Archive for March, 2012

The first sunday after the first full moon after the vernal equinox

March 31, 2012

This year the vernal equinox happened on different dates on the east and west coasts of the US. The equinox happened at 05:14 UTC, 20 Mar¹. But that’s 12:14AM EDT or 9:14PM PDT 19 Mar. Now suppose, just suppose that the full moon were at 5:14 UTC, Sun, 8 Apr. Then the full moon would happen on Sunday on the east coast and on Saturday on the west coast. Would Easter happen a week earlier on the west coast than the east?

So when does “Sunday” begin? What timezone should it be measured in?

Would it be the dateline? Jerusalem? Rome? Constantinople? Canterbury? Nicaea? For the sake of argument, I’m going to pretend it is Jerusalem. Which is GMT+3 hours.

Except it isn’t. Back in 325 at the council of Nicaea, there was no concept of mean time or timezones or daylight savings, so presumably “Sunday” was decided by apparent solar time (possibly at Jerusalem). Now mean solar time in Jerusalem is GMT+2:20 or there-abouts (depending on exactly WHERE in Jerusalem you choose).

Suppose you chose the wrong part of Jerusalem? It’s big. Every mile east or west would mean an error of roughly four seconds (4.1 seconds) in determining the start of a new day. So with just a mile error, if the full moon were at 23:59:58 Sat. you might think it happened on Sunday. Or vice versa.

I assume the day begins at midnight. But did it in 325? Did they use the Jewish idea that the day begins at sundown?

But that’s mean solar time, not apparent. Of course in April the difference between mean and apparent solar time is slight (it usually reaches 0 in the middle of the month somewhere) but on most potential “Easter” days there will be a discrepancy. This means that even if you had a moon calendar accurate for Jerusalem’s mean solar time there will be some full moons which will be on the wrong day because of the difference between mean and apparent time.

Now people like to calculate Easter in advance. Unfortunately we can’t predict the earth’s rotation very accurately and the time lords who determine UTC can throw in a leap second at the end of any month (though so far it has come either 31 Dec or 30 June). In fact at about 6 months in the future the prediction of when a “day” begins can be off by as much as a second.

So some day we’ll have a full moon which is predicted to be at 23:59:59.5 on Saturday, but which is actually at 00:00:00.5 on Sunday. And people would have to reschedule Easter for the following week, and we’d get two Palm Sundays.

The same confusion over the the earth’s rotation means that the vernal equinox can’t be predicted accurately either. So someday, if the full moon is very close to the equinox the predicted order will be wrong and Easter will be off by a whole month (lunar cycle). Possibly coming a month earlier, possibly a month later than expected.

The timing of the full moon, and the earth’s rotation round the sun have their own uncertainties, but my understanding is that these are much less than those involved in the rotation of the earth.

I’ve been puzzling this riddle for years and I could never find anything about timezones in the calculation of Easter. And it turns out that just about everything I thought I knew was wrong.

The council of Nicea did not decide how to determine Easter — it just said that everyone should use the same day. And Easter isn’t decided by “the first sunday after the first full moon on or after the vernal equinox,” but by a peculiar algorithm decided on by the church which approximates the above statement.²

Interesting to see that in the 18th century Germany and Sweden used a method based on Kepler’s data which produced a different sunday 4 times in that century.

It’s sort of like the Hitchhiker’s Guide which “make[s] the reassuring claim that where it is inaccurate, it is at least definitively inaccurate. In cases of major discrepancy it was always reality that’s got it wrong.” [10th fit of the radio series]

Hmm. In 1928 parlement decided that Easter should be “the first sunday after the second saturday of April”.

Identifying Fritillaries

March 22, 2012

About this time last year I was running down Forbush trail toward the Grotto when I blundered into a patch of fritillaries.

Now I was a little perplexed by them because the didn’t look like any of the fritillaries that Cal Flora says bloom in SB county. But the SB Hikes website had a picture that matched along with a comment that SB had an odd color morph. Going back to Cal Flora I discovered that the latin name used by SB hikes had changed and F. lanceolata was now called F. affinis.

Hmm. And Clifton Smith doesn’t list either name as blooming in SB. Disturbing.

A few months later I was handed a species list for the back side of Arroyo Burro trail which included a rare species F. ojaiensis, and no other fritillary. I have an automatic assumption that I’m not likely to see any rare species — I just don’t look hard enough — but there, on the trail, were some fritillary seedpods. So I knew something was growing there.

A couple of weeks ago I found fritillary plants with flower buds growing on both Forbush and Arroyo Burro trails.

Yesterday I went out for a hike on Arroyo Burro, but before I went I got out my Jepson and read up on both species. And I began to think that what I had seen on Forbush trail might really be F. ojaiensis. It was the right color, in the size range, the whorls of leaves seemed to be within the range for them…

When I got to the fritillary patch on Arroyo Burro the plants were in full bloom, but the flowers were tiny. The blooms looked just like the ones on Forbush trail from last year — except they were about a third the size.

So I was perplexed. Were they both ojaiensis and the size difference was unimportant? had I found plants that were at the two far edges of the size range? After all, they weren’t the standard color for affinis.

I went back home and spent some quality time with Jepson. The bits I understood seemed to say that both flowers might be ojaiensis, while, yes, the bigger one might be affinis. The bulbs were different, but I wasn’t going to dig up bulbs on a rare species. And the nectaries were different. Well what on earth is a nectary? Actually it’s pretty clear what a nectary, it’s something that gives out nectar, but what does it look like?

Ah. Thank you Fritillary Group. The nectary is a differently colored blot at the base of the petal (technically tepal, or perinath part). And yes, close inspection reveals that the nectaries of the two flowers are different. The larger flower has a dark broad line, while the smaller flower has a light diamond shape. So the large flower is affinis and the smaller one is ojaiensis.

Yay! Now I understand how to look at fritillaries. Or at least these ones

Nope. My memory wasn’t accurate. The flowers on Forbush are blooming now (7 April) and they are the same size as the ones on Arroyo Burro. And the nectaries look just the same. Both sites appear to have F. ojaiensis.


March 7, 2012

I was hiking in the backcountry, near the top of (the back side of) Arroyo Burro trail when I turned a corner and saw a bobcat trotting down the trail ahead.

He didn’t seem to hear me.

After a few seconds he sat in the trail, still not noticing me.

I stopped and pulled out the camera as fast as I could; expecting every tiny sound to send the bobcat scurrying off. But he just sat. I took one quick shot.

Not the best image, I fear. I had the camera adjusted for taking macro pictures of wildflowers in the direct sun, not for bobcats in the shade twenty feet away.

But I know from past experience that fiddling to get the perfect shot often means the animal leaves and I get no shot. So I took a quick shot, then I moved slightly to get a better view (so the bushes weren’t obscuring the cat), and — the cat was gone, crashing into the chaparral. Oh well.

I’ve seen bobcats 4 times in the last 5 years. Once on More Mesa, once on Island View trail, once on the front side of Arroyo Burro, and now on the back side.

Track workouts

March 6, 2012

I hate them.

Or I hate doing them. I admit there is a certain satisfaction after having completed one.

A couple of years ago I convinced myself that running “fast” (for me) caused injuries, so I stopped doing them. Now I’m not so sure. Running “fast” exacerbates injuries (I’m still sure of that), but I’m less sure it actually causes them. Anyway I’ve started doing track workouts recently — every other week, rather than every week, just to be on the safe side — and no injuries have been caused yet.

I’m not sure what group to go into on the track… I seem to be able to do a tempo run relatively faster than a track workout, which means that the group I have been running with for tempos wants to go a little faster than I’m able to.

I listened to the paces Rusty assigned. My tempo group was told to run 91 second quarters for the mile, the next slower group was 94 second quarters. Well 91 second quarters for a mile is still sounds easy to me.

The workout was 3×800 (at 88sec/quarter), 1600 (91sec/quarter), 2×800 (88), 1600 (91), 2×400 (87). I thought I could do that. But… we didn’t run the pace. We’d all run together a little faster than the pace for the first bit and then everyone else would speed up and pass me. I’d struggle along seconds behind them, but still seconds ahead of the desired pace. I did 2:54,2:53,2:54,5:56,2:55,2:54,5:54,84,87.

I looked back in my notes. Five years ago a randomly selected track workout looked like: 3×800 (86), 1600(87), 2×800 (86), 3200 (89). About 1% faster than what I actually did (the age graded tables suggest a much greater decline from 47 to 52). That’s kind of consoling…

Now the workout is over. I did it.

And, yeah, I’m kinda proud of it now.