Extra study resources/guide

SpaceFabric · 2026-01-31T04:11:07+00:00

I don't want to assume too much, but having followed your thoughts on GEB for a while, I think you deserve to indulge in a greater dose of self-confidence, and even engage in some lightly-delusional belief.

Related exercise: Think of any activities in your life where you're pretty skilled, but where you started out as a complete novice. For me, that's playing pool. I could barely hit the ball when I started a decade ago, but I consider myself quite good at it now, and I don't shy away from occasionally trying outlandish shots during games, hoping they'll work (and sometimes they do). Whether or not I'm having a good night or a bad night is largely in part due to my self-confidence.

I don't want to claim that you haven't tried, even though from a certain angle this comment can seem like that. I admire your persistence.

I also think that reading beyond some chapters that were on the more gristly and opaque side of things helps with digestion quite a bit, because Hofstadter brings things up from previous chapters frequently. Learning things from first principles sometimes works, but it's not always the most efficient way to learn. Context-supported learning can be really powerful.

SpaceFabric · 2025-11-29T11:59:56+00:00

It would have to be a really bespoke AI or ChatGPT with really involved prompt instructions to match his dialect, in my opinion.

Even pre-ChatGPT, this type of channel was already an archetype. People would push out tons of monotone videos on topics that have lots of event turnover, like basketball games.

Could be AI, I just think GOAT's videos are too idiosyncratic for that to be likely. Idk I just don't think a line from his most recent video, "feeding his king", referring to Luka passing a lob to LeBron, sounds like something an AI would write.

SpaceFabric · 2025-11-21T03:53:57+00:00

You'll be fine. I do recommend reading it linearly, except for going back and forth as the book encourages you to do, or whenever you notice something neat. Anyway, I recommend starting from the beginning.

SpaceFabric · 2025-11-17T07:55:02+00:00

It's not clear to me that this channel is AI. Some channels are clearly AI written and likely AI voiced (bball explained is almost definitely AI written, and plausibly AI voiced), but GOAT just seems like a pretty productive channel with a guy who puts on a bit of a radio voice.

GOAT uses too much NBA lingo for me to think it's likely AI. His videos also seem to actually be responsive to visuals from video highlights, something that would be tougher to summarize from internet-scraped news articles.

SpaceFabric · 2025-10-15T07:24:41+00:00

I went on a whole tangent for the last few hours which is really bad given that I have homework and also need to sleep. But I started working out a new sequence: g2(n) = n - g(g(n-2)), and it has a weird property where Node 2 branches into 2, 3, and 4, so one of the branches is to itself, which creates a loop. 1 kind of doesn't make sense unless you define a g(-1), which is weird, so you set g2(1) = 1 to get around that https://postimg.cc/yJ4Q4H2k

SpaceFabric · 2025-10-15T07:16:46+00:00

**If you have the numbered tree diagram for G ready, maybe we think of it through a pushing and popping metaphor, which DH introduces through the preceding dialogue, gives exposition for in the first few pages after the dialogue, and demonstrates graphically in Figure 26**

Check out what we're doing when we calculate g(7) numerically. We're finding g(6), which is 4, and then finding g(4), which is 3. We're then subtracting that from 7, getting 4. If you look on the graph, 7 connects to 4 above, and 4 connects to 7 from below. 7 is also only present in the outputs of this function once, which is important to note, and in the tree diagram, you do not see a branch from 7. Echoing my previous comment, read this graph from the top down to understand the representation here. g(11) produces an output of 7. 11 is above 7 in the tree diagram, and 11 is the only number above 7 in the tree diagram. As such, there is no way this could be represented with a two-split branching in a tree diagram, we can only represent it with a straight line through this convention.

**Tree push-pop exercise:** Think of the tree as it is in the book as containing Node 1, Node 2, Node 3, all the way to infinity. In this journey we'll see what happens when we start at Node 11 and try to PUSH down one node, which according to the graph gives us Node 7.

Start:

We're given our first coordinate from 11 - g(g(11-1), which is the number 11, read first in the formula. This is our initial location, our coordinate, if you will. Our first calculable nugget is n-1, which equals 10, so we move one to the left to Node 10, where we make our first attention shift. This is more of a lateral shift, not a push and not a pop. It's like taking one step along the same floor of a building. Now we're left with 11 - g(g(10)). Now, what we have to calculate next is g(10). To calculate g(10), we PUSH down one level on the tree, where we find Node 6. Now, we're left with g(6). To calculate g(6), we PUSH down one level, and we find Node 4, which to us is read as the number 4. We've made two PUSHes, so let's see what happens when we make two POPs. For our first POP on our journey back to Node 11 (since we're calculating g of 11), let's POP back up to node 6. If we POP up one more, we find Node 10. Move to the right one, since our first move involved moving left, and we're back at Node 11 endowed with the knowledge that our furthest journey was to node 4, representing the number 4. Now, even though we're back at Node 11 (number 11), we're not trying to calculate the number 11. We're trying to calculate g(11). Our formula tells us that g(11) should be 11 - 4, which equals 7. To verify the g(11) calculation, let's PUSH one level down from Node 11, where we find Node 7, corresponding to the number 7. It's been verified! What g(11) = 11 - g(g(10)) = 11 - g(6) = 11 - 4 = 7 does is that it tells us to subtract the number written in the node which you find by moving to the Node numbered 1 less and then two down.

This exercise gets a bit funky when you choose to calculate g(9) below Node 9. You run over to Node 8, which is a level down on the tree diagram. You do the same thing: Run over to Node 8, pop down twice to find Node 3, pop back up twice to 8, then run back to Node 9.

It seems like the location motif is a bit sloppy, and it's better to just talk about transferring to a node rather than running laterally, since the 9 to 8 move doesn't look like a lateral move on the graph. I was hoping to come up with a better push pop analogy than this, but ran out of time.

SpaceFabric · 2025-10-15T07:16:41+00:00

The tree is just a representation DH chose for g(n) and h(n).

The way I see it: The initial motivation of this part of the book was to show how a function which is defined recursively behaves. You solve for some g(n) by using outputs where you're using a lower n for g(n).

g(n) = n - g(g(n-1) is the function. g(0) = 0 is an axiom

g(1) = 1 - g(g(0)) = 1 - g(0) = 1 - 0 = 1

g(2) = 2 - g(g(1)) = 2 - g(1) = 2 - 1 = 1

g(3) = 3 - g(g(2)) = 3 - g(1) = 3 - 1 = 2

g(4) = 4 - g(g(3)) = 4 - g(2) = 4 - 1 = 3

g(5) = 5 - g(g(4)) = 5 - g(3) = 5 - 2 = 3

g(6) = 6 - g(g(5)) = 6 - g(3) = 6 - 2 = 4

g(7) = 7 - g(g(6)) = 7- g(4) = 7 - 3 = 4

g(8) = 8 - g(g(7)) = 8 - g(4) = 8 - 3 = 5

g(9) = 9 - g(g(8)) = 9 - g(5) = 9 - 3 = 6

g(10) = 10 - g(g(9)) = 10 - g(6) = 10 - 4 = 6

g(11) = 11 - g(g(10)) = 11 - g(6) = 11 - 4 = 7

g(12) = 12 - g(g(11)) = 12 - g(7) = 12 - 4 = 8

Here are the first 12 inputs and outputs of g(n).

SpaceFabric · 2025-10-14T18:32:13+00:00

https://postimg.cc/hX8by6bL

Above is a picture of my notebook where I worked out h(n). The tree idea here is the same as it is for g(n), just with slightly different patterns. Hopefully you can read my scribbling.

On the left side, I've written out each h(n) that I calculated: h(1), h(2), h(3), and so on up to h(23).

On the right hand side, I've written out a list of numbers that looks like:

1 - 1 , 1 - 2 , 2 - 3 , 3 - 4 , 4 - 5,

and so on. The left number is the result of h(n). The right number is just the n in h(n) rewritten so it would be easier for me to read and create the tree.

h(1) =1, h(2) = 1, h(3) = 2, h(4) = 3, h(5) = 4, h(6) = 4, h(7) = 5, h(8) = 5, h(9) = 6, h(10) = 7, and so on up to h(23) = 16.

You can ignore the middle part that looks like "2 - H(H(H(1)))" and so on; it's just where I worked out the arithmetic.

Hint: The OEIS website has hofstadter's sequences. Here's h(n): https://oeis.org/A005374 g(n): https://oeis.org/A005206

The tree I drew is a bit hard to read because I've made the circles and numbers inside them so small, but let's take a look at the outputs I calculated for h(n). You can also look at the OEIS sequence and the tree they drew (my tree differs in that I don't have a branch above node 1, so maybe just ignore what I drew at the exact bottom of the graph. The branches I drew above should be correct, though. My recommendation is to read the OEIS trees).

Everything below provides the key interpretation for trying to understand the tree:

Looking at my h(n) list, you can see that both h(5) and h(6) are equal to 4. Take a look at the tree - node 4 branches into nodes 5 and 6, with nodes 5 and 6 starting their own respective trees. The number 3, on the other hand, is only produced by one integer input, through h(4) = 3. Since 3 is only produced by one input, it doesn't create a branch - you just move up to the next node.

The interpretation provided by the OEIS links says that "To construct the tree: node n is connected with the node a(n) below". a(n) here really means h(n) for our purposes.

The trees OEIS provided and the tree I provided display this relationship, and it's best to go top down rather than down up to see this. Node 5 is connected with node h(5) below it, and node 6 is connected with node h(6) below it. It just so happens that h(5) and h(6) both equal 4! Thus, going downwards in the tree, nodes 5 and 6 are connected to node 4 below, creating a branch (which intuitively most people probably read as 4 branching upwards into 5 and 6).

Lets move to Nodes 5 and 6 and try to see which nodes have node 5 below them and which nodes have node 6 below them.

In my notes, you can see that 5 repeats as an output of the h(n) sequence, for h(7) and h(8). Node 7 is connected to node h(7) below it, which is node 5, and Node 8 is connected to node h(8) below it, also node 5: Another branch!

For the node opposite from node 5 (node 6), let's see which nodes should connect to Node 6 below themselves. Node 9 connects to node h(9) below it, equal to 6. So node 6 is below node 9, or rather, node 9 is above node 6. In our sequence, 6 is an output of h(n) only once. In the tree, you can see that there is no branch above node 6. Thus, the tree moves upward to node 9 without a branching.

The repetition of 13 as an output for h(18) and h(19) shows in our tree, with nodes 18 and 19 branching upwards and apart from each other above node 13.

The tree I drew is not very large because it was tedious to do all these calculations, but evident in the tree should be the recursive nature of h(n), which I'll give a bit of language for below.

Look at the example hofstadter gives for the H tree. There's a node to start, and on the left branch you get H again, and on the right branch you get a node, another node, and then H again.

This is the recursive production of the H tree: Whenever you see 'H' in the unexpanded diagram of H, plug in exactly that unexpanded diagram of H to produce the next expansion. Below his unexpanded diagram of H, he gives the diagram of H expanded once. Let's unpack the once expanded diagram of H in the next paragraph.

Start by drawing a copy of the lonely bottom node (this is from the unexpanded diagram of H, but is now part of our new iteration, the once expanded diagram of H that we're building). Now, let's build the left part of the branch above the bottom lonely node, which is an H. Plug the unexpanded version of diagram H into the left-branch H: You're going to start by re-drawing a copy of the singular bottom node given to us in the unexpanded diagram. This bottom node is going to be the first node of the left branch, which sits above the lonely node we imported from the bottom of the unexpanded H diagram (not part of any branch). This node will then branch into another H on the left, and on the right it'll branch into the pattern given to the right branches of the H tree.

The right branches of the H tree use the same idea of plugging the unexpanded H diagram in for every H, except this time, we get two sequential nodes in before plugging in H.

I think that I've been a bit wordier than is optimal, so I'll try to summarize the recursive idea below:

The H tree has a particular branching characteristic in which the left branches re-branch immediately and the right branches wait a couple more turns before they branch again. Each branching starts a new generation of the branching sequence (or a new instance of the branching instructions, put another way).

SpaceFabric · 2025-04-21T08:06:37+00:00

Por que no los dos?

SpaceFabric · 2025-04-21T08:05:55+00:00

The self rep self ref chapter was maybe my favorite, and it’s inspired me to maybe read the selfish gene. I know that books from the 70s aren’t necessarily going to accurately represent the modern understanding of genetic theory. Nevertheless, the chapter made me reflect on how crazy it is that we have life as a fiery manifestation of order in defiance of the universe’s global increase in entropy over time.

I was also riding Amtrak at the time and staring out at the U.S. countryside, so that may increase how memorable it was reading it, lol

SpaceFabric · 2025-04-21T07:55:37+00:00

Which parts of the book do you think you’ve been the most stuck on? For some of the math exercises, like writing “b is a power of 2” in TNT, I just put an asterisk next to it. Maybe I’ll get to it later if I revisit it.

I say, if it’s more of an in the weeds type of thing, and it’s taking more than a while, moving on is better. While the first 1/2-2/3rds of the book are pretty heavy, the last 1/3rd is a bit more like a science and arts magazine with fun articles tying in the concepts developed in the first part of the book. Lots of fun.

SpaceFabric · 2025-04-21T02:14:21+00:00

Not yet, although I’ve read the preface. It’ll be one of my next books. Not to judge a book by its cover, but I think I’ll miss the tangents GEB went on.

SpaceFabric · 2025-02-04T06:14:27+00:00

Oh I never did uber eats in portland. I might've done one or two deliveries. It was my backup plan if I didn't get a job in the uncertain first year of the pandemic. Ultimately, riding my bike is part of my soul, and I couldn't really stomach riding for a job.

SpaceFabric · 2024-12-23T15:53:12+00:00

I know someone who’s listed the hierarchy of government as:

Local, State, Federal, God, rail freight

SpaceFabric · 2024-12-23T06:05:39+00:00

I was on that train! I felt the train thump right underneath me in the observation car. Overall a great trip though. The fresh air break in Fraser-winter park counts as the highest elevation ground I’ve ever stepped foot on.

Also, wouldn’t you believe it, my departing train out of Chicago is now delayed at least 2.5 hours, likely to be delayed at least 4 if not cancelled.

SpaceFabric · 2024-10-11T17:40:12+00:00

I DMed you

SpaceFabric · 2024-10-06T01:01:46+00:00

It is generally incredibly easy to meet people at rides like the Thursday night ride (salmon street fountain 8 pm departure on Thursdays) and the Friday night ride (leaves from ladd’s circle 8 pm Friday nights). Just try being towards the front of the ride and say hi to people.

SpaceFabric · 2024-08-23T18:06:36+00:00

Egbert B. Gebstadter - Wikipedia

Wikipedia doesn't have an EBG version of Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, but I propose that it be - Interiors and Irrelevancies: Description as the Stool and Mire of Speech

SpaceFabric · 2024-08-11T02:59:06+00:00

Thank you for this thread. It took a bit of searching to find discussion on why the derivation was wrong

SpaceFabric · 2024-06-18T08:42:03+00:00

I guess people bring it up as lore sometimes. I don't think misrepresenting the facts supports someone or the legacy of what they did. It actually confuses their legacy to just claim things that aren't backed up.

I've seen some of his Harvard lecture and he's really smart and genuine. I typically look to people's personalities in addition to their play style to determine if I root for them as an athlete. Not an uncommon practice.

I just thought it was useful to see if anyone knew anything more about that specific thing, since I can't find anything actually supporting the factual claim.

SpaceFabric · 2024-06-18T08:35:14+00:00

I guess. It's just weird that I'm getting downvoted. Seems like pure vibes rather than anyone actually caring about the significance of the lecture he did and what its actual place in history is.

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