Comment by Double_Cast | Hacker News Reader

Comment by Double_Cast | Hacker News Reader

> You’re free to think about computation as acting on bits… but for those bits to do us any good, they have to actually represent something (e.g., data structures).

I suspect this is a case of confusing epistemology with ontology.

Galaxies are ontologically composite in that they're the highest holonym in the supervenience hierarchy [0]. Atoms are ontologically fundamental in that they're the the lowest meronym in the supervenience heirarchy.

Galaxies are epistemically abstract in that the notion of galaxy is far removed from everyday experience. Atoms are also epistemically abstract in that the notion of atoms are also far removed from everyday experience. What's epistemically fundamental are the immediate objects of our everyday experience, like chairs and food. (My impression of Zen is that it advises to focus more on things like chairs and food [1].)

https://www.xkcd.com/435/

In the xkcd, which is more "fundamental", Math or Economics? Well, it depends. Likewise, what's more "fundamental", bits or ADT's? Well, it depends.

[0] powers of 10: https://www.youtube.com/watch?v=0fKBhvDjuy0

[1] http://www.itsokblog.com/2011/01/wash-your-bowl-zen-of-mothe...

Well, in this case all models are quite abstract, and there's a very real computational complexity difference between them. The key, if I were to use your way of presenting the issue, is the recognition that some epistemological abstractions are more computationally costly than others. So it's true that you can choose either representation as a foundation, but the representations objectively and radically differ in their computational complexity.

The key is to recognize how it's not just that TOP and TOC both measure X with different models. It's that TOP measures X while TOC measures Y.

It's as if we claimed Spell Checking were as complex as Natural Language Processing because they were both called "linguistics". Yes, they both abstract over language. But the primitives of Spell Checking are glyphs while the primitives of NLP are morphemes. Glyphs don't exhibit the same patterns as morphemes. Which is why Spell Checking uses a Trie while NLP uses a Matrix. Debating whether glyphs or morphemes are "more fundamental" is a distraction.

Likewise, bits don't follow the same patterns as ADT's. Calling both the study of bits and the study of ADT's "Complexity Analysis" is misleading, which I believe is what Pressler was getting at. But we've put bits and ADT's in the same bucket for the entire history of computing, because the Church Turing thesis (i.e. anything a TM can do, lambdas can do too) lead us to believe Turing and Church were studying the same primitives.

What I was getting at in the article is that:

1. TOC and TOP ask different questions.

2. The disparity of the computational complexity involved in the two classes of models is so great, that it is objective proof that they represent two distinctly different things, and therefore comparing them directly is meaningless. That a jet and a bicycle require vastly different amounts of energy to power is conclusive and objective proof that completely different tradeoffs must be involved in choosing them.

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