There is one little piece of information that everyone seems to have missed. This fuse box is indeed supplied by a 1 phase 3 wire service and the circuits on the left side are supplied by the red hot wire whereas the ones on the right are supplied by the black wire however, this box supports a total of 8 circuits (4 on the left and 4 on the right) since each circuit has both a fused hot and neutral. Therefore each circuit has two fuses.
Fusing both the neutral and hot (phase) of a circuit was very common in the early 20th century however, by the end of the 1920s this practice was banned. This is because a circuit would appear to be off if only the neutral fuse burnt out since the circuit will break however in this case it would be dangerous to assume the circuit is dead since the hot is still connected and the circuit is energized and waiting for a path back to a grounded conductor (i.e. the neutral wire or someone assuming the circuit is dead touching the bare conductors) in order to complete the circuit.
In order to eliminate this dangerous situation it has been standard practice and required by code for many decades to only fuse the hot (phase) conductors. That way if a fuse blows the equipment/wiring it is protecting is guaranteed to not be live/energized unless it is being feed by multiple circuits and/or phases, which is a whole other issue which is dealt with using common trip breakers with multiple poles as well as multi pole switches.
Since your fuse box is likely close to 100 years old each circuit has both a fused neutral and a fused hot wire. That is why the fuse/wire in every other row of your fuse box will not register as hot if you touch it with a non contact voltage tester or measure its voltage relative to ground. Keep in mind the neutral is a grounded conductor since it is bonded to ground at the main disconnect/service switch as well as at the utility company’s transformer.
