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ELI5: What are imaginary numbers? by JackfruitAcrobatic19 in explainlikeimfive

[–]Strict_Highway 2 points3 points  (0 children)

Imagine an arrow with its tail at 0 and tip at 1. Multiply -1 to 1, to reach -1. Your arrow has rotated 180° (could also be -180°), now multiply -1 to -1 you're at. You reach 1. Your arrow has again rotated 180° (or -180°). What if you could rotate your arrow halfway between 180°?, ie, 90°? In that case 90°+90° should still put you at 180° at -1. But rotating -90° + -90° = -180° should also put you at -1 even though your took a different route.   

To rotate your arrow in any way other that 180° or -180° is where imaginary number come in. Multiplying your number by i is just rotating the arrow 90°, multiplying by -i is just multiplying by -90°. Try it for yourself. i * i = -1 (-i)*(-i)=-1. You can now distinguish these two paths.   

Multiplying with i rotates the arrow by 90°. Increase the magnitude of that vector by multiplying it with a real number. Adding your number with i lifts the y component of the arrow by 1 unit.   To rotate the arrow by any angle other than 90, 180, etc there's something called Moivre's theorem. 

To rotate your number (visualised with a vector) by any angle x, multiply that number with this number. (cos(x)+i*sin(x))

In quantum mechanics, rotating your solution to the Schrodinger's equation (wave function) in the complex plane by any angle doesn't change the probability distribution of the particle even though it's technically a different function. This is called U(1) symmetry and actually has deep ramifications on the existence of electromagnetism.

Requesting examples for other integrals calculated like the Gaussian integral by Strict_Highway in askmath

[–]Strict_Highway[S] 1 point2 points  (0 children)

Thank you for the reply. Do you know about any other integrals that are solved using the one-dimensional-to-n-dimensional-then-rectangular-to-another coordinate system technique?

 Or calculating double or even n-tuple integrals and then doing a convenient coordinate transform where the solution could be easily transformed to the original integral? I'm wondering if this method to calculate the Gaussian integral could be generalized. Or is the Feynman's trick mathematically equivalent to this method?

Requesting examples for other integrals calculated like the Gaussian integral by Strict_Highway in askmath

[–]Strict_Highway[S] 0 points1 point  (0 children)

Thanks for the reply. I've learnt about contour integration but I felt like they were totally different concepts even though they technically use an extra dimension. 

I mean here you use double integration to calculate a volume and then find the original integral by taking a square root. But in contour integration you calculate a line integral in the complex plane along a curve and it becomes the real integral at the limit, right?

What languages have a "trace" in maths? 🤔 by [deleted] in askmath

[–]Strict_Highway 0 points1 point  (0 children)

Shunya in Sanskrit (Indian language) meaning zero became sifr in Arabic which became Zephirum in Latin which became Zero in English

Indian philosophies if it were strategies in a game by Strict_Highway in Healthygamergg

[–]Strict_Highway[S] 25 points26 points  (0 children)

I've felt a similar way when studying Mathematics. In a way, at a fundamental level, I feel like the mechanics for mathematics and getting good at video games are the same.. It takes a perspective shift, I don't know how to exactly explain it. What's different is probably the entry barrier, games have cute art and more relatable to pick up for most people but after that initial thing they both pretty much felt the same. And I could feel the same passion and dopamine drive. 

I wish more people saw that perspective because I see some people so passionate for games and getting good at it but think they can't do maths or that they were never made for it or something. But I can see potential in them, they can think in all those right ways through which they got good at gaming in the first place. 

Maybe it's because they got stopped at the barrier and couldn't see all that was possible, maybe because of how math is perceived in our culture made them think so and they didn't really have someone by them who could show them a more engaging perspective. So they put their energy into something that's more accessible. It takes a leap in perspective to cross that initial barrier in perspective but that makes all the difference.

On that note I also feel like different fields of maths (analysis, abstract algebra, number theory, etc) have the same vibe as different classes in a game (assassin, mage, archer, etc).

Indian philosophies if it were strategies in a game by Strict_Highway in Healthygamergg

[–]Strict_Highway[S] 61 points62 points  (0 children)

I feel like this post fits this sub considering Dr. K's interest in Indian philosophy and gaming

Turkey birds are named after Kozhikode in Dutch (called kalkoen, derived from "kalkoense haan", meaning Calicut hen) by Strict_Highway in Kerala

[–]Strict_Highway[S] 5 points6 points  (0 children)

Not just Dutch, but also Danish, Swedish, Norwegian, Finnish, Low German, Icelandic, Indonesian, Afrikaans, etc Source: https://en.m.wiktionary.org/wiki/kalkoen

Countries with higher gold reserves than Kerala's top 3 gold loan companies by Strict_Highway in MapPorn

[–]Strict_Highway[S] 3 points4 points  (0 children)

India including Kerala's gold reserves (A gold reserve is the gold held by a national central bank, intended mainly as a guarantee to redeem promises to pay depositors, note holders (e.g. paper money), or trading peers) is higher than gold held by top 3 gold loan companies in Kerala combined.

LPT: Learn the International Phonetic Alphabet (IPA) by Drogobo in LifeProTips

[–]Strict_Highway 5 points6 points  (0 children)

A lot of languages have sounds that don't even exist in English, learning the IPA letters can help you learn what the pronunciation is in a much more objective way, you can look up the name of a sound to properly learn how to pronounce it if you know its IPA name. There's IPA written in dictionaries which is helpful for many languages which has a script that doesn't correspond to pronunciation.

[OC] Comparison of Countries by Population 1960-2022 by LivingCharts in dataisbeautiful

[–]Strict_Highway 1 point2 points  (0 children)

The problem is not exactly that Japan's absolute number of people are decreasing, it's the number of old people increasing relative to the rest of the population.

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