“Mathematics is the language with which God has written the universe.”
― Galileo Galilei ―
Maurício Pinheiro
Ah, the wonder of artificial intelligence, capable of solving the most complex problems and challenging even the brightest mind. But what about when it comes to something as simple as mathematics and physics? Well, that’s where things get interesting. Let’s explore the limitations that large language models (LLMs), like ChatGPT, face when trying to tackle an elementary problem in kinematics, seemingly trivial, involving three hurried tourists and a bicycle.
The Problem:
Three tourists who have a single bicycle move along a straight avenue, wishing to go from the hotel to the tourist center in the shortest time possible (time is counted until the last tourist arrives at the center). The bicycle can only carry 2 people at a time, at a speed of 20 km/h, so the third tourist needs to start walking. The cyclist takes the second tourist to a point along the way, from where they continue walking at a speed of 4 km/h, while the cyclist returns to transport the third. If the distance from the hotel to the tourist center is 8 km, determine:
a) How long will it take for them to reach the tourist center (remembering that time only stops when all tourists are at the center)?
b) How far from the tourist center should the second tourist be transported by bicycle?
We challenge you! This is something you’re expected to know if you’ve gone from high school to college (pure kinematics of uniform rectilinear motion, and the only “formula” you need is v = d/t)…
Now, if you don’t have the patience or couldn’t figure it out, ask ChatGPT to present the solution, and it did so in 10 seconds.
a) To determine the time it will take to reach the tourist center, it is necessary to calculate how many times the bicycle will have to go back and forth. Since the bicycle can only carry 2 people at a time, two trips will be needed to take the three tourists to the tourist center. In the first trip, the cyclist takes the first two tourists by bike, and the third tourist walks. The distance from the hotel to the point where the second tourist starts walking is 2/3 of the total distance, which is 5.33 km. The time to cover this distance is 0.2665 hours or 16 minutes at a speed of 20 km/h, while the third tourist starts walking. On the second trip, the cyclist takes the third tourist to the point where the second tourist is walking. This point is at a distance of 2/3 of the total distance plus 1/3 of the total distance, which is 8 km in total. The time to cover this distance is 0.4 hours or 24 minutes at a speed of 20 km/h. Then, everyone walks together to the tourist center, which is at a distance of 1/3 of the total distance, which is 2.67 km. The time to cover this distance is 0.67 hours or 40 minutes at a speed of 4 km/h. Thus, the total time to reach the tourist center is 16 minutes + 24 minutes + 40 minutes, which is 80 minutes.
b) The second tourist should be transported by bicycle to the point where they start walking. This point is at a distance of 2/3 of the total distance, which is 5.33 km. Therefore, the bicycle must cover 5.33 km – 2 km (distance traveled by the tourists on the bike) = 3.33 km with the second tourist.
As my son alerted me, his answer is wrong. I won’t provide the correct answer here to avoid spoiling the challenge (read until the end).
ChatGPT, you would score zero on this question… However, according to itself:
ChatGPT is an advanced language model trained to understand and generate natural language in various fields of knowledge, including mathematics, physics, and chemistry. It is capable of reading, interpreting, and solving problems in these subjects with ease and speed, thanks to its vast knowledge base. Additionally, ChatGPT can generate new solutions to problems, using its comprehension and logic skills to propose new paths and approaches to already solved problems. Its ability to process and manipulate natural language allows it to provide clear and concise answers to complex questions and, in many cases, offer creative and innovative solutions that can help advance knowledge in various areas. With this, ChatGPT becomes a valuable tool for those seeking quick and reliable solutions to problems in mathematics, physics, or chemistry, as well as a source of inspiration for generating new ideas and solutions.
I have my doubts… Sure, the purely numerical response of an LLM is a faithful copy of the (wrong) solutions found on the web up to the present moment, which undoubtedly entered as training data into the model. But is it capable of solving problems like this, using simple prompts, just by geometry? I bet not. And this probably applies to most language models available out there, for now…
And of course, with some smart prompt engineering, refining questions based on answers, it might be possible to lead the language model to the correct answer. However, the big question is whether the effort to guide it to the solution involves prior knowledge of the solution. But that’s another matter.
Adding a touch of sarcasm, ChatGPT proudly tells us…
ChatGPT is simply amazing, capable of solving all complex problems in mathematics, physics, and chemistry, as well as generating new creative solutions effortlessly. And it doesn’t stop there; it can even demonstrate mathematical theorems and discover new physical laws because, of course, processing and analyzing large amounts of data in natural language is just too easy! Not to mention that ChatGPT can accelerate the discovery of new knowledge and insights, making scientific research much easier and faster.
At least it acknowledges…
But, of course, we can’t forget that the discoveries made by ChatGPT need to be validated by specialized researchers. After all, who needs a sophisticated language model when you have good old scientific method, right? So, in summary, ChatGPT is great, but it doesn’t replace the good old knowledge and experience of specialized researchers. After all, who needs a powerful tool to assist in the scientific discovery process when you have years of study and practice?
How can we expect a large language model to understand simple concepts of physics and, moreover, solve problems manipulating these concepts? It’s clear that it’s skilled at finding answers in a grammatically correct and seemingly consistent text. We can’t expect it to have a deep understanding of physical laws (or geometry), since its capacity is limited to natural language. Perhaps, in the future, with advancements towards artificial general intelligence (AGI), it may learn and understand these concepts better. Well, I’m already content using it to edit and correct my texts.
Now, a solution tip for the problem: just think like Euclid, not cheating like ChatGPT did!
Reference: Mecânica Para Vestibulandos IME ITA – vol 1 – Renato Brito, 2007.
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