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It started with a conversation I overheard.
“Once I knew this furry,” D. said. “He always smelled, and he couldn’t keep his hands to himself.”
“You only knew one like that?” H. laughed. “I don’t know many furs who act normal.”
I had my pen and paper out, working on a problem with partial orders that has picked at me for a few years: some partial orders have a pair of linearizations that can generate the whole order, and sometimes a diagram involving them can show you possible linearizations they have. But I didn’t realize until later that I was restricting my attention to interval orders, which is known to not include all possible partial orders. There were still interesting questions about what I was trying to do: did any partial orders allow for two completely different sets of linearizations to generate them? Were there any linearizations that were never really completely necessary to keep in the set of generating linearizations?
In any case, I was distracted by the conversation. How many furs did I know who always smelled? It’s sad but I could list a few by name. How many were likely to be inappropriately trying to touch folks they had just met? Again, anecdotes led me to quite a few I could put on this list.
I created a Venn Diagram word problem based on real life.
“I have seventeen friends…” I started to write. Were they really friends? I started over.
I have seventeen acquaintances who are furry. Ten of these acquaintances always smell. Eight of these acquaintances cannot keep their hands to themselves. Six of them both always smell and cannot keep their hands to themselves.
1. How many of them only smell, and could be helped by a dose of soap?
2. How many of these acquaintances are normal?
As if they’d been listening in, I heard R. answer D. and H. “They’re furry. None of them act ‘normal.’ Smelly, inappropriate, or not. I wouldn’t introduce most of them to ordinary friends or want to be seen with them publicly.”
“Good point,” I thought to myself. I crossed out “normal” and wrote “furry and tolerable.”
Just in time for AnthroCon.
“Once I knew this furry,” D. said. “He always smelled, and he couldn’t keep his hands to himself.”
“You only knew one like that?” H. laughed. “I don’t know many furs who act normal.”
I had my pen and paper out, working on a problem with partial orders that has picked at me for a few years: some partial orders have a pair of linearizations that can generate the whole order, and sometimes a diagram involving them can show you possible linearizations they have. But I didn’t realize until later that I was restricting my attention to interval orders, which is known to not include all possible partial orders. There were still interesting questions about what I was trying to do: did any partial orders allow for two completely different sets of linearizations to generate them? Were there any linearizations that were never really completely necessary to keep in the set of generating linearizations?
In any case, I was distracted by the conversation. How many furs did I know who always smelled? It’s sad but I could list a few by name. How many were likely to be inappropriately trying to touch folks they had just met? Again, anecdotes led me to quite a few I could put on this list.
I created a Venn Diagram word problem based on real life.
“I have seventeen friends…” I started to write. Were they really friends? I started over.
I have seventeen acquaintances who are furry. Ten of these acquaintances always smell. Eight of these acquaintances cannot keep their hands to themselves. Six of them both always smell and cannot keep their hands to themselves.
1. How many of them only smell, and could be helped by a dose of soap?
2. How many of these acquaintances are normal?
As if they’d been listening in, I heard R. answer D. and H. “They’re furry. None of them act ‘normal.’ Smelly, inappropriate, or not. I wouldn’t introduce most of them to ordinary friends or want to be seen with them publicly.”
“Good point,” I thought to myself. I crossed out “normal” and wrote “furry and tolerable.”
Just in time for AnthroCon.
Category Story / Human
Species Human
Size 120 x 85px
File Size 125.2 kB
Listed in Folders
That's actually in the preview image: the Venn diagram for this problem.
The intersection of the two sets contains six people who always smell and cannot keep their hands to themselves.
We are told that the number of people who always smell is is ten, so there must be four people who smell but are not handsy.
Similarly, we are told that the number of people who cannot keep their hands to themselves is eight; we've already noted the six in the intersection so there must be two who do not smell, but inappropriately put their hands on others.
The circles contain a group of six, a group of four, and a group of two, which amounts to twelve of the seventeen. So five would be in neither set; there are five who do not smell and can behave appropriately.
Without a diagram we could use the inclusion/exclusion principle, but I feel the visual approach conveys the answer to the other question (How many of them only smell, and could be helped by a dose of soap?)
The intersection of the two sets contains six people who always smell and cannot keep their hands to themselves.
We are told that the number of people who always smell is is ten, so there must be four people who smell but are not handsy.
Similarly, we are told that the number of people who cannot keep their hands to themselves is eight; we've already noted the six in the intersection so there must be two who do not smell, but inappropriately put their hands on others.
The circles contain a group of six, a group of four, and a group of two, which amounts to twelve of the seventeen. So five would be in neither set; there are five who do not smell and can behave appropriately.
Without a diagram we could use the inclusion/exclusion principle, but I feel the visual approach conveys the answer to the other question (How many of them only smell, and could be helped by a dose of soap?)
Ah, but the REAL question: How many "normal" people did they meet that they just assumed weren't furry?
"All furries smell and/or are handsy. I know this, because every furry I've ever known has been like that." That group of five on the exterior portion of the graph, how many of them go unnoticed, assumed by D and H to just be non-furs on the basis that they didn't inhabit either circle? ^_~
(Honestly, who'd want to be normal anyway, or hang around such boring people? Give me furries any day, though preferably ones who can get out of those circles...)
"All furries smell and/or are handsy. I know this, because every furry I've ever known has been like that." That group of five on the exterior portion of the graph, how many of them go unnoticed, assumed by D and H to just be non-furs on the basis that they didn't inhabit either circle? ^_~
(Honestly, who'd want to be normal anyway, or hang around such boring people? Give me furries any day, though preferably ones who can get out of those circles...)
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