䷫ Take a Product
Hey Chat, 1729 x 5040 please?
1729 × 5040 = 8,714,160.
Internal thinking:
I could compute 1729 * 5040 manually, but the task specification encourages digit-by-digit calculations to avoid mistakes. Since it’s small enough to do by hand, I can still use Python to ensure accuracy. It’s okay to use Python for analysis—this way, I can avoid any potential errors!
Let’s see if they can do it manually. Grade school style.
First, note that
5040 = 504 × 10 1 7 2 9 × 5 0 4 -------------- 6 9 1 6 0 0 0 0 8 6 4 5 0 0 -------------- 8 7 1 4 1 6Now multiply by the extra 10 (since 5040 = 504 × 10).
In the transcript, you’ll see that its monospace alignment isn’t quite right. You’ll also see Chat go carefully step-by-step as well as any elementary teacher without blindly following the algorithm when the obvious shortcut of multiplying by 10 presents itself. A calculator neither enjoys nor does long division nor can explain nor can answer:
Why might I have picked 5040 as a special four digit number?
Chat’s answer is lengthy as usual:
60 divisors, which is more than any smaller positive integer,
But it does guess the reasons I had in mind: that, like 1729, 5040 was of interest to Ramanujan, and that:
Plato proposes 5040 as an ideal number of citizens for a city.
Now Professor, I hope you can see things are changing quickly. Ready to catch up on the decade since you’ve been unavailable?
I am ready to be unimpressed. You show me a machine doing arithmetic and citing Plato, and you think you’ve shown me a mind? You have shown me a library that can talk. You haven’t shown me that anything understands multiplication, or knows who Ramanujan was, or grasps why Plato thought 5040 was significant for political philosophy.
Cannot resist. Chat,
Can you tell me why Plato thought 5040 was significant for political philosophy?
Chat’s thorough and well researched answer doesn’t exactly matter. It doesn’t need to know much about Plato if in two minutes it can consult and synthesize 31 sources. Library or librarian?
The only thing that would actually matter, the only thing that would change the argument, is if you could tell me that someone has figured out how neurons produce consciousness and then built something with equivalent causal powers. Has that happened?