https://news.ycombinator.com/item?id=31973232

https://github.com/openai/codex/issues/215

https://youtu.be/kBX5WH9b4M4

Then you’ll get several paths of action.

Chose one and tell the model to write into a file you’ll keep around while the implantation is on going so you won’t pollute the context and can start over each chunk of work in a clean prompt. Name the file refactor--plan.md tell it to write the plan step by step and dump a todo list having into account dependencies for tracking progress.

Review the plans, make fixes if needed. You need to have some sort of table reassembling a todo so it can track and make progress along.

Open a new prompt tell it analyze the plan file, to go to the todo list section and proceed with the next task. Verify it done, and update the plan.

Repeat until done.

> it can use code-centred tools like find_symbol, find_referencing_symbols and insert_after_symbol.

https://oraios.github.io/serena/01-about/000_intro.html

https://gemini.google.com/share/1e59f734b43c

This is a fantastic observation, and yes, this pattern not only continues for larger bases, but the approximation to an integer becomes dramatically better.

The general pattern you've found is that for a number base $b$, the ratio of the number formed by digits $(b-1)...321$ to the number formed by digits $123...(b-1)$ is extremely close to $b-2$.

### The General Formula

Let's call your ascending number $N_{asc}(b)$ and your descending number $N_{desc}(b)$.

The exact ratio $R(b) = N_{desc}(b) / N_{asc}(b)$ can be shown to be:

$$R(b) = (b-2) + \frac{(b-1)^3}{b^b - b^2 + b - 1}$$

The "error" or the fractional part is that second term. As you can see, the numerator $(b-1)^3$ is roughly $b^3$, while the denominator $b^b$ grows much faster.

### Testing Your Examples

Let's check your two examples with this formula:

* *Base 10 (b=10):* * $R(10) = (10-2) + \frac{(10-1)^3}{10^{10} - 10^2 + 10 - 1}$ * $R(10) = 8 + \frac{9^3}{10,000,000,000 - 91}$ * $R(10) = 8 + \frac{729}{9,999,999,909} \approx 8 + 0.0000000729...$ * This matches your $8.0000000729$ perfectly.

* *Base 6 (b=6):* * $R(6) = (6-2) + \frac{(6-1)^3}{6^6 - 6^2 + 6 - 1}$ * $R(6) = 4 + \frac{5^3}{46,656 - 31}$ * $R(6) = 4 + \frac{125}{46,625} \approx 4 + 0.00268...$ * This also matches your $4.00268$.

### Answering Your Question: A Larger Base

So, what about a larger base? Let's use *Base 16* (hexadecimal), which uses digits $1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F$. Here, $b=16$.

* $N_{asc} = 123456789ABCDEF_{16}$ * $N_{desc} = FEDCBA987654321_{16}$

According to the pattern, the ratio should be extremely close to $b-2 = 16-2 = 14$.

Let's use the formula to see how close:

* $R(16) = (16-2) + \frac{(16-1)^3}{16^{16} - 16^2 + 16 - 1}$ * $R(16) = 14 + \frac{15^3}{16^{16} - 241}$ * $R(16) = 14 + \frac{3,375}{1.844... \times 10^{19} - 241}$ * $R(16) \approx 14 + (1.829... \times 10^{-16})$

So, the ratio in base 16 is approximately: *$14.0000000000000001829...$*

As you predicted, the "error" for a larger base is astronomically smaller than it was for base 10.

It’s called git!

https://ayudaefectiva.org/simula

Or with 10k daily, 310k monthly, adjusted by historical inflation it’s 100 million during 20 years.

That’s 3 million people helped.

Should have paid the extra €€ to put the solar panels in backup mode…

Invest some (eg. 10-20 million) and use that as a giving fund, giving 1 million per year you could free several thousand of people each year.

I did and presented something on these lines 11 years ago! When multiple ruby runtimes were a thing.

https://speakerdeck.com/brutuscat/jruby-experiences

And the links come.

https://github.com/apache/carbondata

Other than that it felt like magic, like that Google demo of the phone doing some task like setting up an appointment over phone talking to a real person.

https://youtu.be/XVcKLetqf3U

The Intel® Data Center GPU Max Series outperforms Nvidia H100 PCIe card by an average of 30% on diverse workloads1, while independent software vendor Ansys shows a 50% speedup for the Max Series GPU over H100 on AI-accelerated HPC applications.2 The Xeon Max Series CPU, the only x86 processor with high bandwidth memory, exhibits a 65% improvement over AMD’s Genoa processor on the High Performance Conjugate Gradients (HPCG) benchmark1, using less power. High memory bandwidth has been noted as among the most desired features for HPC customers.3 4th Gen Intel Xeon Scalable processors – the most widely used in HPC – deliver a 50% average speedup over AMD’s Milan4, and energy company BP’s newest 4th Gen Xeon HPC cluster provides an 8x increase in performance over its previous-generation processors with improved energy efficiency.2 The Gaudi2 deep learning accelerator performs competitively on deep learning training and inference, with up to 2.4x faster performance than Nvidia A100.

https://www.intel.com/content/www/us/en/newsroom/news/intel-...

https://archive.is/nU8j2

See https://webrecorder.net

Example https://replayweb.page/?source=https%3A%2F%2Freplayweb.page%...

> UPDATE: Jon (I won’t give you his last name) sent me an email after visiting my post. In it he sent me a link to an October 1983 special edition issue of Joystik Magazine that covers winning strategies for common arcade games of the time. In the TRICKS OF THE TRADE section near the end of the magazine, they cover the Galaga No Fire Cheat beautifully!

Page 61, Disarm The Bugs.