The Lorentz equations of special relativity unambiguously specify the current age of a distant object (CADO) according to an inertial observer. This paper demonstrates the following points. 1. For an accelerating observer, consistency with special relativity requires that the CADO be defined in one and only one way. 2. There exists an equation for the CADO, derivable from the Lorentz equations, which explicitly shows how sudden changes in the relative velocity of the observer affect the CADO. Sudden velocity changes can cause the CADO, expressed in years, to vary over a range numerically equal to twice the (objectâmeasured) separation, expressed in lightâyears, between the observer and the object. The equation is well suited for handling arbitrary acceleration profiles and piecewiseâconstant accelerations. 3. The CADO thus defined behaves in a very bizarre manner for an accelerating observer. Specifically, the CADO can decrease as the age of the observer increases, even when the observer's acceleration is limited to 1g. The CADO is also, to a large extent, controllable by the observer. 4. According to an accelerating observer, for a 1g acceleration occurring when the separation is sufficiently great, the object's maximum (in magnitude) rate of aging is greater than the accelerating observer's rate of aging by a factor approximately equal to their separation, as measured in the object's frame, in lightâyears.