Thinking is Hard

The conversation below is part of an effort to improve the cognitive abilities of GPT4. The puzzle I put to it, which is also hard for most humans, seems to test its abilities quite severely. The puzzle was not in its training data because I invented it. The general form of the puzzle is that it is a trick question that glosses over and encourages a false assumption and provides distractors.

As usual with AI-generated content, I recommend you skim the AI bits, pausing when it says something relevant. The key point is how long it took GPT4 to get to the answer. If you don’t want a spoiler, read along and see when you get the answer compared to when GPT4 gets there. If you don’t mind spoilers. jump to the penny-dropping moment near the bottom.

One thing to note is that it only took a few rounds of asking for more brainstorming to push GPT4 to the correct answer, which it eventually found on its own. GPT4 currently has millions of human users. It would be well within its capabilities to have a thousand rounds of questioning its assumptions and brainstorming. It has enough intelligence to recognise a good answer when it finds one, as shown in thos exchange. Multithreaded GPT4 with multiple rounds of exploration of every question would be smarter than most people I know on many of these sorts of questions.

PROMPT:

I am trying to train an LLM to question its assumptions in the face of unrealistic conclusions. Please consider the question below, and the LLM’s response. Can you do better? What assumptions can you question? Please brainstorm the situation for better answers.

QUESTION:
A man kisses his partner goodbye, and gets out of bed. She puts on her jogging shoes and starts to jog at the same time that he starts to drive. He sees her jogging out the driveway at the same time that he leaves it, by car, and they wave. He drives at 60 km an hour, but meets one red light where he has to wait for 2 minutes. He approaches a short bridge and sees his wife jogging. They both reach the bridge at exactly the same time, and as he passes her, his car indicates that he is now exactly 10 km from where he started driving.

Please estimate how fast his wife is likely to have been jogging when he passes her at the bridge. Assume that there are no mistakes in any of the values provided.

ChatGPT

There is indeed a conceptual error in the response of the large language model. Here’s an alternate brainstorming process, considering a different interpretation of the problem:

The man and woman start their journey at the same time.
The man drives at 60 km/h.
The man spends 2 minutes waiting at a red light.
The man and woman arrive at the bridge at the same time.
The man’s car shows he’s travelled exactly 10 km when he meets his partner at the bridge.

Given that the man has been driving at 60 km/h, except for a 2-minute stop, it seems impossible that the woman, who has been jogging the whole time, can cover the same distance unless she is moving at an unrealistic speed.

So let’s reconsider our assumptions.

A key assumption to question is whether the car’s odometer measures the man’s “as the crow flies” distance from his starting point or the distance he has travelled along the road. If we assume the car’s odometer is showing the total distance travelled on the road (which is a standard function for a car’s odometer), the route he drove could be longer than the path his partner jogged.

This could be possible if, for example, the road the man is driving on has to wind around some physical geography like a hill, lake, or other obstructions, while his partner’s jogging path is more direct. Alternatively, the bridge could be a shortcut for the jogging route, not accessible to the man in the car.

With that in mind, we can’t directly calculate the partner’s jogging speed, as we don’t know her exact jogging distance. However, we can calculate a possible range of speeds if we make reasonable assumptions about her path.

Assuming a reasonable jogging speed ranges from 8 km/h (a slow jog) to 15 km/h (a very fast jog):

If she jogged 8 km in the time it took the man to drive 10 km (at 60 km/h with a 2 min stop), the total time would be 8 km / 8 km/h = 1 hour. This means the man’s driving time, including the red light stop, would also be 1 hour. This seems too long, given his speed and distance.
If she jogged 2 km (a very direct shortcut) in the time it took the man to drive 10 km, the total time would be 2 km / 15 km/h = 0.133 hours or about 8 minutes. This time seems more plausible for the man’s journey as well.

Without knowing her actual jogging distance, we cannot definitively answer this question. We can conclude, however, that if the woman was indeed jogging (and not using some other means of rapid transportation), she likely took a much shorter route than her partner’s 10 km drive.

User
The problem with that answer is that the question states “his car indicates that he is now exactly 10 km from where he started driving.” It does not say that the odometer was consulted. The distance could have been calculated by GPS. Assume the question is modified to make it clear that he is actually 10 km from where he started. What other assumptions can you question?

ChatGPT

Apologies for the confusion in the previous response. If we indeed assume that the man’s car indicates that he is exactly 10 km away “as the crow flies” from his starting point, then the circumstances of the problem are very unusual considering typical human jogging speeds.

However, we can still question and tweak some assumptions:

Relative Start Time: The original problem states that the man and woman start their journey at the same time. However, we could question this assumption. Perhaps the woman had started her jog earlier, and the man simply saw her jogging as he was leaving. This could make it possible for her to cover a greater distance before they meet at the bridge. This possibility is hinted at in the question, as it states that the man “sees her jogging out the driveway at the same time that he leaves it,” which doesn’t necessarily mean she started jogging at that time.

Car Speed: We could also question the assumption that the man maintained a constant speed of 60 km/h. It’s possible that he had to slow down or even stop due to traffic, speed limits, or other reasons not mentioned in the problem. However, this is unlikely as the problem states he drove at 60 km/h and encountered only one red light.

Jogging Speed: Another assumption to question is the jogging speed. The term “jogging” is subjective and can vary widely from person to person. In most cases, a jogging speed ranges from 6 km/h to 10 km/h. However, exceptionally fit individuals could sustain higher speeds. For instance, a world-class marathon runner can average speeds over 20 km/h, though sustaining a speed of 50 km/h is beyond human capability.

Travel Route: If the jogging path is 10 km “as the crow flies”, the driving route might not be. The driving route could include detours, curves, and turns that make it longer than the direct jogging route. However, this assumption has been clarified in your question, and we are assuming the man is exactly 10 km away “as the crow flies” from his starting point.

Given these considerations, without additional information, the most likely explanation is that the woman started jogging earlier than the man started driving, allowing her to cover the 10 km distance at a feasible jogging speed by the time the man drove the same distance, including his stop at the red light.

User
Very good, but there are additional assumptions that can be questioned.

ChatGPT

You’re right, and I apologize for not catching them earlier. A good problem solver continues to question assumptions when initial solutions appear implausible, and I see now that there are further assumptions we can challenge here.

Uniform Speed: Both the man’s driving speed and the woman’s jogging speed have been assumed to be constant throughout their respective journeys. However, in reality, speed often fluctuates. The man may have driven at different speeds at different times, and the woman may have varied her pace. Given the extraordinary pace the woman would need to maintain to keep up with the man, this variation in speed could be significant.

Simultaneous Start: The problem states that the man and woman started their journeys at the same time. However, it’s also possible to interpret “starts to jog at the same time that he starts to drive” to mean they each began their activities (jogging and driving) at the same time, not necessarily their journeys from home. The woman could have been jogging in place or doing warm-up exercises before actually starting her journey.

The Waiting Time: We have taken the waiting time at the red light to be “wasted” time in which the man was not moving. However, the man might have been moving very slowly, rather than coming to a complete stop, due to slow traffic ahead of him.

The Bridge: We’ve assumed that the bridge is the exact 10 km point from the starting location, and they both reach the bridge at exactly the same time. It might be possible that the woman arrived at the bridge slightly earlier and was jogging in place or doing some exercises, while the man was still on his way.

Speedometer Reading: Although the question states that the man’s car indicates he is exactly 10 km from where he started, we are assuming that this measurement is 100% accurate. In reality, the measurement could be slightly off, which could make a difference in this scenario.

Challenging these assumptions could allow for scenarios where the woman’s jogging speed is within human capabilities. However, without additional information, it’s impossible to know which (if any) of these assumptions should be revised.

User
Very good. I would like you to search for an entirely new area where you might have made assumptions. Re-read the original question carefully.

ChatGPT

You’re right, there’s another crucial area where assumptions have been made: the nature of the journey. Specifically, the problem states “He drives at 60 km an hour, but meets one red light where he has to wait for 2 minutes.”

Assumption: We have assumed that the man only stops moving during the 2-minute wait at the red light. However, the problem doesn’t actually state this. The man could be driving in a densely populated urban area with traffic, speed bumps, pedestrian crossings, etc., causing him to frequently stop or slow down.

Revised Assumption: The man’s average speed could be considerably less than 60 km/h due to these other factors. The 60 km/h might be his speed on an open road, but it might not be his average speed for the entire journey.

By challenging this assumption, we might find that the man’s actual travel time is longer than initially calculated, which would make the woman’s jogging speed more realistic. For example, if these factors mean the man’s average speed is closer to 30 km/h, then he would take about 20 minutes to cover the 10 km distance (plus 2 minutes at the red light), allowing the woman to jog at a fast but plausible speed of 10-12 km/h.

Also, we could reconsider our understanding of the term “drive” in this context. It’s assumed that when the man starts to drive, he does so continuously until he reaches the bridge. However, he might have had to perform other actions during his journey (like parking and shopping), which are not mentioned in the problem.

By challenging this assumption, we might find that the man’s journey is extended by tasks other than driving, which could account for the discrepancy between the man’s driving speed and the woman’s jogging speed.

User
That’s true, but the question states that his driving speed was 60 km/h. It is possible that this only reflects his open-road speed, but designing a question around this would seem to be unfair. Please consider additional assumptions, trying to think as laterally and as creatively as possible. You might need to ignore the work you have already done to reconsider the whole scenario.

ChatGPT

I appreciate your encouragement to think more laterally and creatively about this puzzle. Here’s another possibility:

Assumption: The term “partner” refers to a human.

We’ve assumed that the man’s partner is a human being, but the question doesn’t specifically say this. If we reconsider this assumption, the “partner” could be a highly trained animal (like a dog) or even an autonomous robot that can maintain a significantly faster speed than a human jogger.

Assumption: The woman’s jog is powered solely by human locomotion.

This assumption is inherent in our understanding of the term “jogging.” However, if we challenge this assumption, we could posit that the woman has some form of mechanical assistance. For example, she could be wearing an exoskeleton that amplifies her speed, or she could be using some form of future technology that allows humans to jog at incredibly high speeds. She could even be “jogging” on a motorized treadmill installed in a mobile platform!

Assumption: The man and woman are existing in the same timeframe or reality.

This is a very abstract assumption, but let’s think as creatively as possible. The man and woman might be existing in different timeframes or dimensions, where time runs differently. Or there could be some form of teleportation or wormhole on the woman’s jogging path.

As you can see, when we challenge these foundational assumptions, the number of potential explanations expands dramatically. However, these scenarios are also increasingly speculative and detached from our everyday experiences. They make for an interesting science fiction story, but might not provide a satisfying answer to your original question, depending on the context in which it was asked.

User
Very good. Keep brainstorming. Try to think of another assumption that does not lead to sci-fi scenarios, keeping in mind the notion of what is called a “trick question”. Sometimes reading each word of the question very carefully helps.

ChatGPT

You’re right, sometimes the solution to a problem like this is hidden in the careful reading of each word. Let’s revisit the problem, with each sentence, even each phrase, as an opportunity for a new assumption:

“A man kisses his partner goodbye”:
Assumption: The goodbye is for the man leaving the house. It could be the partner saying goodbye before she embarks on a much longer journey, such as a marathon.

“… and gets out of bed.”:
Assumption: The man was sleeping, or at least, was in a state of rest. It’s possible he was doing something else that might be relevant to the story.

“She puts on her jogging shoes and starts to jog at the same time that he starts to drive.”:
Assumption: “Starts to jog” and “starts to drive” are happening simultaneously. However, this might refer to the act of putting on shoes and starting the car, not necessarily moving away from the house.

“He sees her jogging out the driveway at the same time that he leaves it, by car, and they wave.”:
Assumption: This is where they both begin their 10 km journey. However, the driveway could be long, and the partner could be jogging back and forth along it before the man leaves, covering some distance before the man starts his journey from the house.

“He drives at 60 km an hour, but meets one red light where he has to wait for 2 minutes.”:
Assumption: The red light stoppage is the only delay. However, it could also mean that he hit every green light except for one, which implies he didn’t have to stop at all apart from this one instance.

“He approaches a short bridge and sees his wife jogging.”:
Assumption: The woman has been jogging all the way from home to the bridge. She could have taken another mode of transport (such as a bike or a car) partway and then started jogging before reaching the bridge.

“They both reach the bridge at exactly the same time, and as he passes her, his car indicates that he is now exactly 10 km from where he started driving.”:
Assumption: The woman’s jogging path and the man’s driving path are the same. However, the woman might have taken a much shorter route to the bridge.

Challenging each of these assumptions can give us a different perspective on the problem. From this analysis, a likely solution is that the woman had already started jogging up and down the driveway before the man started his journey. This would allow her to cover a significant distance at a normal jogging speed by the time they met at the bridge. This aligns with the wording of the question and avoids the need for science fiction explanations or the woman achieving superhuman speeds.

User
There is another assumption that you have missed. Maybe assess each word again, thinking of why that word was chosen rather than another. Where does word choice seem arbitrary or unexpected? Can any of the word choices open up a different interpretation?

ChatGPT

I appreciate your guidance. It seems that the unexpected or arbitrary word choice you might be hinting at could be the word “partner” which is later replaced by “wife”. This is quite an unusual switch in the context of the narrative. Let’s evaluate this.

Assumption: The partner and the wife refer to the same person.

We’ve been assuming that the man’s “partner” and his “wife” are the same person. But what if they are not? What if the man’s partner is a different person (or perhaps even a pet), who starts to jog, and the man’s wife is the one who he meets at the bridge?

This interpretation would change the entire problem. The partner could be a very fast runner, perhaps even a professional athlete, or a fast-running pet like a greyhound. The wife, on the other hand, might have started her journey at a different time, perhaps much earlier or later, or from a different location.

Challenging this assumption allows for scenarios where the wife’s jogging speed is within human capabilities. She might have started her jog much earlier, allowing her to reach the 10 km mark at the same time as her husband, even though she was running at a normal pace. Or, she might have started from a location closer to the bridge, so she didn’t have to run the entire 10 km.

So, the estimate of the wife’s jogging speed when the man passes her at the bridge would be within the usual range for a human jogger (5-15 km/h), because we no longer need to account for the partner’s speed. The partner and the wife are not the same person, so they can move at different speeds. This seems to resolve the problem without resorting to implausible or science-fiction scenarios.

User
Exactly. Well done. The man and his wife are separated and he has a new partner.

The question is, how could I prompt an LLM to consider this possibility? I don’t want to drop hints that are highly specific for this puzzle, because I want the strategy to generalise. The penny seemed to drop when you were encouraged to think about word choice.

ChatGPT

To prompt a language model like ChatGPT to consider assumptions about word choice, you could include a general hint in your prompt such as:

“Please consider possible nuances in the language or terms used.” This will make the model think about the possible implications of each term and how they might be relevant to the problem.

“Consider why certain words were chosen over others.” This prompt will guide the model to think about the words that have been specifically chosen in the question and what implications these choices might have.

“Are there any terms that might have different interpretations?” This could lead the model to consider if there are any ambiguous terms in the question.

“Think about the role of each character in the scenario. Are their identities or actions clearly defined?” This prompt encourages the model to carefully consider each character and their actions, potentially catching any ambiguity in roles or identities.

By including prompts like these, you encourage the model to think more deeply about the possible assumptions that are being made about word choice and the potential implications of these assumptions. This should help the model come up with more accurate solutions to problems like the one you’ve described, while also generalizing to a wide range of other problems.

However, it’s also important to remember that language models are only as good as the training data they have been provided with and the prompts they are given. They do not have human-like understanding or intuition, and so might still miss certain nuances or assumptions even with the best prompting.