Many of the ideas he's talking about are discussed therein; perception and "reality" is an assemblage of ideas, not an objective "truth" waiting to be discovered.
It's not just about the ideas -- it's about how they are explained and with what rigor.
The same way that 19th chemistry didn't "got where Democritus was" when he formulated his atomic theory -- it came to the same concept, yes, but what for him was just an idea put out there, for them it was a solid theory, with experiments, deductions made of it, etc.
Nah - these are just the same ideas in a different intellectual framework, the level of rigor is only apparent because we're attuned to mathematical models as the best means of reasoning. It's just about what you accept as valid proof (math rather than sociology), I don't think they're actually more profound understandings of the underlying concept.
Funny, because (from what I've seen around here) you actually chanced upon a rare person on HN (me) that doesn't consider math/hard science automatically "more profound" than sociology and informal argumentation/reasoning on a subject.
That said, though, having it in math enables ways to re-use and test that knowledge that having it in sociological reasoning does not -- even if the understanding both methods reached is comparable.
I disagree that math is that great. A mathematical model is a formal description of some sort, but a mental model is just a different kind of ontological descriptor; both are merely machines to process inputs and produce some sort of output. You might argue that it's better to be able to observe and tweak the mathematical model than to use one built on purely human semantics, but, mathematical models, by virtue of their simplicity, are generally poor at dealing with complexity (see my other comment in this thread for a critique of his model). This is why we're tending these days towards more complex, harder-to-understand learning systems like neural networks; you get an answer composed of primitives you don't really understand very well. This is basically the same as sociology.
>I disagree that math is that great. A mathematical model is a formal description of some sort, but a mental model is just a different kind of ontological descriptor; both are merely machines to process inputs and produce some sort of output.
That doesn't say much though.
A cheap numeric calculator (not turing complete, the plain type) and a high end PC are both "merely machines to process inputs and produce some sort of output".
It's the precise kind of machines that each is and the exact kind of processing that it can do that's important -- not just their general similarities.
>You might argue that it's better to be able to observe and tweak the mathematical model than to use one built on purely human semantics, but, mathematical models, by virtue of their simplicity, are generally poor at dealing with complexity
Yes, but they're very good at dealing with very precise formulations. It's not necessary when doing an analysis of field X to deal with the whole of X's extend and complexity at all times. A very specific answer to a small non-complex part of X can be very worthy itself.
(The same way Newton's theory is very good to determine the angle of cannon shots with even if it's a bad model for anything really complex speed and mass wise -- only in this case, the "less complex" theory gives more precise answers for its subdomain, whereas with Newton vs Einstein it's the inverse).
Newton's theory is a simple three-variable model that describes a simple power law relationship between them. Holy fuck, would it be fantastic if ANY ASPECT of biochemistry or biology could be modeled with such a simple description. As a biologist I can tell you this is very far from the case. This is a huge problem with the field of biology, actually, that the models (and ideas of complexity) we have to bring to bear were developed in physics where the parametrizations are simple and clean and provide high predictive value.
This math simply doesn't work when you throw it against a biology problem. Precise formulations don't exist when you're dealing with, say, the interactions between two 100-amino acid folded proteins. Physics operates on simple rules that work everywhere; biology operates on complex rule sets that are often broken. The math is just not up to snuff, here.
He's not just talking about constructionism, although he touches upon it with "remove W" - rather he's talking about potentially pan-specietal constructionism - all life perceives the universe through some fundamental and potentially inaccurate constructs.
Many of the ideas he's talking about are discussed therein; perception and "reality" is an assemblage of ideas, not an objective "truth" waiting to be discovered.