Theorems have characteristics that aren't obvious to non-mathematicians. Hofstatder's goal was to convey some of these characteristics. A metaphor that says "if a theorem were a record and a mathematical system were a record player, here is what would happen to the record player when it played a self-referential theorem record" is an excellent way to show how theorems are different than anything we normally deal with.
A more modern book would have been able to rely on the metaphor of a program "crashing" which would have been sad and inept. There are a thousand ways a program can crash and very few of them reflect any aspects of Gödelian incompleteness. They're just poorly made, like a record with a big hole in the track that breaks the record needle.
There are essays in Hofstadter's collection "Metamagical Themas" that expand significantly on his idea of what metaphors and analogies actually are and what he thinks they're capable of doing. Reading those makes it very clear why he'd use broken metaphors in GEBEGB.
I think GEBEGB is most useful in exposing people who don't yet have any formal training in mathematical theory to some deeper concepts and inspiring them to find the subtle edges of these systems. I read it at about 12 and it changed my life by exposing subtle fripperies of thought. If I'd read it at 20, as the author of this article did, I too would probably have experienced these little amusements as lack of rigor. Instead I experienced them as mysteries, and now as an adult I experience them as very dry jokes and thought prompts.
Also adding to this. A main point of the book is also that there is no logical system that can be complete, so someone trying to get the real big picture needs to be able to live outside logic comfortably as well.
A little bit like Zen thinking. You cannot make a clapping sound with one hand. But you have to accept that the question can exist in a space with zero answers.
I can't recommend that course enough too. I guess I couldn't find the book on my own. So anyone that can, great! But having someone who knows the book take your through it, at least for me, made it a lot more fun. It was, in my experience, kind of a rare book in how I wanted to share what I was looking at with someone but didn't have anyone to share it with really. Having the prof giving a breakdown made it a lot more digestable for me.
0. The Mind's I
1. Metamagical Themas
2. Fluid Concepts and Creative Analogies
This was very true of the first (several) times I read through the book. I pulled the book off the shelf of my Dad's library at the age of maybe 10-12 (it had the coolest cover), and couldn't make head nor tail out of most of it. It did have a bunch of interesting pictures and I skipped most of the prose to read the funny and intriguing dialogues.
Each time I re-read the book I felt like I got more out of it, I think I'd read it more than ten times over by the time I was 20.
Having been through GEB a few times made Metamagical Themas easier too, and the same rule of "skip to the next section, or just take a break if I'm not getting it" worked well there too.
GEB is not a book for consume only once. I came back again and again. The profound meaning of the book and Godel theorem goes beyond many people can imaging. GEB itself is a metaphor.
I need to double down on meal planning and just really quit it.
Here is a refresher: https://www.varsitytutors.com/hotmath/hotmath_help/topics/co...
Also, who says the intellectually disabled can't be vegans?
If I have that knowledge, potentially I have moral imperative to use it. Compassion for things that I don't have to have it for might be something I'm supposed to do with my time piloting this homunculus.
However I suspect we agree some lives are so filled with suffering that the compassionate choice is to not breed a sentient being into that life. Imagine choosing to get pregnant if you had certain evidence it'd damn your future child to a life of physical and mental anguish -- you'd refuse. That's the life of pigs and chickens on modern farms: too much suffering[1], below the threshold of "worth living."
Moreover, the state of the animal welfare movement is bleak[2] compared to the scope. Farm animal advocacy is a niche and regularly ridiculed. Progress is constantly on shaky ground: recent initiatives in MA and CA prohibiting animal products from animals raised in cages too small to turn around in is at serious risk of being overturned by the federal government's "King amendment," which would prevent any state-based welfare reforms. I'm passionately in support of this work, but under no delusion we're near the end of it.
Given that, the strategy I advocate for is both improved treatment of farm animals and reduced breeding of them -- at least until farm animal treatment improves. Hoping that treatment will catch up soon so that it'll obviate the need for dietary change is unrealistic today, though I sincerely hope (and will support those trying) to get there[3].
[0] Caveat that slaughter today is not always humane, in particular for chickens and fish.
[1] E.g. gestation crates and lifetime of small cages, genetic breeding that causes chickens to grow so fast they break their own legs, debeaking practices, and more.
[2] Progress is happening, and in fact the wins we've had are hugely beneficial to animals -- but I suspect decades before we're at "enough" of an improvement. Within that time billions of animals will be raised and slaughtered for food; the scale is hard to fathom.
[3] And frankly, I expect cultured meat and sophisticated plant-based meats like Beyond Burger to gain wide adoption before that.
I mean, c'mon. The only way for there to be something good, or great, from a first-person experience, is for there to be a first person to actually do the experiencing.
Caveat, of course, bringing something into an existence that is only suffering is probably not so great. This is why we need to treat our food animals well (not to mention our kids!)
https://en.wikipedia.org/wiki/David_Benatar
https://en.wikipedia.org/wiki/Antinatalism
Edit: though several weaker views are more common in animal rights advocacy, for instance that being born in order to be raised for food is not a benefit to an animal, that being born in order to be raised for food in a factory farm is not a benefit to an animal, or that being born is a benefit but that conferring a benefit on an animal doesn't make conferring harms on the same animal legitimate or appropriate even if the benefits and harms are structured as a "package deal".
As for the animals - hey, I said I want them treated decently. I don't extend them the same courtesies as I extend to humans because they're not human, and I don't shed a tear for their deaths because to do so is to anthropomorphize them, a quintessentially childish way of viewing the world.
> being born in order to be raised for food in a factory farm is not a benefit to an animal
Said animal wouldn't exist otherwise, and could not benefit from not existing, so the potential for benefit is always higher on the existence side, even if the probability is very low - it's still higher than a guaranteed 0.
> Simple teleology defeats it, in the sense that everyone who holds this view will probably die childless, and will not be very successful at spreading their views generationally.
This seems like a particularly raw invocation of
https://en.wikipedia.org/wiki/Argumentum_ad_populum
The same reasoning would seem to suggest that religions that successfully encourage people to have many children are most likely to be correct because they provide one method for spreading their views (that is, having children and then teaching them to believe in the religions' doctrines). This is one way that religious views do get spread in the world and one demographic factor in religious belief, but it's hard to see the connection between this and the correctness of each belief as we might otherwise understand correctness.
This is very silly, it plainly conflates truth and popularity.
> As for the animals - hey, I said I want them treated decently.
Suggests "decent" treatment of animals is preferable to "indecent" treatment; this is broadly accepted.
> I don't extend them the same courtesies as I extend to humans because they're not human
Suggests animals/animal suffering are/is of less moral importance than humans/human suffering. This is also broadly accepted.
> I don't shed a tear for their deaths because to do so is to anthropomorphize them, a quintessentially childish way of viewing the world.
Suggests anthropomorphisation of animals is undesirable because it is stereotypically childish; childishness is bad. Seems like quite a silly argument, kids are also fond of breathing etc.
> Said animal wouldn't exist otherwise, and could not benefit from not existing, so the potential for benefit is always higher on the existence side, even if the probability is very low - it's still higher than a guaranteed 0.
You care about the expectation, not the "potential for benefit".
In any case, the way in which you've presented these ideas suggests that you're a consequentialist maximiser (eg think that it's the outcomes of actions/choices/rules that matter, and that there exists some partial order of the desirability of possible worlds). I'd suggest that if you keep thinking about animal welfare and how to balance the lives and living conditions of animals against your own social and dietary needs, you may well decide that you want to reduce your meat intake. Peter Singer's "Animal Liberation" is fairly classic, "The Possibility of an Ongoing Moral Catastrophe "[0] is much more general but pretty great.
[0] https://link.springer.com/article/10.1007/s10677-015-9567-7
The bigger issue is not that nature of the math but the notion that you believe you can subject the matter to it like what is the answer to 42 + banana.
The simpler answer is that we ought to do less immoral things not to find interesting justifications for doing so.
Maybe your life. I feel pretty good. Have you considered doing things to reduce your suffering? There are a lot of great options. Take a few deep breaths and consider whether it's really as bad as all that.
Suffering in the human context is also very relative to tolerance. Experiencing the occasional great suffering (whether physical or emotional) puts your daily aches and pains and disappointments into proper contrast so you can tell that you should learn how to not take them very seriously.
Ahem, what?
i live with my own temptations in this realm, so i'm not coming from a "i've done it" POV, but from a "this is where i lean when i'm pretty sure i need to give it a real go" one.
I think the trick to reading GEB is to not take it so seriously. You can skim sections, you can skip parts, you don't have to understand everything, not everything has to make sense. I think the author here misses that when he complains such about the quality of the metaphors. They're not meant to help understand, as much as being there to give a vague idea about what's coming in a fun way.
If you still don't enjoy GEB, then it's not for you, and that's OK too.
I found 'I am a Strange Loop' a more dry and less enjoyable read than GEB, but it was certainly a lot clearer, and better written in many ways. I would probably recommend it before GEB for most people.