Monday, March 9, 2015

Section 8-5: Areas of Triangles (Day 127)

This weekend was the time change to mark the beginning of Daylight Saving Time. And so the debate over whether we should keep DST as it is, have year-round DST, or year-round standard time continues this weekend.

For many people, "springing forward" is more difficult than "falling back." It's easier to get an extra hour of sleep than it is to lose an hour. Because of this, here's another DST proposal, by someone named Richard S. Holmes:

                              Richard S. Holmes

It happens every spring: crocuses, baseball (with any luck), and the switch to
Daylight Savings Time (DST).

Coming off DST is not hard.  In the Fall, we set our clocks back one hour.  We
all get an extra hour to sleep, and those who forget find themselves at church,
or the airport, or wherever an hour early.  Embarassing [sic], but not catastrophic.

But in the Spring we set the clocks forward, and the trouble begins.  We lose
an hour of sleep.  Forgetful people miss Mass, planes, breakfast, and the big
game on TV.  Some are thrown into disarray for up to a full week.  Annual
losses due to DST confusion have been estimated (by me) at over a million
dollars.  I myself have missed a flight to Washington and a showing of The
Seven Samurai because of DST.

There is no need for such tragic waste.  We can -- we should and must -- urge
our lawmakers to reform Daylight Savings Time as follows:

Setting clocks back is easy; setting them forward is difficult.  Therefore, let
us keep the fall ritual as it is.  However, one Sunday each Spring, let us set
our clocks not one hour forward, but TWENTY-THREE HOURS BACKWARD.

Think of all the advantages.  We will not lose an hour of sleep; we will gain
(almost) a day of rest.  It will be Saturday all over again.  You will never
again miss Confession, or an airplane, or the Redskins game.

Naturally, if this were the whole plan, our calendars would fall behind one day
in each year.  However, the second part of the Revised DST Plan deals with
this.  Every four years, instead of adding a day, let us SUBTRACT THREE DAYS. 
Furthermore, let these be Monday, Tuesday, and Wednesday, which according to
recent polls are the least popular days.

If done in February, which seems reasonable considering what a miserable month
it is, this would have the beneficial side effect of shortening the
excruciating presidential primary season by an effective four days.

The advantages of this plan are clear.  Let us waste no time.  With a determined
effort we can have Reformed Daylight Savings Time by Spring of next year.

Write your congressperson today!

Now the Holmes proposal is mostly a joke. But it's interesting to see what would happen if Revised DST were actually implemented:

-- First of all, Holmes makes an error here. No one has ever missed a Redskins game due to springing forward, since the Redskins don't play in the spring.

-- If the time change happens at 2 AM on a Sunday, then setting it 23 hours backwards means that it would now be 3 AM on Saturday. It may be awkward to have a full Saturday, then two hours of Sunday, and then back to Saturday again. Instead, I recommend that the time change happen at, say, 11:30 PM on Saturday night, to become 12:30 AM Saturday morning. Instead of having the day change to yesterday, we now have a Saturday lasting 47 hours.

-- In practice, what actually happens is that the clocks are still set forward an hour, but there is a second Saturday and thus a three-day weekend. There is an extra day to adjust to the time change before returning to work on Monday.

Indeed, we see that the seven-day week isn't sacred to Holmes, since he has no problem with dropping Monday, Tuesday, and Wednesday every four years. Therefore, Revised DST is actually a calendar reform proposal. But instead of dropping three days, I'd have a 364-day year (with one of the days 47 hours long). I like this because a 364-day year can be evenly divided into seven-day weeks! 

In other words, we could have a 364-day calendar like, say, the World Calendar (that I mentioned back during my New Year's Eve post on calendar reform), but instead of a blank day at the end of the year, we have a 47-hour Saturday some time in the spring. Since every quarter in the World Calendar begins on a Sunday, April 1st must be a Sunday. So the last day of March can be the long Saturday. (I point out that if one finds a 47-hour day to be too long, one can split the extra 23 hours between Saturday and Sunday, a plan called the Long Sabbath Calendar.)

-- One problem with the Holmes DST plan is that it's USA-centric, and therefore favors the Northern Hemisphere and its seasons. Those living in the Southern Hemisphere would set the clock back 25 hours in their autumn, and still have to set the clock forward an hour in their spring. One can partially balance this by setting the Leap Day to occur in the Southern spring, so at least once every four years, Australians get to enjoy setting the clock back 23 hours as well.

Which boxes on the Calendar Reform list would be checked by this plan? Let's see -- since this plan still involves changing the clock twice a year, all of these boxes must be checked:

(x) requiring people to manually adjust their clocks is idiotic
(x) local time should not be discontinuous
(x) local time should not go backwards
(x) local time should not repeat itself
(x) no amount of clock-moving can increase the amount of solar energy received by Earth
(x) "daylight saving" doesn't

If we accept the original Holmes plan, it disturbs the seven-day week by having a second Saturday some weeks and skipping from Sunday to Thursday during others, then we'd have:

(x) every civilisation in the world is settled on a seven-day week

If we use my version which attaches Revised DST to the World Calendar, then we'd either have:

(x) having one or two days per year with no day of the week is asinine

if the extra 23-hour days are called "blank days" as in the World Calendar, or if we instead consider them to be 47-hour Saturdays, we'd have to check:

(x) solar days are real and the calendar day needs to sync with them

There's also a non-calendar reform to achieve a similar effect to Revised DST. Sometimes people propose that the time change occur Saturday morning rather than Sunday morning. Then one would have two days to adjust to the time change. One can also declare the Monday after the time change to be a holiday. If done at the start of April (as the time change occurred from 1987-2006), then it could result in baseball's Opening Day being a holiday, as is often proposed. (Some sport fans often propose that the day after Super Bowl Sunday be a holiday, but that's too early to spring forward.)

Meanwhile, I've already mentioned the Sheila Danzig plan, where not only is there a single time the whole year, but there are only two timezones in the lower 48, with only a two-hour time difference between the east and west coasts. Alison Schrager repeated her similar plan where there is only one hour between the coasts:

But now Schrager extends her plan around the world. She eventually states that there would be only 10 or 12 time zones, each about two hours apart. So basically, it would be a worldwide Danzig plan.

Some states, such as Colorado, are considering have a single year-round time. The proposal would be for Colorado to have year-round DST, which may occur on the November 2016 ballot:

My opinion of this proposal is mixed. If individual states change to a single time year-round, I'd argue that whether year-round Standard Time or year-round DST is chosen should be based on the surrounding states -- in particular, to avoid the paradoxical situation where one would have to set a clock back one hour to go east or forward an hour to go west. In this sense, the year-round DST proposal is superior to year-round Standard Time, since the latter would result in Colorado being a hour behind Utah to its west in the summer. I suspect that any plan that has a border where the western edge of the border is an hour ahead of the eastern edge of the border, during any part of the year, would be rejected by the Department of Transportation.

But if several states are considering changing to a single time year-round, then I believe that they should work towards the Danzig or Schrager plans. Year-round DST is also the recommendation for Colorado under the Schrager plan. However, the Danzig plan recommends year-round Standard Time for Colorado. This would be awkward unless Utah changes to year-round Standard Time as well.

I prefer the Danzig plan, because I live in California and prefer year-round DST to year-round Double DST, which Schrager recommends for California. Year-round Double DST would have the sun rising here around 9 AM in the winter, which is inconvenient for schoolchildren. If California were to change without other states changing, year-round DST is also preferable since it would keep us the same time as neighboring Arizona, which doesn't change its clocks, the whole year. But actually year-round DST for California is impossible unless Nevada on our east does it as well.

California is not currently considering a DST change, but some western states -- namely Washington, Oregon, and Idaho recently considered changes. The situation in the Pacific Northwest is confusing because the time zone line splits Idaho into Pacific and Mountain time zones. The original proposal was for Idaho to switch to year-round DST, but it ran into problems:

It is claimed that states can only choose year-round Standard Time or the biannual DST clock change, but not year-round DST. But the commenter "Big Jim Swade" pointed out:

Why not just move the whole state to Mountain Standard Time year round and get rid of having the state divided between time zones.

Similarly, my proposal for California wouldn't technically be year-round DST, but instead it would be year-round Mountain Standard Time.

I'd actually oppose year-round DST for Idaho, since then it would be a hour ahead of Wyoming to its east in the winter. I prefer Big Jim Swade's plan, which would keep Idaho on year-round Mountain Standard Time.

As for Washington and Oregon, that depends on what Idaho to their east do. If Idaho doesn't change, then Washington and Oregon would have to choose year-round Standard Time, since year-round DST would put them an hour ahead of Idaho on their eastern border in the winter.

Also, it's possible for Idaho to do what Indiana did a few years ago -- have the eastern side of the state on year-round Standard Time and the western side change its clocks twice a year. But this still wouldn't allow Washington or Oregon to have year-round DST.

Remember, if any changes occur in the west, my preference is for as many states to have the same as Arizona year-round as possible. This is the Danzig plan. But only Idaho, Nevada, and Utah can adopt Arizona time now -- other states must wait for those three to do so first. (Technically New Mexico can adopt Arizona time now as well, but this introduces a two-hour jump between New Mexico and Oklahoma and Texas on its eastern border in the summer. I suspect this would be rejected unless enough other states have already headed towards the full Danzig plan.)

I could go on and on about DST. Actually, I don't have much to say about today's geometry lesson at all, since Section 8-5 of the U of Chicago text is on the areas of triangles. You already know that the area of a triangle is half the product of its base and height. I did point out that this is proved for all three cases -- when the altitude is inside, outside, or aside of the triangle. This roughly corresponds to the acute, obtuse, and right triangles. But notice that if the altitude is drawn from the largest angle of a triangle, the altitude is always inside the triangle even if that angle is right or obtuse.

One of the included questions gives the area of a quadrilateral with perpendicular diagonals as half the product of those diagonals. It applies to all quadrilaterals whose diagonals are perpendicular -- which includes kites (and rhombuses and squares, which are kites under the inclusive definition). In some texts this is a highlighted formula, but in the U of Chicago it is buried in an exercise.

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