Thoughts at the End of a Day - Photography and Fourier Transforms

From: https://www.researchgate.net/figure/Four-Fourier-transforms-and-the-links-between-them-In-the-tempered-distributions-sense_fig1_328163000

A day spent reading produced a few thoughts, sketched here and perhaps expanded in the future.  But mostly just for myself so I don't immediately forget them.

The Rise of Photography

"It is tempting to think [Manet] was impelled to create the new style by the challenge of photography.  The 'pencil of nature,' then known for a quarter of a century, had demonstrated the objective truth of Renaissance perspective, but it established a standard of representational accuracy that no handmade image could hope to rival.  Painting needed to be rescued from competition with the camera.  This Manet accomplished by insisting that a painted canvas is, above all, a material surface covered with pigments - that we must look at it, not through it." - p383, History of Art for Young People, 4th Edition

Reading this today it had me thinking about the effect of photography on painting, and I had this strange thought that it was the same issue that scientific report bore to mythology.  When it comes to establishing the world "as it is" the former in both cases cannot be defeated.  We have mastered, or come close to it, creating precise representations of the world.  The goal of the Renaissance in this respect has been fulfilled.  And it has left us curiously empty, as though something is not quite as fulfilled in these forms.  I feel like until we can properly answer what is missing in a way that isn't just something like "the human touch" we're going to keep passing it by.  

Fourier Transforms and Logic

I've been taking a class on mathematical data analysis and so models and parameter fitting have been on my mind.  For some reason the idea suddenly linked up with what I had known for a while about Fourier Transforms, that any wave can be decomposed into a set of sine waves.  The more complicated the wave, the more sine waves needed to describe it... but also the more particular it becomes as a class.  It felt like an equivalent of overparameterization, that it's always possible to get any model to fit the data, the question is whether it can be done in an elegant enough way to be generalizable. 

Utility.  That seems to lie at the heart of so much of our perceptual and cognitive apparatus.  That we cannot ask so much of the world often whether something is true, only whether it is a good way of representing it.  That somehow rationality and logic are the rules of the average, and that 

There is an idea tickling the back of my mind as well, something from Quantum Reality by Nick Herbert, that:

• All quantum objects have a proxy wave
• All waves can be decomposed into members of any family of waves (Fourier transform generalized)
• Each wave family corresponds with some mechanical attribute (energy/time, position/momentum)
• So using a "prism" of your choice you decompose the proxy wave into a given family, which will come out as a set of individual waves.  These waves, when squared, give the probability of their particular related outcome occurring
• Finally, since waveform families come in pairs, attributes come in pairs, limiting what can be measured by any given device (it takes more unrelated waveforms, more possibilities, to construct a wave)

This has something to do with all of it too, I think.  That the nature of reality is to split into opposites on being measured, and there are more and less efficient choices to do so.  If something looks like a sine wave you're better off using sine waves to decompose it rather than impulse waves, but ultimately there's no fully right or fully wrong answer.  Just more or less effective ones.  This simultaneously anchors and undermines truth, and again it seems like this is just a problem yet to be solved.