An *isodistance* map shows the contours of equal distances from a central point. These would be circles on a map if distance is measured “as the crow flies.” The shapes vary if distance depends on a road network:

But how do you tell if two distances are the same? Different observers have different distance measuring instruments. There must be a way to ensure consistency of the distance measuring instruments – e.g., rigid measuring rods.

The problem is analogous to the need to synchronize clocks for 1D time. The *Einstein synchronization convention* is the standard way to do this:

Position 1 has clock 1 and rod 1; position 2 has clock 2 and rod 2. A light signal is sent from position 1 at time τ_{1} (defined from a specified point in time) to position 2 and immediately back, e.g. by means of a mirror. Its arrival time back at position 1 is τ_{2}. This synchronization convention sets clock 2 so that the time τ_{3} of signal arrival and reflection is defined as

τ_{3} = τ_{1} + ½ ( τ_{2} − τ_{1}) = ½ ( τ_{1} + τ_{2}).

Synchronization is also achieved by slowly transporting a third clock from position ρ_{1} to position ρ_{2}.

Similarly, one needs to *synmacronize* measuring rods for 1D space. As synchronize is from transliterated Greek *syn + chron + ize* (“to occur at the same time”) so synmacronize is from *syn + macron + ize* (“to occur at the same length”). Follow the convention above and then:

Use the constant speed of light, *c*, to convert the times into corresponding distances, setting rod 2 so that the distance of signal arrival and reflection is defined to be

*cτ*_{3} = *cτ*_{1} + ½ (*cτ*_{2} − *cτ*_{1}) = ½ (*cτ*_{1} + *cτ*_{2}), i.e.,

*ρ*_{3} = *ρ*_{1} + ½ (*ρ*_{2} − *ρ*_{1}) = ½ (*ρ*_{1} + *ρ*_{2}), where *ρ*_{1}, *ρ*_{2}, and *ρ*_{3} are the distances corresponding to τ_{1}, τ_{2}, and τ_{3}.

*Synmacronization* can also be achieved by slowly transporting a third measuring rod from position 1 to position 2.

Both space and time require consistent measuring instruments.