I suspect that you two will continue in your naif views, but let me
try one more time, taking first Mr Gilmartin and then Dr Merrill.

The basic sequence, reference standard, is TAI.  UTC is a derived quantity.

The alignment of civil dates with the seasons is a desideratum.
Precession very gradually brings UTC (and other lunisolar calendars
too) out of alignment with the seasons on earth.  Leap seconds correct
for this precession, keeping UTC seasonally aligned, or nearly so.
(There are arguments against this. The  Islamic lunar calendar rotates
the privations of Ramadan/Ramazam through the seasons; a traditional
English Christmas dinner eaten in Australian high summer is
problematic; etc., etc.  It is, however, the prevailing view.)

Sequences like

23h 59m 59s
23h 59m 60s
00h 00m 00s

are [simplistic] expository devices directed at the uninformed.   They
correspond to physical reality in the same way that the
hydrodynamic-analogy diagrams of water flowing through pipes used to
explicate electric-current flow in introductory physics texts
correspond to what goes on in an electric circuit.

The arithmetic  of multiple moduli and several simultaneous cycles
used to convert counter values into calendar dates always numbers
seconds in  the sequence

0, 1, 2, . . . , 59

It knows nothing of and cannot create a time value of the form xx xx 60.

'Splain' is presumably subliterate folksy for 'Explain',  but there
does not seem to me to be anything to much to explain.  Take thought,
Dr Merrill.

As perhaps helpful in your ruminations consider a local time L and a
GMT offset o.
Does the pair (L,0) represent a standard time, EST say?  Or again,
does it represent a daylight-savings/summer/official time, EDT say?
How, in principle, does one distinguish them?

John Gilmore, Ashland, MA 01721 - USA

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