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  34.  @ChibiNyan  Technically, that's a bad idea as a binary search is probably better as the expected value of information (entropy) is higher. Also, Guess Who? has (had?) an actual problem; the completely antiscientific 'male as default' for humans, which is like stating that water flows uphill Before I clarify the expected value of information, let log(b,x) be log base b of x. Also, let's work out the amount of information in bits of finding out a trait: If the trait occurs in half the sample, knowing whether or not it's present gives one bit of information by definition. If you found out that a sample member had two independent traits with (not necessarily) different probabilities, the probability of having both traits is the product of the probabilities for each trait. Since we want the amount of information to be additive, not multiplicative, it's going to involve some base of logarithm for the probability of the trait. Therefore, the amount of information in bits of finding out a trait is -log(2,[probability of trait]). Finally, the expected value of something is defined by taking the probability of getting a certain value multiplied by the value itself, repeating this for all possible values, then adding them up. In other words, the expected value is the sum of the values weighted by the likelihood of each value occurring. In the case of information, given two possibilities 'yes' and 'no' with probabilities p and 1-p respectively, the expected value of information is p*[amount of information gained if 'yes']+(1-p)*[amount of information gained if 'no'], or p*(-log(2,p))+(1-p)(-log(2,1-p)). Therefore, in your example, if you had a binary search, then the expected value would be (1/2)(-log(2,1/2))+(1/2)(-log(2,1/2)), (1/2)+(1/2), or 1 bit of information. If you ask a question that takes out either 2 or 435 possibilities, the expected value would be (2/437)(-log(2,2/437))+(435/437)(-log(2,435/437)) or (approximately) a whopping 0.042155 bits, which shows that it's a terrible, terrible move. Also, Guess Who? did run into a problem, though it wasn't the lack of non-binary genders; the problem was one would expect that 'is it [sex]?' would form a binary search (i.e., either sex would show up in 12 cards out of 24), but it didn't as femaleness (as opposed to maleness) was treated as a 'characteristic' and thus only showed up in 5 cards out of 24, which is completely antiscientific (not to mention sexist) as humans are mammals, not birds, and this is how mammalian sex determination works: Female mammals have XX chromosomes and male ones have XY chromosomes. When mammals procreate, one of the female's X chromosomes unite with the male's X or Y chromosome with equal probability, giving rise to (approximately) equal proportions of male and female offspring. The X chromosome, like the autosomes, are essential for life, whereas the Y chromosome simply signals to produce testes that release androgens, triggering masculine development, as opposed to feminine development, which is the default mammalian pathway. In birds, this is reversed, as I alluded to in the previous paragraph. If you absolutely must treat a human sex as the default (which you shouldn't), it has to be femaleness
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  51. a) The male to female ratio is 19:5, as they had the completely antiscientific 'male as default' assumption for humans, which is like stating that water flows uphill. and b) You'd only need to make eight extra guesses in the modified game a) Femaleness (as opposed to maleness) was treated as a 'characteristic' and thus only showed up in 5 cards out of 24, which is completely antiscientific (not to mention sexist) as humans are mammals, not birds, and this is how mammalian sex determination works: Female mammals have XX chromosomes and male ones have XY chromosomes. When mammals procreate, one of the female's X chromosomes unite with the male's X or Y chromosome with equal probability, giving rise to (approximately) equal proportions of male and female offspring. The X chromosome, like the autosomes, are essential for life, whereas the Y chromosome simply signals to produce testes that release androgens, triggering masculine development, as opposed to feminine development, which is the default mammalian pathway. In birds, this is reversed, as I alluded to in the previous paragraph. If you absolutely must treat a human sex as the default (which you shouldn't), it has to be femaleness b) A yes/no question's response provides one bit of information, the standard two-gender game requires one bit to state the gender (since 2^0<2<=2^1; in fact 2=2^1), the modified version needs nine (since 2^8<437<=2^9, and more specifically, 437<2^9). Therefore, only 9-1, or eight additional bits of information are required
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  154.  @AmericanBrain  Why should it (social democracy, NOT democratic socialism) not be brought into the US? I really don't see how it's worse then what America has. I really don't. "It's not force if it's a contract doesn't refute my point. According to your definition, it was never a contract in the first place. Me: I am lost . I am sure you are not doing it on purpose but it feels like your second strawman argument. But there is nothing to indicate you are doing it on purpose." a) By 'the point' I was referring to the fact that you have to take any job opportunity, no matter how bad (especially if you're in poverty and you're trying to work your way out of it) because a lot of things could happen before you get another one. If you define a contract as something that isn't coercion, it's only a contract by name. b) It implies that's this is a strawman and I've strawmanned your arguments before. Dare I ask for evidence? "Let's look at the equivalent of capitalism, but in government. ME: 1. government jobs are not part of capitalism per se. I fear the analogy will not work. 2. There should be NO pay whatsoever for government jobs. The ONLY way to pay people for government jobs is to STEAL money USING FORCE called taxation from "fair earners' like CEO/FOUNDER of Amazon and all other people in the U.S. You can Not take 1 penny - not even 1 penny from a billionaire (nor any other American)>" 1. You haven't even looked at the analogy. You just said it won't work then took a tangent, which I'll address in points 2 and 3. 2. There is also theft in private companies. The workers provide goods and services to the consumer. Those who don't (CEOs) somehow manages to get most of the money earned and call it 'profit', and you don't seem to want to convert all conventional firms to co-operatives. 3. Economics Explained has a video on taxation. Under a capitalist system, there is no way you can remove taxes, period. If you support capitalism, you support taxes. So pick one. "except if it involves any "unionization" that's supported by law for that is socialism." No. Having a government that is sensible enough not to bust unions (workers that are unified) is not necessarily socialist, just social democratic. This was a long one.
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  175.  @AmericanBrain  "Force will be used against people like you and it should be used. My theory is not one of pacifism but to go to all out against people like you." That's not in self-defence though. I never hurt you. The only way I've affected you is by debunking your almost impenetrable nonsense. Please, at least follow what you preach, please. "You are speaking in logical contradiction. Selfishness is seeking your "rational' self interest. Dictators are not being "Rational' - but they are "Rationalizing"." And may I asked how dictators aren't doing things according to their "rational self interest", because everything Kim Jong-Un does is in his rational self interest. It's logically best for him to fire all of those missiles at America etc. lest he gets out of power from enemy countries educating the North Korean masses. The only reasons that dictators are not rational as rational decisions are decisions that are logically best for EVERYONE (selflessness), not just for themselves (selfishness). Also, if you're allowed to point out my fake 'conflation of ideas', how about I point out your very real conflation of ideas. Selflessness - Doing things in accordance to the interests of everyone around you Being taken advantage of - Doing things in accordance to the interests of someone as they forced you to. TLDR: Selfishness is evil as it results in people being taken advantage of. Selflessness is good. Before we agree on this, we can't agree on capitalism vs democratic socialism.
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  179.  @AmericanBrain  No. a) Why do you keep conflating social democracy (capitalist (CEOs own companies) system in which the government has laws to protect workers like minimum wage laws etc.) with democratic socialism (a socialist (company owners are elected) system + a democratic government.)? b) Why do you conflate selflessness (doing things that are logically best for everyone) and being exploited (Doing something as someone forced you to)? Is it ideologically convenient to mix up those words? The unaddressed comments of mine/points I missed: a) "NO ONE RESTRICTS A SOVEREIGN. NO ONE." I wonder what you think about laws (like not murdering) as that restricts a sovereign b) ""You've been fed these lies from people who "need" to control you and have controlled you and your family for generations like "puppets on a string'..." You never explained how that's not conspiratorial thinking. c) "Your arguments here seem to rely on three foundational principles:..." in which I debunk the foundational principles for all of your arguments. d) The second paragraph onwards of a comment: "...What about desertification, turning the earth into a desert square mile by square mile? We can't just technology-ize our way out of this one. There is less and less arable land, and also less fresh water. If you think that hydroponics will solve everything, you're wrong. There is less fresh water and desalination is expensive. Increasing the costs of food production just means that poorer countries are left in the dust..." You only addressed the first paragraph of this comment. e) "If I have felt explain this in previous posts then let me explain it now. There is a difference between being rational which is dependent upon existential reality or objective reality. And your wishes and once which is based upon subject of reality in other words the subject of perception of reality even if it is fiction." Rational self interest is doing things that are logically best for you, period. You haven't actually refuted anything in the comment you were responding to. f) ""Hard labor and paint them the least possible work them the most possible often 13 hour shifts. Some of them died because they could not keep up. He could find some discovery channel documentaries about these firms the type of invest in . " You don't care about those who died? g) "Environmentalism is bad because it puts the animals and primitive tribes before us" No. The second part of my last comment about environmentalism gives an example of how it harms the common people, so you haven't refuted that part, meaning I still have a case! "...security have just smashed two women from the tribe that tried to stop the logging..." Oh, those poor women. Please listen, TheAmericanBrain. It's perfectly reasonable to want to stop deforestation. "And if you continue your way that you will remain poor because then people like me will hire people like you and make you work your buttocks off for the rest of your life giving you the least relative money possible for the hall of your life to end up living in tiny houses like in the United Kingdom . " False dichotomy is a logical fallacy for a reason. You are making a false dichotomy between not giving two f***s about the environment, and only being able to afford a small apartment because property demand increased."
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  394. ​ @ChibiNyan  log(b,x) is defined such that b^log(b,x)=x. Now, let's define b^k. For positive integer values of k, b^k is defined as b*b*b*b... k times, or more formally: b^1=b, and b^(k+1)=b*(b^k). Here, I'll outline how it is typically defined for arbitrary real k Before we start, let's make it clear that b^(m-n)=b^m/b^n. This is because the right-hand side looks like b*b*b*b... (m times)/(b*b*b*b... (n times), that is, n copies of b in the denominator cancel with m copies of b in the numerator, leaving (m-n) copies of b in the numerator. Similarly, b^(m+n)=(b*b*b*b... m+n times)=(b*b*b*b... m times)*(b*b*b*b... n times)=(b^m)(b^n). Also, let's make it clear that, b^(mn)=(b^m)^n. This is because the left-hand side looks like: b*b*b*b*b...* b*b*b*b*b...* b*b*b*b*b...* ... where each row has m b's and each column has n b's. We can add parentheses as shown: (b*b*b*b*b...)* (b*b*b*b*b...)* (b*b*b*b*b...)* ... =(b^m)*(b^m)*(b^m)... n times, or (b^m)^n, the right-hand side. Now, we can use these two identities to define b^k for all rational k. Let k be equal to m/n, where m and n are integers and n is positive. We want to define b^(m/n) such that the above properties still hold, allowing us to conclude that (b^(m/n))^n=b^(mn/n)=b^m. If m is positive, we can define b^(m/n) such that when you multiply it by itself n times, you get the same result as multiplying b by itself m times. If m is zero, and since we want the above properties to still hold, we can define b^0 as b^(1-1) or (b^1)/(b^1)=1. Also, as a bonus, if m=0, m/n also equals zero, so we're done here. If m is negative, and again, since we want the above properties to still hold, we can define b^m as b^(0-(-m)), or (b^0)/(b^(-m))+1/(b^(-m)). In other words, we can define b^(m/n) such that when you multiply it by itself n times, you get the same result as multiplying b by itself -m times, then taking the reciprocal. Now, assuming that we want b^k to be continuous, we can define b^k for all real k. Let k be equal to the limit of k_1, k_2, k_3... where k_n for all n are rational. b^k can then be the limit of b^(k_1), b^(k_2), b^(k_3)... If we set k such that b^k=x, then k would be log(b,x). Now finally, to see how logarithms turn multiplication into addition, consider that b^(log(b,x)+log(b,y))=(b^(log(b,x)))(b^(log(b,y)))=xy. Taking the base b logarithm of both sides gives the following: log(b,x)+log(b,y)=log(b,xy)
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  477. ​ @allylilith5605  What about climate change? I wouldn't say that long- or short-term thinking have a right- or left-leaning bias respectively. Whilst the long-term view may be more right leaning for some issues, it's more left leaning for others Also, regarding your example, according to Sabine's video on gender-transitions, the conservative view seems to be more about weariness to change, which seems consistent with conservative positions on most topics, as opposed to maybe a few. Though, as you state, the leftist desire to change does stem from the idea of not hurting others. Examples include, but aren't limited to the pandemic response, refugee crisis management, climate mitigation, and, of course, the original example of transgender issues. All of these examples demonstrate the leftist view of not harming others. as you say, (at least in the immediate), since the leftist view on pandemic responses is centred on preventing illness, the leftist view on refugee crisis management is on helping the refugees, leftists advocate action on climate mitigation to prevent crises, and leftists, as you state, advocate gender transitions for gender dysphoria, hoping that it's effective in treating the condition, or at least, more effective than for instance, counselling alone. All of these examples also provide evidence of the conservative view being about weariness of change, since the conservative view on pandemic responses is maintaining a sense of normalcy, for fear that action may set precedent for the systematic stripping of freedoms, the conservative view on refugee crisis management is to minimise the change in the makeup of the native population, conservatives advocate for climate inaction for fears of the effects of other electrical sources, as well as (as you state), not providing gender transitions, due to long-term side effects, some known, and some, potential. Furthermore, whilst your example of gender transition seems to provide evidence that the conservative view is "about giving people the best possible outcome, even if the first steps may be unpleasant", since the conservative position on gender transitions is about avoiding long-term side effects for relief that may potentially be short-term, two of the other examples outlined here (pandemic responses and climate mitigation) provide evidence against this notion, since your description of the general conservative perspective better fits with the leftist viewpoint; sacrificing short-term comfort to prevent mass illness (and the deaths that go along with it), and climate disasters, respectively, are examples of long-term thinking. The left leaning viewpoint, is therefore, as you've stated about minimising harm; however, the conservative view is one about general weariness of the potential consequences of change, and these viewpoints are probably independent of short- and long-term thinking, since the left and the right both exhibit short- and long-term thinking depending on the situation, thereby indicating a lack of correlation, either as you suggest, or opposite to what you suggest. An analogy that I've read somewhere is that the political left and right are like the accelerator and the brakes of a car respectively (so reversed compared to the actual positions of the brake and accelerator pedals on a car); you need the accelerator for the car to start moving (or to increase the velocity, and thus, momentum, of the car in general), including to get out of undesirable places (faster, in the case of the car already moving), and the brakes to stop the car from crashing
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  478. ​ @rianczer  Except I'd argue that it isn't perfectly argument, as per the following response: @allylilith5605 What about climate change? I wouldn't say that long- or short-term thinking have a right- or left-leaning bias respectively. Whilst the long-term view may be more right leaning for some issues, it's more left leaning for others Also, regarding your example, according to Sabine's video on gender-transitions, the conservative view seems to be more about weariness to change, which seems consistent with conservative positions on most topics, as opposed to maybe a few. Though, as you state, the leftist desire to change does stem from the idea of not hurting others. Examples include, but aren't limited to the pandemic response, refugee crisis management, climate mitigation, and, of course, the original example of transgender issues. All of these examples demonstrate the leftist view of not harming others. as you say, (at least in the immediate), since the leftist view on pandemic responses is centred on preventing illness, the leftist view on refugee crisis management is on helping the refugees, leftists advocate action on climate mitigation to prevent crises, and leftists, as you state, advocate gender transitions for gender dysphoria, hoping that it's effective in treating the condition, or at least, more effective than for instance, counselling alone. All of these examples also provide evidence of the conservative view being about weariness of change, since the conservative view on pandemic responses is maintaining a sense of normalcy, for fear that action may set precedent for the systematic stripping of freedoms, the conservative view on refugee crisis management is to minimise the change in the makeup of the native population, conservatives advocate for climate inaction for fears of the effects of other electrical sources, as well as (as you state), not providing gender transitions, due to long-term side effects, some known, and some, potential. Furthermore, whilst your example of gender transition seems to provide evidence that the conservative view is "about giving people the best possible outcome, even if the first steps may be unpleasant", since the conservative position on gender transitions is about avoiding long-term side effects for relief that may potentially be short-term, two of the other examples outlined here (pandemic responses and climate mitigation) provide evidence against this notion, since your description of the general conservative perspective better fits with the leftist viewpoint; sacrificing short-term comfort to prevent mass illness (and the deaths that go along with it), and climate disasters, respectively, are examples of long-term thinking. The left leaning viewpoint, is therefore, as you've stated about minimising harm; however, the conservative view is one about general weariness of the potential consequences of change, and these viewpoints are probably independent of short- and long-term thinking, since the left and the right both exhibit short- and long-term thinking depending on the situation, thereby indicating a lack of correlation, either as you suggest, or opposite to what you suggest. An analogy that I've read somewhere is that the political left and right are like the accelerator and the brakes of a car respectively (so reversed compared to the actual positions of the brake and accelerator pedals on a car); you need the accelerator for the car to start moving (or to increase the velocity, and thus, momentum, of the car in general), including to get out of undesirable places (faster, in the case of the car already moving), and the brakes to stop the car from crashing
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  555.  @Homer-pc6oj  "If you visualize infinity, [infinity] goes to a singularity." Does it? It seems to be well-behaved as infinite cardinals and ordinals are used in set theory. "We call [the singularity] the tenth dimension in quantum physics." Even assuming that there is a 'singularity' involved, there are still so many problems with that statement, I don't know where to start. Firstly, mathematical pathologies aren't physical dimensions. The number of dimensions is simply the smallest number of vectors in a space (or space-time in physics) required to represent every point in said space via linear combination, regardless of how tightly curved some directions may be (I'm assuming you're referring to string theory here). Also, even in an at-least-ten-dimensional space, no dimension would be 'tenth'. For simplicity, let's consider the three-dimensional case (and trying to pin down the first, second and third dimension) before moving on to the notion of a tenth dimension in a space that's at least ten dimensional. What is the first dimension in 3d space? How about the second? How about the third? Notice how you can't answer a specific direction for each. If you, for instance define the 'third dimension' as the vertical dimension, you'll disagree with anyone who is neither near you, nor at the antipode of your location, not to mention that there's no real reason for that dimension to be 'third' as opposed to being 'first', 'second' or a linear combination of the 'first', 'second' and or 'third' dimensions. Similarly, if you, for instance, define the 'second dimension' as north, you'll disagree with anyone not on your latitude (and also anyone not on your longitude, provided you're not on the equator), as well as running into the arbitrariness of calling it 'second'). If it's not possible to pin down a 'first' 'second' and 'third' dimensional space, why on earth would you think that it's possible to pick out a 'tenth' dimension in a space with at least ten dimensions? To summarize, there are no singularities involved here, and even if there were, they a) aren't physical dimensions, and b) there is no 'tenth dimension' even in spaces with at least ten dimensions
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  748.  @AwesomePlaylists888  Do you have any evidence for the notion that your sky daddy's son, who is also sky daddy, somehow, spoke celestial objects into existence and set them in motion? Oh, wait. I forgot that blind faith is a virtue to you. You're going to cite the Bible, to which I ask for proof that it's a credible source, and you'll just state that I just have to have faith in it (i.e., believe it without questioning). Sure! Besides, your god isn't very moral, as evidenced by the following scenario posed in your holy book: An omniscient god sets up a paradise, including Adam, Eve, a tree of knowledge with forbidden fruit, and a talking snake. God tells Adam and Eve to not eat the fruit, and the talking snake he set up tells them to eat the fruit. They oblige with the snake, eat the fruit, and now, all their descendants are destined to die, the females must suffer a really painful childbirth, with many experiencing premenstrual syndrome every month outside of that, as punishment for eating the fruit. When Adam and Eve ate the fruit, they had no sense of right and wrong (as that came from the forbidden fruit), and so had no idea that they were supposed to follow your god and not the snake he set up. Also, your god would have known that this would be the result due to his omniscience. He deliberately set up the scenario, which is a trap, for they didn't know any better, and he, being omniscient, knew that they didn't know any better. Then, if that wasn't bad enough, he then punished every future innocent person, who did not, and will not eat the fruit, to certain death and half of them to some of the most painful childbirths in the animal kingdom. Even if your holy book is right, your god is a piece of $h!t, and isn't worth worshipping and giving up a seventh of your life for. And if it's wrong (which is the stance I take), then it's not worth worshipping and giving up a seventh of your life for a fictional character. So, either way, your god is not worth worshipping, at all, and you can stop trying to convert me. Bye!
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  844.  @MuffinsAPlenty  These problems can be resolved: Motivation: Take the set of natural numbers and put it on the number line. There are gaps everywhere, leaving practically the entire number line unaccounted for. It seems natural to repeatedly halve intervals to fill in the gaps. The gap issue seems solved. However, take the sequence: 1/4, 1/4+1/16, 1/4+1/16+1/64... This sequence clearly has an upper bound: 1/2 (all successive halvings are done to the left of the first halving of the unit interval), yet it's not a number accounted for. Thus, we could 'fill in' these gaps: {-2,-4,-6,-8...} (the number is to the right of the second, fourth, sixth, etc. halving, but not the first, fourth, fifth, etc.) Set restrictions: Yes, it's clear that the sets must have an upper bound. {1,2,3...} for instance makes no sense: the numbers seem to be unbounded. However, if you replace the upper bound rule with a lower bound rule, you get the 2-adic numbers. Equivalence classes: All sets where there's an absent integer with all lower integers present mean the same thing as another set where all the lower integers are replaced with the absent one. This doesn't seem to be an issue either. The motivation for this equivalence relation is that if you took the unit interval and subdivide the right-hand side every time, you'll just get one. Negative numbers: You didn't point this out, but the current system is not a field; we need more numbers. One solution is to switch to negabinary. However, that makes equivalence classes more complicated. Another solution is to re-introduce some of those pathological sets. The complement of the set of all integers and a non-pathological set behaves like its negative and the set of all integers behaves like 0, the empty set. To see this, adding 1 to '...111111.111111...' gives '0.111111...', or 1. However, this solution requires another condition, that the integers and the empty set mean the same and an exception to the set restrictions: that it doesn't apply if there's an integer such that all integers above that are represented. A third solution is to denote the negative of a set as {[empty set], A}, which is I think is the most intuitive solution. However, a new set of operators is required to define interaction with negative sets, like subtracting a positive set
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