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Cake day: June 27th, 2023

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  • Carnelian@lemmy.worldtoLemmy Shitpost@lemmy.worldRAMANUJAN SPECIAL
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    20 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


  • 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





  • Haha yeah it’s a lot, I aim for like 150g of protein every day for strength training. The block of tofu is like 50g and the edamame is like another 40 so it just makes every other meal way easier. I definitely wouldn’t recommend eating nothing but soy tho lol. I think regardless of what you pick you’d eventually get sick if you just ate one thing.

    The rest of my diet mainly consists of a lot of different bags of frozen veggies. Pretty much cycle through every type my store offers, usually pan fried, or soups in the colder months.

    Oatmeal and homemade bread, a few servings of fruit each day including frozen berries and dried fruit, and on the non vegan side I have eggs, cheese, and greek yogurt. Weekends I do more fresh veggie prep as well as have “fun” foods like ice cream or whatever.

    It works great for me, admittedly a lot of soy but I think that particular neuroticism of mine is actually quite tame in context; most bodybuilders pretty much do the same thing but w/ chicken breast or lean ground beef