Ok. But I wouldn't consider Eton as an education system. I do not doubt that it works in isolated cases. Usually even "private" schools receive massive public funding through public research funds.
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Great. 500000$ are maybe 20 teachers (without infrastructure) for 1 year. It is indeed great that Google donates money to schools and I do not want to belittle that fact. However phrases like these leave me baffled:
Google aren't prepared to wait for government or someone else to fix the problems...
Not Google, nor any other private company or entity is going to fix the education system. That is the whole point of having public schools. Without the state committing to education you are screwed. There is not a single example in history where a private education system succeeded in the long run.
You mean the funding of the Taliban? Or the invasion to kill the Taliban... err
Least squares is also often used in parameter fitting. Suppose you have a simulation with an somehow unknown parameter p. First you use a first guess as a value of p. That you run your simulation and get observed values y_obs.
Now you compare the computed values y_obs with the measured values y_mes using squares: cost = (y_obs - y_mes)^2.
By computing d p / d cost you may adapt p and redo the above steps till the squares are minimized... thus a least squares problem.