Spiegel grew up in New York City in the South Bronx with his Yiddish-speaking eastern European parents and his sister, Jeanette.
In 1959, he helped establish the summer Geophysical Fluid Dynamics program for the Woods Hole Oceanographic Institution and was a member of the physical oceanography department there until his death.
His 1966 article entitled "A thermally excited non-linear oscillator," [7] co-authored with D.W. Moore, contains a discussion of chaotic dynamics in terms of the wandering of a trajectory from the vicinity of one unstable periodic orbit to another.
The work also cites some specific cosmic examples where low-dimensional dynamics and chaos theory may provide a key to understanding the astrophysical phenomena.
[citation needed] His work on photo-hydrodynamics is now recognized as potentially important in pulsars, and the Moore-Spiegel oscillator and chaos have become influential ideas since the 1980s.