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ydoaPs last won the day on September 9 2019

ydoaPs had the most liked content!

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About ydoaPs

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    The Oncoming Storm
  • Birthday 04/21/1988

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    Local Group
  • College Major/Degree
    BA in Philosophy, pursuing MA in History and Philosophy of Physics
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    Former Nuclear Mechanic; Current Philosopher

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  1. The Muller Two Step was a prediction of evolution before Behe was even born, let alone before he decided it was somehow a problem for evolution.
  2. And that's not even counting all of the other forms of sameness like adjoint situations. There's so many different forms of "eh, that's sort of the same as this other thing in certain ways".
  3. What LaTeX packages can we use in blogs? If the one we need (say, for commutative diagrams) isn't installed, is there a way to get it installed?
  4. If I'm understanding you correctly, I think you're using different terminology. It might be a geographic thing. As far as I learned, an Equivalence Relation has the properties you detailed in your post, and, by the process I discussed, partitions a set into Equivalence Classes resulting in the quotient set (or monoid or group or category etc). I'm not sure what there is to gain by using "equivalence" only in terms of equivalence classes rather than for either equivalence relations and equivalence classes. If we had to pick, I'd probably make the relation "Equivalence", but that's probably just the categorial bias I have.
  5. Jesus also got mad when a fig tree didn't produce figs when it was not fig season.
  6. That's a great post. Yeah, equivalence relations are much looser than identity. Any bivalent relation will give you an equivalence relation. You can actually even define an equivalence relation out of any function. Take a function f, and you can define the equivalence relation ~ such that a~b iff f(a)~f(b). This is part of a process of decomposing a function. If the domain (what the function is taking as an argument) is A, and the the codomain (what the function points to) is B, then you can decompose a function via ~ in the following way. Make a function f* that takes A and maps each element to the set of other elements of A that it is equivalent to under ~. So, an a in A maps under f* to all of the other a's that map to the same thing under f. For example, take the rule for f to be f(x) = x2. f*, then, will map 1 to {-1, 1}, 2 to {-2, 2}, 3 to {-3, 3} etc, because -1 and 1 both go to the same place under f. We typically write the codomain of f* as A/~. You can then go from A/~ to what is called the "image" of f. And that's just the collection of things in B that actually get pointed to from things in A by f. Often you'll see this just imf. So we have A -> A/~ -> imf. But there's something neat here. Since we have in essence collapsed A into things that don't map to the same thing in imf and all of the things in imf get mapped to, this function is reversible. So we have A -> A/~ <-> imf. Since it goes back and forth like that (assuming the function is structure preserving), A/~ and imf are isomorphic. That's a big word for "for all current intents and purposes, they're the same structurally". A nice fact about isomorphisms is that they are all equivalence relations. We can go further into canonical decomposition and go from imf to B, but, for our purposes, we've gotten what we need for this discussion. Any function gives us two different equivalence relations. So in our example of f(x) = x2 from the Real numbers to the Real numbers, we get the Real numbers being equivalent to sets of Real numbers that have the same absolute value. Those clearly aren't the same thing, in terms of identity. We also get this set of sets of numbers with the same absolute value being equivalent to the set of the squares of the absolute values of the previously mentioned set. Clearly sets containing things like {-2, 2} and sets containing things like 4 aren't identical, but they are equivalent. Any nice back and forth will satisfy the axioms for the equivalence relation. Identity, on the other hand, has extra cool stuff like substitution. Identity is much stronger than equivalence.
  7. How many coin flips does it take to make a free choice?
  8. You'll need to define a function; do you know how? You'll need to take an input from the user; Do you know how? You'll need to make sure the data type of the input is a certain type; do you know what type that is and how to check that the input is that type? Then you'll need to perform the calculation and print the result; Do you know how? Give it a shot, and if you can't figure out how to do any of the above steps, let us know. We won't do your homework for you, but we'll help you figure it out.
  9. That's kind of the definition of UFO.
  10. You could map the wavelengths of visible light to [0,1], map [0,1] to some continuous subset of your time variable, then do a graph for different colors (points in time) for any "granularity" of colors (moments) that you'd like.
  11. Throwing a ball up has it start with a velocity v coming out of your hand. There is no force causing it to accelerate upward, but there is a force causing it to accelerate downward: gravity. So, from v, the velocity slows with the acceleration due to gravity until it stops. But, then, it starts going down, still accelerating due to gravity. This trajectory is symmetric about the point at the top where the velocity is zero. So, for any other point, there is a partner where the ball has the same speed. But for each speed, the ball has that velocity for 0 seconds. There must be a time or two that the ball is at each speed, but it is at each speed for no time at all. Indeed, speed, not velocity. You've earned yet another cookie for catching my mistakes.
  12. For any velocity the ball has along its trajectory, it has it for precisely 0 seconds, and for all but v_y = 0, it has said velocity twice for 0 seconds.
  13. Precisely 0. There must be a time where v_y=0, but the amount of time v_y=0 is precisely 0. This is honestly very unintuitive for a lot of people (Iirc, this might explicitly be a motivating example in the intro to Frames and Locales). Tbh, this is a big part of why I'm not a fan of pointy space. Localic space ftw.
  14. ! Moderator Note Topic moved to General Philosophy
  15. ! Moderator Note Topic moved to General Philosophy
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