Singularity Approaching?

[stoutfellow]

According to Dark Sky, the high tomorrow will be lower than the low today.

I don't think that works, unless the temperature is discontinuous.

Mind you, in my years in Chicago, there were a couple of times that felt like meteorological discontinuities.

Comments

[graydon]

As I am certain you are aware, the temperature isn't discontinuous, but the days are.

[stoutfellow]

Are you suggesting there's a Zenoesque gap between the days? The temperatures epsilon before midnight and epsilon after should be as close as desired, for sufficiently small epsilon.

[graydon]

I think I have fallen off my math limit and don't quite get the joke.

[stoutfellow]

Your pardon, then; I apparently missed the fact that you were joking. (I think the correct explanation is that Dark Sky only looks at the temperature on the hour, so the today's-low temperature at 11 PM can be higher than the temperature at midnight, which then turns out to be the high for the next day.)

[graydon]

Well, what I thought I meant was that days work like "tumbling windows" in database languages; you've got a continuous stream of information, and drop this arbitrary window on it that isn't allowed to overlap with any other window.

So just because temperature is continuous as a physical process (or at least I very much hope so!) doesn't mean adjacent windows can't have the behaviour described. (As you note, it's unlikely they're taking temperature readings continuously.)

[stoutfellow]

In other words, we're looking at an artifact of the data collection, rather than a physical reality. OK, I can buy that. And yet NWS has these nice, continuous-looking data plots for temperature and such...

[jsburbidge]

Absent issues of quantum continuity, adjacent but disjoint sets of temperatures in reality must be an open set next to a closed set, or we have a discontinuity. That is, they behave like the real numbers.

But weather measurements for two periods are adjacent closed sets.

That bring said, I have heard radio weather announcers say things like "The high today is ten degrees" five seconds before saying "the current temperature is eleven", leaving me to wonder what mathematical universe they live in.

[graydon]

Somewhere nearby, someone has a backyard weather station where the barometer is terribly, terribly wrong. It's about forty hectopascals low.

So a lot of weather underground graphs and various weather applications warnings go off because, so far as the data stream about pressure is concerned, there's a major hurricane out there.

I don't think the immense mass of weather data is checked all that thoroughly in immediate terms.

[ndrosen]

Weather reports aren’t intended for professors of mathematics. 8-;