Gödel, Escher, Bach: An Eternal Golden Braid

Author: Douglas R. Hofstadter
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Comments

by stcredzero   2017-08-19
If you want a good feel for this stuff, try downloading and going through this course, "NAND to Tetris": (Link is not the course, but a talk about it.)

http://video.google.com/videoplay?docid=7654043762021156507

The book is only $26, last I looked. The course software is all Open Source.

You'll see how digital logic is used to construct components like logic units and memory, which is then used to construct a computer, for which you create a computer language, which you then use to write an operating system, and finally, you program games on it.

This will then give you the wherewithal to really understand Godel-Escher-Bach:

http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/04...

If you want, you can read the book first, but then go through the course and read it again. The 1st time you read it, much of it will be lost on you, but the 2nd time, you'll have many Ah-HA! moments.

One key is Automata Theory. Understand that, and you can understand what you are trying to ask about.

by pook   2017-08-19
MIT's OpenCourseWare is an excellent way for him to study CS on his own while in high school.

I would recommend, at 14, getting him utterly hooked on the mindset of CS and related subjects. Godel, Escher, Bach, etc. If you can get him fascinated with the field, he'll find all the information he needs on his own better than any list of required reading you'll get.

http://ocw.mit.edu/OcwWeb/web/home/home/index.htm

http://www.amazon.com/dp/0465026567

by p1-o2   2017-08-19

Repeated exposure to formal systems will yield a greater ease with which you engage those systems. Force yourself to read and evaluate theory more often. Read books such as Godel Escher Bach if you need practice.

It worked for me, but it wasn't easy by any means.

by sz23   2017-08-19

Gödel, Escher, Bach: An Eternal Golden Braid - Strongly recommended by a teacher of mine at uni.

by kyp44   2017-08-19

Because in any formal system with sufficient power (like modern mathematics) Gödel showed that it is possible to construct a statement that is true but cannot be proven. IIRC the statement boils down to "This statement is not a theorem". If it is a theorem (meaning it can be proven within the system) then it is true and so leads to a contradiction because it asserts that it is NOT a theorem. Assuming it is not a theorem does not lead to such a contradiction but then means that the statement is in fact true. So since one possibility leads to a contradiction while the other doesn't it must be that this statement is true but not a theorem (and therefore unprovable). If you are interested in this at a pretty informal level check out the fun and interesting book Gödel, Escher, Bach .