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## hidden periodicity idea

### Zulfikar Ahmed<wile.e.coyote.006@gmail.com>

2:36 PM (10 minutes ago)

 to David, bcc: aimee
Dear Professor Donoho,

The fractional derivative as interpreted by Cattani in the attached paper is a convex combination of derivatives.  To understand this a bit better, I looked at the simple functions f(x)=sin(x) and f'(x)=cos(x) in octave and considered their convex combinations.

One simple idea behind occurrence of fractional derivatives in nature where it is understood what is meant by f(t) and f'(t) is the occurrence of a periodic hidden system where observable signals are convex combinations of quantities that have classical interpretation.  Of course this would be a great speculative leap but it’s an intuition that makes sense to me because it is intuitively appealing.

Thus when we observe that some natural process has alpha=0.3 derivatives, then it could occur from some differential equation involving some f(t) and f'(t) as 0.7*f(t) + 0.3*f'(t).  I’d have to check but classical physics and Hamiltonian systems often contain such differential equations.  This is not a serious suggestion but simply a learning example of explanations for what these fractionals mean in nature that differ from more stochastic view of nature modeled as Gaussian white or other fractional 1/f noises.  This also appeals to the determinist in me who agree with Einstein 100% that nature is not stochastic on his first reaction to quantum mechanics, regardless of how he compromised on that position possibly accepting what his initial intuition correctly posited; Einstein’s initial reaction to ballooning universe theories of Lemaitre were a great inspiration for my attempts at showing a static universe produce an artifact clear redshift-distance slope that matches the observed quite well in the following analysis:

https://zulfahmed.wordpress.com/2012/12/09/preparation-of-redshift-distance-dataset/

This simply to give determinism another chance for nature.

### Zulfikar Ahmed<wile.e.coyote.006@gmail.com>

2:38 PM (8 minutes ago)

 to David, bcc: aimee
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## optimism and pessimism for determinism

### Zulfikar Ahmed<wile.e.coyote.006@gmail.com>

3:17 PM (0 minutes ago)

 to aimee