There are now two alleged instances of full chains of thought leaking (use an appropriate amount of spepticism), both of which seem coherent enough.

I think it's more likely that this is just a (non-model) bug in ChatGPT. In the examples you gave, it looks like there's always one step that comes completely out of nowhere and the rest of the chain of though would make sense without it. This reminds me of the bug where ChatGPT would show other users' conversations.

I hesitate to draw any conclusions from the o1 CoT summary since it's passed through a summarizing model.

after weighing multiple factors including user experience, competitive advantage, and the option to pursue the chain of thought monitoring, we have decided not to show the raw chains of thought to users. We acknowledge this decision has disadvantages. We strive to partially make up for it by teaching the model to reproduce any useful ideas from the chain of thought in the answer. For the o1 model series we show a model-generated summary of the chain of thought.

o1-preview and o1-mini are available today (ramping over some number of hours) in ChatGPT for plus and team users and our API for tier 5 users.

https://x.com/sama/status/1834283103038439566

Construction Physics has a very different take on the economics of the Giga-press.

Tesla was the first car manufacturer to adopt large castings, but the savings were so significant — an estimated 20 to 40% reduction in the cost of a car body — that they’re being adopted by many other car manufacturers, particularly Chinese ones. Large, complex castings have been described as a key tool for not only reducing cost but also good EV charging performance.

I think Construction Physics is usually pretty good. In this case my guess is that @bhauth has looked into this more deeply so I trust this post a bit more.

I wonder how much my reply to Adam Shai addresses your concerns?

Very helpful, thank you.

In physics, the objects of study are mass, velocity, energy, etc. It’s natural to quantify them, and as soon as you’ve done that you’ve taken the first step in applying math to physics. There are a couple reasons that this is a productive thing to do:

1. You already derive benefit from a very simple starting point.
2. There are strong feedback loops. You can make experimental predictions, test them, and refine your theories.

Together this means that you benefit from even very simple math and can scale up smoothly to more sophisticated. From simply adding masses to F=ma to Lagrangian mechanics and beyond.

It’s not clear to me that those virtues apply here:

• I don’t see the easy starting point, the equivalent of adding two masses.
  • It’s not obvious that the objects of study are quantifiable. It’s not even clear what the objects of study are.
  • Formal statements about religion must be unfathomably complex?
• I don’t see feedback loops. It must be hard to run experiments, make predictions, etc.

Perhaps these concerns would be addressed by examples of the kind of statement you have in mind.

Re the choice of kernel, my intuition would have been that something smoother (e.g. approximating a Gaussian, or perhaps Epanechnikov) would have given the best results. Did you use rect just because it's very cheap or was there a theoretical reason?

Thanks for this! I ended up reading The Quincunx based on this review and really enjoyed it.

As an aside, I want to recommend a physical book instead of the Kindle version, for a couple reasons:

1. There are maps and genealogy diagrams interspersed between chapters, but they were difficult to impossible to read on the Kindle.
2. I discovered, only after finishing the book, that there's a list of characters at the back of the book. This would have been extremely helpful to refer to as I was reading. There are a lot of characters and I can't tell you how many times I tried highlighting someone's name, hoping that Kindle's X-Ray feature would work, and remind me who they were (since they may have only appeared hundreds of pages before). But it doesn't seem to be enabled for this book.

(Also, without the physical book, I didn't realize how long The Quincunx is.)

Even with those difficulties, a great read.

If, for instance, one minimum’s attractor basin has a radius that is just 0.00000001% larger than that of the other minimum, then its volume will be roughly 40 million times larger (if my Javascript code to calculate this is accurate enough, that is).

Could you share this code? I'd like to take a look.