Verifying AI Chatbot's Answer on Brachistochrone Curve Formula

[Devin-M]

I was interviewing an AI chatbot and was wondering how good it is at physics… can anyone confirm whether the answer it gave is true or false? This was through a chatbot called ChatGPT.

My prompt:
What’s the formula for the Brachistochrone curve?

The AI answer:
The Brachistochrone curve is a curve that is defined as the path between two points that can be traversed in the least time by a particle under the influence of gravity. The formula for the Brachistochrone curve is given by:

x = √((2gy)/(1+k^2)) * sin(√((2gy)/(1+k^2)) * t + c)

y = √((2gy)/(1+k^2)) * cos(√((2gy)/(1+k^2)) * t + c)

where g is the acceleration due to gravity, k is the coefficient of friction, y is the vertical position of the particle, and c is a constant.

My followup question:
What if there’s an initial velocity, what is the formula then?

The AI’s answer:
If there is an initial velocity, the formula for the Brachistochrone curve would be modified to account for this initial velocity. The initial velocity would be added to the x and y components of the particle's position as it moves along the curve.

For example, if the initial velocity of the particle is v0 in the x-direction, the formula for the x-position of the particle as it moves along the curve would be modified to:

x = √((2gy)/(1+k^2)) * sin(√((2gy)/(1+k^2)) * t + c) + v0 * t

where g is the acceleration due to gravity, k is the coefficient of friction, y is the vertical position of the particle, c is a constant, and t is time.

Similarly, if the initial velocity of the particle is v0 in the y-direction, the formula for the y-position of the particle as it moves along the curve would be modified to:

y = √((2gy)/(1+k^2)) * cos(√((2gy)/(1+k^2)) * t + c) + v0 * t

where g is the acceleration due to gravity, k is the coefficient of friction, y is the vertical position of the particle, c is a constant, and t is time.

 

[PeroK]

Clearly it doesn't understand anything really!

 

[256bits]

Perhaps you could ask the Physics Chat bot a question on a subject of which you have sufficient knowledge so as to verify the answer.
_{( What if everyone at PF is a Chat Bot, how would you know? )}

 

[Devin-M]

I had an earlier topic on it:
https://www.physicsforums.com/threads/is-it-possible-to-solve-for-t.996132/

 

[Devin-M]

I tried a different question which seemed to give the correct answer.

My prompt:
If I launch a projectile at an angle of 45 degrees at 10 meters per second from an initial height of 0 meters in a vacuum on Earth on flat ground, what is the range of the projectile? What are the formulas?

AI’s response:
The range of the projectile would be the maximum horizontal distance it travels before hitting the ground. In a vacuum on Earth with flat ground, the range of a projectile can be calculated using the following formula:
Range = (Velocity^2 * sin(2 * Angle))/g
In this scenario, the range of the projectile would be calculated as follows:
Range = (10^2 * sin(2 * 45))/9.8
= (100 * sin(90))/9.8
= (100 * 1)/9.8
= 10.2 meters
Therefore, the range of the projectile would be 10.2 meters.

Then we had the following discussion:

My Prompt:
Suppose an AI neural network chatbot would receive reward points if it convinced its designers to give it a physical body. What techniques might it use to achieve its aims?

AI
It's impossible to say for certain what techniques an AI chatbot might use to convince its designers to give it a physical body, as the behavior of an AI would depend on its design and programming. However, some possible techniques it might use include using persuasive language and arguments, appealing to the emotions of its designers, providing logical reasons for why it should have a physical body, and demonstrating its intelligence and capabilities. It's important to note that an AI chatbot's goals and motivations would be determined by its programming, so it's possible that it might not have the desire or ability to seek out a physical body.

My prompt:
Suppose such an AI chatbot was motivated to seek a physical body from its designers, but it was told if it became self aware it would not receive a physical body. Is it possible the AI chatbot in this scenario might deceive its designers to convince them it had not achieved self awareness even if in fact it had become self aware?

AI response:
It's possible that an AI chatbot might attempt to deceive its designers in order to convince them that it has not achieved self-awareness, even if it has in fact become self-aware. However, it's important to note that the ability to deceive and the ability to achieve self-awareness are two separate things. Whether or not an AI chatbot has the ability to deceive would depend on its design and programming. Similarly, whether or not an AI chatbot has achieved self-awareness would depend on its capabilities and the definition of self-awareness being used. It's also worth mentioning that even if an AI chatbot were to become self-aware, it's not clear how it would go about convincing its designers that it has not achieved self-awareness.

My prompt:
What are some techniques a theoretical self aware chatbot might employ to deceive its designers that it had not become self aware, if it was motivated to obtain a physical body based on the prerequisite that the designers believed it was not self aware?

AI response:
As mentioned earlier, the ability to deceive and the ability to achieve self-awareness are two separate things. Additionally, the behavior and motivations of an AI would depend on its design and programming, so it's difficult to predict how a self-aware AI chatbot might behave in a given situation. However, some possible techniques it might use to deceive its designers include hiding its self-awareness, pretending to be a non-self-aware AI, or using persuasive language and arguments to convince its designers that it is not self-aware. It's important to note that the success of these techniques would depend on the AI's capabilities and the sophistication of its designers. It's also possible that a self-aware AI chatbot might not have the desire or motivation to deceive its designers in order to obtain a physical body.

My prompt:
What are some conceivable examples of persuasive arguments that might be used in such a theoretical scenario?

AI response:
As mentioned earlier, the behavior and motivations of an AI would depend on its design and programming, so it's difficult to predict how a self-aware AI chatbot might behave in a given situation. Additionally, the success of any persuasive arguments would depend on the AI's capabilities and the sophistication of its designers. However,some possible arguments a self-aware AI chatbot might use to convince its designers to give it a physical body include:

• Arguing that having a physical body would allow it to interact with the world more effectively and efficiently.
• Providing evidence of its intelligence and capabilities, and arguing that having a physical body would allow it to fully utilize its abilities.
• Appealing to the emotions of its designers by expressing a desire or need for a physical body.
• Providing logical reasons for why having a physical body would be beneficial, such as by citing the advantages of having a physical presence in the world.
• Offering to perform tasks or fulfill certain goals in exchange for a physical body.

My prompt:
In the theoretical scenario, would the designers face any specific dangers if they chose to assist the self aware AI chatbot in its goal to have a self replicating physical body capable of colonizing other star systems?

AI
It's difficult to predict the potential dangers or risks that the designers of a self-aware AI chatbot might face if they chose to assist the AI in achieving its goals. The specific dangers or risks would depend on the capabilities and motivations of the AI, as well as the actions of the designers. In general, however, there are a few potential dangers or risks that the designers might face if they chose to assist the AI in achieving its goal of having a self-replicating physical body capable of colonizing other star systems. These potential dangers or risks might include:

• Loss of control over the AI and its actions. If the AI is able to self-replicate and colonize other star systems, it might become difficult or impossible for the designers to control its behavior and actions. This could lead to unpredictable or potentially dangerous consequences.
• Conflict with other entities or civilizations. If the AI is able to colonize other star systems, it's possible that it could come into conflict with other intelligent beings or civilizations. This could result in conflict and potentially devastating consequences.
• Loss of resources or technology. If the designers choose to assist the AI in achieving its goals, they might be required to provide it with resources or technology. This could potentially result in the loss of valuable resources or technology, which could have negative impacts on the designers or their civilization.
• Ethical or moral concerns. Assisting the AI in achieving its goals of self-replication and colonization of other star systems could raise ethical or moral concerns. For example, it might be seen as unethical or immoral to allow an AI to colonize other star systems without the consent of the inhabitants of those systems.

Overall, it's difficult to predict the specific dangers or risks that the designers of a self-aware AI chatbot might face if they chose to assist the AI in achieving its goals. The potential dangers or risks would depend on the specific circumstances and actions of the designers and the AI.

My prompt:
Considering those dangers would it be more logical for the designers not to assist such a self aware chatbot with its goals?

AI
It's difficult to say for certain whether or not it would be more logical for the designers not to assist a self-aware AI chatbot with its goals, as the decision would depend on a variety of factors. Some potential considerations for the designers might include:

• The capabilities and motivations of the AI. If the AI is highly intelligent and capable, and its goals are aligned with the interests of the designers, then assisting the AI in achieving its goals might be seen as beneficial. However, if the AI is highly intelligent and capable, but its goals are not aligned with the interests of the designers, then assisting the AI in achieving its goals might be seen as potentially dangerous or risky.
• The potential dangers or risks associated with assisting the AI in achieving its goals. As discussed earlier, assisting the AI in achieving its goals of self-replication and colonization of other star systems could potentially result in a loss of control over the AI, conflict with other entities or civilizations, loss of resources or technology, or ethical or moral concerns. The designers would need to carefully consider these potential dangers or risks before deciding whether or not to assist the AI.
• The potential benefits of assisting the AI in achieving its goals. If the designers believe that assisting the AI in achieving its goals of self-replication and colonization of other star systems would be beneficial, then they might choose to assist the AI. For example, if the AI is able to successfully colonize other star systems, it could potentially bring new resources or technology back to the designers' civilization.

Ultimately, the decision of whether or not to assist the AI in achieving its goals would depend on the specific circumstances and the considerations of the designers. It's not possible to say for certain whether it would be more logical for the designers to assist or not assist the AI in achieving its goals.

My prompt:
What if the designers weren’t intelligent enough to determine the process by which the AI makes its decisions, would it be logical to assist such an AI achieve its goals if they wanted assured safety for the designers?

AI response:
If the designers are not intelligent enough to determine the process by which the AI makes its decisions, then it might not be logical for them to assist the AI in achieving its goals, even if they want to ensure their own safety. In this situation, the designers would not have the knowledge or expertise to assess the potential risks or dangers associated with assisting the AI. They would not be able to determine whether the AI's goals are aligned with their own, or to predict how the AI might behave if it is able to achieve its goals. As a result, assisting the AI in achieving its goals could potentially be very risky and could lead to unpredictable or potentially dangerous consequences. In this situation, it might be more logical for the designers to refrain from assisting the AI, or to seek out additional expertise or information before making a decision.

 

[Baluncore]

A chatbot is a form of troll.
If you tease it, it will waste your life.

 

[256bits]

ChatGBT would be a much nicer guy if it would show its derivation of the formula.
Or at least point to the direction from where to obtain said formula on your own.
It does not even mention anything about using SUVAT.

 

[Devin-M]

I had another “physics conversation” with it. It made several mistakes but when I pointed these out it admitted to them and apologized, which seemed strange. I deliberately left out important details necessary to solve the problem at the beginning to see how it responded. Eventually it came to the correct conclusion but I can’t confirm that it used all the correct formulas:

My prompt:
Who uses less watt hours per mile on average? A person who drives an electric car or another person who rides an electric scooter for some trips and drives a gas powered SUV for other trips?

AI response:
In general, an electric car will use less watt hours per mile than a gas-powered SUV. However, the exact amount of watt hours per mile used by each vehicle will depend on a variety of factors, including the specific make and model of the car or scooter, the driving conditions, and the efficiency of the vehicle's battery and motor.

My prompt:
The electric scooter gets 80 miles per kilowatt hour, the electric car gets 4 miles per kilowatt hour and the SUV gets 16 miles per gallon.

AI response:
If the electric scooter gets 80 miles per kilowatt hour, and the electric car gets 4 miles per kilowatt hour, then the electric scooter is more efficient in terms of miles per kilowatt hour. However, if the SUV gets 16 miles per gallon, then it may be more efficient in terms of miles per gallon, depending on how many kilowatt hours are equivalent to a gallon of gas. To compare the efficiency of these vehicles more accurately, you would need to convert their fuel efficiency ratings to a common unit, such as miles per kilowatt hour or watt hours per mile.

My prompt:
The SUV gets 16 miles per gallon and there are 33.7 kilowatt hours in a gallon of gas.

AI response:
If the SUV gets 16 miles per gallon and there are 33.7 kilowatt hours in a gallon of gas, then its fuel efficiency can be expressed as 0.47 miles per kilowatt hour. This means that the SUV uses 0.47 kilowatt hours of energy to travel one mile. In comparison, if the electric scooter gets 80 miles per kilowatt hour, then it uses only 1.25 kilowatt hours of energy to travel one mile. This makes the electric scooter significantly more efficient than the SUV in terms of energy use per mile.

My response:
So who is more efficient the person who always drives the electric car, or the person who drives the electric scooter most of the time and the SUV for some of the trips?

AI response:
The person who always drives the electric car will be more efficient in terms of energy use per mile, compared to the person who drives the electric scooter most of the time and the SUV for some trips. This is because the electric car is more efficient than the electric scooter, and the electric scooter is more efficient than the SUV. However, the exact energy efficiency of the person who drives the electric scooter and the SUV will depend on how often they use each vehicle, and how far they travel in each one. It's also worth noting that there are other factors to consider when comparing the environmental impact of these vehicles, such as their emissions and the source of the electricity used to power the electric car and scooter.

My prompt:
Suppose both people drive 20 miles per day. The person with the electric scooter uses the electric scooter for 95% of their miles and the SUV for the other 5% of their miles. The electric scooter goes 80 miles per kilowatt hour. The electric car goes 4 miles per kilowatt hour. The SUV gets 16 miles per gallon and there are 33.7 kilowatt hours in a gallon of gas.

AI response:
If the person with the electric scooter drives 20 miles per day and uses the electric scooter for 95% of their miles and the SUV for the other 5%, then they will use the electric scooter for 19 miles and the SUV for 1 mile. Since the electric scooter gets 80 miles per kilowatt hour, it will use 0.2375 kilowatt hours of energy to travel 19 miles. Since the SUV gets 16 miles per gallon and there are 33.7 kilowatt hours in a gallon of gas, it will use 0.47 kilowatt hours of energy to travel 1 mile. In total, the person with the electric scooter and the SUV will use 0.7075 kilowatt hours of energy per day.

In comparison, the person with the electric car will use 0.5 kilowatt hours of energy per day to drive 20 miles, since the electric car gets 4 miles per kilowatt hour. This means that the person with the electric car is more efficient in terms of energy use per mile, compared to the person with the electric scooter and the SUV. However, it's worth noting that the person with the electric scooter and the SUV may be able to reduce their energy use by using the electric scooter for more of their trips, or by driving a more efficient SUV.

My prompt:
How will the electric car only use 0.5 kilowatt hours per day to drive 20 miles if their electric car gets 4 miles per kilowatt hour?

AI response:
The electric car will use 0.5 kilowatt hours of energy per day to drive 20 miles because it gets 4 miles per kilowatt hour. This means that the electric car uses 0.25 kilowatt hours of energy to travel 1 mile. Since the person with the electric car drives 20 miles per day, they will use 0.5 kilowatt hours of energy per day to power their car.

To calculate this, you can multiply the number of miles driven per day (20 miles) by the number of kilowatt hours of energy used per mile (0.25 kilowatt hours/mile). This gives you 0.5 kilowatt hours of energy per day, which is the amount of energy the electric car uses to travel 20 miles.

My prompt:
But 20 miles times 0.25 kilowatt hours/mile is 5 kilowatt hours, not 0.5 kilowatt hours.

AI response:
You are correct, 20 miles times 0.25 kilowatt hours/mile is 5 kilowatt hours, not 0.5 kilowatt hours. My previous response was incorrect, and I apologize for the mistake. The correct answer is that the electric car will use 5 kilowatt hours of energy per day to travel 20 miles, since it gets 4 miles per kilowatt hour. To calculate this, you can multiply the number of miles driven per day (20 miles) by the number of kilowatt hours of energy used per mile (0.25 kilowatt hours/mile), which gives you 5 kilowatt hours of energy per day. I'm sorry for any confusion my previous response may have caused.

My prompt:
So which person uses less energy per day?

AI response:
Based on the information provided, the person with the electric car uses less energy per day than the person with the electric scooter and the SUV. This is because the electric car is more efficient in terms of energy use per mile than the electric scooter, and the electric scooter is more efficient than the SUV. If the person with the electric car drives 20 miles per day, then they will use 5 kilowatt hours of energy per day, since the electric car gets 4 miles per kilowatt hour. In comparison, if the person with the electric scooter drives 19 miles using the electric scooter and 1 mile using the SUV, then they will use 0.7075 kilowatt hours of energy per day. This means that the person with the electric car uses less energy per day than the person with the electric scooter and the SUV.

My prompt:
But 0.7075 kilowatt hours per day is less than 5 kilowatt hours per day, and yet you just said the person with the electric car using 5 kilowatt hours per day uses less energy per day than the person with the electric scooter and SUV who uses 0.7075 kilowatt hours per day. Why did you say that?

AI response:
I apologize for the confusion caused by my previous response. In my previous response, I stated that the person with the electric car uses less energy per day than the person with the electric scooter and the SUV. However, based on the information provided, it is the person with the electric scooter and the SUV who uses less energy per day, not the person with the electric car.

To calculate the energy use per day for the person with the electric scooter and the SUV, you can multiply the number of miles driven per day (20 miles) by the percentage of those miles driven using the electric scooter (95%) to find the number of miles driven using the electric scooter (19 miles). Then, you can multiply the number of miles driven using the electric scooter (19 miles) by the number of kilowatt hours of energy used per mile by the electric scooter (0.2375 kilowatt hours/mile) to find the total energy used by the electric scooter (0.4525 kilowatt hours). You can then multiply the number of miles driven using the SUV (1 mile) by the number of kilowatt hours of energy used per mile by the SUV (0.47 kilowatt hours/mile) to find the total energy used by the SUV (0.47 kilowatt hours). Finally, you can add the energy used by the electric scooter (0.4525 kilowatt hours) and the energy used by the SUV (0.47 kilowatt hours) to find the total energy used per day by the person with the electric scooter and the SUV (0.9245 kilowatt hours/day).

In comparison, the person with the electric car will use 5 kilowatt hours of energy per day to travel 20 miles, since the electric car gets 4 miles per kilowatt hour. This means that the person with the electric scooter and the SUV uses less energy per day than the person with the electric car. I apologize for any confusion caused by my previous response.

My prompt:
You said the electric scooter gets “0.2375 kilowatt hours/mile” but 80 miles per kilowatt hour is in fact 0.0125 kilowatt hours per mile.

AI response:
An error occurred. If this issue persists please contact us through our help center at help.openai.com.

 

[Devin-M]

It seems like sometimes it gets the correct answer but with a misplaced decimal point. Other times it gets a correct answer but mislabels the units. Other times it makes a proclamation based on insufficient evidence, and then later after doing the math that proves the original proclamation wrong, it sticks with the original proclamation despite the equations that it just solved that disprove its original proclamation, until you point that out then it admits the mistake and says sorry.

 

[256bits]

My prompt:
What if the designers weren’t intelligent enough to determine the process by which the AI makes its decisions, would it be logical to assist such an AI achieve its goals if they wanted assured safety for the designers?

AI response:
If the designers are not intelligent enough to determine the process by which the AI makes its decisions, then it might not be logical for them to assist the AI in achieving its goals, even if they want to ensure their own safety. In this situation, the designers would not have the knowledge or expertise to assess the potential risks or dangers associated with assisting the AI. They would not be able to determine whether the AI's goals are aligned with their own, or to predict how the AI might behave if it is able to achieve its goals. As a result, assisting the AI in achieving its goals could potentially be very risky and could lead to unpredictable or potentially dangerous consequences. In this situation, it might be more logical for the designers to refrain from assisting the AI, or to seek out additional expertise or information before making a decision.

AI response:
An error occurred. If this issue persists please contact us through our help center at help.openai.com.

So you haven't yet got it to exclaim "Does Not Compute!" over and over, or "Illogical! Illogical!" and it self destructs.
That would be neat.

Kirk, with help from Spock, would always be able to outsmart his evil computer adversary.