5 ms·

You ignore that it's entirely possible to have an infinite, monotonically increasing sequence with a fixed upper bound. Yes, people could keep getting taller wi

by dkbrk 10y ago

You ignore that it's entirely possible to have an infinite, monotonically increasing sequence with a fixed upper bound. Yes, people could keep getting taller without ever exceeding some defined limit. However we would begin to encounter problems as the sequence of heights approached said limit. The deltas would become smaller than the precision of our equipment, and later would become smaller than physically meaningful scales (i.e. length scale of an atom). In this limit, I think it would be reasonable to generalise "keep getting taller" to "probabilistically grow by the smallest physically meaningful amount on an arbitrarily long timescale", in which case this continues to be well defined as t→∞ even if it would be difficult to physically observe.

pklausler 10y ago
I omitted reference to convergence on a limit from my brief note because it's self-evidently obvious to even the most casual observer that the argument is no less specious than saying that one cannot simply walk into Mordor. There is a practical limit to human height, and rather than simply converging upon it while remaining less than that limit by some nonzero amount, humans will actually reach that height in a finite duration of time and then stop evolving altogether, at least along that particular dimension.
khc 10y ago
You would be right if humans are made of numbers and not atoms.
- tlb 10y ago
  But humans are made of many atoms, and the measurement is averaged over some time period in which molecules vibrate many times, so there is no limit to the precision with which they can be measured.
personjerry 10y ago
Forgive me if I've misunderstood, but isn't your proposed problem akin to Zeno's paradox of infinite distance, where we never reach anywhere because first we need to go 1/2 the distance, then 1/2 of that, etc.? Which, of course, is resolved in math by limits, and in the real world by discrete units (i.e. atoms).
- vacri 10y ago
  Zeno's paradox also conveniently ignores that the time chunks are getting smaller alongside the distance chunks. An item going at 1m/s will cover half a meter in half a second, and still have half a meter to go. Then after another quarter of a meter, it still has a quarter of a meter to go... but now only a quarter of a second has passed. If you keep on making the time units smaller, then of course it will 'never arrive'. It's not much of a paradox if you take a time-based characteristic and then don't give it enough time to occur :)

by dkbrk 10y ago

pklausler 10y ago

I omitted reference to convergence on a limit from my brief note because it's self-evidently obvious to even the most casual observer that the argument is no less specious than saying that one cannot simply walk into Mordor. There is a practical limit to human height, and rather than simply converging upon it while remaining less than that limit by some nonzero amount, humans will actually reach that height in a finite duration of time and then stop evolving altogether, at least along that particular dimension.

khc 10y ago

You would be right if humans are made of numbers and not atoms.

tlb 10y ago
But humans are made of many atoms, and the measurement is averaged over some time period in which molecules vibrate many times, so there is no limit to the precision with which they can be measured.

personjerry 10y ago

Forgive me if I've misunderstood, but isn't your proposed problem akin to Zeno's paradox of infinite distance, where we never reach anywhere because first we need to go 1/2 the distance, then 1/2 of that, etc.? Which, of course, is resolved in math by limits, and in the real world by discrete units (i.e. atoms).

vacri 10y ago
Zeno's paradox also conveniently ignores that the time chunks are getting smaller alongside the distance chunks. An item going at 1m/s will cover half a meter in half a second, and still have half a meter to go. Then after another quarter of a meter, it still has a quarter of a meter to go... but now only a quarter of a second has passed. If you keep on making the time units smaller, then of course it will 'never arrive'. It's not much of a paradox if you take a time-based characteristic and then don't give it enough time to occur :)