5 ms·
Slightly cheating by using complex numbers so there is 8 degrees of freedom instead of 4. But bravo anyway, it was a great exercise.
by tlarkworthy 9y ago
Slightly cheating by using complex numbers so there is 8 degrees of freedom instead of 4. But bravo anyway, it was a great exercise.
- 983 9y agoOne might also argue that choosing a non-continuous sequence of Fourier-coefficients is not perfectly honest, since it allows for encoding information in the coefficient indices.
- soVeryTired 9y agoI'm not sure counting the number of real numbers that you have to input is quite the right way to think about this. I could encode instructions to draw an arbitrary shape in a single real number if I wanted: .00011110 could be interpreted as a square if I take pairs of digits to be successive (x,y) coordinates (my example becomes (0,0), (0,1), (1,1), (1,0)).
- tlarkworthy 9y agoDegrees of freedom expresses a bound on the complexity of things you can represent. The motivation of this work was a conversation about the over complexity of a scentific model. You literally count the free params and if there are loads of parameters you need zillions of observations to pin them down due to the curse of dimensionality. It's the same concept in parametric statistics: https://en.m.wikipedia.org/wiki/Degrees_of_freedom_(statistics) https://en.m.wikipedia.org/wiki/Degrees_of_freedom_(statisti... Non-parametric statistics work by fitting models of infinite degrees of freedom. But then you need fancy math to figure out how complex your model currently is and how your data supports it.