
All horses are the same color
Paradox arising from an incorrect proof
From Wikipedia, licensed CC BY-SA 4.0.
Loading…
Logs
★ 2.5 average from 5 people · 5 entries
Most liked
A bit of context, a few years back I took a discrete math course. Very hard, but very fun! The way the course was structured around is that you went to TA sessions with your classmates and did the homework together. Anyways, one of our questions was a question on induction, specifically that we had to analyze a proof and then point out at which part did this proof mess up. One part was along the lines of this: "Claim: We have a set S containing only real numbers. Then every member of S has the same sign." As I was wrapping my head around this proof, I could not for the life of me understand where this proof messed up. Looking back, this seemed elementary, but it took me a solid 30 minutes to finally understand what is going on. We now introduce another character into this story. jan Misali is a youtuber best known for their work in linguistics and game design, although my introduction and appreciation largely stems from their incredible but sadly unfinished WarioWare fanfic called "Wario Faces Consequences for His Actions". They have also published a video by the name of "the five kinds of paradox" in which I learned about various different paradoxes and the ways they kind of suck (sorry to any paradoxes in the audience). I watched this video when it initially came out (so a few months before my story takes place), but it didn't occupy my mind that much. Back to the story. About 45 minutes have passed and I severely do not know how to begin answering this question. It is very agonizing, because I am often the slowest among my fellow math majors, especially with more abstract concepts. It makes me feel like a fraud sometimes, since a lot of proofwriting comes naturally for them, but for me it takes a long time to formulate (and I often need help from others in order to make progress). However, as I reread the question again, it hits me, and I blurt out loudly in the classroom: "It's the fucking horses." I am subsequently told by one of the TAs to be quiet, not out of the fact I've blurted out something loudly (there is a bit of walla walla in this classroom as students are working together), but rather I had unlocked the secret to this question, that this is indeed a rewriting of the horse problem, and that I should be quiet as to not spoil the answer for everyone else. I had gained secret horse knowledge to gain an edge against my peers in this class, and for that I am very grateful for this funny and memorable paradox for helping me in this class. As someone who also has gotten into horses through another avenue (in this case, the media franchise Uma Musume: Pretty Derby), I come back to this claim with a more burning question: What would this claim look like in the Uma Musume universe? As a franchise revolving around a gacha game, I find it unlikely that racism exists in the in-game universe and thus the claim of all horses being the same color could possibly exist as a normal paradox- calling all horses the same color is inoffensive in their utopian world. But on the other hand, the people who are writing Uma Musume come from our real world, a world where things are not so perfect. Thus, it could be possible for the writers of Uma Musume to exclude or rewrite the claim to prevent offending people. This is another paradox which I consider to almost be on the same level of the claim of "all horses are the same color". I've actually seen a few horses before. I've often driven in rural backroads, and I often crane my neck to see the livestock out on the road. This is very unsafe but I've never gotten into a crash from doing this before, so I keep on doing it. I've actually only seen one color of horses, specifically bay horses, with a brown coat. Sometimes, they wear external coats too. This is called a horse blanket though. However, if we consider horse blankets, there are n*m combinations of colors the horses can be, where n is the number of different coats a horses have, and m is the color blanket the horses have. We conclude by saying that there are only two combinations of colors though. I've only ever seen bay horses, and I've only seen one horse with a blanket, and thus there are only two different types of horses that exist. Overall, I recommend memorizing this paradox. If you happen to take a high level mathematics course, or want to impress your friends, this can be a very useful tool in your back pocket to get out of a sticky situation. I would not recommend this for a job interview though.