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A trajectory $u_n := F^n(u_0), n = 0,1,2, \dots $ is quasiperiodic if thetrajectory lies on and is dense in some $d$-dimensional torus, and there is achoice of coordinates on the torus $\mathbb{T}$ for which $F$ has the form$F(\theta) = \theta + \rho\bmod1$ for all $\theta\in\mathbb{T}$ and for some$\rho\in\mathbb{T}$. There is an ancient literature on computing three rotationrates $\rho$ for the Moon. %There is a literature on determining thecoordinates of the vector $\rho$, called the rotation rates of $F$. (For $d>1$we always interpret $\bmod1$ as being applied to each coordinate.) However,even in the case $d=1$ there has been no general method for computing $\rho$given only the trajectory $u_n$, though there is a literature dealing withspecial cases. Here we present our Embedding Continuation Method for computingsome components of $\rho$ from a trajectory. It is based on the TakensEmbedding Theorem and the Birkhoff Ergodic Theorem. Rotation rates are oftencalled "rotation numbers" and both refer to a rate of rotation of a circle.However, the coordinates of $\rho$ depend on the choice of coordinates of$\mathbb{T}$. We explore the various sets of possible rotation rates that$\rho$ can yield. We illustrate our ideas with examples in dimensions $d=1$ and$2$.

Solving the Babylonian Problem of quasiperiodic rotation rates