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Reddit mentions of Gödel, Escher, Bach: An Eternal Golden Braid

Sentiment score: 85
Reddit mentions: 183

We found 183 Reddit mentions of Gödel, Escher, Bach: An Eternal Golden Braid. Here are the top ones.

Gödel, Escher, Bach: An Eternal Golden Braid
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Release dateFebruary 1999
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Found 183 comments on Gödel, Escher, Bach: An Eternal Golden Braid:

u/samort7 · 257 pointsr/learnprogramming

Here's my list of the classics:

General Computing

u/kevroy314 · 43 pointsr/compsci

I first heard about these when reading Godel Escher Bach back in later high school. That book was a long, difficult read, but man did it blow my brain wide open. Quines are definitely the thing that I remember most vividly (probably because it was the easiest to understand), but that book was full of awesome stuff like this.

You should totally check it out! You can get it super cheap at used book stores since it was such a successful book.

u/veryreasonable · 35 pointsr/RationalPsychonaut

As one of the people who commented on that thread, I feel the need to respond to this as rationally as humanly possible.

For starters, let's clear up the difference between fractal mathematics, fractal woo, and what Douglas Hofstadter might call fractal analogy.

  1. From the wiki - Fractal Mathematics would be the study of "natural phenomena or a mathematical sets that exhibits repeating patterns that display at every scale" as well as the study of self similarity and iterated functions. While it has grown complex and vast, the studies of fractals and their geometry started out as literally what you say it isn't: people asking questions about self-similarity in nature and asking how to describe it mathematically.

  2. Fractal Woo would be, as OP said:

    >“Everything big is just like everything small!” they exclaim, “the universe is self-similar!”

    ...and then using such logic to thereby justify whatever silly energy-Reiki-mystical-connectedness-telepathy-de-jour they want.

  3. Fractal Analogy (my term, but run with it) would be seeing patterns in the world which are, indeed, self similar, as tons of stuff in nature is. This includes plant and animal system, as well as consciousness and human experience. The reason I mention Douglas Hofstadter is that he is a PhD physicist who literally used fractal mathematics to predict some pretty nifty real world stuff 35 years before it was confirmed - but Mr. Hofstadter is also an incredibly enjoyable author who muses at length about cognitive science and AI research, often using the analogy of self-similar shapes to help describe what we understand of consciousness in a way that most layman readers can understand. Even if you are not a very capable mathematician, I highly recommend his Godel Escher Bach, which uses fractals and loads of other creative stuff to help conceptualize how the "mind" arises from the brain.

    As well, Chaos Theory - the study of how immensely complex patterns emerge from seemingly simple preconditions - is full of fractal mathematics. Given that the universe is absolutely packed with iterated functions and self-similarity almost everywhere we look, I think you can absolutely take the point of view that the universe is fractal in nature, especially when you are in a self-induced state where your brain makes a lot of connections you might normally overlook or not even bother to think about.

    My point is that discussing things in the universe as self-similar is useful to mathematicians and non-mathematicians alike; using the word "fractal" to describe natural systems that exhibit those familiar patterns might not be perfectly correct, but it's not itself offensive or an affront to reasonable discourse. I manage a business; so what's your problem if I visualize the structure of my company as a fern leaf with departments and employees as branches off the main stem? What would be the issues of discussing how incredible human cellular morphology really is with my biologist roommate, and citing some cool research someone decided to do about fractal geometry in the way our bodies build themselves?

    EDIT: OP's edit makes it more clear his statements were more about irrational folk seeing the universe as a single continuous fractal (that would be the "fractal woo"), and that he is not denying the existence of fractal-like patterns in nature, or that using fractal models can be useful in understanding phenomena. Sorry for any confusion and thanks for the discussion!

    EDIT2: /u/ombortron commented pretty well in regards to the utility of the concept of fractals in scientific discourse and otherwise:

    >The universe itself doesn't have to be a fractal for fractals to be important.

    >Fractals are quite common in our reality, and as a result, that means they are an important facet of reality, and as such they are a legitimate and common topic of discussion amongst people, and this is particularly true of people who do psychedelics.

    >Does this mean the universe is 100% fractal in nature? No.

u/cronin1024 · 25 pointsr/programming

Thank you all for your responses! I have compiled a list of books mentioned by at least three different people below. Since some books have abbreviations (SICP) or colloquial names (Dragon Book), not to mention the occasional omission of a starting "a" or "the" this was done by hand and as a result it may contain errors.

edit: This list is now books mentioned by at least three people (was two) and contains posts up to icepack's.

edit: Updated with links to Amazon.com. These are not affiliate - Amazon was picked because they provide the most uniform way to compare books.

edit: Updated up to redline6561

u/darawk · 22 pointsr/compsci

Godel Escher and Bach is precisely what you're looking for.

u/MyrddinE · 21 pointsr/programming

Gödel, Escher, Bach: An Eternal Golden Braid

This book is not exactly a programming book... maybe... kinda. It teaches no practical programming language. It explains no useful design patterns. It does not deal with any practical computer applications. And yet had I never would have really gotten into programming had I not read it long ago. Written in the late 70's, it's still relevant today.

u/I_make_things · 20 pointsr/AskReddit

Godel Escher Bach

It's ultimately about the self-referential nature of consciousness, but it explores so many fascinating concepts that I couldn't even begin to do it justice

u/chrndr · 17 pointsr/HPMOR
I wrote a quick script to search the full text of HPMOR and return everything italicized and in title case, which I think got most of the books mentioned in the text:

Book title|Author|Mentioned in chapter(s)|Links|Notes
Encyclopaedia Britannica| |7|Wikipedia|Encyclopaedia
Financial Times| |7|Wikipedia|Newspaper
The Feynman Lectures on Physics|Richard P. Feynman|8|Wikipedia|Full text is available online here
Judgment Under Uncertainty: Heuristics and Biases|Amos Tversky|8|Amazon|
Language in Thought and Action|S.I. Hayakawa|8|Amazon Wikipedia |
Influence: Science and Practice|Robert B. Cialdini|8|Wikipedia|Textbook. See also Influence: The Psychology of Persuasion
Rational Choice in an Uncertain World: The Psychology of Judgment and Decision Making|Reid Hastie and Robyn Dawes|8|Amazon |Textbook
Godel, Escher, Bach|Douglas Hofstadter|8, 22|Amazon Wikipedia|
A Step Farther Out|Jerry Pournelle|8|Amazon|
The Lord of the Rings|J.R.R. Tolkien|17|Wikipedia|
Atlas Shrugged|Ayn Rand|20, 98|Wikipedia|
Chimpanzee Politics|Frans de Waal|24|Amazon|
Thinking Physics: Understandable Practical Reality|Lewis Carroll Epstein|35, 102|Amazon|
Second Foundation|Isaac Asimov|86|Wikipedia|Third novel in the Foundation Series
Childcraft: A Guide For Parents| |91|Amazon|Not useful if your child has a mysterious dark side

Also, this probably isn't technically what the OP was asking, but since the script returned fictional titles along with real ones, I went ahead and included them too:

Book title|Mentioned in chapter(s)
The Quibbler|6, 27, 38, 63, 72, 86
Hogwarts: A History|8, 73, 79
Modern Magical History|8
Magical Theory|16
Intermediate Potion Making|17
Occlumency: The Hidden Arte|21
Daily Prophet|22, 25, 26, 27, 35, 38, 53, 69, 77, 84, 86, 108
Magical Mnemonics|29
The Skeptical Wizard|29
Vegetable Cunning|48
Beauxbatons: A History|63
Moste Potente Potions|78
Toronto Magical Tribune|86
New Zealand Spellcrafter's Diurnal Notice|86
American Mage|86

As others mentioned, TVTropes has a virtually-exhaustive list of allusions to other works, which includes books that aren't explicitly named in the text, like Ender's Game
u/My_6th_Throwaway · 16 pointsr/INTP

American amazon link

u/[deleted] · 16 pointsr/books


Seriously, this is a brainfuck of a book.

u/osirisx11 · 14 pointsr/math

If you like stuff like this you may be interested in my favorite book: Godel, Echer, Bach: The Eternal Golden Braid:


Edit: Also see the great MIT course with video lectures:


u/drzowie · 13 pointsr/AskPhysics

Reductionism is important, but pure reductionism denies the existence of emergent phenomena (phenomena that depend on collective behavior of many simpler things). A very enjoyable book that covers this and many other topics at a popularly-accessible level is
Gödel, Escher, Bach: an Eternal Golden Braid. First published in the late 1970s, GEB is still delightfully fresh and exciting although a few minor elements are dated (e.g. computers now can beat humans at chess).

u/LongUsername · 13 pointsr/compsci

I'd second unplugging completely: no computer, TV, electronics. If you insist on doing something CS related, Godel, Escher, Bach comes highly recommended.

u/jacobolus · 11 pointsr/math

Your post has too little context/content for anyone to give you particularly relevant or specific advice. You should list what you know already and what you’re trying to learn. I find it’s easiest to research a new subject when I have a concrete problem I’m trying to solve.

But anyway, I’m going to assume you studied up through single variable calculus and are reasonably motivated to put some effort in with your reading. Here are some books which you might enjoy, depending on your interests. All should be reasonably accessible (to, say, a sharp and motivated undergraduate), but they’ll all take some work:

(in no particular order)
Gödel, Escher, Bach: An Eternal Golden Braid (wikipedia)
To Mock a Mockingbird (wikipedia)
Structure in Nature is a Strategy for Design
Geometry and the Imagination
Visual Group Theory (website)
The Little Schemer (website)
Visual Complex Analysis (website)
Nonlinear Dynamics and Chaos (website)
Music, a Mathematical Offering (website)
Mathematics and its History
The Nature and Growth of Modern Mathematics
Proofs from THE BOOK (wikipedia)
Concrete Mathematics (website, wikipedia)
The Symmetries of Things
Quantum Computing Since Democritus (website)
Solid Shape
On Numbers and Games (wikipedia)
Street-Fighting Mathematics (website)

But also, you’ll probably get more useful response somewhere else, e.g. /r/learnmath. (On /r/math you’re likely to attract downvotes with a question like this.)

You might enjoy:

u/c_d_u_b · 10 pointsr/AskHistorians

Computer scientist here... I'm not a "real" mathematician but I do have a good bit of education and practical experience with some specific fields of like probability, information theory, statistics, logic, combinatorics, and set theory. The vast majority of mathematics, though, I'm only interested in as a hobby. I've never gone much beyond calculus in the standard track of math education, so I to enjoy reading "layman's terms" material about math. Here's some stuff I've enjoyed.

Fermat's Enigma This book covers the history of a famous problem that looks very simple, yet it took several hundred years to resolve. In so doing it gives layman's terms overviews of many mathematical concepts in a manner very similar to jfredett here. It's very readable, and for me at least, it also made the study of mathematics feel even more like an exciting search for beautiful, profound truth.

Logicomix: An Epic Search for Truth I've been told this book contains some inaccuracies, but I'm including it because I think it's such a cool idea. It's a graphic novelization (seriously, a graphic novel about a logician) of the life of Bertrand Russell, who was deeply involved in some of the last great ideas before Godel's Incompleteness Theorem came along and changed everything. This isn't as much about the math as it is about the people, but I still found it enjoyable when I read it a few years ago, and it helped spark my own interest in mathematics.

Lots of people also love Godel Escher Bach. I haven't read it yet so I can't really comment on it, but it seems to be a common element of everybody's favorite books about math.

u/distantocean · 10 pointsr/exchristian

That's one of my favorite popular science books, so it's wonderful to hear you're getting so much out of it. It really is a fascinating topic, and it's sad that so many Christians close themselves off to it solely to protect their religious beliefs (though as you discovered, it's good for those religious beliefs that they do).

As a companion to the book you might enjoy the Stated Clearly series of videos, which break down evolution very simply (and they're made by an ex-Christian whose education about evolution was part of his reason for leaving the religion). You might also like Coyne's blog, though these days it's more about his personal views than it is about evolution (but some searching on the site will bring up interesting things he's written on a whole host of religious topics from Adam and Eve to "ground of being" theology). He does also have another book you might like (Faith Versus Fact: Why Science and Religion are Incompatible), though I only read part of it since I was familiar with much of it from his blog.

> If you guys have any other book recommendations along these lines, I'm all ears!

You should definitely read The Selfish Gene by Richard Dawkins, if only because it's a classic (and widely misrepresented/misunderstood). A little farther afield, one of my favorite popular science books of all time is The Language Instinct by Steven Pinker, which looks at human language as an evolved ability. Pinker's primary area of academic expertise is child language acquisition, so he's the most in his element in that book.

If you're interested in neuroscience and the brain you could read How the Mind Works (also by Pinker) or The Tell-Tale Brain by V. S. Ramachandran, both of which are wide-ranging and accessibly written. I'd also recommend Thinking, Fast and Slow by psychologist Daniel Kahneman. Evolution gets a lot of attention in ex-Christian circles, but books like these are highly underrated as antidotes to Christian indoctrination -- nothing cures magical thinking about the "soul", consciousness and so on as much as learning how the brain and the mind actually work.

If you're interested in more general/philosophical works that touch on similar themes, Douglas R. Hofstadter's Gödel, Escher, Bach made a huge impression on me (years ago). You might also like The Mind's I by Hofstadter and Daniel Dennett, which is a collection of philosophical essays along with commentaries. Books like these will get you thinking about the true mysteries of life, the universe and everything -- the kind of mysteries that have such sterile and unsatisfying "answers" within Christianity and other mythologies.

Don't worry about the past -- just be happy you're learning about all of this now. You've got plenty of life ahead of you to make up for any lost time. Have fun!

u/ThomasMarkov · 10 pointsr/math

Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter is perhaps the most thought provoking book I have ever read. It unifies music, art, and mathematics and will simply blow your mind.

u/SharmaK · 9 pointsr/books

For some physics :
Penrose - Road to Reality

Gleick - Chaos

Some math/philosophy :
Hofstadter - Godel, Escher, Bach: An Eternal Golden Braid

Anything early by Dawkins if you want to avoid the atheist stuff though his latest is good too.

Anything by Robert Wright for the evolution of human morality.

Pinker for language and the Mind.

Matt Ridley for more biology.

u/stonedead78 · 9 pointsr/IWantToLearn

Read this book: Gödel, Escher, Bach: An Eternal Golden Braid at least 3 times, and take your time.

u/chindogubot · 8 pointsr/compsci

I get teased by people that I am one of only 3 people in the world to have actually finished this book, one of those being the author and the other being the person who recommended to me, but Godel, Escher, Bach: An Eternal Golden Braid was pretty interesting. It covers the profoundness of the topic and is interspersed with Alice in wonderland style dialog that comes at the topic from another angle. Deep but captivating overall.

On a tangent, Goedel's theorem and Turing's incompleteness theorem, along with some other mathematicians who have gazed out over the edge of logic and gone somewhat mad are covered in the BBC documentary Dangerous Knowledge.

u/help_me_will · 8 pointsr/actuary

Against The God: the remarkable story of Risk- Outlines the history of probability theory and risk assessment through the centuries


When Genius Failed - A narrative of the spectacular fall of Long Term Capital Management, a hedge fund which had on its board both Myron Scholes AND Robert Merton (you will recall them from MFE)

Black Swan/ Antifragility- A former quant discusses the nature of risk in these controversial and philosophical books. Some parts of this book are actually called out and shamed in McDonald's Derivative Markets, one or the both of them are worth reading


Godel, Escher, Bach- Very dense look into recursive patterns in mathematics and the arts. While not actuarial, it's obviously very mathematical, a must read.


Endurance- This was recommended to me by a pure mathematics professor. Again, not actuarial, but more about the nature of perseverance though problem solving(sound familiar). It's about Shakleton's famous voyage to the south pole.


u/PsychedelicFrontier · 7 pointsr/RationalPsychonaut

What a great question, and an interesting example. For those confused by OP's example, check out Gödel's Incompleteness Theorem on Wiki. Better yet, read the insightful and very trippy Pulitzer Prize winning book, Gödel, Escher, Bach. Gödel's theorem is a bit abstract but it was both a monumental and surprising discovery. It's not just mathematical -- it's meta-mathematical, in that it reveals the limitations inherent to any mathematical framework or system. From wiki:

>The first incompleteness theorem states that no consistent system of axioms...is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.

I'll point out an obvious one, though it's more to do with the aesthetics of the psychedelic experience rather than insights or ideas. Psychedelic hallucinations tend to be geometric, with lattices, grids, spirals, and perhaps most intriguing of all, fractals. All these are geometric forms that can be rigorously defined and analyzed by math. Fractals are especially fascinating because they exhibit self-similarity at every scale, appear sometimes in nature (for example, coastlines), and look extremely trippy. (Seriously, just look at these zoom-ins of the Mandelbrot set, discovered in 1978.)

u/Mythiees · 7 pointsr/todayilearned

I don't follow?

At some point we started asking questions about the world. There came a time where 'something' emerged in us and we started questioning the world around us.

Questions are investigations about how the world (and here 'world' is everything in the immediate environment) works. This leads to 'what if' scenarios, equivalencies 'is this thing like the other?' and sets 'I belong to the group called 'men', she belongs to the group called 'women'. In the group called 'women' there is the subset of 'women' that are my offspring. Godel, Escher, Bach yourself on sets and other concepts.

So, we learned how to ask questions and the answers to those questions lead to more questions. All this leads to the internet and us meeting. Our interaction is the result of an unbroken chain of questions that has brought us from the savanna all the way to here. Think about that.

u/HarlequinNight · 7 pointsr/math

You would love Godel Escher Bach by Douglas R Hofstadter. It won the pullitzer prize and is basically just a really good popular math/computer science/art book. But a really excellent jumping off point. Yes it lacks mathematical rigor (of course) but if you are a bright clever person who likes these things, its a must read just for exposure to the inter-connectivity of all of these topics in a very artistic and philosophical way. But be prepared for computer code, musical staff notation, DNA sequences, paintings, and poetry (all themed around Godel, Escher and Bach).

u/shobble · 7 pointsr/books

In Search Of Schrodinger's Cat by John Gribbin is a very readable physics and quantum physics history sketch. Might be slightly dated now, although I can't think of anything directly contradicted by recent work. Then again, I'm not actually a physicist :)

The Quark and the Jaguar is quite a bit more complicated, but still quite accessible to the layperson and has a lot of interesting stuff.

Slightly less sciency, more maths/logic/computation is Gödel, Escher, Bach: An Eternal Golden Braid

A Guinea Pig's History of Biology is pretty much what the title says, although there's an awful lot about fruit-flies too. Quite a good review of the history of biological experimentation, especially genetics.

H2O: A Biography of Water from a previous editor of Nature, covers water across a variety of fields. The second half of the book is mostly a rant about cold fusion and homoeopathy though, from what I recall, but the first half makes up for it.

Most general-audience things by Richard Feynman are well worth the read. He's got some great physics lectures, and his autobiography (Surely You're Joking, Mr Feynman?) is fun, but more for the anecdotes than the science.

Those are off the top of my head. If its something in a particular field, I might have some other ideas I'm currently forgetting.

u/justanothercactus · 7 pointsr/DesignPorn

You might like this [book] (https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567)...Gödel, Escher, Bach: An Eternal Golden Braid, the cover has an even better whatever you call that effect/illusion.

u/gerundpu · 7 pointsr/philosophy

Yes, and if you want to follow this deeper into the context of consciousness, check out this book: GEB

There's a series of chapters discussing the localization of brain functions. The author discusses a study on rat brains, in which maze-running rats had significant portions of their brains removed, and were allowed to heal. Most rats were still able to re-learn the maze.

u/SuperConductiveRabbi · 5 pointsr/INTP

Here's the inevitable recommendation for Gödel, Escher, Bach (Amazon page, so you can see the reviews).


>Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.

>Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here.

It may be strange, but during the biology and nature-of-thought-related sections of GEB I decided to read the neurology chapters of Gray's Anatomy (no, not Grey's Anatomy). It's pretty heady and slows you down quite a bit, but it results in a really interesting mix of deep biological knowledge about the structure of neurons and functioning of the nervous system with GEB's higher-level, cognition-focused discussion.

Note that that's the 40th, British edition of Gray's Anatomy. There are cheaper ones if you don't need the most up-to-date version, including leather-bound reprints of the classic 1901 American reprint. I doubt the old versions have much accurate information about neurology, however.

u/MmmCurry · 5 pointsr/compsci

Not specific to algorithms or even to CS, but Douglas Hofstadter (Gödel, Escher, Bach, I Am a Strange Loop) touches on many of the logical fundamentals in a relatively layman-digestable manner.

I wouldn't call him easy reading compared to Sagan or Kaku, and don't know a "pop computer science" equivalent to those two, but you definitely don't need a CS or math degree to get through GEB. Whether it's on-topic enough here is definitely questionable.


Edit: I haven't read it, but from the description this one by Thomas Cormen looks like it might be close to what you're looking for: Algorithms Unlocked.

"This is a unique book in its attempt to open the field of algorithms to a wider audience. It provides an easy-to-read introduction to an abstract topic, without sacrificing depth."

From the TOC, it looks like it's probably fairly light on math but gets into code or pseudocode relatively quickly. I still wouldn't call it pop-CS, but if that sounds like a fit, maybe give it a shot!

u/1337_Mrs_Roberts · 5 pointsr/suggestmeabook

Hofstadter's Gödel, Escher, Bach

If you like things a bit more prose-y, try Pirsig's Zen and the Art of Motorcycle Maintenance

u/resisttheurge · 5 pointsr/reddit.com

It becomes useful to replace concepts such as equivalence relations (and other relations) with symbols in order to facilitate understanding, actually. I'm sure you've used the =, <, >, the greater-than-or-equal-to, or the less-than-or-equal-to symbols before. These symbols allow those that read equations, definitions, or proofs to quickly and unambiguously understand what is being discussed. If you end up studying higher math for a while, you become familiar and comfortable with this style of notation.

Interestingly, notation like this and the thought process it represents is important in understanding the structure of mathematical logic, forms a large part of the basis of automata theory (aka why you're able to enjoy complex technology, like computers), and may hold key insights into the nature of consciousness and sentience itself.

If you've got the stomach for the notation, wide worlds of fascinating information await!

u/scottklarr · 4 pointsr/books
u/jsprogrammer · 4 pointsr/science

If that question interests you you'd probably enjoy Godel, Escher, Bach

u/isarl · 4 pointsr/AskReddit

If you don't understand why you are getting downvoted, it is due to the difference between the centre for thought and the origin of consciousness. If you don't think there's a difference, go educate yourself; there are many resources. You might try Gödel, Escher, Bach, for starters.

u/tuber · 4 pointsr/atheism

If I understand you correctly, the principle you've stumbled upon was mathematically proven by Kurt Goedel in 1931. I think you would enjoy this book a lot. It won a Pulitzer prize.

u/proverbialbunny · 4 pointsr/awakened

lawl, that's a fun one.

>You had no choice.

Some fun with semantics: This isn't going to fit into words right, so you're going to have to explore it to understand it, but you do have a choice, but control isn't quite what it seems to be. You obviously get the bit about control, but calling it a choice is misleading. I made the same mistake for a while, until I tried explaining it to people and realized the misunderstanding:

A choice is when there are multiple options, and you pick the best option. You're still picking that option, despite the delusion of control. Even if there is no you, and control is made up, there is still a choice.. a decision, a process. It just isn't real; choice is formless, it is language, it is psychological.

Have you explored consciousness yet? If you're the type that likes to nerd out and go beyond simple teachings checkout I Am a Strange Loop and it's more advanced cousin Gödel, Escher, Bach: An Eternal Golden Braid.

u/butchdogt1234 · 3 pointsr/AskReddit

How about Godel, Escher, Bach? I currently have the book and have read a good bit of it. I'd highly recommend it to anyone. As a matter of fact, you should buy it for yourself and use it within your class.

u/ichmusspinkle · 3 pointsr/math

Gödel, Escher, Bach gets recommended a lot, but for good reason. And it has a good layman's explanation of the incompleteness theorems.

u/introspeck · 3 pointsr/eldertrees

First book I recommend to any programmer, no matter what they're working on, is The Pragmatic Programmer. Excellent stuff.

If you don't get a shot at low-level coding at work, get yourself an Arduino kit and just hack away. Apparently the language is similar to / based on the C programming language. I use C every day.

To do well with embedded systems, real-time, device driver, or kernel type stuff, you have to really, really, really, understand what the hardware is doing. I was able to learn gradually because I started programming when there was one CPU and no cache memory. Each hardware operation was straightforward. Now with multi-core CPUs, multi-level cache memory, multiple software threads, it becomes a bit more complex. But something like the Arduino will teach you the basics, and you can build on that.

Every day I have to think asynchronously - any operation can happen any time, and if they share memory or other resources, they can't step on each other. It can get hairy - but it's really fun to reason about and I have a blast.

There's a lot more I'm sure, but get started with some low-level hacking and you can build from there.

If you want to get meta, many of the best programmers I know love Godel, Escher, Bach because it widens your mental horizons. It's not about programming per se, but I found that it helps my programming at a meta level. (and it'll give you a lot to meditate on when you're baked!)

u/higz · 3 pointsr/AskReddit

Gödel, Escher, Bach: An Eternal Golden Braid

I still haven't finished it though, it's demanding and very rewarding when you do understand it.

u/jbigboote · 3 pointsr/programming

I am surprised this book has not been mentioned yet:


u/dr_entropy · 3 pointsr/InsightfulQuestions

Douglas Hofstadter talks about something like this in I am a Strange Loop. Here's an interview that talks about it a bit. I recommend reading the book, though you may enjoy it more after reading Godel, Escher, Bach: An Eternal Golden Braid.

u/violinplayer · 3 pointsr/violinist

Jaap Schroder wrote a book detailing his study of the Solo violin works, and he's recorded the concertos as well. That's a good place to begin. There are some really brilliant insights that most students would never consider.

Don't get caught up thinking you are handcuffed and can only imitate an anemic baroque style or a warbly, romantic style. This video is one sort of hybrid, where the soloist and conductor are very aware of performance practice, but modern instruments and techniques are relied upon heavily. Remember that no recordings exits before 1900ish. There's still a lot of personal judgment in a good historically informed performance.

There are many great Bach interpretations, and you should listen to many recordings (Grumiaux is often held in high esteem, and Schroder, as good models) to find out where your preferences lie. You should attempt to play with all sorts of expressive devices (Non vib, lots of decay, faster bow, different bow strokes, bowing patterns, holding the bow higher, gut strings?, baroque bow) and find out what you have to say about Bach. I think any successful interpretation will at least have two major things: a tremendous sense of line (form, rhythm, a large-scale view) and an expressive use of the tone color (bright, warm, deep, thick, feathery, etc.).

Leopold Mozart also wrote a treatise on violin playing. In terms of playing style, he was more familiar with the Baroque than with the music of W.A mozart. He wrote about a sense of "affect" in Baroque music. He wrote that overall, there is one overriding feeling that should come across in Barque works (especially dances and binary form movements.) In the E major Bach, I bet it would be helpful to decide what the "affect" is for each movement. Is there only one, is the narrative single-minded? More simply, come up with something other than "happy" or "sad."

Don't let anyone tell you Bach was a stodgy, strict person. He was ridiculously smart, as shown by his ability to improvise multi-voice fugues. Hofstader wrote eloquently about Bach's puzzles and intellectualism. He was a jokester - the crab canon and the Coffee Cantata or good examples. He was sometimes compensated for his work with large amounts of beer. Bach had somewhere around 20 children, about half of which survived childhood. Bach was a very complex person, with lots of life experience. Don't let a careless caricature influence how you think about his music.

u/PatricioINTP · 3 pointsr/INTP

The most INTP book I know is Godel Escher & Bach, though the second half is harder to get through. The first half more than makes up for it.

Other favs include Frank Herbert’s Dune series and his lesser known semi-stand alone book The Dosadai Experiment. That said, The Golden Age Trilogy by John C Wright is jam packed with sci-fi ideas. If you rather read modern fantasy, look at Night Watch series by Sergei Lukyanenko. Meanwhile as a history buff I also like the Temeraire series by Naomi Novik, where European powers in the Napoleonic era have a draconic Air Force.

Right now I am redoing and continuing the Thursday Next series byJasper Fforde, which combines alt history, sci-fi, British humor, and meta level shenanigans. A must for classic lit fans who don’t mind its wackiness. (Others can’t stand it) I also recently finished a reread of Roadside Picnic, which Stalker movie and game were loosely based on.

Edit: one other. If you want a “Lovecraftian Simulator”, get House of Leaves ASAP. It is less of a book to sit down and read and more of an interactive experience.

u/jackthehobo · 3 pointsr/compsci

Gödel, Escher, Bach: An Eternal Golden Braid is a fantastic read.

Hofstadter discusses Gödel's incompleteness theorems, computability, AI, music, and art, and generally about how complexity arises out of self reference.

u/HeyHesRight · 3 pointsr/math

I too love fun math[s] books! Here are some of my favorites.

The Number Devil: http://www.amazon.com/dp/0805062998

The Mathematical Magpie: http://www.amazon.com/dp/038794950X

I echo the GEB recommendation. http://www.amazon.com/dp/0465026567

The Magic of Math: http://www.amazon.com/dp/0465054722

Great Feuds in Mathematics: http://www.amazon.com/dp/B00DNL19JO

One Equals Zero (Paradoxes, Fallacies, Surprises): http://www.amazon.com/dp/1559533099

Genius at Play - Biography of J.H. Conway: http://www.amazon.com/dp/1620405938

Math Girls (any from this series are fun) http://www.amazon.com/dp/0983951306

Mathematical Amazements and Surprises: http://www.amazon.com/dp/1591027233

A Strange Wilderness: The Lives of the Great Mathematicians: http://www.amazon.com/dp/1402785844

Magnificent Mistakes in Mathematics: http://www.amazon.com/dp/1616147474


u/senzei · 3 pointsr/reddit.com

I'd recommend having a read of Godel, Escher, Bach: An Eternal Golden Braid. The book that taught me that consciousness happens somewhere between hormone propogation and the physiological manifestations of our biochemical state.

That and it is just plain good reading.

u/lechnito · 3 pointsr/AskReddit


u/gipp · 3 pointsr/askscience

I'm assuming you're looking for things geared toward a layman audience, and not textbooks. Here's a few of my personal favorites:


Cosmos: You probably know what this is. If not, it is at once a history of science, an overview of the major paradigms of scientific investigation (with some considerable detail), and a discussion of the role of science in the development of human society and the role of humanity in the larger cosmos.

Pale Blue Dot: Similar themes, but with a more specifically astronomical focus.


The Greatest Show on Earth: Dawkins steers (mostly) clear of religious talk here, and sticks to what he really does best: lays out the ideas behind evolution in a manner that is easily digestible, but also highly detailed with a plethora of real-world evidence, and convincing to anyone with even a modicum of willingness to listen.


Godel, Escher, Bach: An Eternal Golden Braid: It seems like I find myself recommending this book at least once a month, but it really does deserve it. It not only lays out an excruciatingly complex argument (Godel's Incompleteness Theorem) in as accessible a way as can be imagined, and explores its consequences in mathematics, computer science, and neuroscience, but is also probably the most entertainingly and clearly written work of non-fiction I've ever encountered.


The Feynman Lectures on Physics: It's everything. Probably the most detailed discussion of physics concepts that you'll find on this list.


Connections: Not exactly what you were asking for, but I love it, so you might too. James Burke traces the history of a dozen or so modern inventions, from ancient times all the way up to the present. Focuses on the unpredictability of technological advancement, and how new developments in one area often unlock advancements in a seemingly separate discipline. There is also a documentary series that goes along with it, which I'd probably recommend over the book. James Burke is a tremendously charismatic narrator and it's one of the best few documentary series I've ever watched. It's available semi-officially on Youtube.

u/iLikeSpegettiWestern · 3 pointsr/cheatatmathhomework

Have you read Gödel, Escher, Bach? There are some great analogies between math, music, art, and other really neat stuff.


u/actualscientist · 3 pointsr/askscience

The book that kindled my interest in Artificial Intelligence and started my journey toward getting a PhD in Computer Science was Gödel, Escher, Bach: An Eternal Golden Braid. It's not current with respect to the state of the art, but it is a compelling, high-level tour through some of the biq questions in Artificial Intelligence, Cognitive Science, and Computer Science in general.

u/habroptilus · 3 pointsr/suggestmeabook

Uncle Tungsten: Memories of a Chemical Boyhood by Oliver Sacks. Sacks is best known for writing case studies of his patients as a neurologist, such as The Man Who Mistook His Wife For a Hat. Uncle Tungsten is part memoir, part history of and introduction to chemistry. There's nothing quite like it out there.

The Selfish Gene by Richard Dawkins. Dawkins's Twitter antics notwithstanding, this book is an unmissable classic in biology.

Godel, Escher, Bach by Douglas Hofstadter. An ode to consciousness, full of puns, music and metamathematics.

Mind, Body, World by Michael Dawson. This is a textbook, but it's (legally!) available for free online, and it's totally engrossing. The author uses his work in music cognition to introduce the major theories and paradigms of cognitive science and show how there isn't as much separation between them as it seems.

u/voyetra8 · 3 pointsr/AskReddit

To OP: You should read Godel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter: http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567

It's a GREAT book. They cover this mental exercise, as well as a ton of others that would likely enjoy.

u/OdwordCollon · 3 pointsr/pics

I'm reminded of this book

u/noveltyimitator · 3 pointsr/atheism

The Eternal Golden Braid

For a collection of simple elements with enough resources and time, emergence of structure occur. Recursion, and the system of seemingly simple neurons can lead to consciousness.

u/SchrodingersLion · 3 pointsr/math

Gödel, Escher, Bach is a popular one. If you're looking for fiction, then I highly recommend Flatland.

u/unverified_user · 2 pointsr/philosophy

Before you read this, check out this Amazon review: here

u/airshowfan · 2 pointsr/atheism

Read naturalist explanations of decision-making, the image of the self, how thoughts work, qualia, etc. You probably want to start with I am a Strange Loop, then Consciousness Explained, and work your way to Godel Escher Bach. There are also many essays online about the non-supernatural nature of the mind, this one being one that atheist Redditors link to often. Also see Wikipedia articles about the mind, free will, etc.

Even after I became an atheist, I could not shake the feeling that consciousness could not be just patterns of atoms. Even in a universe that follows rules and that was not deliberately created as part of a plan, I thought that maybe there's some kind of "soul stuff" that interacts with our brains and is responsible for consciousness. But then, if I can tell that I am conscious, then 1) the soul stuff impacts the natural world and is thus observable and not supernatural, and 2) I am no different from a computer that understands itself well enough to say it is conscious. (It helped me to think of AIs from fiction, like HAL and Data, and try to think of what it would be "like" to be them. Books like The Mind's I are full of such thought experiments). So after thinking about it for a while, I was able to shed that last and most persistent bit of supernaturalism and embrace the naturalistic view of the mind.

u/tanglisha · 2 pointsr/FCJbookclub

I read the first two books of Saga and Promethea. Both are great!

I also started on Gödel, Escher, Bach: An Eternal Golden Braid, which is going to take me a while to get through.

u/eatsleepravedad · 2 pointsr/philosophy

Useless, conceited, futurist masturbation.

You want the theoretical framework of AI, go study math and programming, then go read Russell & Norvig, or if you want philosophy without the practicality, Hofstadter.

u/Meinsilico · 2 pointsr/booksuggestions

I don't believe fiction is the place to go, I'd suggest:

Gödel, Escher, Bach: About Music, Arts, Consciousness, Math, Zen... There is actually an On-going Read-Through of it here on Reddit

Thus Spoke Zarathustra by Nietzsche

& if your into psychology, Psychoanalysis literature is characteristically deep & philosophical!

u/garblz · 2 pointsr/IWantToLearn

Very Special Relativity a simple explanation of a complex phenomena

Thinking, Fast and Slow explains why we actually do live in a Matrix, and how, focusing on statistics instead what your guts tell you, to be able to break the veil of lies sometimes.

Gödel, Escher, Bach: An Eternal Golden Braid how music is connected with art and mathematics? Exploration of symmetries, where none are expected to be found.

Watch everything Richard P. Feynman related on YouTube, start with interviews and the rest will probably follow.

I seriously think you should start with science. Getting a glimpse of how world works at the quantum levels can surprisingly enlighten someone on topics one thought were philosophical. E.g. recent Reddit post asked whether true randomness exists, and the answer to read almost pointless kilograms of philosophy made me cringe. Quantum physics has tonnes more to say, and it's actually verifiable by experiment. So I guess my advice is, before going the way of philosophical banter about the existence of coffee shop around the corner, you can just walk the few steps and take a look yourself. Hence, science as a first suggestion.

u/AlotOfReading · 2 pointsr/math

To understand the general history of math, you won't need to understand what you most likely consider to be math. You will, however, need to understand how to put yourself in the shoes of those who came before and see the problems as they saw them, which is a rather different kind of thinking.

But anyway, the history of math is long and complicated. It would take years to understand everything and much of it was work done on paths that are now basically dead ends. Nevertheless, here are some other resources:

u/RandomMandarin · 2 pointsr/zen

Looks like someone's been reading GEB!

u/A_Downvote_Masochist · 2 pointsr/changemyview

This isn't going to change your views... in fact, it may very well reaffirm them... but you should definitely read Gödel, Escher, Bach by Douglas Hofstadter if you haven't already done so.

Among many other things, Hofstadter discusses Gödel's incompleteness theorem. The gist of this theorem is that no formal system can ever be complete. In the formal system of mathematics, that means that there is always a true statement which is not a provable theorem within the system. In other words, "provability is a weaker notion than truth." Hofstadter also discusses the concept of "leveled realities" and intelligent AI.

One implication of the book is that, even if we are inside some sort of program... it is impossible for us to realize that. It is impossible for us to "escape" the program. The program will necessarily be incomplete, but the only way to see the "holes" - the incompleteness - is to be outside the program, looking at it from above.

The only way I can think to change your views, though, is to argue that our universe is not a formal system. Formal systems are functional - given one input, there is only one output. Math is a formal system. Computers are formal systems. All "randomness" in a computer is actually just the output of another program designed to simulate randomness – pseudorandomness, if you will.

Our universe kind of seems like a formal system on a macro level - there are laws that govern interactions. But at the level of subatomic physics, that all breaks down. The universe is no longer deterministic; it's random. Here's an article about an experiment in quantum physics which concluded that quantum randomness is not computable.. And while that may not matter much to us, quantum randomness probably had huge repercussions on the development of the universe beginning with the Big Bang due to chaos theory.

Now you may say, "Well, maybe in the next highest reality they have better computers than we do which can produce/compute quantum randomness." And there's really no argument I can posit against that, because all my arguments are based on the physical and mathematical laws present in our world. Gödel says that neither of us can ever see beyond the system in which we operate; what you are positing is essentially a science-y argument for the existence of a God or gods – maybe not gods in the traditional sense, but intelligent higher beings on another plane that created our universe and do not obey its laws. It's a matter of "faith."

u/banachball · 2 pointsr/books

Here is the Amazon link.

u/sheep1e · 2 pointsr/AskReddit

> SO lets say I want to play "As Time Goes By". On paper, all it says is Gm7 C7, Cm6 C7, F6 Gm7 (to the words 'You must remember this, a kiss is still a kiss, a sigh is still a sigh.) Those chords are locked together perfectly, like a jigsaw puzzle.

You've described a written language, expressed in symbols of some sort (Gm7 C7, Cm6 C7, F6 Gm7). This written language "maps" to actual music, i.e. symbols correspond to musical chords or notes the same way that points on a map correspond to places in the real world.

This is a perfect example of how most of mathematics works: you analyze some problem and come up with a way to express and manipulate models of the problem in a useful way. Just as written music lets you express and manipulate a model of actual music, written mathematics lets you express and manipulate models of... almost anything.

There's not just one single kind of mathematics, there are many kinds of mathematics for dealing with many kinds of problems. This includes the usual things you've probably heard of, like numbers, geometry, sets, and topology, but also more abstract things like groups and categories (terms with specific meanings in mathematics.) Then there are more applied things, such as the mathematics used in phyics or engineering, to model subatomic particles or buildings and bridges.

In many cases, in pure mathematics, the problem being modeled may be something very abstract. In areas like applied math, physics, and computing, the problems are more concrete. But in both cases, what mathematics does is focus on essential elements of the problem, and capture them in a system of symbols (usually), and rules for manipulating those symbols that match the rules of the problem being modeled.

Mathematics is then about analyzing problems and creating these models and the languages to describe them; manipulating models in these languages; and "proving" things by following the rules of a given language to show that it is or isn't possible to achieve certain results.

I don't know if anyone else has suggested this, but you should try to get hold of a copy of the book Godel, Escher, Bach: An Eternal Golden Braid (at Amazon and Powell's). It's quite well-known, so you can probably find a copy in any decent library. The Powell's page includes the following description:

"A mixture of art, philosophy, music, math, technology, and cognitive science, the book's title only reflects one aspect of its subject matter; namely, the connection between the work of mathematician Kurt Gödel, the artist M. C. Escher, and the composer J. S. Bach. [...] Douglas Hofstadter’s book is concerned directly with the nature of 'maps' or links between formal systems."

Those formal systems that the book discusses, very accessibly, in many respects are mathematics - or at least, simple examples of the kinds of languages that mathematics creates and deals with. The ongoing connection to music in the book may also provide more insight into the relationship between music and mathematics.

u/winnie_the_slayer · 2 pointsr/JordanPeterson

Has Peterson ever spoken about somatic psychotherapy? Embodied cognition? I feel his approach to psychology is entirely intellectual, and as somatic research is showing thoughts are just a way to make sense of lived experience, and when the lived experience is changed (through exercise, yoga, diet, somatic psychotherapy, etc) the previous thoughts often become irrelevant. GEB discusses this as "jumping levels of context." Perhaps Peterson is stuck in a level of context, trying to figure it out intellectually, instead of jumping out of that to a bigger context, a "whole organism" approach to therapy. In other words, it is not possible to sort oneself out just by thinking about it. It runs right into Freud's/Jung's ideas about the unconscious: you can't become conscious of things about aspects of existence of which you are unconscious without some kind of action to break out of conscious thinking. Perhaps underlying the intellectual approach of Peterson is an inherent hostility to feelings and emotions, which would correlate with his conservative position and history of depression and misery.

u/Notlambda · 2 pointsr/dataisbeautiful

Sure. Without anything to go on, I'll just recommend some of my favorites. :)

  • Godel Escher Bach - Mindbending book that delves into connections between art, music, math, linguistics and even spirituality.
  • Code - The Hidden Language of Computer Hardware and Software - Ever wondered how the black box you're using to read this comment works? "Code" goes from transistor to a fully functioning computer in a sequential way that even a child could grasp. It's not at the "How to build your own computer from Newegg.com parts". It's more at the "How to build your own computer if you were trapped on a desert island" level, which is more theoretical and interesting. You get strong intuition for what's actually happening.
  • The Origin of Consciousness in the Breakdown of the Bicameral Mind - An intriguing looking into the theory that men of past ages actually hallucinated the voices of their gods, and how that led to the development of modern civilization and consciousness.
u/karlbirkir · 2 pointsr/Psychonaut

The, err, idea you're talking about is a pretty big one and a lot of cool stuff has been written about it. You might really enjoy reading some of it, if you haven't already, and even writing some of your own. The question if we make words for ideas or if we get have ideas because we have words for them is a mind boggling. You can probably find wikipedia articles through the article for structuralism. Then there's this amazing book which goes into the question about the neurons and consciousness, called "Gödel, Escher, Bach." here: http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567/ref=sr_1_1?ie=UTF8&qid=1335752053&sr=8-1
And the obligatory reading-guide subreddit: http://www.reddit.com/r/GEB/

u/iDante · 2 pointsr/philosophy

Ooooooh my friend you have entered into the realm of a particular book that I recommend to anyone who is able to think: Gödel, Escher, Bach. From the intro, "In a word, GEB is a very personal attempt to say how it is that animate being can come out of inanimate matter. What is a self and how can a self come out of stuff that is as selfless as a stone or a puddle." It won the Pulitzer Prize long ago and is overall amazing. Its author has worked with Dennett on other publications about intelligence too, such as The Mind's I.

That being said, it's quite a difficult and mathy read, but well worth it IMO.


u/acamann · 2 pointsr/todayilearned

If someone reading this is interested in this idea of a unified theory but doesn't feel like diving into principa mathematics, check out Douglas Hofstadter's book Godel Escher Bach: an eternal golden braid. It is intense in its own right, but glorious nerd entertainment!


u/float_into_bliss · 2 pointsr/askscience

Child development researchers have found a lot of interesting "milestones" that seem to differentiate our cognition from that of other primates. An interesting one is called Theory of Mind -- basically the ability to reason that other people are conscious beings as well.

At around 2-5 years old, children tend to understand that other people have a mind too, and the children learn to empathize with others (empathize in this context just means being able to imagine what a situation appears like from another person's point of view). The "Theory of Mind" clip on [this episode] (http://science.discovery.com/videos/through-the-wormhole-did-we-invent-god/) of the excellent series Through the Wormhole has a really great explanation.

At around 6-7 years old, children add another level of indirection -- a child not only realizes that other people have minds, but they realize that other peoples' minds are aware of their own minds. First you realize that you have a mind, then around 2-5 years old your mind can imagine other minds, then at around 6-7 you realize that those other minds can imagine your mind as well. That's the point when kids learn what deception is and become sneaky little bastards.

There's a lot of other really interesting child development milestones. For example, most animals lack the ability to realize that what they see in the mirror is actually themselves instead of another animal. Part of what it means to be human appears to be this ability to think about and layer self-referential concepts -- you've got a mind, this other person has a mind, but in the same way that your mind can think about the other mind, the other mind can think about you, and you can use that understanding of awareness to then change how you interact with the other mind (i.e. "I didn't steal the cookie from the cookie jar!", "These white lines on a blueprint show you how you build a skyscraper"). If you're up for a challenge, the 1979 classic [Godel, Escher, Bach: An Eternal Golden Braid] (http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567) touches on a lot of these self-referential concepts. Be warned: it's not an easy nor a short book.

: The worst thing "Through the Wormhole" has going for it is its incredibly cheesy name that mares an otherwise fantastic documentary series about the "rockstars" of current science. Other shows that have fallen into the terribly-cheesy-name-but-otherwise-excellent-show trap include "Battlestar Gallactica".

u/kyp44 · 2 pointsr/math

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.

u/piratejake · 2 pointsr/math

Escher's work with tessellation and other mathematical ideas are fairly well-known and documented so I'll try to mention a few examples of things I learned in an art history course a while ago.

DaVinci's Vitruvian Man used Phi in the calculation of ratios. Example: the ratio of your arm to your height or your eyes to your face is nearly always Phi. I'm not sure if I'm correct in the body parts mentioned, my art history class was nearly 6 years ago so I'm a bit rusty. I'll try to think of some more examples and post.

EDIT: a few more examples have come back from memory. DaVinci was a master of perspective as well. As you can see DaVinci used linear lines to draw attention to the subject of his works. In the case of The Last Supper, the lines from the structure of the building, to the eyes and gestures of the disciples aim towards Jesus.

Botticelli's Birth of Venus uses a triangle to bring the subject into the viewer's mind. The two subjects on the left and right form the lines that meet at the middle of the top and close off a triangle with the bottom of the work. Venus herself is in the middle of the triangle which brings your attention to her immediately upon viewing the work.

Michelangelo's Pieta also uses a triangle to highlight its subjects. Mary's figure creates a triangle (which is considered to be quite intentional based upon her size, both in relation to Jesus, a full grown man, and from her upper and obviously enlarged lower body). Her triangle makes the outline for the subject, Jesus. He is nearly in the center of both the horizontal and vertical axises. The way he is laying, from near the top of the left and then draping to the bottom of the right, depicts a very lifeless form because of the unnatural laying. Moving the viewer's gaze from the top to the bottom of the triangle strengthens the emotion of the scene.

Moving on to architecture, vaulted ceilings also use triangles to draw your eyes down a line also make an awe-inspiring impression.

In contrast to the European's love of straight lines and geometric figures, the traditional Japanese architectural style was opposed to using straight lines. As you can see, nearly every line in a traditional Japanese building is curved. The traditional belief was that straight lines were evil because they thought evil spirits could only travel in straight lines. This design criteria made for very interesting formations and building methods which I would encourage you to check out because of the sheer dedication to the matter.

The Duomo in Florence is a great example of Renaissance architecture and has a really cool octagonal shaped dome. I could go on and on about how awesome Brunelleschi's design was, but I'll just let you read about it here.

I could talk all day about this sort of stuff, just let me know if you want anything else or have any questions. Good luck with your class!

EDIT2: I've found some more links about the subject of mathematics in art and architecture. It looks like University of Singapore actually has a class on the subject. There's also a good Wikipedia page on it as well. This article is pretty lengthy and knowledgeable, but doesn't include pictures to illustrate the topics. Finally, as almost anybody in r/math will testify, Godel, Escher, Bach by Douglas Hofstadter is a fantastic read for anybody interested in mathematics and cool shit in general.

EDIT3: LITERATURE: I know we've all heard what a badass Shakespeare was, but it really hits you like a bus when you find out that how well the man (or for you Shakespeare conspiracy theorists, men) could use words in rhyme and meter. Here's a Wikipedia article about his use of iambic pentameter and style. Nothing else really comes to mind at the moment as far as writers using math (other than using rhyme and meter like I mentioned Shakespeare doing); however, I can think of a few ways to incorporate math. If you would like to go into any sort of programming during the class, you could show how to make an array out of a word. Once that concept is understood, you could make them solve anagrams or palindromes with arrays... a favorite of mine has always been making [ L , I , N , U , X ] into [ U , N , I , X ] ( [ 3 , 2 , 1 , 4 ] for the non-array folks ).

u/moreLytes · 2 pointsr/DebateAnAtheist

Ah, I too have wrestled with Gödel's theorems, and how they seem to necessitate fallibilism. You might also find Heisenburg Uncertainty Principle to be disconcerting. :)

> I can now see maybe how religious people might look at something in their holy book that opposes modern science (lilke evolution) and say "hey there's always a chance this is wrong!" And I guess i can't fault them there.

I fault them for lazy, mystical, and unsophisticated thinking.

That said, I feel like I understand where you're coming from, and wanted to share some resources that benefited me:

  • Godel, Esher, Bach. I haven't finished this highly acclaimed book yet, but its lucid explorations of consciousness, fallibilism, and paradox have proved quite formative.

  • Critical Rationalism. A theory of knowledge (epistemology) that dominates how many professionals view science today.

  • Bayesian Epistemology sequence. This directed collection of musings has (more than most) resonated with my own discoveries and experiences. Highly recommended.
u/TsaristMustache · 2 pointsr/suggestmeabook

You might really dig Gödel, Escher, Bach

u/alittleperil · 2 pointsr/AskAcademia

If you haven't read GEG:EGB yet, you should

u/scomberscombrus · 2 pointsr/Meditation

Could you explain how his ideas are fallacious?

The question is not "Do I have free will?", but "What am I?"; It's not like the ideas are his own, see Sweeping Zen - Karma, Free-will, and Determinsm.

Also, look up the Taoist concept of wu-wei.

You might also be interested in Gödel, Escher, Bach by Douglas Hofstadter. Essentially, the I appears to be the result a continuous process of self-reference within the brain. There really is no room for the typical Western idea of free will, because the I that is supposed to have the free will does not actually exist as we normally think of it.

Saying that humans exist separate from what we normally think of as the nature of cause and effect would be like saying that humans exist separate from karma, or that atman is separate from brahman. It's just that Western culture is so focused on ideas of separation and individualism that it forgets our fundamental unity with all of nature.

He's not really attacking free will; He's attacking the dualistic view of nature that gives rise to ideas of free will.

u/SirClueless · 2 pointsr/GEB


Not sure if this is exactly what you're asking for.

u/HenryJonesJunior · 2 pointsr/compsci

GEB is a single book, not a list of recommended authors.

u/iemfi · 2 pointsr/Futurology

As I've said many times in this thread, I do not think that Watson is general AI. Watson would not be able to do any of these things today. Please don't ask me to repeat this again.

The point is that the ability to break questions into relevant sub-questions is intelligence. Watson does this. It does not do it as well as a human but it still does it scarily well. There's nothing "just" about recursing your way to intelligence, the complexity involved is staggering.

>Understanding the equation is not the same as having to ability to ask yourself "Can I use this equation?", and having the ability to ask yourself "Can I use this equation?" is actually quite useless if you also have to ask yourself if you can use every other possible equation in existence (of which there are infinite).

Understanding the usage of an equation is being able to answer the question "What can I use this equation for?" Understanding how to derive an equation is being able to answer the question "How do I derive this equation?" When we say someone understands an equation we really mean understanding the usage of an equation, understanding how to derive the equation, and a whole host of other types of understanding. Understanding a myriad of other foundation concepts is also implied when we say someone understands an equation. It is a huge tangled web you have to traverse to solve the simplest of problems. We do it quickly and without being conscious of it but there isn't some magical "understand" symbol which allows us to skip the whole process.

I think I'm just doing a terrible job at explaining myself in general. I really would recommend the book GEB, he explains it amazingly well.

u/roboticjanus · 2 pointsr/outside

This one is a good alternate for the meta-game/mechanical perspective, I've found. Really helps look at some of the underlying connections between different mechanics in-game, so things start to make sense on a broader scale.

Also, to add my own 2¢... If you get too caught up in grinding and the game starts to feel empty and boring, this essay on grinding and the idea of 'the endgame'/global goal conditions not really existing consistently across the playerbase was written by a last-gen player, whose other writings I also happen to like quite a bit.

u/darkardengeno · 2 pointsr/artificial

What else does it do? What low-level function of the brain is incapable of being emulated ('consciousness' is not an answer; that is a high-level result of the low-level machinery)? What observed data breaks with the model I have described?


To expand upon this: mathematical models of single neurons and groups of neurons behave basically just as we would expect them to behave and just as we observe neurons behaving in the lab. Obviously no one has ever made a conscious mathematical model in silicon, paper, or anything else.

However, we observe that our brains are made of neurons (which we understand) and demonstrate consciousness (which we don't). We are left with two possibilities: either there's some 'magic' that makes consciousness happen to large groups of neurons but is more or less unrelated to the individual actions of the neurons themselves, or something in the structure of groups of neurons and groups of groups of neurons (and groups of groups of groups of neurons) creates the phenomenon that we call 'consciousness'.

The 'magic' hypothesis is unfalsifiable and I assign it very low probability. If you have religious or dualist inclinations then you might think it more likely or even certain. The 'composition' hypothesis is testable and almost certainly true. I don't just say this to discredit the magic hypothesis but because there are some serious hints that higher level structures of neurons can do some very interesting things.

If you are interested in this topic I cannot recommend Douglas Hofstadter's Gödel, Escher, Bach enough. It's almost 40 years old so a lot of the science is out of date, but it is genius in basically every meaning of the word and goes into much more detail about this debate between taking things holistically versus reductionistically.

u/sun_tzuber · 2 pointsr/Showerthoughts
  1. Yes, but pirates. I would try to join their cause. Would you?

  2. For now. Some day maybe there will be a user friendly wrapper.

  3. We're much closer to this now than we were in the age of pen-and-paper.
u/SuperC142 · 2 pointsr/explainlikeimfive

I recommend reading: The User Illusion by Tor Norretranders, Gödel, Escher, Bach by Douglas R. Hofstadter, and I Am a Strange Loop also by Douglas R. Hofstadter for some interesting reading on the subject (Warning: Gödel, Escher, Bach isn't for everyone- it's a bit strange, but I love it). I read a lot of books on science in general and, based on that, it seems like many believe consciousness and also free will is just an illusion. In fact, just a few days ago, physicist Brian Greene sorta-kinda said as much in his AMA - granted, he's talking specifically about free will and not consciousness per se, but I think the two must be very related.

I, too, believe in God and also have a very strong belief in and enthusiasm for science, so this is an especially fascinating question for me.

BTW: if you're interested in the way the brain works in general, I highly recommend How the Mind Works by Steven Pinker.

u/gr33nsl33v3s · 2 pointsr/math

You'd probably really like Godel, Escher, Bach.

u/tubameister · 2 pointsr/Meditation

I am a strange loop is essentially a summary of GEB, I remember reading it a few years ago and dropping it halfway through for some reason... I'm reading GEB right now and it's fascinating, though. Amazon. Pdf.

u/lordlicorice · 2 pointsr/compsci

The famous tome Gödel, Escher, Bach covertly explains a lot of important concepts at about your level. And it's meant to be entertaining, not a textbook. I think it's perfect for you!

u/TalkingBackAgain · 2 pointsr/intj

24 years ago was a better time for me as well.

"The Prince" [Niccolò Machiavelli]

"The Demon-Haunted World [Carl Sagan]

"Gödel, Escher, Bach: An Eternal Golden Braid" [Douglas Hofstadter]

"On War" [Carl von Clausewitz]

"Intuition Pumps And Other Tools For Thinking" [Daniel C. Dennett]

u/xelf · 1 pointr/AskReddit

From a discrete math class.

> Gödel, Escher, Bach: An Eternal Golden Braid (commonly GEB) is a book by Douglas Hofstadter, described by the author as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll".[1]

u/_angel · 1 pointr/Meditation

You have to be above the bar to begin with. If you can understand exactly what intelligence is then you can increase it.

Meditation can be used as a way to gain insight. This is not all types of meditation, but there are definitely types of meditation with the goal of enlightenment in mind. Using the Buddhist definition of enlightenment and overly simplified explanation is insight, specifically the type of lower level type of insight that not everyone can get to and for the most part needs to be unlocked. Once it is unlocked, how one utilizes it can be a large intelligence booster, but you have to be able to comprehend how your mind works. If you can't fully recognize a lot of advanced and abstract concepts then knowledge gain is possible but hardly any intelligence gain.

Using the example you mention, math is utilized on the other part of the brain in such a way that you can multitask while solving advanced math problems. A way this can be figured out is solving math problems in your sleep. It is like a piece of your brain is a math coprocessor and it can chug along while you are talking to someone, reading writing, sleeping, or generally not paying attention to it, much like cooking something in the oven.

It depends what you want to learn. The most direct path is raw insight. For advanced logic, paradoxes, and other mathy nerdy stuff you might want to checkout GEB. Meditation doesn't skip the learning step. You still have to learn things the same way everyone else does. Meditation just helps you realize you can utilize your brain to a more full potential.

If you are really interested and think you can can push forward, I highly recommend you try a 300µg+ dose of lsd. Tripping is the same thing as a deep meditation state, but it doesn't stay. It is like driving a car over the mountain instead of walking. In a deep state under the influence you can do all of the more insightful things one can do in a deep meditative headspace. However, figuring it out could take multiple trips as sometimes insight will take 6 hours to come full circle. When meditating in a deep headspace the answer can come much quicker.

The idea is if you can figure it out while tripping, then you can remember what you've learned and migrate it into meditative practices, as it can literally take a life time to get to the level of meditation skill as one night of dropping acid will bring you to.

It is definitely possible. If you don't ask very specific detailed questions about how your brain works, I will not be able to explain in detail, and without asking yourself you can't move towards figuring things out either.

An efficient way to get to a deep headspace from meditation is a map, so you have an idea of which direction to go in. This tends to be pretty good.

u/Solvoid · 1 pointr/AskReddit

Drive yourself sane

Godel, Escher, Bach

Geometry of meaning

Hypnotic Writing

Holographic Universe

Let me know if any of these sound interesting to you and I can refer you to more similar ones. These books have changed my life and helped me learn a lot, they are some of the best books I have ever read.

u/geocar · 1 pointr/AskReddit

> Yeah, but how does a NOT gate work?

A NOT gate can be implemented as a NAND gate where the other input is directly attached to the power supply.

> I want to know on the absolute lowest level how this works

Go eat Godel Echer Bach: an Eternal Golden Braid. I suspect strongly you are trying to ask a question that you lack the language to express. This book covers an awful lot on the subject of computability, and may help you ask your question.

u/ScoopTherapy · 1 pointr/DebateReligion

> It's entirely possible that you had a professor with a specific view of mathematics and told you that their view was right and dismissive or other views, and that you've internalized this attitude.

I formed my views on the matter after I had left school - no professor opined on any philosophical underpinnings of the field that I can remember.

In the same vein, it's entirely possible you have only studied this topic so far as to justify your already-held beliefs in a god, and no more. It's more than possible since you are not using language common to the field, and are talking about formal systems in ways that are radically different than experts.

> The point is that when math and science conflict we believe the math. This would not be the case of math was invented to describe reality.

This is demonstrably false. We believe the observations. When observational evidence conflicted with Newton's laws of gravitation (which were a completely consistent mathematical system), well...we needed new models of gravity, new math.

> You are not a square circle.

Ha, I'm sure this seems self-evidently true, but define what you mean by "you" and I'm sure you'll see that it refers to something that you have empirical evidence for. Unless you are claiming "you" is also an abstraction, and not a real object?

> You need to read this -

I will read it. For an introductory look at formal systems and many other related topics, I would suggest the fantastic GEB by Douglas Hofstatdter.

u/oldredditname · 1 pointr/computerscience


u/jalabi99 · 1 pointr/AskMen

Just a few I've gone through in the past half-year:

The 4-Hour Workweek by Tim Ferriss

A People's History of the United States by Howard Zinn

Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter

The Accidental Billionaires: The Founding of Facebook: A Tale of Sex, Money, Genius and Betrayal by Ben Mezrich

Long Walk to Freedom by Nelson Mandela


The South African Gandhi: Stretcher-Bearer of Empire by Prof. Ashwin Desai and Prof. Goolam Vahed

u/ClarSco · 1 pointr/computerscience

I would give Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter a go.

u/kodemizer · 1 pointr/AskReddit

Hmm, I don't have any specific advice. It sounds to me like a depression - Google that shit and see if fits and if there is any good standard stuff you can do about it. It certainly doesn't help that it's November (assuming you are in USA/Can/EU).

Last time I was in a similar place I got the fuck out of dodge - it didn't 'solve' my issues, but it gave me enough new energy that I could refocus and deal with my shit from a better place.

Another time I was depressed (middle of winter and no money, so travelling was out of the question), I just hermited it up with some good books:

  1. http://www.amazon.com/Ego-Archetype-Edward-Edinger/dp/087773576X
  2. http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567

    and went for a lot of late night walks by myself in the cold all bundled up. Did a lot of thinking - didn't even try to socialize. It was cathartic and I processed a lot. When spring came I was in a much better place.

    Just my experience, take what you can from it.

u/sstults · 1 pointr/reddit.com

What you really need to read is Gödel, Escher, Bach: An Eternal Golden Braid. It's a very readable analysis of computers and algorithms made in the hopes of either proving or disproving the possibility of artificial intelligence. It even won a Pulizter.

u/lfborjas · 1 pointr/Buddhism

That sounds really cool, the fact that you've had the time to research and now to explore, I wish there were buddhist temples/centers/what-have-you in my area, but I live in latin america so it's highly unlikely (I'll ask around anyway, though :P). And now that you mention that

> Zen tends to lean more towards the belief that we are already enlightened and just have to discover that enlightenment as compared to other schools that hold the view that enlightenment comes after this life

I realize that one of the books on buddhism I have read, "Buddhism plain and simple" is Zen-based! Maybe that, the book by D.T. Suzuki I'm reading right now and the mentions about Zen in "Gödel, Escher, Bach" have biased me towards Zen, I'll definitely look into other schools to see what's there.

u/roger_pct · 1 pointr/math

Godel, Escher, Bach: an eternal golden braid by Douglas Hofstadter is a great book that talks about this.


u/thrilljockey · 1 pointr/AskEngineers

I'm not an ME, but these are some of my (more computery-ish) favorites that might have general engineering appeal:

The Difference Engine - proto-steampunk!

Gödel, Escher, Bach - essays on logicians' wet dreams.

Anathem - mathy and fantastic.

House of Leaves - you'll either love it or it will just piss you off...

Also, anything by Phillip K Dick or Kurt Vonnegut. And Feynman's (first) autobiography is definitely a must.

u/Chocklatesoop · 1 pointr/houston

I got a book :D

u/UncomfortablyHonest · 1 pointr/AskReddit

Sorry, I've been playing around with quines and reading too much Godel, Escher, and Back lately.

u/baddox · 1 pointr/programming

Nice. My plan is to buy them all once they're done; they should make a great trophy to have on my bookshelf for life.

I've been reading The Lifebox by Rudy Rucker over break. I'm about a third of the way in and I'm liking it so far. I've already had many of the epiphanies he's trying to install, coming off of reading Hofstadter's GEB over the summer. So far, I consider GEB the superior book, but I appreciate the narrower focus of The Lifebox (Rucker stays strictly on the topic of Computer Science with some very elementary explanations of some advanced physics concepts). The section on molecular biology in the middle of GEB read at a snail's pace for me.

u/quite_stochastic · 1 pointr/philosophy

If you're going to quote me, don't skew my meaning

> My argument was that minds are turing machines because as far as we know, minds are matter, and as far as we know minds are matter because that's what science tells us, and i will certainly revise should science come up with something else.

As my complete quoted statement should show, I am fully aware that science is no dogmatic source of authority with a single voice. Science is always revising itself, and there are always debates within it.

>[the mind== matter hypothesis] is one hypothesis among several, and with less evidence than the other available ones.

>There are thousands of scientists, who issue books which are contradictory to one another. For example Raymond Tallis, a prominent neuro-scientist, argues that mind =/= matter:

It seems that you've been reduced to simply protesting that there exists disagreement among intelligent people. I will allow that the mind body problem isn't a simple problem, many years from now if a consensus is reached, many smart people will be proven wrong. Even so, your characterization of the controversy on this topic that exists within the field of neuroscience specifically is hyperbolic, like so many other things you say.

Importantly, you say you have evidence but the only evidence you've given that the mind isn't matter is your very controversial interpretation of godel and turing that every professor of logic I've spoken to or heard of (not the least of which is OP) absolutely do not endorse, godel's own side musings notwithstanding.

Furthermore, I must ask you, what then is mind? You by your own admission several posts ago, have no idea, you don't even have a guess. Now imagine yourself a neuroscientists, trying to figure out how the mind works. You have before you a human brain, in or outside of a living human body, all of which is matter. What else are you possibly going to study? You cannot step outside of this without stepping into some kind of religion, platonism, or mysticism, neither of which can be studied by science, induction, or even logic. I've spoken to lots of neuroscience professors, and this was their clear consensus. Some respectfully did not rule out religion or platonism but they certainly decried its presence in science. As I said, within neuroscience, the presumption that mind==matter isn't controversial.

By the way if you're gonna throw a book at me, I will return the favor, in fact you may have even heard of this book by cognitive scientist Douglas Hofstadter.


>The reason it is circular is because in OP, the author omitted one of Kurt Godel's explanations for the Incompleteness Theorem -- the one that said that mind =/= matter -- and I corrected him on that. 4-5 replies later you jump in, and presuppose that mind = matter, oblivious to the fact that this was already discussed and challenged before you ever were in the picture.

I will only say that this is a completely unreasonable caricature of what was said in this thread.

u/CSMastermind · 1 pointr/learnprogramming

Entrepreneur Reading List

  1. Disrupted: My Misadventure in the Start-Up Bubble
  2. The Phoenix Project: A Novel about IT, DevOps, and Helping Your Business Win
  3. The E-Myth Revisited: Why Most Small Businesses Don't Work and What to Do About It
  4. The Art of the Start: The Time-Tested, Battle-Hardened Guide for Anyone Starting Anything
  5. The Four Steps to the Epiphany: Successful Strategies for Products that Win
  6. Permission Marketing: Turning Strangers into Friends and Friends into Customers
  7. Ikigai
  8. Reality Check: The Irreverent Guide to Outsmarting, Outmanaging, and Outmarketing Your Competition
  9. Bootstrap: Lessons Learned Building a Successful Company from Scratch
  10. The Marketing Gurus: Lessons from the Best Marketing Books of All Time
  11. Content Rich: Writing Your Way to Wealth on the Web
  12. The Web Startup Success Guide
  13. The Best of Guerrilla Marketing: Guerrilla Marketing Remix
  14. From Program to Product: Turning Your Code into a Saleable Product
  15. This Little Program Went to Market: Create, Deploy, Distribute, Market, and Sell Software and More on the Internet at Little or No Cost to You
  16. The Secrets of Consulting: A Guide to Giving and Getting Advice Successfully
  17. The Innovator's Solution: Creating and Sustaining Successful Growth
  18. Startups Open Sourced: Stories to Inspire and Educate
  19. In Search of Stupidity: Over Twenty Years of High Tech Marketing Disasters
  20. Do More Faster: TechStars Lessons to Accelerate Your Startup
  21. Content Rules: How to Create Killer Blogs, Podcasts, Videos, Ebooks, Webinars (and More) That Engage Customers and Ignite Your Business
  22. Maximum Achievement: Strategies and Skills That Will Unlock Your Hidden Powers to Succeed
  23. Founders at Work: Stories of Startups' Early Days
  24. Blue Ocean Strategy: How to Create Uncontested Market Space and Make Competition Irrelevant
  25. Eric Sink on the Business of Software
  26. Words that Sell: More than 6000 Entries to Help You Promote Your Products, Services, and Ideas
  27. Anything You Want
  28. Crossing the Chasm: Marketing and Selling High-Tech Products to Mainstream Customers
  29. The Innovator's Dilemma: The Revolutionary Book that Will Change the Way You Do Business
  30. Tao Te Ching
  31. Philip & Alex's Guide to Web Publishing
  32. The Tao of Programming
  33. Zen and the Art of Motorcycle Maintenance: An Inquiry into Values
  34. The Inmates Are Running the Asylum: Why High Tech Products Drive Us Crazy and How to Restore the Sanity

    Computer Science Grad School Reading List

  35. All the Mathematics You Missed: But Need to Know for Graduate School
  36. Introductory Linear Algebra: An Applied First Course
  37. Introduction to Probability
  38. The Structure of Scientific Revolutions
  39. Science in Action: How to Follow Scientists and Engineers Through Society
  40. Proofs and Refutations: The Logic of Mathematical Discovery
  41. What Is This Thing Called Science?
  42. The Art of Computer Programming
  43. The Little Schemer
  44. The Seasoned Schemer
  45. Data Structures Using C and C++
  46. Algorithms + Data Structures = Programs
  47. Structure and Interpretation of Computer Programs
  48. Concepts, Techniques, and Models of Computer Programming
  49. How to Design Programs: An Introduction to Programming and Computing
  50. A Science of Operations: Machines, Logic and the Invention of Programming
  51. Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology
  52. The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation
  53. The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine
  54. Computability: An Introduction to Recursive Function Theory
  55. How To Solve It: A New Aspect of Mathematical Method
  56. Types and Programming Languages
  57. Computer Algebra and Symbolic Computation: Elementary Algorithms
  58. Computer Algebra and Symbolic Computation: Mathematical Methods
  59. Commonsense Reasoning
  60. Using Language
  61. Computer Vision
  62. Alice's Adventures in Wonderland
  63. Gödel, Escher, Bach: An Eternal Golden Braid

    Video Game Development Reading List

  64. Game Programming Gems - 1 2 3 4 5 6 7
  65. AI Game Programming Wisdom - 1 2 3 4
  66. Making Games with Python and Pygame
  67. Invent Your Own Computer Games With Python
  68. Bit by Bit
u/1311854 · 1 pointr/PhilosophyofScience

I hate to say this but you do not have a very good understanding as to what "Math" actually is... Mathematical systems are based on axioms. Math itself is just the logic that defines a system (i.e. the system must be consistent, etc) and it is the mathematical logic that backs up the system. In other words, you were looking for something of the scientific method in mathematics... It's mathematical logic.

You can even change the axioms all you want but if the result leads you to contradictions, then it is inconsistent. Look at Gauss's work with non-euclidean systems for example. It is not that math is based on certain axioms but it does use axioms in the construction of systems.

To use you ethics example: It is one thing to say that such ethical axioms could exist (there are a lot of things that could exist) but coming up with a consistent set of ethical axioms (of sufficient size, etc, etc) or a mathematical ethical system, is a whole other ball of wax. While I can't prove that a consistent set of ethical axioms doesn't exist (enter problems of proving a negative here), the odds of such a systems existing is (very, very, very, ... ) low by my estimation.

No mathematician worth their salt would say that mathematics describes "the real world", physics (for the most part) does that. Mathematics is just applying a specific process to different systems (different sets of axioms) and working out the result (consistency, figuring out theories in that system, trying to find mappings to other systems, etc).

I'm not sure this explanation has helped... It's hard to explain these ideas without a wall of text. But if you are interested in philosophy of mathematics, GEB is a good book and A Profile of Mathematical Logic is a great book but a little dense.

u/p1-o2 · 1 pointr/cscareerquestions

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.

u/dmazzoni · 1 pointr/explainlikeimfive

Here's a simple hand-wavy version of the proof.

First let's assume that it is possible to write a program that decides the halting problem. That means it's a program that takes another program as input, and tells you if that program will halt or not. This is what we're going to prove doesn't exist, so to prove it we'll assume it DOES exist and then show that results in a contradiction.

Now take that halting program, which we've assumed to exist, and modify it so that if the answer is "no" then it returns "no", but if the answer is "yes" then it runs forever.

Now take that second program, and feed it to the first program - in other words, you're asking it if that second program halts or not.

If it says "yes, it halts", then that's a contradiction, because it just said that it halts - and yet we just passed it the code to itself but modified so that if it halts, it runs forever.

But if it says "no it doesn't halt", then that means it just said that the halting program itself doesn't halt, which means it doesn't work.

So either way it's a contradiction, and therefore there doesn't exist a program which decides whether any other program will halt or not.

This is not a complete or correct proof, I left out important details. But that's the idea behind it.

If you want more, the book Godel, Escher, Bach is a fascinating take on a very related problem. It takes one of the most surprising mathematical theorems of the last 100 years and explains it by way of language, storytelling, analogy, and metaphor. It doesn't quite explain the halting problem proof but it comes so close that once you've read the book, the halting problem will seem easy. :)

Also, Wikipedia's proof is pretty good and concise, and doesn't involve any higher math.

If you want, try to read through that proof and ask any questions about things that are unclear.

u/insandrium_heart · 1 pointr/IAmA

That doesn't really sound like AI to me. When I think of AI, I imagine some sort of machine that changes state when given certain inputs, and the responses can be "trained" or biased a certain way if the right sorts of inputs are given.

My original question was really angling to make you think in the other direction -- how does the physical material of our brain become conscious? Is the concept of consciousness something that can only arise from cellular material, or can it be implemented with different underlying materials?

I really suspect that there's nothing exclusive about the material our brains are made out of. Take a peek at Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid if you're interested possible mathematical ideas for how consciousness could be an emergent phenomenon.

u/Linguist208 · 1 pointr/tipofmytongue

I can't think of it, but I think it's a movie production company. It's like this cover of "Goedel Escher Bach"

u/themusicgod1 · 1 pointr/computerscience

The skill which cannot be named, that you can only access with u-mode thinking.

u/not_lexihu · 1 pointr/mbti

[2 of 4]

  • How curious are you? Do you have more ideas then you can execute? What are your curiosities about? What are your ideas about - is it environmental or conceptual, and can you please elaborate?
    • I think this is something I struggle with on a daily basis. I like many things, or so I like to believe. Like I feel that everything’s interesting and everything is connected somehow through symbols. I like thinking about these symbols and connections constantly. So my ideas are about concepts mostly. I can’t remember facts if I can’t attach them to concepts that make sense to me.
    • This has been my latest conflict I have to say. I started a career in EE, and then I shifted to computer science. I’ve wanted since I was an undergrad to start a research path, but I’ve been struggling to find something I really really love. I am not good at taking decisions, but an academic path looks now like my best bet for not working in a desk never again (I like having my own desk at home, though).
    • I’m confident everything will be good at the end, and I am confident I can do almost anything. Not trying to be cocky, is just that I know I’m physically and mentally capable of learning anything (in the realm of normal stuff, of course I won’t build a heavy falcon myself), so unless that does not change, I’m good. On the other hand, being so certain about that backfires at me, filling my head with “what ifs”
    • I have this bad habit of reading (and most of the time not finishing) books in parallel, now I’m reading about
    • I pick a chapter until I finish it, and then I move on to the next book, when I have time. I’ve lost interest in reading fiction, I get that from reading graphic novels and manga, mostly. If it matters something, currently ongoing mangas I like are Hajime no Ippo, One Piece, Vinland Saga and The Promised Neverland.
  • Would you enjoy taking on a leadership position? Do you think you would be good at it? What would your leadership style be?
    • I’m not very good at getting stuff done so I would probably suck as a leader of anything. But hey, I am good listening to people and helping them improve. I also don’t think I’m a good teamplayer. I’m bad at following instructions if I don’t trust them. During college I was the guy that ended redoing the work of others during group assignments, because I either I was not satisfied with their work or I was not good at giving instructions. I didn’t know at that moment I was being a dick and I know now, and it’s not something I’m proud of. I'm working on it.
  • Are you coordinated? Why do you feel as if you are or are not? Do you enjoy working with your hands in some form? Describe your activity?
    • I used to draw more when I was younger, and did a bit of woodwork also. I had plants. I like to cook, and have strong opinions on food. I like creating stuff with my hands, I consider myself a creative person. In short, I am coordinated, but not so with team activities like team sports.
  • Are you artistic? If yes, describe your art? If you are not particular artistic but can appreciate art please likewise describe what forums of art you enjoy. Please explain your answer.
    • It’s hard to pin down what kind of art I like, I just know I like something after I’ve seen it or told about, with no particular topic. I don’t understand sculpture, and I vaguely get poetry. Regarding drawing, I appreciate the flow and light in shapes. I was into human figure for some years, and I did a lot of drawings that were good.
    • I know a bit of guitar and ukulele, but I never played for others than girls I like. I am too shy of my voice, my singing and technique, I know it needs improving. I took singing classes once but with only the gist of it I got it’s something that requires more discipline and time than what I’m willing to spend.
  • What's your opinion about the past, present, and future? How do you deal with them?
    • uhm, now I strive to live a life that maximises happiness and minimizes regret. At my age I think I know enough about the things I can control, and play along with that hand, always with the best intentions, and I am optimist about the future.
    • Sometimes I regret not being like this in the past, however, and I see myself revisiting things I would have done better, like studying more, eating better, loved more.
  • How do you act when others request your help to do something (anything)? If you would decide to help them, why would you do so?
    • I always help, I believe in karma as a thing (I mean, not religiously) and that life has been really good to me. I don’t help when I know I can’t help, or when I’m being ordered to or asked in a bad way i.e. makes me feel bad. I have trouble noticing these situations though.
u/NotFreeAdvice · 1 pointr/atheism

I am not totally sure what you are asking for actually exists in book form...which is odd, now that I think about it.

If it were me, I would think about magazines instead. And if you really want to push him, think about the following options:

  1. Science News, which is very similar to the front-matter of the leading scientific journal Science. This includes news from the past month, and some in-depth articles. It is much better written -- and written at a much higher level -- than Scientific American or Discover. For a very intelligent (and science-interested) high school student, this should pose little difficulty.
  2. The actual journal Science. This is weekly, which is nice. In addition to the news sections, this also includes editorials and actual science papers. While many of the actual papers will be beyond your son, he can still see what passes for presentation of data in the sciences, and that is cool.
  3. The actual journal Nature. This is also weekly, and is the british version of the journal Science. In my opinion, the news section is better written than Science, which is important as this is where your kid's reading will be mostly done. IN addition, Nature always has sections on careers and education, so that your son will be exposed to the more human elements of science. Finally, the end of nature always has a 1-page sci-fi story, and that is fun as well.
  4. If you must, you could try Scientific American or Discover, but if you really want to give your kid a cool gift, that is a challenge, go for one of the top three here. I would highly recommend Nature.

    If you insist on books...

    I see you already mentioned A Brief History of the Universe, which is an excellent book. However, I am not sure if you are going to get something that is more "in depth." Much of the "in depth" stuff is going to be pretty pop, without the rigorous foundation that are usually found in textbooks.

    If I had to recommend some books, here is what I would say:

  5. The selfish gene is one of the best "rigorous" pop-science books out there. Dawkins doesn't really go into the math, but other than that he doesn't shy away from the implications of the work.
  6. Darwin's Dangerous Idea by Dennett is a great book. While not strictly science, per se, it does outline good philosophical foundations for evolution. It is a dense read, but good.
  7. On the more mathematical side, you might try Godel, Escher, Bach, which is a book that explores the ramifications of recrusiveness and is an excellent (if dense) read.
  8. You could also consider books on the history of science -- which elucidate the importance of politics and people in the sciences. I would recommend any of the following: The Double Helix, A man on the moon, The making of the atomic bomb, Prometheans in the lab, The alchemy of air, or A most damnable invention. There are many others, but these came to mind first.


    edit: added the linksssss
u/andrecunha · 1 pointr/brasil

Em janeiro, terminei de ler Fundação, do Isaac Asimov. É um livro sensacional; super recomendo. Agora, estou terminando The Foundational Falsehoods of Creationism e Gödel, Escher, Bach: An eternal golden braid. O próximo que eu vou ler provavelmente será Consciousness Explained, do Daniel Dannet.

u/mennomo · 1 pointr/exmormon

>What brought you that position?

My path included convert parents, BIC, a very happy childhood in a huge loving family, RM, 30ish years TBM, 10 years agnostic (closeted 7 or 8 years), going on I think 7ish years now as a Christian. I'm bookish - PhD in engineering. My agnostic period kind of grew out of the full term surprise stillbirth of our second child. I was already starting to question BoM historicity, I had issues with the whole "I know the church is true" thing / epistemology, and it was a fairly quick worldview failure after that. Then with the discovering church history. You get the idea. During my agnostic period, I held a position pretty much identical to what I hear you describing: I cared deeply about truth (still do, very much), I knew logic works (still a big fan, but more aware of its limits now), eventually felt called to try to 'get off the fence' of agnosticism, if I could do it authentically. My approach was to start reading more. Things I read: Godel Escher Bach, Tolstoy's War and Peace, Pilgrim's Progress, a bunch of CS Lewis, the bible in modern english, and a bunch of other stuff I can't remember. Some things that most impressed me about the bible: stories about what goes on in people's hearts that I could see in myself, in my loved ones, and around me in the world, the coherence of the entire narrative around the theme of redemption, the concept of Grace implied in God's relationship to His people and later extended to the individual by Paul.

> what makes you believe in the Christian God?

Here is one thing I wrote about that before.

u/sgnn7 · 1 pointr/askscience


Math is everywhere and it's just about seeing the patterns emerge from simplicity. My knowledge on this topic has mainly been from my own work in Artificial Life and encoding AI genetic knowledge combined with my general interest in biological patterns (which are everywhere in nature) but the first thing that got many things to click for me was playing around with Turtle Logo in high school that is all about using simple constructs to create amazingly complex structures (i.e. one, two - look familiar?).

Sadly I don't work on my AI research anymore due to ethical concerns so I'm a bit out of date but I'd highly recommend the following that weren't mentioned in the original post though:

u/steveeq1 · 1 pointr/AskReddit

Currently only 1/4th through it, but so far it's the most amazing book I've ever read: Godel, Escher, Bach

u/CalvinLawson · 1 pointr/atheism

Wow, awesome list, I've read way to many of those books.

You need to add G.E.B.; that book is amazing and fits in quite well on that list.

u/IRBMe · 1 pointr/Christianity

> If it is about how we interpret our experiences, we can't but fall prey to confirmation bias.

When you're aware of confirmation bias, it is possible to overcome it. That is one of the most important parts of the scientific method: that it accounts for and eliminates the problem of confirmation bias. We can take lessons from the scientific method and eliminate our own confirmation bias in the same way. How we do this is by not trying to prove what we want to prove, but by trying our hardest to disprove it with objective tests, then have others check our work (like peer review).

> Assuming they existed, if you were to witness the sighting of a real ghost, you would likely interpret it as a wisp of fog.

Actually you're just projecting. I would not jump to any conclusions if I didn't know what it was. If it disappeared before I could investigate, the most I could conclude would be that it was something unexplained that disappeared before I could investigate it. I might say that it was probably a wisp of fog and I could back that up with evidence and reasoned arguments, but I wouldn't just jump to whatever conclusion happens to fit my beliefs best as you clearly would.

> It doesn't matter which view you favor, for confirmation bias to occur. It only matters that you favor one over the others and that this can influence your perception of the event.

Which is why, for important conclusions, we should make sure to eliminate confirmation bias using the methods I described above, or some other method that would also take account of it and correct for it. When we do this for any supernatural claims, they quickly fall apart or retreat to the untestable.

> You don't tell people who don't share your basic assumptions to look at things objectively, because it will mean different things to both of you.

I don't think you quite know what the word "objective" means. If it means different things to both of you, it's subjective, not objective.

> If you tell someone who believes in God to look at this objectively, it isn't an unfounded leap at all.

Yes it is. Asserting otherwise doesn't make it true. It does not logically follow from the fact that a dying man sees some light and feels calm that he is seeing an afterlife. There is no logical connection between the two. The only thing that connects them is pure speculation and wishful thinking.

> It is actually very reasonable: A belief predicts that after death my soul will go to heaven, a place filled with light, warmth, and joy. When I am close to death I experience a feeling of floating up, out of my body, and sensations just as predicted by my faith.

Actually I would be willing to bet that near death experiences far out-date religion. But even if not, there is a rather large disconnect between "Seeing some tunnel of light and feeling high" and "Seeing the afterlife". You are making a completely unfounded assumption (actually quite a lot of them), but you are too steeped in your own web of beliefs and superstitions to see it.

The absolute most you can reasonably conclude is that there is an unknown reason why people close to death experience what you described above. To conclude anything above that without demonstrable evidence is unfounded.

> Where a leap of faith is necessary, is at the level of basic assumptions: Belief in God and truth of the Bible. And nobody even disputes that...

They do, actually. Plenty of people, especially on Reddit, claim that their beliefs in God and the truth of the Bible are supported by evidence and reasoning, just as you are doing right now. Like you, they are too tangled in their own web of beliefs and confirmation bias to see that they are just making unfounded leaps.

> Welcome to the mind-body problem, and the deep waters of philosophy.

You need not welcome me. My girlfriend is pursuing a PhD in this very problem, and I myself have been interested in it for a long time. I've already heard and read far more about it than I could possibly digest. The more I've researched it, by the way, the more it seems to be true that there is no such thing as a separate soul or some entity that can survive the death of our physical brains. All of the evidence points away from such a thing. As a starting point, may I recommend Consciousness Explained by philosopher, Daniel Dennet. It attempts to provide a possible explanation of how consciousness is a distributed process in the brain with each part working together, rather than centered in some Cartesian theater. For a heavier read, I would recommend Gödel Escher Bach by physicist, Douglas Hofstadter. It explores the deep meaning that comes from recursion and self reference in art, music, mathematics, logic and in the world itself, and explains how consciousness could be the result of many layers of self referential recursive systems and structures.

u/ruberik · 1 pointr/AskReddit

One thing that's cool about math is that sometimes there are easily-understood examples for even the most mind-blowing stuff. In my last sentence I mentioned something that's (probably) true, but cannot be proven. Weird, right? Example:

"This sentence is true, but cannot be proven."

It's true, but go ahead and try to prove it. If this stuff interests you, you should take a look at this book.

u/pkbooo · 1 pointr/depression

Sometimes depression isn't about circumstances or perspective, it's entirely chemical.

I've thought of the answers to these questions hundreds of times. But the thing about depression is that sometimes it makes it impossible to find a happy answer.

Here are my thoughts:

  1. I have a goal. I'm going to school for Computer Science and Philosophy. I'm hoping to go into AI research. I want to improve the world through new discoveries. That's not my reason to live, though. The only reason I'm alive is because I don't want to hurt the people who love me. I only feel more awful when I think of the wasted potential that my death would cause, which makes me feel even more depressed. Having a goal and dreams does little to curb my depression, and only increases my anxiety.

  2. I'm doing absolutely everything I can to get better. I'm taking my meds, I'm going through therapy, I'm doing everything I'm supposed to do. I think every person deserves to be happy, including me. Happiness is just much, much, harder for some to achieve than other. It's frustrating when so much work doesn't get you very far.

  3. I am connected to everything around me, I am a part of this universe. Even when my consciousness ceases, I (well, maybe not "I") will continue to impact everything around whether through ideas or the physical decomposition of my body. I think I contribute a lot even while alive, and the world has so much to offer. I just lack the capacity to enjoy so much of it.

    I'll try to keep the philosophical bit short, because I could really lose myself in a rant otherwise :p

    I think that an existentialist philosophy can have a lot to offer on a human level. In a way, everything is functionally meaningless, in the sense that so much meaning is beyond our understanding. However, I think that rather than a complete lack of meaning in the universe, meaning is an inherent part of the universe.

    To quote Hofstadter (taken from P-6 of Godel, Escher, Bach:
    >Shouldn't meanings that one choooses to read into strings of meaningless symbols be totally without consequence?

    >Something very strange thus emerges from the Godelian loop: the revelation of the causal power of meaning in a rule-bound but meaning-free universe.

    Basically, by the way that matter is related to other matter, meaning emerges from even the tiniest connection. And that meaning can push matter around in the same way that matter can cause meaning. Ideas are not only meaningful, they have causative power. I think that's pretty cool!

    So basically, I agree that humans may have insignificance on some scale. But in the grand scheme of things, there is something so much more magnificent that we are a part of.

    Anyway...while I appreciate your thoughts and respect your desire to help others, I think that you are a bit misinformed. That's okay! It's nearly impossible for someone who hasn't experienced depression to know what it's like. But there are ways to better understand and help. Here is a great resource from /r/SuicideWatch that shares some ways that you can connect with depressed or suicidal people. I think it may help a lot!

    Oh, and sorry for what turned out to be a philosophical rant anyways; I just can't resist invoking Hofstadter and isomorphism in the face of existentialism :p
u/FatFingerHelperBot · 1 pointr/consciousness

It seems that your comment contains 1 or more links that are hard to tap for mobile users.
I will extend those so they're easier for our sausage fingers to click!

Here is link number 1 - Previous text "GEB"

^Please ^PM ^/u/eganwall ^with ^issues ^or ^feedback! ^| ^Delete

u/ooohnowigetit · 1 pointr/exmuslim

That depends on what you're interested in. There's a bunch of philosophy, psych books I could recommend but I'll go for some more general but still amazing books.




u/winnen · 1 pointr/AskReddit

I can't offer you a lot in the way of non-fiction. If you haven't read it, Gödel, Escher, Bach by Douglas Hofstadter is a good read. It is very dense and slow reading, but can be rewarding. If you like computer science, biology, math, or music in any combination, this could be a good book for you.

The secret to picking good non-fiction is to find something you're interested in or curious about and read a book about it. Things like neuro-linguistic programming, cryptography, riding horses, biking, running, cacti of the saguaro desert, Trees of the Eastern Forests, Scuba diving, Lockpicking, Prestidigitation (aka "magic tricks"), etc.

Of other books I've loved but could not mention in my top 3, I include:

  • Kushiel's Dart by Jacqueline Carey
  • Black Sun Rising by C.S. Friedman
  • Cryptonomicon by Neal Stephenson
  • Slaughterhouse Five by Kurt Vonnegut (or any book by Kurt Vonnegut)

    That's all I can think of right now at work, but if you want more, PM me and I'll see what I can dig up.
u/TheBB · 1 pointr/AskReddit
u/zubzub2 · 1 pointr/AskReddit

(GEB being Hofstadter's Godel, Escher, Bach). I think that it might get a bit more buzz than it really deserves, but it is really a good book to read, as it brings up a number of computer science and philosophy problems like this one, makes you consider them. I'm not really a huge fan of the novel format, and some of the content went over my head, but if you like this sort of problem, I think that it presents a lot of similar-such issues. In GEB, the teleportation question is asked in the form of "replacement" -- that is, if I swap out one carbon molecule in you for another, have I made a new you? What about two molecules? Three? The whole thing?

u/CassandraVindicated · 1 pointr/todayilearned

GEB by Douglas R. Hofstadter

u/looeee · 1 pointr/math

some amazing books I would suggest to you are:

  • Godel Escher Bach

  • Road to Reality By Roger Penrose.

  • Code by
    Charles Petzold.

  • Pi in the Sky by John Barrow.

    All of these I would love to read again, if I had the time, but none more so than Godel, Escher, Bach, which is one of the most beautiful books I have ever come across.

    Road to Reality is the most technical of these books, but gives a really clear outline of how mathematics is used to describe reality (in the sense of physics).

    Code, basically, teaches you how you could build a computer (minus, you know, all the engineering. But that's trivial surely? :) ). The last chapter on operating systems is pretty dated now but the rest of it is great.

    Pi in the Sky is more of a casual read about the philosophy of mathematics. But its very well written, good night time reading!

    You have a really good opportunity to get an intuitive understanding of the heart of mathematics, which even at a college level is somewhat glossed over, in my experience. Use it!
u/adamwong246 · 1 pointr/programming

Well, meta-think about this: a "strong AI" like ourselves might seem mysterious, but consider the fact that our brains are really just nueral nets, which can be mathematically approximated. The process of learning and thinking, in the neurological sense, is really nothing a blind search of your cells for optimal solutions. Using a fairly simple set of rules (See Conway's Game), complicated, intelligent behavior emerges. So I'm not really sure what you mean, but I'm guessing you're implying that intelligence cannot be designed, it must emerge. And don't forget that a method of discovering algorithms, is itself, still "just an algorithm!" Cornell's Eureqa project can do this, to a degree. I think my most important point is this: Intelligence is different between individuals and even animals. Don't judge machine intelligence by it's resemblance to the human mind. Both are machines but they process data in profoundly different ways.

PS http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567

u/DorkRawk · 1 pointr/skeptic

Read this... Godel, Echer, Bach, it's interesting.

u/portal2 · 1 pointr/books

Gödel, Escher, Bach (Amazon, Goodreads, Wikipedia )

That thing is half typography, font, indentation, ... puns and metaphors. For example this holism/reductionism joke: http://i93.photobucket.com/albums/l76/orestesmantra/MU.jpg

I can't think of a way that could work on Kindle. You could try, and some things might not make sense, and some you might miss altogether, just because the font is different.

u/lokikali · 1 pointr/Showerthoughts

you should read this book

u/tigrrbaby · 1 pointr/suggestmeabook

One book that i didnt see mentioned in a casual skim of the posts is Off to be the Wizard

A very silly series where a modern day guy ends up in an alternate dimension where he can do magic/control the world via programming. Super light reads, fun and funny, and pulls in your computer interest. If you enjoy the first one, you can pick up the others.

If you want something a bit meatier, check out some Douglas Hofstadter.

Le Ton Beau de Marot (it's in English) is about the process and problems of translating languages, and makes surprisingly good bathroom reading because the chapters are short. He starts the scope small, talking about whether to focus on literal meaning or the spirit of the words, and then brings in more concepts like artificial constraints (poetry, or even writing without certain letters, for one example). It is philosophical, informative, and amusing. https://www.amazon.co.uk/dp/B012HVQ1R0/ref=cm_sw_r_cp_awdb_L2sgAbDYFK1XK

He also wrote Godel Escher Bach: an Eternal Golden Braid. https://www.amazon.co.uk/dp/0465026567/ref=cm_sw_r_cp_awdb_b3sgAbQ79TTGS better writers than I have written reviews (this one is from Amazon)

>Twenty years after it topped the bestseller charts, Douglas R Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.

u/mrhorrible · 1 pointr/learnmath

Thanks for the conversation. I'd need to think this over some more before commenting further. Much appreciated.

And as for Hofstadter, he's a writer who deals with many topics but largely mathematics and philosophy. I especially recommend "Escher Godel and Bach". Some of your comments, in particular the Magritte painting, could be right out of his writing.

u/simism66 · 1 pointr/Psychonaut

Beyond the obvious choices, Watts' The Book, Ram Dass' Be Here Now, Huxley's Doors of Perception, Leary’s The Psychedelic Experience, and of course Fear and Loathing (all of these should be on the list without question; they’re classics), here are a some others from a few different perspectives:

From a Secular Contemporary Perspective

Godel Escher Bach by Douglass Hofstadter -- This is a classic for anyone, but man is it food for psychedelic thought. It's a giant book, but even just reading the dialogues in between chapters is worth it.

The Mind’s Eye edited by Douglass Hofstadter and Daniel Dennett – This is an anthology with a bunch of great essays and short fictional works on the self.

From an Eastern Religious Perspective

The Tao is Silent by Raymond Smullyan -- This is a very fun and amusing exploration of Taoist thought from one of the best living logicians (he's 94 and still writing logic books!).

Religion and Nothingness by Keiji Nishitani – This one is a bit dense, but it is full of some of the most exciting philosophical and theological thought I’ve ever come across. Nishitani, an Eastern Buddhist brings together thought from Buddhist thinkers, Christian mystics, and the existentialists like Neitzsche and Heidegger to try to bridge some of the philosophical gaps between the east and the west.

The Fundamental Wisdom of the Middle Way by Nagarjuna (and Garfield's translation/commentary is very good as well) -- This is the classic work from Nagarjuna, who lived around the turn of the millennium and is arguably the most important Buddhist thinker after the Buddha himself.

From a Western Religious Perspective

I and Thou by Martin Buber – Buber wouldn’t approve of this book being on this list, but it’s a profound book, and there’s not much quite like it. Buber is a mystical Jewish Philosopher who argues, in beautiful and poetic prose, that we get glimpses of the Divine from interpersonal moments with others which transcend what he calls “I-it” experience.

The Interior Castle by St. Teresa of Avila – this is an old book (from the 1500s) and it is very steeped in Christian language, so it might not be everyone’s favorite, but it is perhaps the seminal work of medieval Christian mysticism.

From an Existentialist Perspective

Nausea by Jean Paul Sartre – Not for the light of heart, this existential novel talks about existential nausea a strange perception of the absurdity of existence.

The Myth of Sisyphus by Albert Camus – a classic essay that discusses the struggle one faces in a world inherently devoid of meaning.

I’ll add more if I think of anything else that needs to be thrown in there!

u/jchiu003 · 1 pointr/OkCupid

Depends on how old you are.

  • Middle school: I really enjoyed this, this, and this, but I don't think I can read those books now (29) without cringing a little bit. Especially, Getting Things Done because I already know how to make to do list, but I still flip through all 3 books occastionally.

  • High school: I really enjoyed this, this, and this, but if you're a well adjusted human and responsible adult, then I don't think you'll find a lot of helpful advice from these 6 books so far because it'll be pretty basic information.

  • College: I really enjoyed this, this, and started doing Malcolm Gladwell books. The checklist book helped me get more organized and So Good They Can't Ignore You was helpful starting my career path.
  • Graduate School: I really enjoyed this, this, and this. I already stopped with most "self help" books and reading more about how to manage my money or books that looked interesting like Stiff.

  • Currently: I'm working on this, this, and this. Now I'm reading mostly for fun, but all three of these books are way out of my league and I have no idea what their talking about, but they're areas of my interest. History and AI.
u/MysteryOfTheAges · 1 pointr/read_more

Godel, Escher, Bach: An Eternal Golden Braid
> By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach, GEB expounds concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself.

Read it. Trust me. There's also a course on this by MIT available here

u/glennonymous · 1 pointr/slatestarcodex

First of all, let's establish something about the audience for whom I'm writing: People who have read and are reasonably familiar with Eliezer's great work of fan fiction Harry Potter and the Methods of Rationality.

Paragraph 1, while necessary in order to set up what follows, is mostly just silly, but already playing with little self-referential jokes. The self-consciously weird use of "isomorphism" is meant to remind readers of Gödel, Escher, Bach, which will come up again later. If the reader thinks that nonsensical phrases such as "All characters are fictional" are mistakes by a dimwitted author in a hurry: They are not. Read more Nabokov.

u/roboticc · 0 pointsr/math

You definitely, definitely want to give him Gödel, Escher, Bach: An Eternal Golden Braid . If he's into mathematical thinking, this book will expand his mind in ways that no other book can. More than books that are directly about mathematics, Godel, Escher, Bach is an exploration of ideas and their relationships that will expand the way he thinks.

u/GerardDG · 0 pointsr/DebateReligion

That was an unsatisfying answer, I suppose. You want me to make a genuine play before we continue, fine, I'll give it a shot. But the supposed delineation between literal and symbolic is the first thing you'll have to discard. It is entirely wrongheaded. It's not even wrong. On one end a literal interpretation has Christians eat the body of Christ and drink his blood, and you end up painting them as vampire cannibals. Which was probably your agenda anyway. On the other, everything is symbolic and the new testament might aswell be referring to Jesus' covert war against clown reptiles. These answers are silly because the question is silly.

In the early 20th century, mathmetician Kurt Gödel set out to create his incompleteness theorem. The theorem was originally intended to show Russel and Whitehead's system for working with natural numbers as complete. This is important, because what use is an incomplete system? Not only did he end up proving the system as incomplete (humiliating two people he actually admired), he ended up proving no consistent system of logic can ever be complete, and vice versa. Neither can the system prove it's own axioms, any more than you can lift yourself by pulling your hair. Why is this crucial to a debate about religion? Because divinity is complete.

Source: Godel, Escher, Bach by Douglas Hofstadter.

So math and science arrive at what religion already knew. All is one. Duality is false. Symbolic and literal interpretations do not exclude one another, they show aspects of the same complete divine thing. They are shifts in perspective. An unsolved rubix cube does not disprove the solution. One implies the other.

And so the singular divine splits itself into male and female. One becomes two. And the coupling of two will beget a third. But duality is false, division is false. Man is fallible and incomplete, so he stifles the world through his ego. The benevolent king becomes the tyrant. The mighty creator becomes Holdfast, the enemy, the dragon.

It's been awhile since I've actually seen a bible, but as I recall the new testament does not start with Mary or God. It was Herod who called the census and set the whole thing in motion. The bad, unjust king strangles the land in an attempt to secure his reign. Thereby his actions create the very thing he fears most: the hero.

The tyrant-father is just a different face of the holy creator. When the arch-enemy holds the entire world in his stranglehold, new life springs from the void itself. The story of the savior is the story of every single human being. It shows the hero ascending the dominance hierarchy, dethroning the evil tyrant, slaying the dragon and reuniting with the divine. The hero's special weapon is the ability to tell good from evil in all their different guises. And again good and evil are just a perspective shift away from being truth and untruth. What difference does it make if the dragon is an actual dragon, mankind's sin, or the duality of all existance itself? All of it is symbolic. And in the sense that all of us are heroes, all of it is real.

Source: Hero with a thousand faces by Joseph Campbell.

>Clearly we can infer the Apostles and many early Christians believed that these things literally happened, and whether or not you think this is zealotry, the number of Christians who believe this literally is greater than those who see this symbolically.

This part brings a particular quote to mind, and besides there's a third book that I can show off as having read:

>The sun signifies first of all gold. But just as philosophical gold is not common gold, so the sun is neither just the metallic gold nor the heavenly orb...Redness, heat and dryness are the classical qualities of the Egyptian Set (Greek Typhon), the evil principle which, like the alchemical sulphur, is closely connected with the devil. And just as TYphon has his kingdom in the forbidden sea, so the sun, as sol centralis has its sea, its "crude perceptible water" and as sol coelestis its "subtle imperceptible water." This sea water (Aqua pontica) is extracted from sun and moon...
>We can barely understand such a description, contaminated as it is by imaginative and mythological associations peculiar to the medieval mind. It is precisely this fantastical contamination however that renders the alchemical description worth examining- Not from the perspective of the history of science, concerned with the examination of outdated objective ideas, but from the perspective of psychology, focused on the interpretation of subjective frames of reference...The alchemist could not sperate his subjective ideas from the nature of things, from his hypotheses (emphasis by prof. Peterson)...The medieval man lived in a universe that was moral- where everything, even ores and metals, strived above all for perfection.

Source: Maps of meaning by Jordan Peterson.

u/josephsmidt · -1 pointsr/mormondebate

Physicist here so don't pretend I don't know what science is. (Though like the ancient Pythagoreans I'm sure as soon as I discuss something that has been proven that goes against a purely scientific worldview out comes the pitchforks.) And though I love science, unlike some people here I am willing to admit to the limits of science. Science can lead to all truth in the same way that rational numbers define all numbers: it can't! and Godel proved it.

The real problem with science is that it has been mathematically proven by Godel that there are more things that are true then are provable and thus you can't ever have a scientific theory that can determine the truth or falsity of all things. As soon as you write down that theory, assuming it allows for arithmetic, Godel's incompleteness theorem immediately shows if the theory is true there will be true statements about reality that are beyond provability. Read Godel Esher Bach or Incompleteness or work through it yourself in this textbook as I have.

So like I said above, science is great in it's sphere (and in that sphere let me emphasize it is awesome!) but leads to all truth in the same way that rational numbers leads to all numbers. (And the analogy is precise since Godel used the famous diagonizational argument in his proof.) Russell and Whitehead set out to show in the early 1900s that if we could determine the axioms of reality then through logic work out everything that was true and Godel spoiled the party.

It it would be one thing if these truths were trivial things, but they are not. Some examples of true or false statements that may fall into this category of being unprovable are:

  • Goldbach's conjecture and an uncountable number of mathematical theorems (by the diagonalization argument) for that matter.. (Search the pdf for Goldbach)

  • Issues related to the halting problem in computer science.

  • Issues related to recursive logic and artificial intelligence.

  • And again, this list goes on uncountably.

    Now, at this point critics almost always tell me: but Joe, Godel's incompleteness theorem is only relative to your set of logic. (Ie... we can prove Goldbach by just adding axioms needed to do so.) Fine. But two things: (first) adding axioms to prove what you want willy nilly is not good science. (Two) You now have a new set of axioms and by Godel's theorem there is now a new uncountable set of things that are true (and non-trivial things like I listed) that are beyond proof.

    Now usually comes the second critique: But Joe, this doesn't prove God exists. And this is true. But at least it has been proven God gives you a chance. It has been proven that an oracle machine is free from the problems that hold science and logic back from proving the truth of all things. At least something like God gives you a chance (whereas science falls short).

    Or, like Elder Maxwell says so well: it may only be by the "lens of faith" that we can ever know the truth of all things. He maybe be right, and hence the importance to learn by study, and also by faith...
u/kaosjester · -1 pointsr/philosophy

Calculus is a bullshit excuse for mathematics. It's pure computation, and it's freaking useless. You have no idea what a formal proof is, or what an axiom is, or anything related to talking about math in an abstract, metamathematical fashion. Pick up a copy of Gödel, Escher, Bach and introduce yourself.

Abstract mathematics, or `pure mathematics', is a specific field of mathematics that spends time examining and proving theorems. It is, in some regard, the study of metamathematics - you use math to prove other math. Check out a basic explanation here.

u/emporsteigend · -1 pointsr/lisp

>Ah, this is another troll tactic, the misleading statistic. Many DO disagree. Many MORE, at least twice as many, agree.

I personally tend to weight negative reviews a bit higher.

See the other book I named:


>Maybe you did not try asking non-inflammatory questions in the places where people are willing to answer, such as here and #lisp.

My memory of the chanop in #lisp (though this was years ago) was that he was exceedingly surly for no real reason. In fact, pretty much everyone there had a bug up their ass. There again, IRC in general has that same problem.

u/kruchone · -1 pointsr/compsci

This really isn't a textbook, but it might as well be: Gödel, Escher, Bach

All of these suggestions are spot on, I can second Sipser's textbook, as well as Structure and Interpretation of Computer Programs.