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Randomness thread, part two.

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  1. #13276
    bigred's Avatar
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    Guys. I'm really struggling with life. I'm at a bar on Tuesday night in Austin, elephant room. Blues are all around.
  2. #13277
    Quote Originally Posted by bigred View Post
    Guys. I'm really struggling with life. I'm at a bar on Tuesday night in Austin, elephant room. Blues are all around.
    How long have you felt this way?
  3. #13278
    bigred's Avatar
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    GUYS.

    Name a song that better sums up our generation than Everlong. I fucking dare you.
    LOL OPERATIONS
  4. #13279
    bigred's Avatar
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    AND IF YOU CHOOSE CHUMBA WUMBA I SWEAR TO GOD I WILL STRIKE YOU DOWN WILL ALL OF MY VENGEANCE
    LOL OPERATIONS
  5. #13280
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    Quote Originally Posted by bigred View Post
    GUYS.

    Name a song that better sums up our generation than Everlong. I fucking dare you.
    bittersweet symphony?

    ?wut
  6. #13281
    bigred's Avatar
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    Quote Originally Posted by bikes View Post
    bittersweet symphony?
    True. But let me clarify. A song we want to represent our generation!
    LOL OPERATIONS
  7. #13282
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    CAUSE BRO, SONG 2 IS UP THERE THEN
    LOL OPERATIONS
  8. #13283
    bigred's Avatar
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    bikes, get in irc so we walk talk RAWK
    LOL OPERATIONS
  9. #13284
    bigred's Avatar
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    New thread since shit ain't so random: http://www.flopturnriver.com/pokerfo...27#post2193427
    LOL OPERATIONS
  10. #13285
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    Quote Originally Posted by bigred View Post
    GUYS.

    Name a song that better sums up our generation than Everlong. I fucking dare you.
    46 and 2

    or

    Whip It

    Can we use Whip It again? If it's an option, it's always a winner. It's motivational and 'tarded at the same time... that's our generation.
  11. #13286
    Quote Originally Posted by bigred View Post
    GUYS.

    Name a song that better sums up our generation than Everlong. I fucking dare you.
  12. #13287
    bigred's Avatar
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    omg, shut up you guys
    LOL OPERATIONS
  13. #13288
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    Quote Originally Posted by bigred View Post
    GUYS.

    Name a song that better sums up our generation than Everlong. I fucking dare you.

    Too easy.


    The strengh of a hero is defined by the weakness of his villains.
  14. #13289
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    X = 1-1+1-1+1...

    X = 1-1+1-1+1...
    +X = 1-1+1-1....
    --- ------------
    2*X = 1+0+0+0+0... = 1

    X = 1-1+1-1+1... = 1/2

    Y = 1-2+3-4+5...

    Y = 1-2+3-4+5...
    +Y = 1-2+3-4...
    --- -------------
    2*Y = 1-1+1-1+1... = X = 1/2

    Y = 1-2+3-4+5... = 1/4

    Z = 1+2+3+4+5...

    Z = 1+2+3+4+5...
    -Y = -1+2-3+4-5...
    --- -------------
    Z-Y = 0+4+0+8+0... = 4+8+12+16+20... = 4*(1+2+3+4+5...) = 4*Z

    Z-Y = Z - (1/4) = 4*Z

    3*Z = -1/4

    Z = 1+2+3+4+5... = -1/12

    Don't forget to mop up your brains from the floor.
  15. #13290
    Or stop reading after the fourth line because the mistake is obvious.
  16. #13291
    a500lbgorilla's Avatar
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    Do go on.
  17. #13292
    Quote Originally Posted by a500lbgorilla View Post
    X = 1-1+1-1+1...

    X = 1-1+1-1+1...
    +X = 1-1+1-1....
    --- ------------
    2*X = 1+0+0+0+0... = 1

    X = 1-1+1-1+1... = 1/2

    Y = 1-2+3-4+5...

    Y = 1-2+3-4+5...
    +Y = 1-2+3-4...
    --- -------------
    2*Y = 1-1+1-1+1... = X = 1/2

    Y = 1-2+3-4+5... = 1/4

    Z = 1+2+3+4+5...

    Z = 1+2+3+4+5...
    -Y = -1+2-3+4-5...
    --- -------------
    Z-Y = 0+4+0+8+0... = 4+8+12+16+20... = 4*(1+2+3+4+5...) = 4*Z

    Z-Y = Z - (1/4) = 4*Z

    3*Z = -1/4

    Z = 1+2+3+4+5... = -1/12

    Don't forget to mop up your brains from the floor.
    Yeah, it seems like weird voodoo but apparently there are proofs of this, and it's used in string theory and whatnot.
    https://www.youtube.com/watch?v=w-I6...e_gdata_player
  18. #13293
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    Strange, but true. The sum of all the positive integers is -1/12. There are multiple ways to prove it. Some of them are weaker than others, but the funny thing is that they all agree.

    It doesn't make sense unless you really accept that infinity is beyond your direct comprehension.

    If the fastest computer ever to exist were created now, and set to count 1,2,3,... from now until the end of time... (assuming enough memory to hold any size number) ... that would still be the equivalent of counting to 3 in terms of infinity. There is always an infinite amount of numbers left to count.

    Only when you apply mathematics that can deal with this problem can you actually find solutions. The math is counter-intuitive.. well, the results are, at least... but it works.
  19. #13294
    Quote Originally Posted by a500lbgorilla View Post
    Do go on.
    What you've written makes no sense really. Whether it's correct or not, which apparently it is unless google is trolling me, is besides the point.

    I'd also be tempted to call bullshit on most things people do with respect to infinity because it's so easy just to simplify the problem so much that you can make it look like there are no obvious issues when mathematically you can't do what you're doing for some very valid, but non apparent, reason.
  20. #13295
    The answer is obviously 42.
    Some days it feels like I've been standing forever, waiting for the bank teller to return so I can cash in all these Sklansky Bucks.
  21. #13296
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    This makes me hate math.
    I'm the king of bongo, baby I'm the king of bongo bong.
  22. #13297
    this semi reminds me of a book i read in 9th grade, it was about the history of zero.. so there was a bunch of theoretical math in there and there was some fun stuff in the back, including a mathematical proof showing that winston churchill is a carrot. the sad irony of my existence is that i was always genuinely fascinated by math and science (hence me picking up books about zero and reading stephen hawking), but i'm just pitifully, woefully, lamentably, tragically bad at it.
    Free your mind and your ass will follow.
  23. #13298
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    Also, I don't see how 2X=1. Surely it could just as likely equal zero? I mean the way you demonstrate it equalling 1 is pretty much by just adding 1 to the original X. Surely if we slide the 2nd X along for easy math that starts with 1 rather than zero, shouldn't there be a -1 bolted onto the end of it too?
    I'm the king of bongo, baby I'm the king of bongo bong.
  24. #13299
    Quote Originally Posted by rong View Post
    Also, I don't see how 2X=1. Surely it could just as likely equal zero? I mean the way you demonstrate it equalling 1 is pretty much by just adding 1 to the original X. Surely if we slide the 2nd X along for easy math that starts with 1 rather than zero, shouldn't there be a -1 bolted onto the end of it too?
    It's not a proof of any sort so following it is essentially pointless. But no because it goes on forever so you can't think of it as being finite. Everytime you want to try and condense it into a finite thing, essentially what you are doing by saying they should be consistent in length, it can all break down.
    Last edited by Savy; 02-12-2014 at 06:02 PM.
  25. #13300
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    Quote Originally Posted by rong View Post
    Also, I don't see how 2X=1. Surely it could just as likely equal zero? I mean the way you demonstrate it equalling 1 is pretty much by just adding 1 to the original X. Surely if we slide the 2nd X along for easy math that starts with 1 rather than zero, shouldn't there be a -1 bolted onto the end of it too?

    I actually really like the first one. A buddy asked me about a light switch where after 30 seconds it would flip, then 15 later, then 7.5 later, then 3.75 later... etc will it be on or off at 60 seconds. After accepting that the switch could handle infinite rate of switching and the signal had no delay to the light, I guessed that the impossible combination of on and off would give it a half current. He said that's what mathematicians preferred and hit me with that first proof.

    The math of it works out because there's an infinity of elements in the series. For every next +1 in one series there is a -1 in the partner, no exceptions. It makes some sense to me as if it were the 'superposition' of the two possible results 0 and 1. It's also cool because you can indent the second series as much as you want and you either get 2X = 2-2+2... or 1+0+0....

    The second one I'm a bit iffy on.
  26. #13301
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    Quote Originally Posted by aubreymcfate View Post
    this semi reminds me of a book i read in 9th grade, it was about the history of zero.. so there was a bunch of theoretical math in there and there was some fun stuff in the back, including a mathematical proof showing that winston churchill is a carrot. the sad irony of my existence is that i was always genuinely fascinated by math and science (hence me picking up books about zero and reading stephen hawking), but i'm just pitifully, woefully, lamentably, tragically bad at it.
    Only bad until you're not so bad. Not that it's worth getting into, mind you. Just that math is not a super power.
  27. #13302
    Quote Originally Posted by a500lbgorilla View Post
    Only bad until you're not so bad. Not that it's worth getting into, mind you. Just that math is not a super power.
    You're right. I lived a self-fulfilling prophecy when it came to things like that. One of my biggest regrets is not thinking more of myself when it came to athletics and the maths and sciences. I could've been good, I just needed to work really hard, and I didn't want to do that. I found literature and music more enjoyable, and they came more easily to me, so that was my comfort zone. And I was a self-congratulating slacker.

    Then again I'm 24 so they don't really need to be "big regrets."

    I've entertained the notion before of having some kind of mathematical side project, slowly working myself up to calculus over a period of years, lol. I dunno.
    Free your mind and your ass will follow.
  28. #13303
  29. #13304
    MadMojoMonkey's Avatar
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    Saying something is valid, or important, or "correct" because it's used by string theorists is glorifying string theory into something useful, which it's not (yet... but it's been decades with no results). Also, the brilliant people who've dedicated their careers to string theory are not infallible.

    Nonetheless, these counter-intuitive results are confirmed from multiple approaches, so there's no need to invoke the magic of string theory.
  30. #13305
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    Quote Originally Posted by aubreymcfate View Post
    I've entertained the notion before of having some kind of mathematical side project, slowly working myself up to calculus over a period of years, lol. I dunno.
    Calculus could be taught to 8 year olds. It's really not hard. It's just one step past arithmetic. Sure, there's algebra, but that's not strictly needed for calculus. So... if you can understand the basic concepts of algebra, then you can understand the basic concepts of calculus.

    Here's calculus:

    There's some bowl, with a very funny shape, and we want to determine the volume. Unfortunately, we can't use liquids, only solid blocks. If we use a small number of large blocks, we count the blocks and multiply by the known volume of each block. As we use smaller and smaller blocks, we can fit more and more of them in the bowl. As we fit more and more of them in the bowl, we more adequately fill in the little funny nooks and crannies in the bowl's shape. If we could use smaller and smaller blocks, without restraint, then we could ultimately know the volume of the bowl exactly.

    That's calculus. Finding the volume (or area or ...) if you could measure only with crude shapes. The advantage of the crude shapes is that they have a volume (or area ...) which is known exactly. The disadvantage is that they don't fit well. To overcome the disadvantage, we assume that we can make the blocks "infinitely small".
    calculus

    "calculus" means "stone" and literally means the counting of stones, as in the counting of tiny stones to fill a building.
  31. #13306
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    Something that I was going to post anyway but that happens to follow science/math posts (even randomness should appear to have order, sometimes)

    Are perpetual motions machines possible in a universe with different physical laws than our own?
  32. #13307
    Quote Originally Posted by Lukie View Post
    Something that I was going to post anyway but that happens to follow science/math posts (even randomness should appear to have order, sometimes)

    Are perpetual motions machines possible in a universe with different physical laws than our own?

    If baseball were rugby, could the the fire department win the space race?
  33. #13308
    Quote Originally Posted by boost View Post
    If baseball were rugby, could the the fire department win the space race?
    Excelsior!
  34. #13309
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    Quote Originally Posted by boost View Post
    If baseball were rugby, could the the fire department win the space race?
    Technically, if baseball were rugby then the fire department already won the space race.
  35. #13310
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    Quote Originally Posted by boost View Post
    If baseball were rugby, could the the fire department win the space race?
    nes, yo, maybe ho
  36. #13311
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    Quote Originally Posted by Lukie View Post
    Something that I was going to post anyway but that happens to follow science/math posts (even randomness should appear to have order, sometimes)

    Are perpetual motions machines possible in a universe with different physical laws than our own?
    Quote Originally Posted by boost View Post
    If baseball were rugby, could the the fire department win the space race?
    I guess that says it all without actually saying it.

    As long as you're throwing out physical law as we know it, then anything's possible.

    It's the conservation laws that trip this up in our universe. Entropy doesn't really help, but from a QM point of view, entropy doesn't exist. As long as mass-energy can neither be created nor destroyed, then a device that produces energy (or mass) output with no energy (or mass) input can not run forever.

    There must be a fuel that burns. The energy you wish to extract from the machine must come from somewhere. It can not be created by the machine.
  37. #13312
    Lukie's Avatar
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    I know that the bit about the energy having to come from somewhere. There was more implied in the question itself though. It seems to be a more growing consensus that there is more than one universe (correct me if I'm wrong) and perhaps the more pressing implication of that is that should those universes have the same physical laws as our own? Do they have to? Why or why not? What would the universe be like if light traveled at 1 mile per hour and all that affects?
  38. #13313
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  39. #13314
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    Quote Originally Posted by Lukie View Post
    I know that the bit about the energy having to come from somewhere. There was more implied in the question itself though. It seems to be a more growing consensus that there is more than one universe (correct me if I'm wrong) and perhaps the more pressing implication of that is that should those universes have the same physical laws as our own? Do they have to? Why or why not? What would the universe be like if light traveled at 1 mile per hour and all that affects?
    It seems to me that either these "other universes" can be observed, and the physical laws that hold there are the physical laws that hold here... OR they cannot be observed and there is no intelligent prediction to be made about the nature of physical laws there.

    In the first case, even if it were discovered that something contradictory with our current theory was going on, then the theory would be amended to include the new observations. Anything which can be observed is under the purview of physical law, if a physical law is shown to be incorrect, then it is discarded from the canon of law.

    By this hand-waving, I declare that any universe we will encounter will share the same physical laws are this universe we know today.

    EDIT: accepting that our current understanding of the laws may be laughably foolish and mostly wrong.
  40. #13315
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    Quote Originally Posted by rong View Post
    Probably because clean equations are just easier. You'll get your ire up chewing through an unnecessarily unintelligible one.
  41. #13316
    Is the universe a perpetual motion machine?
  42. #13317
    rong's Avatar
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    It's a marble.
    I'm the king of bongo, baby I'm the king of bongo bong.
  43. #13318
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    Quote Originally Posted by MadMojoMonkey View Post
    It seems to me that either these "other universes" can be observed, and the physical laws that hold there are the physical laws that hold here... OR they cannot be observed and there is no intelligent prediction to be made about the nature of physical laws there.

    In the first case, even if it were discovered that something contradictory with our current theory was going on, then the theory would be amended to include the new observations. Anything which can be observed is under the purview of physical law, if a physical law is shown to be incorrect, then it is discarded from the canon of law.

    By this hand-waving, I declare that any universe we will encounter will share the same physical laws are this universe we know today.

    EDIT: accepting that our current understanding of the laws may be laughably foolish and mostly wrong.
    This seems like as good of an explanation as any.
  44. #13319
    I feel very snarky and old today. All i want to do is get d0zer on skype and berate him for playing digital card games.
    So you click their picture and then you get their money?
  45. #13320
    lol wife's in bed soon bud! go download hearthstone while yer waiting!
  46. #13321
    Quote Originally Posted by d0zer View Post
    lol wife's in bed soon bud! go download hearthstone while yer waiting!
    you know what that means. it time fo some BATTLE SEX.
  47. #13322
    or wait maybe i'm confusing that with something else. the girl is conscious during battle sex, right? isn't there another one where she's unconscious and the goal is to try and finish before she awakes?
  48. #13323
    im pretty goddamn sure any time dozer has sex there's a battle going on
  49. #13324
    even if only in my mind, yes
  50. #13325
    rong's Avatar
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    Fuck! I forgot Valentine's day. Not going down well.
    I'm the king of bongo, baby I'm the king of bongo bong.
  51. #13326
    Quote Originally Posted by rong View Post
    Fuck! I forgot Valentine's day. Not going down well.
    Ouch

    I was in Tesco last night and they had basically made a huge display right at the front of the store for wine, flowers, chocolates. Loads of half panicked guys milling around it lol
    Congratulations, you've won your dick's weight in sweets! Decode the message in the above post to find out how to claim your tic-tac
  52. #13327
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    I figure at least I can get stuff for half price today.
    I'm the king of bongo, baby I'm the king of bongo bong.
  53. #13328
    Quote Originally Posted by rong View Post
    I figure at least I can get stuff for half price today.
    False economy, you have to buy more because you forgot
    Congratulations, you've won your dick's weight in sweets! Decode the message in the above post to find out how to claim your tic-tac
  54. #13329
    http://www.treehugger.com/culture/wh...tines-day.html

    "If you thought slavery had ended, think again. In Côte d’Ivoire and Ghana, children are often kidnapped from neighbouring Mali and Burkina Faso in order to provide slave labour on cocoa plantations. In Bitter Chocolate, journalist Carol Off describes the conditions in which these child slaves work:

    “The farmers were working the young people almost to death. The boys had little to eat, slept in bunkhouses that were locked during the night, and were frequently beaten. They had horrible sores on their backs and shoulders… Farmers were paying organized groups of smugglers to deliver the children to their cocoa groves, while police were being bribed to look the other way.”

    These children are responsible for climbing cocoa trees, cutting down bean pods, and chopping them open with machetes, which leads to inevitable accidents. They are exposed to hazardous pesticides that they spray without protective equipment. They are fed corn paste and bananas, the cheapest food available, and they’re not paid.

    When one former child slave was asked what he’d stay to chocolate-eating Westerners, he answered, “When people eat chocolate, they are eating my flesh.”"
    Free your mind and your ass will follow.
  55. #13330
    Quote Originally Posted by aubreymcfate View Post
    When one former child slave was asked what he’d stay to chocolate-eating Westerners, he answered, “When people eat chocolate, they are eating my flesh.”"
    This will not stop me eating chocolate. Sorry.
    Congratulations, you've won your dick's weight in sweets! Decode the message in the above post to find out how to claim your tic-tac
  56. #13331
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    Quote Originally Posted by Luco View Post
    False economy, you have to buy more because you forgot
    The £25 of chocolate I just bought tells me you're right.
    I'm the king of bongo, baby I'm the king of bongo bong.
  57. #13332
    Quote Originally Posted by Luco View Post
    This will not stop me eating chocolate. Sorry.
    Not all chocolate. You can buy fair trade chocolate. Might be a bit pricier but I think it's worth it, if it's within your means.
    Free your mind and your ass will follow.
  58. #13333
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    Quote Originally Posted by rong View Post
    Fuck! I forgot Valentine's day. Not going down well.
    You have already solved your own problem. Go down well, and the day will be saved.

    btw, I worked in a large grocery store many moons ago, and one of my favourite annual events was the flocking to the greeting card aisle on the morning of Feb. 14 every year. The crowd was obviously 98% male.


    Quote Originally Posted by sauce123
    I don't get why you insist on stacking off with like jack high all the time.
  59. #13334
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    I think the 25 quid of chocolate saved it all by itself.
    I'm the king of bongo, baby I'm the king of bongo bong.
  60. #13335
    Galapogos yet again proves why he is the king
  61. #13336
    Quote Originally Posted by Galapogos View Post
    You have already solved your own problem. Go down well, and the day will be saved.

    btw, I worked in a large grocery store many moons ago, and one of my favourite annual events was the flocking to the greeting card aisle on the morning of Feb. 14 every year. The crowd was obviously 98% male.
    I got mine wine and chocolate and she got me wine and chocolate.
    Congratulations, you've won your dick's weight in sweets! Decode the message in the above post to find out how to claim your tic-tac
  62. #13337
    Quote Originally Posted by Lukie View Post
    This seems like as good of an explanation as any.
    Yeah, it's fun thinking about this stuff-- like if the physical laws were only slightly altered, it's easy to imagine how insanely different the universe would be. As a parallel, look at predictions of what alien life might look like on planets with different atmospheres, levels of gravity, etc. Or you can take the guess work out of it and look at animals which are at home in the extreme deep sea. Changing the physical laws in the slightest would surely have a butterfly effect.
  63. #13338
    Lukie's Avatar
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    ^ agreed

    I just made a ham bone and navy bean soup. Ham bone came from a precooked 9-10 lb ham I had a while back which I baked in the oven, mangled it in all sorts of different ways (i.e. attempted to cut it up), and froze a fairly meaty ham bone for a while in the fridge.

    Today I added to my crock pot: Said ham bone, a diced onion, a few diced carrots, a few diced celery stalks, navy beans (1lb. dry that soaked in water overnight), a small amount of sea salt, parsley flakes, garlic powder (I forgot to add the real stuff in the beginning, so I put this in a little later), and several cups of water.

    It cooked on low for 8 hours or so, I took the bone out, put whatever was left of the good meat back in, pureed a few cups of the soup in the blender, and poured it back into the crock pot.

    It is really good.
  64. #13339
    Sounds awesome. Only suggestion would be: in the future don't salt legumes until they are done cooking. Depending on the bean it can make a huge difference in texture.
  65. #13340
    MadMojoMonkey's Avatar
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    Just watched "House of Cards" Season 2 Ep 1.

    Def. a good episode. Loved the last seconds.
  66. #13341
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    Quote Originally Posted by boost View Post
    Sounds awesome. Only suggestion would be: in the future don't salt legumes until they are done cooking. Depending on the bean it can make a huge difference in texture.
    How does that affect the texture of the beans? Mostly in general but also for this recipe, considering there will be a good amount of sodium because of the ham/ham bone anyway. I didn't put much extra salt in for that reason.

    But yeah it turned out really well, I just had a bowl and am kind of blown away by how flavorful it is.
  67. #13342
    Quote Originally Posted by boost View Post
    Sounds awesome. Only suggestion would be: in the future don't salt legumes until they are done cooking. Depending on the bean it can make a huge difference in texture.
    gordon ramsey told me not to salt my scrambled eggs until they're done cooking. But meats you salt before searing, so what's the theory there? Are there any generalizations about salting foods before/during/after cooking?
  68. #13343
    Yeah, beans are great man! Like potatoes, they are a really nutrient dense food, and are cheap cheap cheap.

    I can't explain the exact chemistry behind the early salting on legumes have undesired effects, but I know it's true. It seems to vary by bean, but it can make them never get fully tender, and/or make them split and shed their husks, leaving a pot of empty skins and mush. The latter isn't a problem if you're planning to puree anyways, I guess, but the former can ruin a whole pot a beans.
  69. #13344
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    Interesting, I have read stuff to that effect before. Just to be clear, I only pureed a small portion of the soup (perhaps a quarter of it), but the beans that remained still had what seemed like perfectly good texture.
  70. #13345
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    I don't know the chemistry, but I think the general advice is to add the salt last, because a tiny amount of salt right on your tongue is equivalent in intensity to a much higher amount of salt dissolved into the dish.

    I'm not convinced that salt is bad for you, but if you have a reason to limit salt, then leaving it out until the end significantly reduces the amount you use, while giving the same flavor.
  71. #13346
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    Generally the advice is to add salt early in the cooking process, as it helps to intensify and develop other flavors. Maybe Boost can comment more on that.

    Also people have their own preconceived notions and like to label various nutrients as good or bad, salt is one that often gets labeled as bad, but it is a lot more complicated than that.

    Might be relevant (I say might because I only read a few paragraphs and got too damn bored): http://www.ncbi.nlm.nih.gov/books/NBK50958/
  72. #13347
    Quote Originally Posted by a500lbgorilla View Post
    X = 1-1+1-1+1...

    X = 1-1+1-1+1...
    +X = 1-1+1-1....
    --- ------------
    2*X = 1+0+0+0+0... = 1

    X = 1-1+1-1+1... = 1/2

    Y = 1-2+3-4+5...

    Y = 1-2+3-4+5...
    +Y = 1-2+3-4...
    --- -------------
    2*Y = 1-1+1-1+1... = X = 1/2

    Y = 1-2+3-4+5... = 1/4

    Z = 1+2+3+4+5...

    Z = 1+2+3+4+5...
    -Y = -1+2-3+4-5...
    --- -------------
    Z-Y = 0+4+0+8+0... = 4+8+12+16+20... = 4*(1+2+3+4+5...) = 4*Z

    Z-Y = Z - (1/4) = 4*Z

    3*Z = -1/4

    Z = 1+2+3+4+5... = -1/12

    Don't forget to mop up your brains from the floor.
    So then we can also do this:

    X = 10 - 10 + 10 - 10 + ..
    + X = +10 - 10 + 10 - ..
    2X = 10
    X=5

    or X = any number you want.
  73. #13348
    Which is consistent with the idea?
  74. #13349
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    Quote Originally Posted by jackvance View Post
    So then we can also do this:

    X = 10 - 10 + 10 - 10 + ..
    + X = +10 - 10 + 10 - ..
    2X = 10
    X=5

    or X = any number you want.
    Yes, that means you get it... as long as you recognize that this

    1 - 1 + 1 - 1 + ....

    is totally different than this

    10 - 10 + 10 - 10 + ...

    and is also quite different than this

    1 - 1 + 0 + 1 - 1 + 0 + ...

    Adding a finite number of zeros doesn't change the sum, but adding an infinite number of zeros in a recurring way changes the sum of the infinite series.
  75. #13350
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    Last night I tried out those sticky strips that you put on your nose to open up your airways as you sleep.

    It was amazing!

    I didn't realise I had issues breathing through my nose when I was laying down until I heard someone else speak about it, but apparently it's really common to have things like one nostril shutting off when you lay on your side and various other little things that effect your breathing and htese strips solve those issues. It's a noticeable difference in how I breath and I have a much better nights sleep.

    Not that sexy though.
    I'm the king of bongo, baby I'm the king of bongo bong.

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