Talk:2435: Geothmetic Meandian - Revision history

82.132.244.183 at 07:41, 22 October 2025

2025-10-22T07:41:20Z

Jukamala: /* Proof - Possibly by Induction */

2025-02-10T18:30:24Z

‎Proof - Possibly by Induction

Jukamala: /* Proof - extension to negative values */

2025-02-10T18:27:29Z

‎Proof - extension to negative values

172.70.206.163 at 02:40, 1 April 2022

2022-04-01T02:40:41Z

198.41.238.117: /* Better Python implementations */

2021-07-28T01:35:04Z

‎Better Python implementations

198.41.238.107 at 01:33, 28 July 2021

2021-07-28T01:33:34Z

198.41.238.108 at 00:08, 24 July 2021

2021-07-24T00:08:11Z

Nullcline: /* Why is this funny? */

2021-07-20T17:34:57Z

‎Why is this funny?

Quillathe Siannodel: /* Does anyone know why this is incomplete? */

2021-04-07T13:20:19Z

‎Does anyone know why this is incomplete?

Xorg: /* Proof - extension to negative values */

2021-03-31T16:43:03Z

‎Proof - extension to negative values

← Older revision		Revision as of 07:41, 22 October 2025
Line 407:		Line 407:
	Short proof that the thing converges. Basically there are three cases, one is that the median is larger than both one is that it is smaller than both and one is that it is in between. If it is in between, both he max must decrease and the min must increase. If it is greater, then the minimum must increase. If it is less, the maximum must decrease. In all three cases max(F(n+1))-min(F(n+1))<max(F(n))-min(F(n)) so by monotonic convergence theorem it must converge.		Short proof that the thing converges. Basically there are three cases, one is that the median is larger than both one is that it is smaller than both and one is that it is in between. If it is in between, both he max must decrease and the min must increase. If it is greater, then the minimum must increase. If it is less, the maximum must decrease. In all three cases max(F(n+1))-min(F(n+1))<max(F(n))-min(F(n)) so by monotonic convergence theorem it must converge.
	[[Special:Contributions/172.70.206.163\|172.70.206.163]] 02:40, 1 April 2022 (UTC)		[[Special:Contributions/172.70.206.163\|172.70.206.163]] 02:40, 1 April 2022 (UTC)
		+
		+	== Example table formatting ==
		+	Just seen (and slightly adjusted the edit of) the edit that gives the minima numbers in the table italics, to go with the maxima numbers being bold. But normal-weight italics is relatively indistinct from normal-weight unsloped, next to strongly-weighted bold. Contemplated changing it to <u>underline</u>, instead. Then wondered if that means we could <span style="text-decoration: overline">overline</span> the values that are maximum, and reassign bold (or maybe italics; but, no, not strikethough... similarly symbolic though that might be!) to median. <br/><br/> So <span style="text-decoration: underline">minimum</span>, '''median''' and <span style="text-decoration: overline">maximum</span>, in whatever order they might appear. Just an idea for another editor, though... [[Special:Contributions/82.132.244.183\|82.132.244.183]] 07:41, 22 October 2025 (UTC)

@@ Line 352: / Line 352: @@
 Edit: Note that this proof holds only assuming the values are nonnegative. Some sets of values including negative ones, such as gmdn(-4,-4,1), do not converge.
 [[Special:Contributions/141.101.98.16|141.101.98.16]]
 == Why is this funny? ==

@@ Line 392: / Line 392: @@
 Given <code>M<sub>n</sub> := max(abs(inputs<sub>n</sub>))</code> and <code>min<sub>n</sub> < 0 < max<sub>n</sub></code>, we still have <code>abs(AM<sub>n</sub>) ≤ M<sub>n</sub>*2/3</code> (by dropping a summand with different sign from AM<sub>n</sub>), <code>abs(AM<sub>n+1</sub>) ≤ M<sub>n+1</sub>*2/3 ≤ M<sub>n</sub>*2/3</code> and <code>abs(mid<sub>n+1</sub>) ≤ abs(AM<sub>n</sub>) ≤ M<sub>n</sub>*2/3</code>, because AM<sub>n</sub> shares a sign with one of the others. <code>abs(GM<sub>n+1</sub>) = abs(GM<sub>n</sub>*mid<sub>n</sub>*AM<sub>n</sub>)<sup>(1/3)</sup> ≤ M<sub>n</sub>*(1*1*2/3)<sup>(1/3)</sup> ≤ M<sub>n</sub>*(2/3)<sup>(1/3)</sup></code>.
 Consequently <code>M<sub>n+2</sub>/M<sub>n</sub> ≤ (2/3)<sup>(1/3)</sup></code>, which shows convergence to 0. □ -- [[User:Xorg|Xorg]] ([[User talk:Xorg|talk]]) 16:43, 31 March 2021 (UTC)
 Edit: Deleted comment. Sorry for the accidental spam. [[User talk:Quillathe Siannodel|<sup>{)|(}</sup>]][[User:Quillathe_Siannodel|Quill]][[User talk:Quillathe Siannodel|<sub>{)|(}</sub>]] 14:54, 25 March 2021 (UTC)

← Older revision		Revision as of 02:40, 1 April 2022
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	Since it uses F(F(F...)) someone should write a Hascal version that actually uses the fixedpoint function. [[Special:Contributions/172.69.35.175\|172.69.35.175]] 22:56, 30 March 2021 (UTC)		Since it uses F(F(F...)) someone should write a Hascal version that actually uses the fixedpoint function. [[Special:Contributions/172.69.35.175\|172.69.35.175]] 22:56, 30 March 2021 (UTC)
		+
		+	Short proof that the thing converges. Basically there are three cases, one is that the median is larger than both one is that it is smaller than both and one is that it is in between. If it is in between, both he max must decrease and the min must increase. If it is greater, then the minimum must increase. If it is less, the maximum must decrease. In all three cases max(F(n+1))-min(F(n+1))<max(F(n))-min(F(n)) so by monotonic convergence theorem it must converge.
		+	[[Special:Contributions/172.70.206.163\|172.70.206.163]] 02:40, 1 April 2022 (UTC)

@@ Line 165: / Line 165: @@
 I'd like to add my own implementation:
-from math import *
+ from math import *
-def getMeans(n=list):
+ def getMeans(n=list):
-    n.sort()
+     n.sort()
-    mean=sum(n)/len(n)
+     mean=sum(n)/len(n)
-    if len(n)%2==1:
+     if len(n)%2==1:
-        median=n[len(n)//2]
+         median=n[len(n)//2]
-    else:
+     else:
-        median=(n[1+floor(len(n)/2)]-n[floor(len(n)/2)])/2
+         median=(n[1+floor(len(n)/2)]-n[floor(len(n)/2)])/2
-    prod=1
+     prod=1
-    for i in n:
+     for i in n:
-        prod*=i
+         prod*=i
-    gmean=prod**(1/len(n))
+     gmean=prod**(1/len(n))
-    return [mean,median,gmean]
+     return [mean,median,gmean]
-def gmdn(tol,n=list):
+ def gmdn(tol,n=list):
-    mList=n
+     mList=n
-    mList=getMeans(mList)
+     mList=getMeans(mList)
-    while not (isclose(mList[0],mList[1],rel_tol=tol) and isclose(mList[1],mList[2],rel_tol=tol) and isclose(mList[0],mList[2],rel_tol=tol) ) :
+     while not (isclose(mList[0],mList[1],rel_tol=tol) and isclose(mList[1],mList[2],rel_tol=tol) and
-        mList = getMeans(mList)
+ isclose(mList[0],mList[2],rel_tol=tol) ) :
-    return (mList[0]+mList[1]+mList[2])/3
+         mList = getMeans(mList)
+     return (mList[0]+mList[1]+mList[2])/3
+ print(gmdn(1e-15,[1,1,2,3,5]))
 which gives me 2.089057949736859

@@ Line 362: / Line 362: @@
 :Yes, here's a bit more on that.. I agree with [[User:Elektrizikekswerk|Elektrizikekswerk]] the joke is explained. The stat tip: "If you aren't sure whether to use the mean, median or geometric mean, just calculate all three, then repeat until it converges." is funny because there are many situations in the physical sciences where the arthmean, geometric mean and median for some data are different values. It is perhaps common that scientists not well versed in statistics are unsure which to use. The funny bit is imagining this less-statistically-versed-scientist throwing up their hands and just accepting the fixed constant given by iterating GMDN as the 'answer' irrelevant of any physical meaning. Also the name "geothmetic meandian" is funny because the word meandian is similar to both median, which it uses, and to ''meander'' which is indicated by the alternate assignment of the median on each iteration -- informally, this function meanders. [[User:Ramakarl|Ramakarl]]
 :Thanks to all who shared the absurdity so I could also enjoy the joke, and the joke is on me for needing to have a joke "explained". Now where is the button for me to give credit to the best answer? I want to be sure you get points toward your next-level badge. ;-) [[User:Rtanenbaum|Rtanenbaum]] ([[User talk:Rtanenbaum|talk]]) 16:23, 13 March 2021 (UTC)
+:This is actually one of my favorite xkcd comics. Even before seeing this comic, one thing I would always do was take the AM(AM,GM) instead of using either average on it's own. [[User:nullcline|nullcline]] ([[User talk:nullcline|talk]]) 17:33, 20 July 2021 (UTC)
 == PyPi-package ==

@@ Line 390: / Line 390: @@
 Consequently <code>M<sub>n+2</sub>/M<sub>n</sub> ≤ (2/3)<sup>(1/3)</sup></code>, which shows convergence to 0. □ -- [[User:Xorg|Xorg]] ([[User talk:Xorg|talk]]) 16:43, 31 March 2021 (UTC)
-== Does anyone know why this is incomplete? ==
+Edit: Deleted comment. Sorry for the accidental spam. [[User talk:Quillathe Siannodel|<sup>{)|(}</sup>]][[User:Quillathe_Siannodel|Quill]][[User talk:Quillathe Siannodel|<sub>{)|(}</sub>]] 14:54, 25 March 2021 (UTC)
 :The joke is still not explained, as far as I can tell. Maybe it's too obvious but since people asked (see three sections above in the comments) I think the explanation of the actual joke shoudl be added. As I too find it quite obvious what the joke is I find it hard to really explain it which is the reason why I didn't. Besides of that, the incomplete tag actually says why it's incomplete (in this case). AND there is already a comment section (again, three sections above) about this problem. [[User:Elektrizikekswerk|Elektrizikekswerk]] ([[User talk:Elektrizikekswerk|talk]]) 07:41, 26 March 2021 (UTC)
+::Sorry. That wasn't a thing when I added this section.
 can someone help me with my python code of this? i dont get why this isnt working! https://replit.com/@Bumpf/geothmetic for my code. if you want i can paste my code here. i also commented in the code the error and why i dont understand it. thank you in advance! (also the geometric formula thing in the table on the page is showing a big red error. Maybe fix that?) [[Special:Contributions/172.70.38.56|172.70.38.56]] 13:35, 26 March 2021 (UTC)Bumpf
 Since it uses F(F(F...)) someone should write a Hascal version that actually uses the fixedpoint function. [[Special:Contributions/172.69.35.175|172.69.35.175]] 22:56, 30 March 2021 (UTC)

@@ Line 386: / Line 386: @@
 : this is not yet sufficient proof.
 [[User:Xlf|Xlf]] ([[User talk:Xlf|talk]]) 18:05, 15 March 2021 (UTC)
 == Does anyone know why this is incomplete? ==