Sunday, July 24, 2016

Virtual parts, compressed files and divine ideas

Suppose I record some video to a file on my phone. The video on my phone then is made up of frames, say, 30 of them per second. The frames are parts of the video that it sure seems like we can quantify over. But what is a frame of the video? Well, it's natural to say: The file consists of a sequence of bits implemented as flash memory states arranged spatially in the flash memory of the phone (though not always in the "logical" order, because of wear-leveling and filesystem issues). A frame then would seem to be a subsequence of these flash memory states. But that is in general false. Video files are typically compressed. While some frames--the "key frames"--are stored as a whole as a discrete sequence of bits, typical frames are not stored as a whole. Instead, what is stored is basically a set of instructions on how to modify one or more other frames in order to get the current frame. For instance, if you are panning smoothly across a static object from left to right, the non-key frames will presumably say something like: "Take most of the previous frame, shift it over a little, and then add such and such pixels on the right." But we cannot identify the bits of an instruction like that with the video frame itself, because the video frame does not supervene on the instruction: it supervenes on the instruction and the previous frame.

Even a liberal materialist ontology with unrestricted composition that allows for fusions of arbitrary disconnected sequences of bit-encoding states, the parts of the video do not exist. Noentheless, we correctly (and truthfully) say in ordinary language that the video is made up of frames as parts.

This is a rather nice illustration, I think, of the Thomistic concept of virtual parts. Virtual parts are not fundamental ingredients in the ontology. Nonetheless it is correct (and truthful) to talk of them in ordinary language. There are other such illustrations in computing. For instance, images and sounds are compressed by algorithms that transform them from spatial or temporal sequential data to frequency data or wavelet coefficients. The "natural" parts of the image or sound (say, "the left half", or "the last third") will typically not correspond to a physical part of the device memory storage.

A more homely example is, I am pretty sure, the human visual system. I see an image composed of a variety of parts. There is a lit-up rectangular part (the laptop screen), which has a left half and a right half, and so on. But even without looking up any brain research, I am willing to bet quite a lot that the disjoint spatial parts of the visual image do not correspond to particular things in my brain: I do not have an array of pixels in the brain whose parts correspond to the parts of the image (I do not even have an array of pixels in the retina corresponding to the parts of the image, as the image is stitched together by the brain over time from a variety of images produced by eyes that are constantly moving across the image).

(Can the Platonist avoid talking of virtual parts, insisting that videos and pictures are abstract objects? But even if videos and pictures are abstract objects, I doubt that they have frames and subpictures as parts.)

One thing I would like to use this story for is divine ideas. God is fundamentally simple. But we can meaningfully and truthfully talk of a multiplicity of divine ideas, in much the way that we can talk of the parts of the visual image, which are all encoded in God's one idea of all possibility. And this grounds worlds, propositions and the like.


Walter Van den Acker said...

Dr Pruss

"...a multiplicity of divine ideas in much the way that we can talk of the parts of the visual image, which are all encoded in God's one idea of all possibility."

If a mutiplicity of divine ideas is encoded in God's one idea, is the encoding algorithm a simple one or a complex one? If it is a simple one, I think the analogy with compressed images and sounds fails because they require a relatively complex algorithm. It's hard to see how a fundamentally simple algorithm could encode a multiplicity of ideas, which, in the case of god, should consist of (virtually) infinitely many ideas.

On the other hand, is it really maningful to call a being that 'contains' a complex algorithm simple?

Alexander R Pruss said...

I'd say that the algorithm is complex but it doesn't have to be implemented in God. God sees all truth at once and doesn't need to break it up or decode. It's we who would need the algorithm to attribute particular beliefs or ideas to God.

Walter Van den Acker said...

The decoding algorithm doesn't have to be implemented in God, but what about the encoding algorithm? It somehow has to be a sort of 'encoded description' of a relatively complex reality and I think this description is implemented in God. Is that description simple or is it complex?

Alexander R Pruss said...

God simply and necessarily has a single representation of all of the space of possibilities. :-)

awatkins909 said...

Materialists agree with you about perception and the brain. In 'Image and Brain' (p. 5) Stephen Kosslyn says:

"In a depictive representation, [e.g., mental images] each part of an object is represented by a pattern of points, and the spatial relations of those patterns **in the functional space** correspond to the relations among the parts."

"spatial relations ... in the functional space"!

A bit more recent: Elisabeth Camp also says something similar toward the end of her paper, "Thinking with Maps."

Of course, the ontology of "the functional space" is presumably not fundamental (in some appropriate sense of "fundamental"). So the visual system example is nice.

awatkins909 said...

Somewhat tangential question, but I'm actually curious:

Why do you feel the need for worlds, propositions, etc.? Especially if quantificational statements over things like "virtual parts" in ordinary language are true even though these do not (fundamentally) exist.

Or is debate about possible worlds, propositions, etc. part of "non-fundamental" metaphysics?

I tend to think they "exist" in some very loose sense (maybe), but there's not much to be said about their nature or anything like that, because there's not much to them. It's not as if Kripke discovered worlds just like Pauli discovered the neutrino. Semantics isn't like physics. Worlds, propositions, etc. are useful idealizations, or something like that (if they're anything at all).