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Comment by eterevsky | Hacker News Reader

Aaronson wrote a great book "Quantum Computing since Democritus" discussing not just quantum mechanics and computing, but also such topics as algorithmic complexity and anthropic principle. It is located somewhere between science and pop-science: it contains quite a few proofs and technical details, while remaining quite approachable for a non-expert.

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I disagree that it is “quite approachable for the non-expert” assuming you meant a general audience without a background in high school mathematics. They probably wouldn’t exactly understand the Löwenheim–Skolem theorem or ZFC, or consistency arguments and so forth as presented in the book.

Some parts require more math than probably the general audience will be able to grasp but if they gloss over those sections they could still get the gist of what follows.

I think I’d rephrase it as “quite approachable for a talented high schooler / someone with knowledge in undergraduate mathematics”

> assuming you meant a general audience without a background in high school mathematics

Why assume that ? Isn't the whole point of high school to provide a basic foundation of knowledge that everyone should have ?

The parent comment said “quite approachable for the non-expert” not “quite approachable for the uneducated”.

Depends what “non-expert” means. Because I actually think even if you have an undergraduate knowledge in mathematics then you still may not be able to follow some of his arguments unless you specifically studied mathematical logic. I have a more advanced background in math but not in logic and don’t understand some of his arguments. He sometimes makes loose statements without proof or without providing strong background knowledge to closely follow those things if you don’t already know them. Some of the ZFC stuff I didn’t follow either, but I never really needed to know set theory to the extent Aaronson uses it. I think the statement it’s quite approachable isn’t very accurate. If you want to gloss over it and still get the main idea then it’s good for that but not for rigorously understanding all the mathematical arguments without preexisting background knowledge. It’s between a pop sci book and textbook with a casual tone. It’s a fun book.

You may well be right. I haven't read that book, though I have found much of Aaronson's writing to be quite approachable. But I think your previous comment was an inaccurate way of phrasing those critiques.

Ok, I think I generally agree with your categorisation.

Personally I did study mathematical logic in the University a little bit, but it was 20 years ago and I don't think I remember much about it past what all undergraduates are taught.

Yes, to understand all of the contents in this book you'd need to have knowledge of Math on the level of an undergraduate in a STEM discipline. To me it still meets the definition of "non-experts". It is much more involved than your average pop-science book, but at the same time is much more fun and easy to read than a typical Math college textbook.

Also, about half of the book can be read without any Math background.

I tried reading that book and I can't say I followed everything smoothly. For each chapter, I had to read 10 other articles to better understand the material, though I admit I am not very well versed with the subject matter.

But yeah, it is a very good book, one of its kind. I wish there were more accompanying books written in similar fashion.

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