Turning Turing upside down

I am probably not alone in visualizing Turing’s Universal Machine as a little animacule walking over a linear landscape of ones and zeros:

The great innovation of thinkers such as Turing and others was to reduce the complex world of algorithms and functions into something simple and elemental: all computable functions can be thought of as state machines operating over a large collection of ones and zeros, presence and absence.

There are arguably many differences between a Turing Universal Machine and a modern browser (quite apart from the fact that, being a Javascript interpreter makes a browser a TUM). But for me, one of the most striking differences is that where a TUM is an animacule in a universe of one and zeroes, the browser is an animacule in a universe of HTML, CSS, HTTP and so on.

The browser understands a different world than Turing’s computer. Were we to draw a browser as an animacule, it should look like:

There are similarities, and if you were to look at it from the perspective of a binary TUM, you would be hard put to see a significant difference between a browser and a regular TUM. But that would be missing an essential difference.

The browser understands a different world than the TUM because the concepts that underlie its state machine are concepts from the world of the web, not the world of ones and zeros. Its semantic engagement with the world is different; arguably higher level than the binary TUM. The browser stands on the shoulders of the binary TUM, but nevertheless reaches higher.

What, one may ask, would the level above the browser’s level look like? And is there an infinite stack of levels waiting for our discovery?