Well, a half hour before bedtime. It’s getting dark, and that means that everything turns blue in Antarctica. Here’s the view from my balcony: lots of floating ice, with an occasional big iceberg.

Tomorrow you will see a beautiful field station, a passel of molting juvenile penguins, a snow chute that you slide down on your butt, and you’ll learn that I ate abstemiously today.

5:15 seems a bit early for bedtime. I’m in Pennsylvania. How do time zones work in Antarctica and does the fact that you are so close to the pole have an effect on the day’s length?

I’m not sure how time zones work here; Google may help. The ship’s time is constant, though we may cross some time zones. We are three hours ahead of Chicago time, and I go to sleep around 9:30 pm ship’s time.

It appears that there is no simple answer – it is a kind of “roll your own” zone. Per Jerry’s suggestion, there is a good discussion of some of the issues and options by the Hurtigruten expedition Line in wikipedia at https://www.hurtigruten.com/destinations/antarctica/inspiration/antarctica-time-zone/

The Hurtigruten page makes one mistake. Time zones are defined by longitude lines, not latitude. As you get really close to either pole, well south of the Antarctic Circle and north of the Arctic Circle, the lines of longitude get so close together that time zones are so narrow as to be not useful. At the pole, you could walk through all 24 time zones in a minute just by tramping a circle around the marker. This effect is not yet pronounced at Jerry’s latitude. Communities in northern Canada above the Arctic Circle can use standard time zones effectively….and of course everywhere they bend around a lot to accommodate commerce and political administration.

@Jean Hess, We are just 2 weeks away from the March equinox. Jerry’s hours of daylight are therefore close to what everyone in the world is getting right now, about 12 hours. A bit more for him because it’s still summer and he’s so far south but it will be shortening rapidly. In the high latitudes, the sun sinks and rises at a shallow angle with the horizon, prolonging the dawn and dusk twilight substantially when it’s not overcast. You can see this even in Jasper National Park. My wife tells me that in the Canadian Arctic (Iqaluit and Cambridge Bay, still south of the Circle,) it is quite striking. Even in full summer the sun never climbs very high, though, even though it’s up over 20 hours a day.

Well, at the moment we’re also quite close to the March equinox.

Antarctica sunlight hours

Does the Amundsen run at night? I know that she is armored for polar expeditions but some of that sea ice looks a bit foreboding if it were to smack a ship at any significant speed.

Sometimes it runs at night if we’re moving between places. It’s never stopped because of ice; this ship is capable of jamming itself into pack ice without damage (we did that in 2019). But the bridge is occupied with one captain or another 24 hours a day, and the top captain’s own cabin is right next to the bridge. We have sophisticated radar and sonar and I tink we’re capable of seeing any large berg. Small floating ice poses absolutely no danger to the ship. (We visited the bridge in 2019, and it was amazing what with all the computer screens and equipment. Sadly, we won’t be doing that this year because of Covid.

Beautiful photo!

I’m not sure whether Jerry has access to the Economist while at sea, but the obituary in the latest issue is apropos. It’s about Cristina Calderón, the last full-blooded member of the Yaghan people of Tierra del Fuego. She spent much of her later years recording the culture and language of her people. Yes, Darwin is mentioned.

I saw Calderon’s obituary. Really fascinating and poignant.

No, I don’t, but a passenger told me that she died. She is on the last slide about the Fuegians in my lecture, and I checked when preparing my lectures in Chicago. Then she was still alive at 93. But she died a few weeks ago, I think, and was the last full-blooded member of the Yamana: the group that Darwin and the Beagle encountered in Tierra del Fuego.

I’m curious what the Weather app says – or, indeed, what time is displayed – how about the compass?

I should plan a trip of my own, is what I’m thinking…

I just found “Antarctica (general)” on the Weather app.

Everyone knows the general type of puzzler of walking a mile north, a mile east, and a mile south (There are in fact numerous solutions to this), right?

PCC(E) could be the first person to show the demonstration in real life – with time too, for extra puzzlement perhaps, and some less obvious biology! (Usually something about either polar bears or penguins is folded into the puzzler).

I doubt if he’ll get close enough to the South Pole to demonstrate that.

As I understand it, the only requirement is the travel along the longitudinal directions on either side of the triangle* meet at the southern-most point _of_that_triangle_. Not that the point has to be located on the south pole.

Triangle of course being non-Euclidean – on a globe.

… and … might be more to that..

Update – this video at 1:33 : https://youtu.be/DkkqhzatasI

Hasty explanation : Walk in a circle _around_ the pole, return to the starting point.

The only places where two different lines of longitude intersect are the poles so there’s only two ways to fulfil the requirements. Either start at the South Pole or start a mile south of the line of latitude that has a circumference of one mile.

Precisely – thanks.

Circumference – walk in a circle around the pole.

But you can’t do that at the South Pole. Even from the South Pole, by the time you’ve walked one mile north, the circumference is already a little over six miles. It works from the South Pole because the meridians intersect there but not from anywhere else in the Southern Hemisphere. So Jerry is unlikely to get there.

“… by the time you’ve walked one mile north, the circumference is already a little over six miles.”

The diagram in that video (from ~1:33 ) shows a O— shaped ring around the pole and a longitudinal path from a point on the circumference extending outward. The longitudinal path is the one taken at the beginning and the end of the complete trip.

… I’m slow to think this out… I think the difference is going _around_ the pole vs. _starting_ at a pole… I think is what you mean.

… I can’t do this by philosophizing only, I’ll have to get my paper and pencil…

Because of finding the discussion here confusing without me looking at that video, I watched it (but didn’t read the too many replies below it to see whether anybody said the following):

Firstly, the video describes the easy solution of the mirror image (south-east-north) problem of #7s (north-east-south) frenetically, but at least correctly. However her diagram on the globe, which unfortunately includes a map with North America, must be utterly confusing to some, since as drawn you’d need to change one mile to several thousands of miles! I wouldn’t recommend that to an inquisitive 6 or 7 year old, who’d get pretty confused about either geographical distances or how lengthy a mile really is (or if the kid is fortunate enough to live in Canada, the kilometre!).

More to the point, the not-so-obvious uncountably infinitely many really interesting solutions down near the south pole (symmetrically up near the North pole for Thyroid’s version) is again correct verbally, but the diagram very confusing when thinking geographically and about the size of the mile.

And surely all that’s needed for even the 6 year old of notable intellectual curiosity is:

1/ find the unique circle of circumference 1 mile exactly centred at the South Pole. Start at any one of the infinitely many points exactly 1 mile north of that circle. Go south to your circle, around it entirely once, then due north to where you started, of course on the same longitude as before.

2/ for all the other, even more interesting and obscure, solutions, first pick any larger natural number from 2 or 3 or 4 or ….. Say choose 13 just to be specific. Now find the circle centred at the South Pole, but this time with circumference 1/13th of a mile. Now, as before, start at any point one mile north of the circle. Go down one mile to it. But this time go round the circle 13 times exactly, not just once. Then back up on the same longitude for a mile to where you started.

I’m being way overly pedantic, unless there happens to be a 5 year old reading!

Maybe not so pedantic if I asked you to prove that there are no other solutions!

Me again, sorry, but something was subconsciously bugging me, so I looked again at the video with the closed captions on, easier, for me anyway, to make out the frenetic dialogue.

In describing the interesting solutions, she says to first find “a” mile-long circle (ONE of the circleS? Surely not!) where going round it you’re always going east (or always west of course). As far as I could see neither of them says it is to be that unique circle with the given small circumference, centred at the South Pole (**)—almost! since, there’s another such little circle around the North Pole, not to be used here.

So that video description would still be more-or less correct, if rather incomplete. On the one hand, the globe used does look like the centre might be the South Pole, by noticing a few ‘maps’ on the periphery. On the other hand, in the centre, the land mass looks like no map of any land I can think of, and certainly very far from any kind of rough map of the Antarctica continent, which it needs to be.

(**)—Of course, it’s also centred at the other, North, Pole, in mathematicians’ geometry precision jargon. We’re just talking about lines of latitude, which really should be called CIRCLES of latitude. If you dislike that ‘two centres’ way of thinking, how about the equator itself—which pole is the centre of that circle? Probably an Aussie would insist on the opposite answer versus a Canuck. I say both centres for all circles of latitude.

Actually, thinking about the equator gives more aspects: take our earth as before to be idealized as a perfect sphere of circumference 40,000 km, as Napoleon’s advisors when inventing the metric system wanted it to be; i.e. 10,000 from equator to pole. We go back to the, so-called by me, uninteresting solution of the video’s form of the problem, as opposed to Thyroid’s mirror image version. So you go straight out from the North Pole (no other ‘choice’ than due south of course) a certain exact distance, but PAST the equator, so some number of km. between 10,000 (the equator) and 20,000. That number must be to get you to that southern latitude such that if you turn left and follow it around the earth once completely, you travel exactly the same distance you had earlier done down from the North Pole. Believe me, there is exactly one such distance by a continuity argument—continuing downwards all the way from the equator to the South pole, distances increase from 10,000 to 20,000, whereas the circumference of the corresponding circle of latitude decreases from 40,000 to zero. So the two numbers must agree at one and only one place by continuity, by one of the first theorems, called the Intermediate Value Theorem, in rigorous elementary calculus. (The theorem is intuitively obvious, but in reality depends on a fundamental property of the real number system.)

Here we get a solution which looks like both the uninteresting one and like the interesting one. We change the problem merely with one mile becoming instead that particular much larger number of miles. This gives hints about how to organize an attempted proof that you’d found all solutions—how the actual size of the Earth might force a division into a few cases when attempted in general.

Ah well, I guess I’ve gotten into the habit of demanding too much clarity—but you’d sure as hell need it to try showing no other solutions exist.

I love the – your – enthusiasm.

The video : the only thing I was using it for is the diagram at ~1:33, because that was the first I heard of the alternate solutions(s). I refrained from opining that it is otherwise unwatchable. In fact, I read (“reed”) videos a lot more now than before.

As for non Euclidean geometry – I still need to get to my pencil and paper for this!

I just tried a quick demo – based on a classic demo – to test the intuition on this problem – this is super easy :

Obtain one cardboard toilet paper tube, or paper towel tube. Cut a slice off the end, to produce a ring. Repeat. Cut one ring to make one straight strip along with the original ring.

Compare the length and circumference by connecting or holding the ring on top of the straight strip’s tip.

I ask – is it obvious, that the distance around the circle is identical to the straight piece? Not to me! The object resembles a cooking utensil shape, not two identical lengths.