After glancing at this post and its comment section I want to make my own unanchored attempt at typing up how I might invent temperature.
Sometimes my nerves report “hot”/”cold”. I’d like to predict this sense input. It’s mostly continuous over time. Most predicted discontinuities are predicted by the part of me that pays attention to what objects I touch. Touching a friend that reports feeling cold causes me to feel cold! I suspect that every object can feel hot/cold, and touching it tells me how it feels. Indeed, when an object touches ice and then I touch the object, I feel cold.
But isn’t that circular? Confused investigation finds that objects that touch each other eventually reach an equilibrium. In which order I introduce them doesn’t matter. If all the objects are copies, they all eventually feel the same, neither hotter than the hottest nor less hot than the least hot. Thus, necessarily[1], how hot a blarg feels is a monotonic[2] function of a hotness scalar that a blarg has, which is eventually averaged between touching blargs.
I prepare many touching blargs, many touching snizzles, and so on for a hundred different objects. I produce a 100x100 heatmap table of how hot the left object feels after equilibrating with the top object. I sort the columns, not by how hot the top objects feel, but by the values in the third row, and find that every row ends up sorted! Apparently, equilibrating a tool with the target and then checking how hot the tool feels gives more consistent data than checking how hot the target feels.
Via the tool, objects that touch each other eventually feel the same, neither hotter than the hottest nor less hot than the least hot. Necessarily, how hot an object feels via a tool is a monotonic function of a hotness scalar that objects have, which is eventually weighted-averaged between touching objects.
technically if they ended up always feeling as hot as the most hot, you would need the hotness scalar to grow more quickly with the felt hotness than our instruments can detect
After glancing at this post and its comment section I want to make my own unanchored attempt at typing up how I might invent temperature.
Sometimes my nerves report “hot”/”cold”. I’d like to predict this sense input. It’s mostly continuous over time. Most predicted discontinuities are predicted by the part of me that pays attention to what objects I touch. Touching a friend that reports feeling cold causes me to feel cold! I suspect that every object can feel hot/cold, and touching it tells me how it feels. Indeed, when an object touches ice and then I touch the object, I feel cold.
But isn’t that circular? Confused investigation finds that objects that touch each other eventually reach an equilibrium. In which order I introduce them doesn’t matter. If all the objects are copies, they all eventually feel the same, neither hotter than the hottest nor less hot than the least hot. Thus, necessarily[1], how hot a blarg feels is a monotonic[2] function of a hotness scalar that a blarg has, which is eventually averaged between touching blargs.
I prepare many touching blargs, many touching snizzles, and so on for a hundred different objects. I produce a 100x100
heatmaptable of how hot the left object feels after equilibrating with the top object. I sort the columns, not by how hot the top objects feel, but by the values in the third row, and find that every row ends up sorted! Apparently, equilibrating a tool with the target and then checking how hot the tool feels gives more consistent data than checking how hot the target feels.Via the tool, objects that touch each other eventually feel the same, neither hotter than the hottest nor less hot than the least hot. Necessarily, how hot an object feels via a tool is a monotonic function of a hotness scalar that objects have, which is eventually weighted-averaged between touching objects.
submits and reads the post to see how I did
technically if they ended up always feeling as hot as the most hot, you would need the hotness scalar to grow more quickly with the felt hotness than our instruments can detect
“if it feels hotter, the hotness scalar is larger”