Thank you SO much for writing/drawing this! Now I’ll know what to tell people the next time they ask me. If after hearing answer #4 they insist that they ARE ready for the answer, I’ll say “Well, … when a Mind and a World get together, a strange and beautiful thing happens: …”
Hammering – pounding one thing with another thing – existed before the “invention” of the hammer.
Math is the language we use (invented) to communicate information about quantities and ratios. Those relationships (more people needed to move a big rock than a little rock, a little salt goes a long way, no eggs with just one chicken) exist independent of human interaction with them.
On the discovery vs invented shtick I’d say some of both. Discovered in that one doesn’t know what a proof means or implies until it’s done. That outcome isn’t known before it’s started even if what wants to be proved is known. The thing is proofs can surprise, even those who do the proof.
Interesting question! I lean towards math being discovered. The underlying principles seem inherent in the universe, we just develop the language to describe them. Like natural laws you discover while playing Moto X3M – physics exist regardless of your skill. Perhaps it’s a bit of both, invention and discovery constantly feeding each other.
This piece humorously captures the long-standing debate by showing that math feels both invented and discovered, depending on Retro Bowl how and where we choose to look at it.
Thank you SO much for writing/drawing this! Now I’ll know what to tell people the next time they ask me. If after hearing answer #4 they insist that they ARE ready for the answer, I’ll say “Well, … when a Mind and a World get together, a strange and beautiful thing happens: …”
Hammering – pounding one thing with another thing – existed before the “invention” of the hammer.
Math is the language we use (invented) to communicate information about quantities and ratios. Those relationships (more people needed to move a big rock than a little rock, a little salt goes a long way, no eggs with just one chicken) exist independent of human interaction with them.
Scratch the bit about the chicken and egg. Should say “one chicken produces eggs but not more chickens”. Sigh.
On the discovery vs invented shtick I’d say some of both. Discovered in that one doesn’t know what a proof means or implies until it’s done. That outcome isn’t known before it’s started even if what wants to be proved is known. The thing is proofs can surprise, even those who do the proof.
I felt sure that Kronecker would be mentioned. He’s usually the one claimed to have said “God made the integers, all else is the work of man.”
“G-d made the integers, all else is the work of man.” Leopold Kronecker, 1800’s.
Interesting question! I lean towards math being discovered. The underlying principles seem inherent in the universe, we just develop the language to describe them. Like natural laws you discover while playing Moto X3M – physics exist regardless of your skill. Perhaps it’s a bit of both, invention and discovery constantly feeding each other.
This piece humorously captures the long-standing debate by showing that math feels both invented and discovered, depending on Retro Bowl how and where we choose to look at it.
Sprunki is a game that may be played several times as well.