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> Of course the "real" numbers have never been controversial Apparently the existence of irrational numbers was a shock to Pythagoreans. There may be also peop

by kgwgk 4y ago

> Of course the "real" numbers have never been controversial Apparently the existence of irrational numbers was a shock to Pythagoreans. There may be also people unhappy with transcendental numbers.

jerf 4y ago
In 21st century hindsight, being annoyed by irrational numbers seems a bit odd to me. I mean this very much as an opinion. I actually partially understand where they were coming from; it makes a bit more sense than the 21st century perspective would indicate, but still, obviously, not something we'd agree with today. Even from a 21st century perspective, I think that the first "two dimensional number" is always going to freak people out and I can see where it's coming from. Imaginary numbers intrinsically involves leaving numbers that can be used to describe the number of apples you have in your hand, and by the time people get there, they've been pretty darned used to numbers looking like that. Real numbers nominally overshoot that too (you can't really have apples in two hands whose size only differs by 10^(-(10^1000))) but people tend to not have their faces rubbed in this until they get a math degree. Matrices nominally are such numbers too, but they are often presented as shortcuts rather than numbers in and of themselves. Of course in the 21st century now we have a zoo of these representations and the community as a whole is comfortable with it.... but for any given person I still think that first number that isn't something that can be a number of meters or apples is a shock.
- kgwgk 4y ago
  > that first number that isn't something that can be a number of meters or apples is a shock. That’s what Pythagoreans thought about irrational numbers, I guess. You don’t need them to denote a fraction of an apple.
- C-x_C-f 4y ago
  Plus Pythagoreans had a much more religious attitude towards number than any present-day mathematician. In fact I think it's almost misleading to remember them chiefly for their mathematical contributions (many of which are disputed anyway) while they were first and foremost mystic philosophers.

by kgwgk 4y ago

> Of course the "real" numbers have never been controversial Apparently the existence of irrational numbers was a shock to Pythagoreans. There may be also people unhappy with transcendental numbers.

jerf 4y ago

In 21st century hindsight, being annoyed by irrational numbers seems a bit odd to me. I mean this very much as an opinion. I actually partially understand where they were coming from; it makes a bit more sense than the 21st century perspective would indicate, but still, obviously, not something we'd agree with today. Even from a 21st century perspective, I think that the first "two dimensional number" is always going to freak people out and I can see where it's coming from. Imaginary numbers intrinsically involves leaving numbers that can be used to describe the number of apples you have in your hand, and by the time people get there, they've been pretty darned used to numbers looking like that. Real numbers nominally overshoot that too (you can't really have apples in two hands whose size only differs by 10^(-(10^1000))) but people tend to not have their faces rubbed in this until they get a math degree. Matrices nominally are such numbers too, but they are often presented as shortcuts rather than numbers in and of themselves. Of course in the 21st century now we have a zoo of these representations and the community as a whole is comfortable with it.... but for any given person I still think that first number that isn't something that can be a number of meters or apples is a shock.

kgwgk 4y ago
> that first number that isn't something that can be a number of meters or apples is a shock. That’s what Pythagoreans thought about irrational numbers, I guess. You don’t need them to denote a fraction of an apple.
C-x_C-f 4y ago
Plus Pythagoreans had a much more religious attitude towards number than any present-day mathematician. In fact I think it's almost misleading to remember them chiefly for their mathematical contributions (many of which are disputed anyway) while they were first and foremost mystic philosophers.