>the result is the same as if it did This isn't quite true. Differently ordered operations can lead to different results due to floating point math, but in gene

>the result is the same as if it did This isn't quite true. Differently ordered operations can lead to different results due to floating point math, but in general, the point of multiple dispatch isn't to produce different results for different types. The example from Stefan's talk does this when contrasting with operator overloading because it's easier to show a difference in results than a difference in performance. I don't know the specifics of how Matlab/Octave do this, but you're probably right about runtime checks. It's true that compilation time will make Julia slower than Octave for a single multiplication, but if you are doing a bunch of them (especially if they are small), Julia can perform the computations with much lower overhead since it doesn't have to do type checks for stable programs. Also, Julia lets you define specialized matrix types which can be asymptotically faster than Octave for specific circumstances. A great example of this is BandedBlockBandedMatrix from https://github.com/JuliaMatrices/BlockBandedMatrices.jl https://github.com/JuliaMatrices/BlockBandedMatrices.jl which are extremely useful solving of PDEs quickly, but aren't implemented in any of the other languages because they have to write all their dispatch systems manually for each algorithm.