A physics thing I think about a lot was this demonstration uses polarized lens filters. The filters block 50% of the light based the orientation of the wave the photon is traveling in. If you take 2 of these filters and rotate one of them 90 degrees, approximately no light is getting through. This is totally expected and makes sense. However, if you place a third filter in between those 2 at a 45 degree angle to the first, more light suddenly comes through. We don’t really know why this happens. It like defies our conventional understanding of how light works, and the theories to explain it involve fuckin quantum entanglement. It’s so fucking weird and cool that there’s this scientific mystery that you can observe yourself at minimal cost.
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Another thing I think about a lot is that the sum of all natural numbers (positive integers greater than zero: 1, 2, 3, …) is -1/12. It’s both negative and a fraction and it’s a summation of strictly positive integers. Like it shows up in physics and replacing the sum of all natural numbers with -1/12 will make equations work and give you accurate predictions or whatever. It’s so fuckin stupid.
Not on topic, but I hate conspiracy brain people when they say “WHAT ARE THE CHANCES!” like it could never happen accidently.
When in reality things are happening every second that have ungodly low chances of probability. With 8+ billion humans, it’s just common sense to realize rare things happen constantly, although humans aren’t built to really think this way.
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a one in a million chance happens every single day
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what if we’re just wrong
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Why do I get recommended this immediately. I want a cravings box so bad
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Wdym
like if we just made an assumption somewhere thats wrong and we’re basing all of physics around it
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Uh. Hm. So like mathematics is a tool we use to help us understand physics, but even if we’re wrong about some things (we almost certainly are), it’s likely like we’re not entirely wrong or we wouldn’t be able to consistently predict how things are going to behave in the universe purely on math alone. Einstein’s work suggested that gravitational waves existed, but he assumed that there was a mistake somewhere and that they didn’t actually exist. We know now that they do after we were finally able to measure some after like 50 years since Einstein first predicted them.
(And we know that our mathematical system is both inconsistent and incomplete and it’s just something we have to deal with. All axiomatic systems will inevitably be inconsistent and incomplete re: Gödel’s incompleteness theorems)
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I think you can only arrive at the sum of all natural numbers being the sum of -1/12 by using something called analytic continuation which is a thing that is somewhat controversial IIRC and you can sometimes get different results based on how you approach a particular function. However like 3 different mathematicians arrived at -1/12 as the answer using 3 different methods over a time span of hundreds of years and entirely independently, and we can use as an real number replacement for the sum of all natural numbers in physics equations and we get useful results from it. It’s confounding.
I’m not a physicist or a serious mathematician so my bad if I’m fucking up some explanations here, but idk I find all of it fascinating.
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i hear that a lot and it’s annoying. it’s a ramanujan sum, which assigns a value to any divergent infinite series that can somehow make it work with physics shit. obviously the sum of the naturals isn’t actually -1/12 but that’s just a number that can work for reasons above my mathematical paygrade
newton and galileo and the like made many assumptions that were wrong and that all of physics was based around for hundreds of years. it’s just that their assumptions happened to work on a human scale and at the time that’s all they really had to work with. how were they supposed to know shit would get fucky once things got too small or too large
I think the thing that’s so confounding is why the fuck does it work if it’s not the sum of all natural numbers
it’s a divergent series so why the fuck does a negative fraction relatively close to zero work
the ramanujan sum of the squares (or any even power, for some reason) is zero. the ramanujan sum of the reciprocals of the naturals is the euler-mascheroni constant (note that this is sometimes referred to as just euler’s constant but is distinct from e, which is euler’s number). i don’t understand the math behind it but i’ll leave ramanujan to it
also I believe there are multiple methods beyond just the Ramanujan summation to arrive at the same result for the sum of all natural numbers
i wonder what the smallest natural number i’ve never thought about is
isnt that impossible to calculate because you’ll then think about it
there’s infinitely many, so there’s gotta be at least one. there’s a good chance you’ve just never thought about, say, 1,593,629. and it’s a question you can never know the answer to because if you somehow ever figure it out the answer changes
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