I have a dump from a version of PostGIS that is no longer supported. It dumps the value of a (lat, long) as 01010000003D2CD49AE6A549409AB1683A3B19F1BF
How can I decode that number (without using PostGIS) to determine the original lat long?
This example is identical to ISO WKB, since it does not have an SRID or use dimensions beyond 2D (such as Z, M, or ZM). The formats are different otherwise.
You can decode geometry data (i.e. longitude and latitude) from WKB using a wide range of tools available in Python, PHP, R, Perl, etc., or any custom implementation that is capable of implementing the specification.
Also note that you might be able to use the PostGIS dump file with newer versions of PostGIS; see the hard upgrade procedure, which uses utils/postgis_restore.pl to read older formats.