What now, Dr. Moebius?  


Prepare your minds for a new scale...                   
of physical scientific values, gentlemen.

Mark Calabretta takes the lazy man's way out and appeals to facts:

Here in a topology-free way is what the axis labels of my graph look
like during the said leap second insertion:

            UTC axis                    TAI axis                 DTAI
       2005/12/31 23:59:58         2006/01/01 00:00:30            32
       2005/12/31 23:59:59         2006/01/01 00:00:31            32
       2005/12/31 23:59:60         2006/01/01 00:00:32            32
                        60.9                        32.9          32
                        60.99                       32.99         32
                        60.999...                   32.999...     32
       2006/01/01 00:00:00         2006/01/01 00:00:33            33
       2006/01/01 00:00:01         2006/01/01 00:00:34            33

The seconds keep step and the graph has no gaps, jumps or kinks.

Now let's look at a leap hour introduced as an extra "fall back" hour:

2600-12-31T23:59:58 2601-01-01T00:00:31 33
2600-12-31T23:59:59 2601-01-01T00:00:32 33
2600-12-31T23:00:00 2601-01-01T00:00:33 33
2600-12-31T23:00:01 2601-01-01T00:00:34 33 (?)
... ...
2600-12-31T23:59:58 2601-01-01T01:00:31 33 (?)
2600-12-31T23:59:59 2601-01-01T01:00:32 33 (?)
2601-01-01T00:00:00 2601-01-01T01:00:33 3633

I chose to introduce the leap hour on December 31 - I don't believe the proposal indicates the date for doing so.  Folks have been tossing around the notion of aligning this with daylight saving time - but DST in what locality?  Does anyone really believe that a leap hour would be introduced on different calendar dates worldwide?  (It seems to me that the one time it is guaranteed NOT to occur is during a daylight saving transition.)

Not satisfied with the ITU position that UTC should merely be emasculated to correspond to TAI - 33s - Nx3600s (which, of course, really has the effect of ensuring that TAI itself will remain a completely irrelevant mystery to the public), some would completely eliminate UTC from the equation (or is it that they would eliminate TAI?) Something like:

2600-12-31T23:59:58 2601-01-01T00:00:31
2600-12-31T23:59:59 2601-01-01T00:00:32
2600-12-31T23:00:00 2601-01-01T00:00:33
2600-12-31T23:00:01 2601-01-01T00:00:34
... ...
2600-12-31T23:59:58 2601-01-01T01:00:31
2600-12-31T23:59:59 2601-01-01T01:00:32
2601-01-01T00:00:00 2601-01-01T01:00:33

But we're to believe that this would be implemented as an omitted "spring forward" hour - ignoring the fact that many localities don't currently have this option because they don't use DST at all - can't omit what you don't have in the first place.  Well - fine, a "spring forward" event might look like:

2600-12-31T23:59:58 2601-01-01T00:00:31
2600-12-31T23:59:59 2601-01-01T00:00:32
2601-01-01T01:00:00 2601-01-01T00:00:33
2601-01-01T01:00:01 2601-01-01T00:00:34
2601-01-01T01:00:02  2601-01-01T00:00:35

But under this interpretation we're to believe that the very notion of international civil time is anathema (except perhaps for TAI with some oddball persistent 33s offset and either a one hour gap or one hour repetition every few hundred years).  What this means is that *local* civil/business/legal time contains this gap or this repetition.  I suspect we can agree that the civilians/businesspersons/lawyers won't care whether the issue is local or not, all they are going to see is a repeated time sequence or a gap - and with no possibility of appeal to standard time, because standard time as we know it simply won't exist anymore.

And historical time?  Well, historians will simply have to get with the program.  Suck it up.  Perhaps loudspeakers will announce the arrival of the leap hour (or leap timezone migration event) with the admonition to refrain from historically significant activity for the space of one hour.  (This announcement would be unnecessary in the Washington, D.C. city limits, of course.)

And more to the point, since international time is a fiction, this gap/overlap in civil/business/legal/historical time would occur twice a year, every year.  Perhaps it could be scheduled to coincide with the State of the Union Address to minimize its historical impact.

I suppose this would be a good way to finally convince folks to do away with DST.

But, of course, one suspects that even the ardent supporters of the "timezone" proposal don't really expect it to be adopted.  The ITU has made it pretty clear that only two options are on the table - the status quo of leap seconds, or the perceived-to-be-politically-expedient, albeit goofy, proposal of leap hours.  As I said in an earlier message (and as Mark has now so clearly delineated), the only viable way to introduce a leap hour is just like a leap second, as additional ticks added to the clock:

2600-12-31T23:59:58 2601-01-01T00:00:31 33
2600-12-31T23:59:59 2601-01-01T00:00:32 33
2600-12-31T24:00:00 2601-01-01T00:00:33 33
2600-12-31T24:00:01 2601-01-01T00:00:34 34
2600-12-31T24:00:02 2601-01-01T00:00:35 35
... ...
2600-12-31T24:59:58 2601-01-01T01:00:31 3631
2600-12-31T24:59:59 2601-01-01T01:00:32 3632
2601-01-01T00:00:00 2601-01-01T01:00:33 3633
2601-01-01T00:00:01 2601-01-01T01:00:34 3633
2601-01-01T00:00:02 2601-01-01T01:00:35 3633

As Mark says:  "The seconds keep step and the graph has no gaps, jumps or kinks."  (Well, some might argue that this whole idea is kind of kinky.)

I'm only speculating about the behavior represented above for DUT1 (or DTAI or whatever) during the progress of the leap hour, of course - of course, because the "proposal" doesn't choose to contemplate such distressing issues.  Ooooh!  It makes their widdle heads hurt!

BTW - thanks to whoever for reminding me of the concept of diffeomorphism.  Really loved topology as an undergrad.  Trying to remember if I finished that course - was about the time I realized I couldn't pursue everything that interested me.  I spend more time in Dilbert Space than Hilbert Space these days - what a shame!  (If only I'd pursued the Math degree instead of Astronomy!  I might now be an ardent supporter of the sane and sensible notion of the leap hour.  :-)  In any event, I doubt whoever wrote the ITU proposal was thinking about Hausdorff Spaces at the time.

Ranger Brad, I'm a scientist.  I don't believe in anything!

I think a little atmospherium is all we need to resolve out troubles.  Let's share!

Rob Seaman
National Optical Astronomy Observatory

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