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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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