Actually a quite interesting article: en.wikipedia.org/…/All_horses_are_the_same_color
The science is divided
Submitted 2 months ago by The_Picard_Maneuver@lemmy.world to [deleted]
https://lemmy.world/pictrs/image/fb4aada2-0875-483f-ae03-7223fa83413b.jpeg
Comments
Tiuku@sopuli.xyz 2 months ago
cmgvd3lw@discuss.tchncs.de 2 months ago
I did do this proof by induction back in the day, but now looking at the article I am clueless.
sp3tr4l@lemmy.zip 2 months ago
Do you mean you went through the proof and verified it, or falsified it?
…
As I understand it, it goes something like this:
You have a set of n horses.
Assume a set of n horses are the same color.
Now you also have a set of n+1 horses.
Set 1: (1, 2, 3, … n) Set 2: (2, 3, 4, … n+1)
Referring back to the assumption, both sets have n horses in them, Set 2 is just incremented forward one, therefore, Set 2’s horses are all one color, and Set 1’s horses are all one color.
Finally, Set 1 and Set 2 always overlap, therefore that the color of all Set 1 and Set 2’s horses are the same.
…
So, if you hold the ‘all horses in a set of size n horses are the same color’ assumption as an actually valid assertion, for the sake of argument…
This does logically hold for Set 1 and Set 2 … but only in isolation, not compared to each other.
The problem is that the sets do not actually always overlap.
If n = 1, and n + 1 = 2 then:
Set 1 = ( 1 )
Set 2 = ( 2 )
No overlap.
Thus the attempted induction falls apart.
Set 1’s horse 1 could be brown, Set 2’s horse 2 could be … fucking purple… each set contains only one distinct color, that part is true, but the final assertion that both sets always overlap is false, so when you increment to:
Set 1 = ( 1, 2 )
Set 2 = ( 2, 3 )
We now do not have necessarily have the same colored horse 2 in each set, Set 1’s horse 1 and 2 would be brown, Set 2’s horse 2 and 3 would be purple.
…
I may be getting this wrong in some way, it’s been almost 20 years since I last did set theory / mathematical proof type coursework.
Iceman@lemmy.world 2 months ago
idunnololz@lemmy.world 2 months ago
I took a peak and it is sort of dumb but logically “sound”. Specifically the indictive step.
In the inductive step you assume the statement is true for some number n and use this statement to prove the statement n + 1 is true. If you can do that then you can prove the induction step.
So in this example the statement we assume is true is given n horses, all of them are the same color. To prove the statement for n + 1 horses we look at the n + 1 horses. Then we exclude the first horse. By excluding the last horse we have a set of n horses. By the induction statement this set of horses must all be the same color. So now we’ve proven the first n horses are the same color.
Next we can exclude the first horse. This also gives us a set of n horses. By the induction statement all these horses must also be the same color. Therefore all n + 1 horses must be the same color.
This sounds really dumb but the proof works in the induction step.
The logical issue is that the base case is wrong which is necessary for a complete proof by induction.
Elgenzay@lemmy.ml 2 months ago
Also related: en.wikipedia.org/wiki/Raven_paradox
WildPalmTree@lemmy.world 2 months ago
A much more interesting question, if you ask me.
Viking_Hippie@lemmy.dbzer0.com 2 months ago
It was stated as a lemma, which in particular allowed the author to “prove” that Alexander the Great did not exist, and he had an infinite number of limbs.[4]
Talk about burying the lede! 😄
sp3tr4l@lemmy.zip 2 months ago
From that link:
Assume that n horses always are the same color.
… I mean… yes, the logic follows… if you… make and hold that assumption… which is ostensibly what you are trying to prove.
This is otherwise known as circular reasoning.
Apparently this arose basically as a joke, a way of illustrating that you actually have to prove the induction is valid every step of the way, instead of just asserting it.
kogasa@programming.dev 2 months ago
No, that’s what induction is. You prove the base case (e.g. n=1) and then prove that the (n+1) case follows from the (n) case. You may then conclude the result holds for all n, since we proved it holds for 1, which means it holds for 2, which means it holds for 3, and so on.
ThatGuy46475@lemmy.world 2 months ago
It’s not circular reasoning, it’s a step of mathematical induction. First you show that something is true for a set of 1, then you show that if it’s true for a set of n it is also true for a set of n+1.
Black616Angel@discuss.tchncs.de 2 months ago
Actually this just refers to the color of their fur. I’d say that a blonde white man and a white read head are the same color, just their hair has a different color.
(I’m not totally serious and will not die on this hill)
thefartographer@lemm.ee 2 months ago
Oh, I’m gonna make sure you die on that hill!
First, by building you a lovely house on that hill and a nearby Denny’s…
Black616Angel@discuss.tchncs.de 2 months ago
Sounds nice, go on!
(I’m gullible and will fall into any trap I come across)
zaphod@sopuli.xyz 2 months ago
I’m not even convinced that horses are real.
idiomaddict@lemmy.world 2 months ago
They’re what the government uses to spy on the Amish.
zaphod@sopuli.xyz 2 months ago
Why can’t they just use birds like for everyone else?
Matriks404@lemmy.world 2 months ago
I’m not convinced that anything outside my thoughts are real. In fact are my thoughts real?
zaphod@sopuli.xyz 2 months ago
You’re not real. I am not real. Nothing is real.
lugal@sopuli.xyz 2 months ago
True. They look too similar to giraffes
the_beber@lemm.ee 2 months ago
Why is there a picture of an empty field?
ignotum@lemmy.world 2 months ago
I assume John Cena is standing there and we just can’t see him
Colonel_Panic_@lemm.ee 2 months ago
This is what arguing with people about politics feels like.
Matriks404@lemmy.world 2 months ago
In some cultures this might be the same color.
Hupf@feddit.org 2 months ago
They are both horse colored, obviously.
danc4498@lemmy.world 2 months ago
Their hair is the same color. What color is the skin?
ZILtoid1991@lemmy.world 2 months ago
Excrubulent@slrpnk.net 2 months ago
Horse blindness is a made up illness designed to gaslight us into believing that horses exist.
CarbonIceDragon@pawb.social 2 months ago
But the reasoning given doesnt apply exclusively to horses. Suppose we follow the same chain that gets us “all horses are the same color”, but replace “horses” with “colors”, we would end up with the statement that all colors are the same color. Thus, this is not a counterexample, because black and brown are the same color.
Tiuku@sopuli.xyz 2 months ago
Brilliancy!
Colonel_Panic_@lemm.ee 2 months ago
That theory assumes that color is real. Color is just some photons smacking into your retina and then the brain deciding what that even means.
Tezzerets_Tea_Time@lemmy.world 2 months ago
Well, sorta. Different materials bounce different wavelengths of light that our eyes catch and send to the brain to piece together and interpret color from. There is a degree of responsibility for what we see on the object the light bounces off of in the form of what wavelengths they absorb or reflect.
Colonel_Panic_@lemm.ee 2 months ago
Aha, but that assumes light is real and materials are real and the universe is real!
UltraGiGaGigantic@lemmy.ml 2 months ago
Oh the inside?
hansolo@lemm.ee 2 months ago
…what?
Horse hair colors vary.
If you shave a horse, any breeds with dark black or blue-ish grey hair will give you a variety of that pallet, getting dark enough to be stopped and frisked in larger American cities. Sometime blueish-black skin and hair pigmentation matches as well.
Most other breeds will give you a pink color range.
artpictures.club/autumn-2023.html
magonlinelibrary.com/…/ukve.2021.5.1.24_f03.jpg
Source: was given a saddle for Christmas once.
kogasa@programming.dev 2 months ago
It’s not actually claiming that all horses are the same color, it’s an example of a flawed induction argument
AlecSadler@sh.itjust.works 2 months ago
If you read the Wikipedia article (or other articles) about “all horses are the same color”, it is really just about an inductive fallacy that can occur.
introvertcatto@lemmy.blahaj.zone 2 months ago
All horses are monkeys
nova_ad_vitum@lemmy.ca 2 months ago
Okay but all monkeys are sharks.
HipsterTenZero@dormi.zone 2 months ago
real
Bishma@discuss.tchncs.de 2 months ago
Mammals only make brown, but we do a lot with it.
Sheldan@programming.dev 2 months ago
This is great. I love stuff like this.
vane@lemmy.world 2 months ago
Maybe author of the sentence was looking at horses in space and wikipedia is completly wrong.
AllNewTypeFace@leminal.space 2 months ago
To be fair, until you can see both sides of each horse, that technically doesn’t disprove it
credo@lemmy.world 2 months ago
Doesn’t “color” (no ‘s’) imply they can’t be more than one? Or… is this theorem proven? Both of these horses are all the same color.
Valmond@lemmy.world 2 months ago
There are Value, Croma(or Saturation) and Hue, so maybe you’re onto something here!