That’s an interesting question. Proxima Centauri b is a planet that orbits Proxima Centauri, the closest star to Earth. The planet orbits its parent star at a distance of roughly 4.6 million miles (7.5 million km) with an orbital period of approximately 11.2 Earth days. Proxima Centauri b is only four light years away from Earth.
A solar sail is a spacecraft that uses the pressure of photons from the sun or other light sources to propel itself. The maximum theoretical speed a solar sail could reach is around 420 kilometers per second, or about 1/4 of the speed of light. However, this would require a very large and thin sail, and a close approach to the sun. A more realistic speed for solar sails is 10% of the speed of light, or 67,100,000 mph.
Assuming a solar sail could reach 10% of the speed of light, it would take about 40 years to travel to Proxima Centauri b. However, this does not account for the time it would take to accelerate and decelerate the spacecraft, or the effects of gravity from other bodies in the solar system. A more accurate estimate would require a detailed trajectory analysis and simulation.
I even asked Bing to calculate the time dilation for the person on earth. It answered correctly with the formula and steps shown clearly.
Then it was pulling its calculations directly from a web source, not using generative large language models. I’m not saying a chatbot can’t do this, I’m saying language models can’t do this.
Apparently Bing Chat is able to do some maths. I asked Bing multiple variations of this question based on different speeds of the solar sail (e.g. what if it travels at 50% the speed of light). It was able to calculate both the travel time and the time dilation.
If it is only pulling the answer from web sources, how did it handle the variable speeds?
Your failure in reasoning here is assuming that all of them are purely and only language models. That they receive no other source of learning other than language models – for example, they aren’t fed any kind of pop science math.
It’s clear that this is true of models like ChatGPT, but isn’t the Bing thing powered by GPT4 with a number of other enhancements? Fixing this “can’t do math” thing is a low-hanging fruit for development improvements.
Bing Chat is doing quite well:
I even asked Bing to calculate the time dilation for the person on earth. It answered correctly with the formula and steps shown clearly.
Then it was pulling its calculations directly from a web source, not using generative large language models. I’m not saying a chatbot can’t do this, I’m saying language models can’t do this.
Apparently Bing Chat is able to do some maths. I asked Bing multiple variations of this question based on different speeds of the solar sail (e.g. what if it travels at 50% the speed of light). It was able to calculate both the travel time and the time dilation.
If it is only pulling the answer from web sources, how did it handle the variable speeds?
It’s also possible that Bing’s chatbot is using a math-specific plugin in addition to its websearching plugin.
Your failure in reasoning here is assuming that all of them are purely and only language models. That they receive no other source of learning other than language models – for example, they aren’t fed any kind of pop science math.
It’s clear that this is true of models like ChatGPT, but isn’t the Bing thing powered by GPT4 with a number of other enhancements? Fixing this “can’t do math” thing is a low-hanging fruit for development improvements.
They announced to build in plug ins like for WolframAlpha, so maybe that is where it is pulling this data from.