why is text written on a piece of paper flipped horizontally when viewed in a mirror -- why is it not flipped vertically?
4. Say we want to generate a random number from 0 to 999 (including both) with uniform probability distribution (i.e. every number is equally likely). In C we often do it using the modulo operator like this: `int num = rand() % 1000`. However there is a problem with this -- describe what the problem is and how its negative effect can be reduced. Hint: it's called *modulo bias*.
5. What's the difference between [data](data.md) and [information](information.md)?
6. Bob has written a program and then committed [suicide](suicide.md) because Alice sued him for sexual harassment. His program is now [unmaintained](maintenance.md). Bob's program uses 10 libraries. The probability that the API of one such library will be [updated](update_culture.md) and changed in any given year is 5%. If this happens, Bob's program will stop working. During the next 5 years what is the probability of his program breaking?
7. What will the following C (C99) snippet print out? `int x = 2; putchar('a' + ((1 == 3 > 2) + ++x));`
8. Order the following software by the date of the release of their 1.0 version from oldest to newest: [TempleOS](temple_os.md), [MS DOS](dos.md), original [Unix](unix.md), [Linux](linux.md), [Windows](windows.md). Also point out which one stands out from others and why.
9. If you're running in a race and overtake the guy who's currently in third place, what place will you be in?
10. When multiplying two *N* bit numbers (unsigned integers, direct representation), what is the minimum number of bits we will need to store their product? Prove it.
11. We have two gears, each of same size and same number of teeth. Gear A is fixed in place, it can't move or rotate, gear B runs around gear A so that it keeps touching it (and therefore rotates along the way) until it gets to the place where it started. How many revolutions around its own axis (from your stationary point of view) has gear B made?
12. What's the worst socioeconomic system in the world? You don't even have to say why because that would take too long.
13. Manually convert the [binary](binary.md) numeral 10110000000010110101 to hexadecimal.
14. Why do astronauts on the ISS feel weightlessness?
15. How would you compute the circumference of a circle with radius *r* without using floating point? Consider just the approximate value of pi ~= 3.14, i.e. write the formula multiplying *2 * r* by 3.14 only using whole numbers (of course the result will be rounded to whole number too).
16. Name at least five licenses commonly used for [FOSS](foss.md) programs, five text editors/IDEs commonly used for programming and five operating systems whose source code is mostly free-licensed (none of these is allowed to be using the same or forked kernel of any other).
17. What is the minimum number of [bits](bit.md) that will allow us to represent 12345678910111213 distinct values?
18. Give at least one example of [analog](analog.md) electronic device and one of [digital](digital.md) mechanical device.
19. Is physical violence every justified?
20. Find a normalized (having length 1) [normal](normal.md) ([vector](vector.md) that's perpendicular to surface) of the [triangle](triangle.md) defined by vertices *A = {1,2,3}*, *B = {5,5,1}* and *C = {1,5,2}*. (Orientation doesn't matter.)
21. Why will (in a typical programming language such as C) an infinite [recursion](recursion.md) crash the program but infinite loop generally won't?
22. Answer yes/no to following: Is base-three number 2101 greater than base-seven number 206? Is [gemini](gemini.md) better than [gopher](gopher.md)? Is there any [triangle](triangle.md) (in Euclidean geometry) whose one side is longer than the sum of lengths of its other two sides?
23. There are two walls 2 meters apart, the right wall is moving left by the speed 0.1 m/s, the left wall is moving right by the same speed 0.1 m/s. There is a fly in the middle between the walls, flying by speed 1 m/s. It is flying towards one wall, then when it reaches it it turns around and flies towards the other wall etc. When the walls completely close in, what distance would the fly have traveled? (There is a simple solution.)
25. At what times, with precision to seconds, do clock hands overlap (just compute AM, PM is the same)?
26. In 3D computer [graphics](graphics.md) what's the difference between [shading](shading.md) and drawing [shadows](shadow.md)?
27. Can we say that the traditional feed forward [neural networks](neural_network.md) are [Turing complete](turing_complete.md)? Explain why or why not.
28. Wicw mx uum yvfe bbt uhmtf ok?
29. What is the *Big O* time [complexity](complexity.md) of worst case scenario for [binary search](binary_search.md)?
30. Does the statement "10 does not equal 10" logically [imply](implication.md) that intelligent alien life exists?
31. What is the principle of [asymmetric cryptography](asymmetric_cryptography.md) and why is it called *asymmetric*?
32. What is the main reason for [Earth](earth.md) having seasons (summer, winter, ...)?
33. WARNING: VERY HARD. There are two integers, both greater than 1 and smaller than 100. *P* knows their product, *S* knows their sum. They have this conversation: *P* says: I don't know the numbers. *S* says: I know you don't, I don't know them either. *P* says: now I know them. *S* says: now I know them too. What are the numbers? To solve this you are allowed to use a programming language, pen and paper etc. { Holy shit this took me like a whole day. ~drummyfish }
34. Did you enjoy this quiz?
2. Use numbers 1, 3, 4 and 6, each exactly once, with any of the basic arithmetic operations (addition, subtraction, multiplication, division) and brackets to get the result 24.
3. Name at least 10 different [programming languages](programming_language.md).
4. Why is text written on a piece of paper flipped horizontally when viewed in a mirror -- why is it not flipped vertically?
5. Say we want to generate a random number from 0 to 999 (including both) with uniform probability distribution (i.e. every number is equally likely). In C we often do it using the modulo operator like this: `int num = rand() % 1000`. However there is a problem with this -- describe what the problem is and how its negative effect can be reduced. Hint: it's called *modulo bias*.
6. What's the difference between [data](data.md) and [information](information.md)?
7. Bob has written a program and then committed [suicide](suicide.md) because Alice sued him for sexual harassment. His program is now [unmaintained](maintenance.md). Bob's program uses 10 libraries. The probability that the API of one such library will be [updated](update_culture.md) and changed in any given year is 5%. If this happens, Bob's program will stop working. During the next 5 years what is the probability of his program breaking?
8. What will the following C (C99) snippet print out? `int x = 2; putchar('a' + ((1 == 3 > 2) + ++x));`
9. Order the following software by the date of the release of their 1.0 version from oldest to newest: [TempleOS](temple_os.md), [MS DOS](dos.md), original [Unix](unix.md), [Linux](linux.md), [Windows](windows.md). Also point out which one stands out from others and why.
10. If you're running in a race and overtake the guy who's currently in third place, what place will you be in?
11. When multiplying two *N* bit numbers (unsigned integers, direct representation), what is the minimum number of bits we will need to store their product? Prove it.
12. We have two gears, each of same size and same number of teeth. Gear A is fixed in place, it can't move or rotate, gear B runs around gear A so that it keeps touching it (and therefore rotates along the way) until it gets to the place where it started. How many revolutions around its own axis (from your stationary point of view) has gear B made?
13. What's the worst socioeconomic system in the world? You don't even have to say why because that would take too long.
14. Manually convert the [binary](binary.md) numeral 10110000000010110101 to hexadecimal.
15. Why do astronauts on the ISS feel weightlessness?
16. How would you compute the circumference of a circle with radius *r* without using floating point? Consider just the approximate value of pi ~= 3.14, i.e. write the formula multiplying *2 * r* by 3.14 only using whole numbers (of course the result will be rounded to whole number too).
17. Name at least five licenses commonly used for [FOSS](foss.md) programs, five text editors/IDEs commonly used for programming and five operating systems whose source code is mostly free-licensed (none of these is allowed to be using the same or forked kernel of any other).
18. What is the minimum number of [bits](bit.md) that will allow us to represent 12345678910111213 distinct values?
19. Give at least one example of [analog](analog.md) electronic device and one of [digital](digital.md) mechanical device.
20. Is physical violence every justified?
21. Find a normalized (having length 1) [normal](normal.md) ([vector](vector.md) that's perpendicular to surface) of the [triangle](triangle.md) defined by vertices *A = {1,2,3}*, *B = {5,5,1}* and *C = {1,5,2}*. (Orientation doesn't matter.)
22. Why will (in a typical programming language such as C) an infinite [recursion](recursion.md) crash the program but infinite loop generally won't?
23. Answer yes/no to following: Is base-three number 2101 greater than base-seven number 206? Is using [gemini](gemini.md) a good idea when [gopher](gopher.md) exists? Is there any [triangle](triangle.md) (in Euclidean geometry) whose one side is longer than the sum of lengths of its other two sides?
24. There are two walls 2 meters apart, the right wall is moving left by the speed 0.1 m/s, the left wall is moving right by the same speed 0.1 m/s. There is a fly in the middle between the walls, flying by speed 1 m/s. It is flying towards one wall, then when it reaches it it turns around and flies towards the other wall etc. When the walls completely close in, what distance would the fly have traveled? (There is a simple solution.)
26. At what times, with precision to seconds, do clock hands overlap (just compute AM, PM is the same)?
27. In 3D computer [graphics](graphics.md) what's the difference between [shading](shading.md) and drawing [shadows](shadow.md)?
28. Can we say that the traditional feed forward [neural networks](neural_network.md) are [Turing complete](turing_complete.md)? Explain why or why not.
29. Wicw mx uum yvfe bbt uhmtf ok?
30. What is the *Big O* time [complexity](complexity.md) of worst case scenario for [binary search](binary_search.md)?
31. Does the statement "10 does not equal 10" logically [imply](implication.md) that intelligent alien life exists?
32. What is the principle of [asymmetric cryptography](asymmetric_cryptography.md) and why is it called *asymmetric*?
33. What is the main reason for [Earth](earth.md) having seasons (summer, winter, ...)?
34. WARNING: VERY HARD. There are two integers, both greater than 1 and smaller than 100. *P* knows their product, *S* knows their sum. They have this conversation: *P* says: I don't know the numbers. *S* says: I know you don't, I don't know them either. *P* says: now I know them. *S* says: now I know them too. What are the numbers? To solve this you are allowed to use a programming language, pen and paper etc. { Holy shit this took me like a whole day. ~drummyfish }
35. Did you enjoy this quiz?
### Answers
1. Though legally similar (but not identical), free software is a movement based on ethics and pursuing freedom for the software user, open source is evil business movement that avoids talking about ethics, it was forked from free software and is solely focused on exploiting free software licenses for making profit.
3. The mirror doesn't really flip the text -- what's left/right in front of it is also left/right in it. It is you who flipped the text when you pointed it at the mirror -- you most likely flipped it horizontally so that's how you see it in the mirror, but you could as well have flipped it vertically; then the text would be flipped vertically in the mirror.
4. Modulo bias happens when the random number generator's range is non-divisible by our desired range that we enforce with modulo operator -- with shown approach some numbers then have higher probability of being generated than others. For example if rand() here return numbers from 0 to 1023, there is only one way to get 999 (999 % 1000) but two ways to get 0 (0 % 1000 and 1000 % 1000), i.e. 0 is more likely to be generated. Common approach to reducing this effect is to repeatedly generate numbers until we get one falling into the "fair" range (this is not guaranteed to end so we should limit the maximum number of attempts).
5. The relationship is commonly described like this: information is interpreted data. I.e. data is just a sequence of symbols, information is the knowledge we extract from it.
6. The probability of program breaking is 1 minus probability of it not breaking. For a program to NOT break during one year, all libraries have to stay unchanged (probability 0.95 for each one): that's 0.95 * 0.95 * 0.95 * ... = 0.95^10. Similarly the probability of it not breaking during 5 years is (0.95^10)^5, so the probability of the program breaking in 5 years is around 92%.
7. `e`
8. Original Unix (around 1970), MS DOS (1981), Windows (1985), Linux (1998), TempleOS (2007). Linux stands out because it's not an operating system, it's a kernel.
9. third
10. *2 * N*. We can multiply the greatest values: *(2^N - 1) * (2^N - 1) = 2^(2 * N) - 2^(N + 1) + 1*; The greatest term *2^(2 * N)* in binary is 1 with *2 * N* zeros after it, subtracting *(2^(N + 1) - 1)* will always definitely shorten this number by at least one bit (1000... minus anything non-zero will shorten the number). So at most we will need *2 * N* bits for the result, but we can't use fewer because for example 11 * 11 = 1001 -- in this case fewer than 2 * 2 = 4 bits wouldn't suffice. So in general we need *2 * N* bits.
11. two (try it, see coin rotation paradox)
12. [capitalism](capitalism.md)
13. B00B5
14. It's not because of the distance from the [Earth](earth.md), the force of gravity is practically the same there (from the Earth's perspective they're really not significantly far away, even the Moon still feels Earth's gravity very strongly so that it doesn't fly away). It's because they are orbiting the Earth, the path they are taking makes them constantly be in a kind of free fall while also preventing them from hitting the Earth (similarly to a comet who is kind of falling towards the Earth but just narrowly misses it, the orbital path of ISS is just much closer to being a circle than an ellipse). I.e. they feel the same kind of weightlessness you will feel in an elevator that's falling down.
17. The number is *N* such that 2^N = 12345678910111213, rounded up, that is ceil(log2(12345678910111213)) = 54.
18. amplifier, voltmeter, analog hardware for [neural networks](neural_net.md), ...; abacus, mechanical calculators such as Curta, Turing machine made of wood, ...
19. no
20. We can use [cross product](cross_product.md) to find a vector perpendicular to two vectors, so we can take e.g. vectors *U = B - A = {4,3,-2}* and *V = C - A = {0,3,-1}*; their cross product is *UxV = {3,4,12} = n* (just look up the formula for cross product). This is the normal, to normalize it we'll first compute its length, i.e. *|n| = sqrt(3^2 + 4^2 + 12^2) = 13* and then divide each component of *n* by this length, i.e. we finally get *n0 = {3/13,4/13,12/13}*. As a check we can compute [dot product](dot_product.md) of this normal with both *U* and *V* and we should get 0 in both cases (meaning the vectors are perpendicular).
21. Infinite loop just performs jumps back to some previous program instruction which can be repeated indefinitely, so unless there is something inside the loop that will lead to a crash after many repetitions, an infinite loop will just make the program run forever. With recursion, however, every successive recursive call allocates a new call frame on the call stack (so that the program knows where to return from the function) which will lead to running out of stack memory and to [stack overflow](stack_overflow.md).
22. no, no, no
23. The walls will collide in 10 seconds during which the fly has been constantly flying with the speed 1 m/s, so it traveled 10 meters.
25. 1:5:27, 2:10:54, 3:16:21, 4:21:49, 5:27:16, 6:32:43, 7:38:10, 8:43:38, 9:49:05, 10:54:32, 12:00:00, you can compute it by making equations for position of the hour and minute hand depending on time, setting them equal and solving, i.e. you get something like *tm / (60 * 12) = (tm / 60) - (tm // 60)* (where *//* is integer division and *tm* is time in minutes); you will find the times are those when minute hand is at multiples of 60 / 11 minues (5:27), i.e. there are 11 such times around the circle and they are evenly spaced.
26. Shading is the process of computing surface color of 3D objects, typically depending on the object's material and done by GPU programs called [shaders](shader.md); shading involves for example applying textures, normal mapping and mainly lighting -- though it can make pixels lighter and darker, e.g. depending on surface normal, it only applies local models of light, i.e. doesn't compute true shadows cast by other objects. On the other hand computing shadows uses some method that works with the scene as a whole to compute true shadowing of objects by other objects.
27. We can't really talk about Turing completeness of plain neural networks, they cannot be Turing complete because they just transform fixed length input into fixed length output -- a Turing complete model of computation must be able to operate with arbitrarily large input and output. In theory we can replace any neural network with logic circuit or even just plain lookup table. Significance of neural networks doesn't lie in their computational power but rather in their efficiency, i.e. a relatively small and simple neural network may replace what would otherwise be an enormously large and complicated circuit.
28. two (or txq); The cipher offsets each letter by its position.
29. *log2(n)*; Binary search works by splitting the data in half, then moving inside the half which contains the searched item, recursively splitting that one in half again and so on -- for this the algorithm will perform at worst as many steps as how many times we can divide the data in halves which is what base 2 logarithm tells us.
30. Yes, a false statement implies anything.
31. The main difference against symmetric cryptography is we have two keys instead of one, one (private) for encrypting and one (public) for decrypting -- neither key can be used for the other task. Therefore encryption and decryption processes differ greatly (while in symmetric cryptography it's essentially the same, using the same key, just in reversed way), the problem looks different in one direction that the other, hence it is called *asymmetric*.
32. It's not the distance from the Sun (the distance doesn't change that much and it also wouldn't explain why opposite hemispheres have opposite seasons) but the tilted Earth axis -- the tilt changes the maximum height to which the Sun rises above any specific spot and so the angle under which it shines on the that spot; the [cosine](cos.md) of this angle says how much energy the place gets from the Sun (similarly to how we use cosine to determine how much light is reflected off of a surface in [shaders](shader.md)).
33. 4 and 13, solution: make a table, columns are first integer, rows are second (remember, both *P* and *S* can be making their own table like this too). Cross out whole bottom triangle (symmetric values). *P* doesn't know the numbers, so cross out all combinations of two primes (he would know such numbers as they have only a unique product). *S* knew *P* didn't know the numbers, so the sum also mustn't be a sum of two primes (if the sum could be written as a prime plus prime, *S* couldn't have known that *P* didn't know the numbers, the numbers may have been those two primes and *P* would have known them). This means you can cross out all such numbers -- these are all bottom-left-to-top-right diagonals that go through at least one already crossed out number (combination of primes), as these diagonal have constant sum. Now *P* has a table like this with relatively few numbers left -- if he now leaves in only the numbers that make the product he knows, he'll very likely be left with only one combination of numbers -- there are still many combinations like this, but only the situation when the numbers are set to be 4 and 13 allows *S* to also deduce the numbers after *P* declares he knows the numbers -- this is because *S* knows the combination lies on one specific constant-sum diagonal and 4-13 lie on the only diagonal that in this situation has a unique product within the reduced table. So with some other combinations *P* could deduce the numbers too, but only with 4-13 *S* can finally say he knows them too.
4. The mirror doesn't really flip the text -- what's left/right in front of it is also left/right in it. It is you who flipped the text when you pointed it at the mirror -- you most likely flipped it horizontally so that's how you see it in the mirror, but you could as well have flipped it vertically; then the text would be flipped vertically in the mirror.
5. Modulo bias happens when the random number generator's range is non-divisible by our desired range that we enforce with modulo operator -- with shown approach some numbers then have higher probability of being generated than others. For example if rand() here return numbers from 0 to 1023, there is only one way to get 999 (999 % 1000) but two ways to get 0 (0 % 1000 and 1000 % 1000), i.e. 0 is more likely to be generated. Common approach to reducing this effect is to repeatedly generate numbers until we get one falling into the "fair" range (this is not guaranteed to end so we should limit the maximum number of attempts).
6. The relationship is commonly described like this: information is interpreted data. I.e. data is just a sequence of symbols, information is the knowledge we extract from it.
7. The probability of program breaking is 1 minus probability of it not breaking. For a program to NOT break during one year, all libraries have to stay unchanged (probability 0.95 for each one): that's 0.95 * 0.95 * 0.95 * ... = 0.95^10. Similarly the probability of it not breaking during 5 years is (0.95^10)^5, so the probability of the program breaking in 5 years is around 92%.
8. `e`
9. Original Unix (around 1970), MS DOS (1981), Windows (1985), Linux (1998), TempleOS (2007). Linux stands out because it's not an operating system, it's a kernel.
10. third
11. *2 * N*. We can multiply the greatest values: *(2^N - 1) * (2^N - 1) = 2^(2 * N) - 2^(N + 1) + 1*; The greatest term *2^(2 * N)* in binary is 1 with *2 * N* zeros after it, subtracting *(2^(N + 1) - 1)* will always definitely shorten this number by at least one bit (1000... minus anything non-zero will shorten the number). So at most we will need *2 * N* bits for the result, but we can't use fewer because for example 11 * 11 = 1001 -- in this case fewer than 2 * 2 = 4 bits wouldn't suffice. So in general we need *2 * N* bits.
12. two (try it, see coin rotation paradox)
13. [capitalism](capitalism.md)
14. B00B5
15. It's not because of the distance from the [Earth](earth.md), the force of gravity is practically the same there (from the Earth's perspective they're really not significantly far away, even the Moon still feels Earth's gravity very strongly so that it doesn't fly away). It's because they are orbiting the Earth, the path they are taking makes them constantly be in a kind of free fall while also preventing them from hitting the Earth (similarly to a comet who is kind of falling towards the Earth but just narrowly misses it, the orbital path of ISS is just much closer to being a circle than an ellipse). I.e. they feel the same kind of weightlessness you will feel in an elevator that's falling down.
18. The number is *N* such that 2^N = 12345678910111213, rounded up, that is ceil(log2(12345678910111213)) = 54.
19. amplifier, voltmeter, analog hardware for [neural networks](neural_net.md), ...; abacus, mechanical calculators such as Curta, Turing machine made of wood, ...
20. no
21. We can use [cross product](cross_product.md) to find a vector perpendicular to two vectors, so we can take e.g. vectors *U = B - A = {4,3,-2}* and *V = C - A = {0,3,-1}*; their cross product is *UxV = {3,4,12} = n* (just look up the formula for cross product). This is the normal, to normalize it we'll first compute its length, i.e. *|n| = sqrt(3^2 + 4^2 + 12^2) = 13* and then divide each component of *n* by this length, i.e. we finally get *n0 = {3/13,4/13,12/13}*. As a check we can compute [dot product](dot_product.md) of this normal with both *U* and *V* and we should get 0 in both cases (meaning the vectors are perpendicular).
22. Infinite loop just performs jumps back to some previous program instruction which can be repeated indefinitely, so unless there is something inside the loop that will lead to a crash after many repetitions, an infinite loop will just make the program run forever. With recursion, however, every successive recursive call allocates a new call frame on the call stack (so that the program knows where to return from the function) which will lead to running out of stack memory and to [stack overflow](stack_overflow.md).
23. no, no, no
24. The walls will collide in 10 seconds during which the fly has been constantly flying with the speed 1 m/s, so it traveled 10 meters.
26. 1:5:27, 2:10:54, 3:16:21, 4:21:49, 5:27:16, 6:32:43, 7:38:10, 8:43:38, 9:49:05, 10:54:32, 12:00:00, you can compute it by making equations for position of the hour and minute hand depending on time, setting them equal and solving, i.e. you get something like *tm / (60 * 12) = (tm / 60) - (tm // 60)* (where *//* is integer division and *tm* is time in minutes); you will find the times are those when minute hand is at multiples of 60 / 11 minues (5:27), i.e. there are 11 such times around the circle and they are evenly spaced.
27. Shading is the process of computing surface color of 3D objects, typically depending on the object's material and done by GPU programs called [shaders](shader.md); shading involves for example applying textures, normal mapping and mainly lighting -- though it can make pixels lighter and darker, e.g. depending on surface normal, it only applies local models of light, i.e. doesn't compute true shadows cast by other objects. On the other hand computing shadows uses some method that works with the scene as a whole to compute true shadowing of objects by other objects.
28. We can't really talk about Turing completeness of plain neural networks, they cannot be Turing complete because they just transform fixed length input into fixed length output -- a Turing complete model of computation must be able to operate with arbitrarily large input and output. In theory we can replace any neural network with logic circuit or even just plain lookup table. Significance of neural networks doesn't lie in their computational power but rather in their efficiency, i.e. a relatively small and simple neural network may replace what would otherwise be an enormously large and complicated circuit.
29. two (or txq); The cipher offsets each letter by its position.
30. *log2(n)*; Binary search works by splitting the data in half, then moving inside the half which contains the searched item, recursively splitting that one in half again and so on -- for this the algorithm will perform at worst as many steps as how many times we can divide the data in halves which is what base 2 logarithm tells us.
31. Yes, a false statement implies anything.
32. The main difference against symmetric cryptography is we have two keys instead of one, one (private) for encrypting and one (public) for decrypting -- neither key can be used for the other task. Therefore encryption and decryption processes differ greatly (while in symmetric cryptography it's essentially the same, using the same key, just in reversed way), the problem looks different in one direction that the other, hence it is called *asymmetric*.
33. It's not the distance from the Sun (the distance doesn't change that much and it also wouldn't explain why opposite hemispheres have opposite seasons) but the tilted Earth axis -- the tilt changes the maximum height to which the Sun rises above any specific spot and so the angle under which it shines on the that spot; the [cosine](cos.md) of this angle says how much energy the place gets from the Sun (similarly to how we use cosine to determine how much light is reflected off of a surface in [shaders](shader.md)).
34. 4 and 13, solution: make a table, columns are first integer, rows are second (remember, both *P* and *S* can be making their own table like this too). Cross out whole bottom triangle (symmetric values). *P* doesn't know the numbers, so cross out all combinations of two primes (he would know such numbers as they have only a unique product). *S* knew *P* didn't know the numbers, so the sum also mustn't be a sum of two primes (if the sum could be written as a prime plus prime, *S* couldn't have known that *P* didn't know the numbers, the numbers may have been those two primes and *P* would have known them). This means you can cross out all such numbers -- these are all bottom-left-to-top-right diagonals that go through at least one already crossed out number (combination of primes), as these diagonal have constant sum. Now *P* has a table like this with relatively few numbers left -- if he now leaves in only the numbers that make the product he knows, he'll very likely be left with only one combination of numbers -- there are still many combinations like this, but only the situation when the numbers are set to be 4 and 13 allows *S* to also deduce the numbers after *P* declares he knows the numbers -- this is because *S* knows the combination lies on one specific constant-sum diagonal and 4-13 lie on the only diagonal that in this situation has a unique product within the reduced table. So with some other combinations *P* could deduce the numbers too, but only with 4-13 *S* can finally say he knows them too.
@ -83,7 +83,7 @@ Besides others gears/wheels can be used to:
*NXOR (equality) gate implemented with gears (counterclockwise/clockwise rotation mean 1/0); the bottom gear rotates counterclockwise only if the both input gears rotate in the same direction.*
## Buttons/Levers/Sliders/Etc.
### Buttons/Levers/Sliders/Etc.
Buttons, levers, sliders and similar mechanism can be used in ways similar to gears, the difference being their motion is linear, not circular. A button can represent a bit with its up/down position, a lever can similarly represent a bit by being pointed left/right. As seen below, implementation of basic logic gates can be quite simple, which is an advantage. Disadvantages include for example, similarly to gears, vulnerability to friction -- with many logic gates in a row it will be more difficult to "press" the inputs.
@ -22,6 +22,8 @@ In 15th century an unofficial version of the Bible, the Wycliffe's translation,
**Can a child consent?** Rather ask if you have good enough reason to prevent it from what it wants to do and what is natural for its healthy development. Can a child consent for going out of house? What if someone abducts it there? What if a car runs it over? Better lock it at home until it's 18 and it's no longer on you if it dies, right? Doesn't matter it will grow up to be a pale unsocialized monster with depression who never saw sunlight, only if it's physically safe and you are legally safe. People nowadays have more trouble with sex than ever before, they don't know what gender they are, they have trouble dating, stay virgins, don't have kids, commit suicides. This wasn't the case in times when this supposed "law protection" didn't exist, how can that be? It's because this "protection" is actually a curse, it makes big deal out of sex and prevents natural development at everyone's pace. It labels people monsters for being attracted to the wrong age group, it labels them marked for life for having been touched by someone from a different age group, it label art a work of Satan if it shows a natural human body. It prohibits the depiction of young face because someone might find it pretty. This you think is a good society? Think again then.
Is there evidence that children can enjoy sex? Sure, tons of it, but this evidence is literally illegal, it's called "child porn", even if it's not porn and if it's not treated as porn at all (e.g. if you just want to use it for research), you will ruin your life sometimes just by saying those words out loud. Let's repeat this: viewing, possession and sharing of this kind of evidence is illegal, and not only that, it is extremely culturally demonized, i.e. it's not the kind of "I stole a bubble gum" illegal, it's the kind of heresy, witchcraft, lynching kind of illegal, you may not officially get a death sentence but it is suggested that if angry mod kills you, the court will leave that be because it was understandable, so you can very easily get a de facto mafia style death sentence. Doesn't this perhaps remind you of some kind of medieval age?
{ I've had people point out to me that pedophobia hurts not only adults but also the minors and children; they told me they had strong sexual desires before the age of 18 they couldn't satisfy because of the age discrimination: even on many social networks they are forced to lie about their age just to be able to join and socialize with others. I myself remember I had the desires LONG before reaching adulthood and would be very glad to satisfy them back then. Sure, abuse can happen, but that's the case for any interaction between children and adults and strong and weak in general -- should we just ban children play parks because that's where many child abductions happen? ~drummyfish }
The fact that they made people believe it is a disorder if your penis can't magically telepathically check a chick's ID and may get erect if she's been born before a date legally established in political region the penis currently resides in shows that at this point an average citizen is more retarded than a braindead chimp. Society believes it is not a disease for a human to [think he's a dog](furry.md) but by law it is considered a disease if by the exact nanosecond of your 18th birthday your brain doesn't magically switch from being attracted to "up to exactly 18" to "exactly from 18 above".
