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Re: Math: Fleeting Thoughts

Posted: Mon Jan 14, 2019 4:35 pm UTC
by Eebster the Great
doogly wrote:
gmalivuk wrote:One's son shouldn't be one's sibling...

The moral injunctions of Exodus can really go take a hike. 2019, brah.

Since this is the math forum, it's worth mentioning that the detrimental genetic effects from such a union are statistically significant but practically very small, in contrast to popular belief that they would typically be large. Also, a child of two first cousins is not significantly more likely to have genetic disorders than a random child.

Re: Math: Fleeting Thoughts

Posted: Mon Jan 14, 2019 5:48 pm UTC
by gmalivuk
If someone's son is their brother, they reproduced with their mother or father. Which, in addition to having a much higher rate of defects, is also fucked up in loads of other ways that often wouldn't apply to (even double first) cousins.

Re: Math: Fleeting Thoughts

Posted: Mon Jan 14, 2019 5:49 pm UTC
by DavidSh
If you are talking about half-siblings, or step-sons, you get the effects Eebster the Great was discussing. If you are genetic father of a genetic full-sibling, I think you have to be your own genetic father. That's not quite as extreme as the situation of the protagonist in All You Zombies, but still requires a causality violation. You might have genes that you inherited only from yourself, which haven't run through the process of human evolution. Who knows how well they will interact with human genes in any of your descendants? (The Time Patrol, that's who.)

Re: Math: Fleeting Thoughts

Posted: Mon Jan 14, 2019 6:00 pm UTC
by Eebster the Great
gmalivuk wrote:If someone's son is their brother, they reproduced with their mother or father. Which, in addition to having a much higher rate of defects, is also fucked up in loads of other ways that often wouldn't apply to (even double first) cousins.

Yeah, the kid's parent is also his grandparent. It's fucked up, but the notion that the rate of genetic defects will be very high is simply incorrect. It will be higher than in the general population, but not by a lot. The examples of inbreeding we are used to seeing result from many generations of isolation, not just a single case of incest.

Re: Math: Fleeting Thoughts

Posted: Mon Jan 14, 2019 6:09 pm UTC
by gmalivuk
Still, the coefficient of inbreeding for a son who's also a (half-)brother is four times higher than it is for the offspring of (non-double) first cousins, which is usually the point where some jurisdictions start allowing marriage. (Though I don't know how often those laws distinguish between double and non-double first cousins. That is, cousins who share one pair of grandparent, vs. those who share both.)

Re: Math: Fleeting Thoughts

Posted: Mon Jan 14, 2019 7:17 pm UTC
by Eebster the Great
A majority of US states actually also prohibit first cousin marriage. North Carolina has the odd distinction of being the only state to allow single first cousin marriages but not double first cousin marriages. Sex is more broadly legal though.

Re: Math: Fleeting Thoughts

Posted: Tue Jan 15, 2019 7:19 am UTC
by PM 2Ring
Wikipedia has lots of info on cousin marriage, including various maps. Also see cross cousin marriage from the University of Manitoba.

Re: Math: Fleeting Thoughts

Posted: Tue Jan 15, 2019 3:31 pm UTC
by gmalivuk
All this info about marrying your cousin is interesting and all, but my initial point was that it would take several generations of cousin marriage to reach the level of inbreeding of a single parent-child pairing.

Re: Math: Fleeting Thoughts

Posted: Tue Jan 15, 2019 10:58 pm UTC
by Pfhorrest
Flumble wrote:In any case, let's not discount any non-human entities that may work for degrees. They're worker-years.

"Person" does not entail "human". Nonhuman people are possible.

Re: Math: Fleeting Thoughts

Posted: Fri Mar 15, 2019 4:37 pm UTC
by Sungura
This year my news feed on fb got flooded with:
PI IS WRONG!
TAU IS RIGHT!
DONT CELEBRATE PI DAY ITS A LIE!

...so using tau cleans up some forumlas and maths. But holy duck people that doesnt mean pi is wrong. Nor does it mean youre so fancy that you know what tau is because you read an article on a nerd site and now feel all superior and can yell at people who like having some fun in life.

Let us enjoy things! Pi is still Pi and will be Pi even if you want to jump on the CHANGE ALL THINGS TO TAU bandwagon. Pi is not wrong, its not fake math or false news. So stop claiming pi is wrong!

Fucking add tau day as a holiday if you want. Bake two pies for tau day for all i care. :roll:

Re: Math: Fleeting Thoughts

Posted: Fri Mar 15, 2019 5:04 pm UTC
by Eebster the Great
But now we have a factor of 2! Sometimes! Surely that's worth getting upset about. Now let me grab my calendar reform proposal and collection of infographics showing how dumb MDY dates are.

Re: Math: Fleeting Thoughts

Posted: Fri Mar 15, 2019 5:14 pm UTC
by Xenomortis
But I like factors of 2.

Re: Math: Fleeting Thoughts

Posted: Fri Mar 15, 2019 6:29 pm UTC
by Soupspoon
Eebster the Great wrote:But now we have a factor of 2! Sometimes! Surely that's worth getting upset about. Now let me grab my calendar reform proposal and collection of infographics showing how dumb MDY dates are.

I shall be celebrating Pi Day on the 31st of April, as I have done every year!

Re: Math: Fleeting Thoughts

Posted: Fri Mar 15, 2019 9:12 pm UTC
by Xanthir
Celebrate it on July 22nd, you heathens. It's more accurate!

Re: Math: Fleeting Thoughts

Posted: Fri Mar 15, 2019 10:16 pm UTC
by Sungura
Soupspoon wrote:I shall be celebrating Pi Day on the 31st of April, as I have done every year!

:lol: This made me literally LOL!

Re: Math: Fleeting Thoughts

Posted: Fri Mar 15, 2019 10:18 pm UTC
by Pfhorrest
Sungura wrote:
Soupspoon wrote:I shall be celebrating Pi Day on the 31st of April, as I have done every year!

:lol: This made me literally LOL!

took me a second

Re: Math: Fleeting Thoughts

Posted: Sat Mar 16, 2019 12:32 am UTC
by Sungura
Eebster the Great wrote: Now let me grab my calendar reform proposal and collection of infographics showing how dumb MDY dates are.

https://xkcd.com/1179/

Everywhere in the world march 14th works. If you use ISO 8601...which you should... :wink:

Re: Math: Fleeting Thoughts

Posted: Sat Mar 16, 2019 4:24 pm UTC
by gmalivuk
The problem with ISO 8601 is that the year can't be added coherently, whereas the American format allows for a once-per-century 3-14-15 9:26:53

Re: Math: Fleeting Thoughts

Posted: Sat Mar 16, 2019 6:26 pm UTC
by Sungura
What do you mean gmal? I love ymd, works amazing for organising files and photos etc. years are quite coherent when first i think.

Re: Math: Fleeting Thoughts

Posted: Sat Mar 16, 2019 7:03 pm UTC
by Soupspoon
He means that putting the digits 31415926… into YYYYMMDD hhmmss doesn't easily work.

(000)3/nope, fourteenth month of year 3
(00)31/nope, forty-first month of year 31
(0)314/nope, fifteenth month of year 314
3141/nope, fifty-first month of year 3141
31415/nope, ninety-second month of the extended YYYYYMMDD format.
•••
31415926535897932384626433832795/02/nope, 88th day of February¹ in 10³¹ years or so.
•••
October 58th a billion billion billion-and-a-bit times later on
•••
July 81st is the next possible-but-impossible month, if I've not missed any. Then, ooh, a June 28th! But at 62-hundred-hours, in the time-of-day field. Scanning the digits a bit further and we seem to be out of luck. And definitely, by this point, we'd have stopped using the current calendar for any number of reasons (up to and beyond the non-existence of the Universe, if not ourselves?) so obviously our Calendar creators hated Pi!

That's what Stardates are for? Of course!

¹ Well, perhaps if we stopped the Leap Days for a while, then splurged!

Re: Math: Fleeting Thoughts

Posted: Sat Mar 16, 2019 11:04 pm UTC
by Sungura
ahh, well, ignore the year and 314 works haha

Re: Math: Fleeting Thoughts

Posted: Sun Mar 17, 2019 1:05 am UTC
by Flumble
Sungura wrote:But holy duck people that doesnt mean pi is wrong.

Yes it does! It's as bad as imperial (US) customary units and current going the wrong way.

Celebrate the 14th of March with baked goods all you like, but don't pretend it's that day specifically that is related to a circle constant. Using the month number as the integer part and the day number as two decimal places? Ludicrous! Even Xanthir's suggestion is better (for people using the slash as a separator)!
Or like Vihart proposed in one of her pi day videos: celebrate every full turn (tau radians) of the Earth. Two pie every day! :D Or maybe I misunderstood and she meant every turn around the Sun. In that case you get two pie every year, but the day on which it happens doesn't matter. Yes, it can be 03-14, but 06-28, 01-01 and your birthday (which is a pie day anyway) are equally valid. Hell, why not celebrate it four times a year with half a pie to demonstrate how silly π is. :wink:

Soupspoon wrote:
Eebster the Great wrote:But now we have a factor of 2! Sometimes! Surely that's worth getting upset about. Now let me grab my calendar reform proposal and collection of infographics showing how dumb MDY dates are.

I shall be celebrating Pi Day on the 31st of April, as I have done every year!

But March 14 is the better day because of ISO 8601. Oh, you!

Soupspoon wrote:He means that putting the digits 31415926… into YYYYMMDD hhmmss doesn't easily work.

Well just like we conveniently drop the year already and use month/day numbers that are really modulo 12/28/29/30/31 (rather than modulo 100) as digits, why not conveniently drop a leading zero in the month or day? A super pi day every century on __31-_4-15 _9:26:53 and super-mega-awesome pi day on 3141-_5-_9 _2:_6:53.



While looking through the tau manifesto (again) I came across a long section about volumes of hyperballs which left me very much unconvinced. The formulation with the gamma function ( π^(n/2) / Γ(n/2+1) eq.14) is elegant and clearly extends to non-integer dimensions. However it leaves me puzzled as to what those n/2s are doing there, let alone why powers of π and Γ are showing up.
I liked the quadrant formulation ( 2^n * λ^⌊n/2⌋ / n!! eq.28) with λ a quarter turn, but again, no (geometric) argument for the n/2 nor the double factorial.
Sweeping through a single quadrant in polar coordinates gives a nice looking integral ∫_0^λ ∫_0^λ ... (sin θ_n)^n*(sin θ_(n-1))^(n-1)*...*sin θ_1. (Incidentally, today I learned what a Jacobian is, or at least what its determinant means.) However, the antiderivatives of (sin x)^n are horrible and their integrals are, of course, gamma functions with half-integers.
Does anyone have a good explanation for why the volume (or surface) of an n-ball is the way it is?

Re: Math: Fleeting Thoughts

Posted: Mon Mar 18, 2019 1:01 pm UTC
by doogly
Flumble wrote:Does anyone have a good explanation for why the volume (or surface) of an n-ball is the way it is?

You mean, better than integrals?

Re: Math: Fleeting Thoughts

Posted: Mon Mar 18, 2019 1:32 pm UTC
by Eebster the Great
doogly wrote:
Flumble wrote:Does anyone have a good explanation for why the volume (or surface) of an n-ball is the way it is?

You mean, better than integrals?

Integrals are the way hyperglobists lie about the shape of the flat hyperearth.

Re: Math: Fleeting Thoughts

Posted: Mon Mar 18, 2019 4:37 pm UTC
by Pfhorrest
Please don't tell me that "globalist" is now used to mean "someone who believes the world is a globe".

I mean, if that's actually true then please tell me, but please don't tell me.

Re: Math: Fleeting Thoughts

Posted: Mon Mar 18, 2019 5:58 pm UTC
by Flumble
doogly wrote:
Flumble wrote:Does anyone have a good explanation for why the volume (or surface) of an n-ball is the way it is?

You mean, better than integrals?

....yes, surely there's an intuitive explanation for the number of points closer than (or at) 1 from the origin in integer dimensions as well as fractal ones. :roll:

Maybe I should start with the question why a factor of sqrt(π) shows up in the gamma function's half-integers while there's no π between integers.

Re: Math: Fleeting Thoughts

Posted: Mon Mar 18, 2019 6:36 pm UTC
by Eebster the Great
Pfhorrest wrote:Please don't tell me that "globalist" is now used to mean "someone who believes the world is a globe".

I mean, if that's actually true then please tell me, but please don't tell me.

No, the term is "globist." The globalists are the Illuminati reptoids that are trying to take over the world by teaching kids Spanish and taking our guns.

Re: Math: Fleeting Thoughts

Posted: Mon Mar 18, 2019 9:03 pm UTC
by Soupspoon
¿Que pistolas? Aquí no hay armas, solo lagartos.

Re: Math: Fleeting Thoughts

Posted: Sat May 25, 2019 9:02 pm UTC
by cyanyoshi
I love whenever you can solve an optimization problem without needing calculus. There's just something really transparent, elegant, and liberating about it.

Re: Math: Fleeting Thoughts

Posted: Wed May 29, 2019 8:58 pm UTC
by gmalivuk
Boltzmann's constant is 8.61733333314159e-5 eV/K.

(Okay, more realistically but still kind of an interesting coincidence, it's 8.617333333(53)e-5 eV/K.)

Re: Math: Fleeting Thoughts

Posted: Wed May 29, 2019 10:29 pm UTC
by cyanyoshi
gmalivuk wrote:Boltzmann's constant is 8.61733333314159e-5 eV/K.

(Okay, more realistically but still kind of an interesting coincidence, it's 8.617333333(53)e-5 eV/K.)

In other words, it is exactly 8617.333...e-8 eV/K.

Re: Math: Fleeting Thoughts

Posted: Thu May 30, 2019 12:10 am UTC
by Eebster the Great
cyanyoshi wrote:
gmalivuk wrote:Boltzmann's constant is 8.61733333314159e-5 eV/K.

(Okay, more realistically but still kind of an interesting coincidence, it's 8.617333333(53)e-5 eV/K.)

In other words, it is exactly 8617.333...e-8 eV/K.

No, it is exactly 1380649/16021766340 eV/K, which is a repeating decimal with period 778716 approximately equal to 0.000086173332621451774336636593340806392012330395775825551.

Re: Math: Fleeting Thoughts

Posted: Thu May 30, 2019 12:31 am UTC
by gmalivuk
Oh right, I forgot that also got an exact value recently.

Re: Math: Fleeting Thoughts

Posted: Thu May 30, 2019 2:13 am UTC
by cyanyoshi
I'm still correct. I didn't say what was after the dot dot dot, did I? :P

Re: Math: Fleeting Thoughts

Posted: Thu May 30, 2019 3:25 am UTC
by gmalivuk
cyanyoshi wrote:I'm still correct. I didn't say what was after the dot dot dot, did I? :P

Yeah, but it means the one with those digits of pi was just wrong, since that was the old value of the eV and the new value of Boltzmann.