Careful what you wish for. Negating the predicate of "A COMPUTER CAN NEVER BE HELD ACCOUNTABLE. THEREFORE A COMPUTER MUST NEVER MAKE A MANAGEMENT DECISION" might open us up to the consequence.
Btw, note that it was not actually a Roman salute (though it may have been adopted by Italian fascists because they incorrectly believed it had been used by the Romans; they were keen on Roman iconography).
A dot product is a weighted sum of two vectors, but not in the way the author suggested. The author's use is that one of the vectors is the weights and the other is 'the' vector, so the dot product is the weighted sum of ONE vector. It just so happens that because the author is not interested in the geometric interpretation of the dot product that they forgo the metric.
On the other hand, it is common to need a metric, which is actually the set of weights in the dot product. If `g` is the metric,
dot(a, g, b) = np.einsum('x,xy,y->', np.conj(a), g, b)
g doesn't have to be diagonal, but if you want the dot product to be symmetric in a and b it ought to be self-adjoint. Then you can find a basis where g is diagonal with real diagonal elements, which you can interpret as the weights.
> A small change in the parameter a can lead to vastly different particle trajectories and the overall shape of the attractor. Change this value in the control panel and observe the butterfly effect in action.
I think this is slightly inaccurate. The butterfly effect is about the evolution of two nearby states in phase space into well-separated states. But the parameter a is not a state. To see the butterfly effect by changing a we would need to let the system settle down, give the parameter a small change, and then change it back. The evolution during the changed time acts as a perturbation on states.
Instead, showing that the attractor changes qualitatively as a function of the parameter is more akin to a phase transition.
