For those who enjoy kind of stuff, I would highly recommend the book Godel Escher Bach
Honestly, these kind of articles don't do justice to the Godel's incompleteness theorems. Infact the reason for this book was to explain what that even means.
But when you read that book you will realise just how much of everything that is beautiful in this world is mathematical.
I think I made it up to 70% of he book, probably 4 or 5 times. Thats pretty much how far I could make it. But I thoroughly enjoyed each of those partial reads
You got further than me... the bookmark has dust on it.
I thought it would be more palettable via audiobook... but even being read to, the concepts are dense and you're not driving down the road fully present...
I got some good stuff out of it... for now. The analogy pattern recognition/consciousness thing clicked...
I loved the visuals in the book. I had 3 copies I think, gave them all to people I met who I thought would appreciate it. Need to buy a new copy for my son who is majoring in Math.
Godel’s incompleteness theorems and Douglas Hofstadter's book Godel, Escher, Bach get hung up (or lost in space in the case of Hofstadter) on self-reference. Granted, Godel uses his overly complicated mathematical "system" as cover to bury self-reference so it isn't as obvious as 2x2=5 but nevertheless it is wrong.
To wit from the article;
Godel’s extra insight was that he could substitute a formula’s own Gödel number in the formula itself, leading to no end of trouble.
This isn't insight or genius it is proof that he made a mistake. Self-reference leads to "infinity" and "no end of trouble" if improperly defined. If you've read the history of mathematics you'll find that many of them (including Godel and Cantor) went insane thinking about infinity but that is what you get when you use an ungrounded base-case for self-reference. Intentional or not, these incompleteness theorems have led to uncertainty and doubt regarding reason.
BTW, we all safely use self-reference virtually every single day when we say "I" but what do you mean by that?
For those who enjoy kind of stuff, I would highly recommend the book Godel Escher Bach
Honestly, these kind of articles don't do justice to the Godel's incompleteness theorems. Infact the reason for this book was to explain what that even means.
But when you read that book you will realise just how much of everything that is beautiful in this world is mathematical.
Agree - Godel Escher Bach is excellent
" But when you read that book you will realise just how much of everything that is beautiful in this world is mathematical."
...tis...
The human mind uses 4 different tools.
" The human mind uses 4 different tools."
...drugs and sex and rock and roll...
...the fourth slips my mind...
...howl on Rdude...
Bacon 😎
https://x.com/ihtesham2005/status/2051296304740069635
IYKYK
Anyone who has fully read and understood that book is a true genius!
Yeah... it's by no means, "light reading" !!!
I think I made it up to 70% of he book, probably 4 or 5 times. Thats pretty much how far I could make it. But I thoroughly enjoyed each of those partial reads
You got further than me... the bookmark has dust on it.
I thought it would be more palettable via audiobook... but even being read to, the concepts are dense and you're not driving down the road fully present...
I got some good stuff out of it... for now. The analogy pattern recognition/consciousness thing clicked...
I loved the visuals in the book. I had 3 copies I think, gave them all to people I met who I thought would appreciate it. Need to buy a new copy for my son who is majoring in Math.
"IYKYK"
...wags tail merrily...
Godel’s incompleteness theorems and Douglas Hofstadter's book Godel, Escher, Bach get hung up (or lost in space in the case of Hofstadter) on self-reference. Granted, Godel uses his overly complicated mathematical "system" as cover to bury self-reference so it isn't as obvious as 2x2=5 but nevertheless it is wrong.
To wit from the article;
This isn't insight or genius it is proof that he made a mistake. Self-reference leads to "infinity" and "no end of trouble" if improperly defined. If you've read the history of mathematics you'll find that many of them (including Godel and Cantor) went insane thinking about infinity but that is what you get when you use an ungrounded base-case for self-reference. Intentional or not, these incompleteness theorems have led to uncertainty and doubt regarding reason.
BTW, we all safely use self-reference virtually every single day when we say "I" but what do you mean by that?