Why not five? Six? Two?
If we have to use a fourth dimension, can it be "reason"?
Let's look at the reasonable uses of the nuclear "waste" here: 96% of the "waste" is uranium that when sent through reprocessing for fuel for present LWRs can use up to 30% of this amount. When fast reactors become more mainstream (only large operational plant is in Russia right now; the U.S. pulled all funding in the 1990's out of shortsightedness) that will allow full re-use of the 96% uranium as well as the 1% that is plutonium (and even a couple other transuranic isotopes).
Now, with that remaining 2-4%, you have a very long-lived, very radioactive source term that would be great for.... anything that needs a long-lived, hot source. Think of the Curiosity Mars rover; it gets it's power from an RTG that is based on a specific long-lived and radioactively hot plutonium isotope. Why should we limit ourselves to producing RTG's based on this one long-lived, hot isotope? Why not use the residual "waste" for applications such as that, or others?
So my point is, with the fourth dimension you suggested of reason, it seems like nuclear waste will actually be quite useful in the near term.