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Cake day: June 27th, 2023

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  • Carnelian@lemmy.worldtoLemmy Shitpost@lemmy.worldRAMANUJAN SPECIAL
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    12 days ago

    Sadly the sum of all natural numbers is not actually -1/12. It’s a divergent sum. You could call it infinity.

    There’s a little parlor trick that maths teachers like to perform where they do algebraic manipulation on a simple formula, eventually cancelling out the variables and arriving at some absurd statement like 1=2. The game is for the students to figure out what went wrong.

    The trick is always that at some point, snuck into the progression, you ended up dividing something by “(X-X)” before moving on, seemingly without violating any algebraic rules. Very astute students (or ones who were warned by students from earlier classes haha) will notice that right at that point in time, you are in fact attempting to divide by zero, which is not possible.

    So the reason you ended up with 1=2 is because you applied rules to something which they definitionally cannot apply to. At that point, the equation became undefined.

    …the funny thing though, is you were able to just…continue. And get something to come out. Now, in this case, that thing was utter nonsense. An amusement for children to help teach them of various pitfalls they might fall into when playing with numbers.

    But what if you were one of the most brilliant mathematicians who ever lived, and you were concerning yourself with questions such as,

    “What would happen if I took [1 + 2 + 3 + 4+ 5….], and subtracted [1 + 1/2 + 1/3 + 1/4 + 1/5…]”

    Now, those are both divergent sums. So we could just call them both infinity. But the second infinity just kind of…feels smaller, doesn’t it? It feels like you should be able to just…perform some type of operation and get…something to come out.

    It wouldn’t be “correct” to do so, but this is basically what Ramanujan did. Illegal math. With a nonsense output of negative -1/12.

    The funny thing though is that this “nonsense output” is actually now a cornerstone of quantum mechanics. It turns out we subtract diverging infinites from each other literally all the time, even just by walking around, and that pesky little -1/12 trick has proven to be consistently useful. Astonishing.

    He died a preventable death at 32. Imagine what the world might have looked like today if only he could have dreamed a little longer, asked more impossible questions, and broken more rules. Specifically he died after a bout of dysentery, in case anyone is confused why they’re reading all this in the shit posting community


  • Just to save the next person the trouble,

    It was introduced in 2009. Inflation calculator says that $0.89 in 2009 is the equivalent of…$1.34 in today’s money.

    Wow.

    I’d be curious to see the whole price history but yeah. Can’t believe how bad a deal all the fast food places have become

    Edit: regarding price history, another commenter said it raised to 2.99 after only a couple of years. So 2011 to 2026 inflation calc results in $4.48. A second user said beef in particular is ahead of general inflation, so this might not be too bad of an example after all


  • As the other commenter said, biking is cardio. It has many overlapping benefits with heavy circles (resistance training), but they each have some unique benefits and they grant you those benefits through different biological mechanisms. So doing one or the other is very good, and doing both is extremely good.

    American heart association has a very good breakdown of the benefits of cardio. They recommend 150 minutes per week of moderate intensity cardio (biking slower than 10mph/16kph) or 75min per week of intense cardio (faster than 10mph) to fully cash in on those benefits.

    On a personal note: before “taking the plunge” with any form of exercise, most people experience the same form of “temporal sticker shock” that you’ve expressed concern with. The “need to reserve time” for it.

    It’s very deceptive though, because the short time you invest into it actually gives back so much more time to your life. Like multiple extra hours per day, every day, where you feel refreshed, energetic, and capable of pursuing your passions fully. It’s extremely worth the time you spend upfront