- Contemporary messages sorted: [ by date ] [ by thread ] [ by subject ] [ by author ] [ by messages with attachments ]

From: David Malone <dwmalone_at_maths.tcd.ie>

Date: Wed, 11 Jan 2006 12:23:58 +0000

[A lot of discussion on this list seem to revolve around people

understanding terms in different ways. In an impractical example

of that spirit...]

*> I do not understand. As a function of TAI, UTC is neither continuous
*

*> nor monotone increasing in the mathematical sense.
*

To say if TAI is a monotone function of UTC, you need to put an

order on the set of possible TAI and UTC values. To say if UTC is

a continious function of TAI, you need to put a topology on both.

To me, TAI seems to be a union of copies of [0,1) labelled by

YEAR-MM-DD HH:MM:SS where you glue the ends together in the obvious

way and SS runs from 00-59. You then put the obvious order on it

that makes it look like the real numbers.

OTOH, UTC seems to be a union of copies of [0,1) labelled by

YEAR-MM-DD HH:MM:SS where SS runs from 00-60. You glue both the end

of second 59 and 60 to the start of the next minute, in adition to

the obvious glueing.

I haven't checked all the details, but seems to me that you can put

a reasonable topology and order on the set of UTC values that

will make UTC a continious monotone function of TAI. The topology

is unlikely to be Hausdorf, but you can't have everything.

*> DTAI jumped
*

*> from 32 s to 33 s; thus, UTC is not a monotone increasing function of
*

*> TAI either.
*

Since DTAI involves subtracting quantities that aren't real numbers,

you can't conclude that a discontinuity in DTAI results in a

discontinuity in UTC.

David.

Received on Wed Jan 11 2006 - 04:24:18 PST

Date: Wed, 11 Jan 2006 12:23:58 +0000

[A lot of discussion on this list seem to revolve around people

understanding terms in different ways. In an impractical example

of that spirit...]

To say if TAI is a monotone function of UTC, you need to put an

order on the set of possible TAI and UTC values. To say if UTC is

a continious function of TAI, you need to put a topology on both.

To me, TAI seems to be a union of copies of [0,1) labelled by

YEAR-MM-DD HH:MM:SS where you glue the ends together in the obvious

way and SS runs from 00-59. You then put the obvious order on it

that makes it look like the real numbers.

OTOH, UTC seems to be a union of copies of [0,1) labelled by

YEAR-MM-DD HH:MM:SS where SS runs from 00-60. You glue both the end

of second 59 and 60 to the start of the next minute, in adition to

the obvious glueing.

I haven't checked all the details, but seems to me that you can put

a reasonable topology and order on the set of UTC values that

will make UTC a continious monotone function of TAI. The topology

is unlikely to be Hausdorf, but you can't have everything.

Since DTAI involves subtracting quantities that aren't real numbers,

you can't conclude that a discontinuity in DTAI results in a

discontinuity in UTC.

David.

Received on Wed Jan 11 2006 - 04:24:18 PST

*
This archive was generated by hypermail 2.3.0
: Sat Sep 04 2010 - 09:44:55 PDT
*