In some fields, e.g. condensed matter physics, you need you need to deal with contracting multidimensional tensors all the time, and with out Einstein notation it would be difficult.
The simples example is so-called matrix product state (http://en.wikipedia.org/wiki/Matrix_product_state), which is similar to Markov process. But for more interesting scenarios (e.g. 2d) one needs to use at least 4 dim tensors.
In some fields, e.g. condensed matter physics, you need you need to deal with contracting multidimensional tensors all the time, and with out Einstein notation it would be difficult.
The simples example is so-called matrix product state (http://en.wikipedia.org/wiki/Matrix_product_state), which is similar to Markov process. But for more interesting scenarios (e.g. 2d) one needs to use at least 4 dim tensors.