During graduate school, not only did I finished my doctoral thesis in molecular biology, but I also somehow wrote a fun manuscript where I allowed myself to freely pour my philosophical—not very scientific!—thoughts on intelligence and on the interpretation of an “intelligence equation” I had come up with many years before. 

Essentially, I had discovered a curious relationship between intelligence, effort and results. This relation I expressed in the following mathematical equation: E x I = R, where E=effort, I=intelligence and R=results. If you solve this equation for the variable I, you get that I=R/E. Thus, this equation states that intelligence is highest when results are obtained with the least effort. Furthermore, I thought that since division by zero is not possible or undefined, this equation also revealed that in an universe where intelligence is present, effort could not be zero or non-existent, suggesting that wherever there is effort, there would be intelligence. If we understand that any effort is in essence a force, then the presence of forces in the universe implies the presence of intelligence. 

But, was I right? Did my intelligence equation make any sense at all or would it have any potential uses in the real world other than in my own head. I engaged ChatGPT’s wonderful artificial intelligence and not only did it stop me on my tracks on some of my arguments (with good reasoning!), it also suggested this equation may be useful in multiple fields. 

So what did ChatGPT say? Below our conversation…

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ChatGPT: The equation you’ve presented, E x I = R, is a mathematical representation of the relationship between effort, intelligence, and results. It suggests that the more effort one puts in, the more intelligent they are and the more results they will achieve. The formula you’ve derived, I = R/E, suggests that intelligence is highest when results are obtained with little effort. However, it’s important to note that this equation is a simplification of the complexity of the relationship between effort, intelligence and results. Intelligence is a multi-dimensional and complex construct, it can be measured in different ways, such as cognitive, emotional, or practical intelligence, and it’s not only related to the effort but also with other factors such as knowledge, skills, and experience. Additionally, the idea that intelligence is only present where there is effort is not universally accepted, and intelligence can be present in the absence of effort.

Regarding the idea that the presence of forces implies the presence of intelligence, it’s important to note that forces are physical concepts that describe how objects interact with each other, and they don’t necessarily imply the presence of intelligence. Intelligence is a cognitive concept that refers to the ability to think, reason and learn, and it cannot be reduced to a physical concept such as force.

Me: Can you give examples of where intelligence can be present in the absence of effort?

ChatGPT: Yes, here are some examples:

1. Natural abilities: Some individuals may possess innate abilities or talents in areas such as music, art, or sports, which can be considered a form of intelligence, without much effort being applied.
2. Evolution: Evolution itself can be seen as a form of intelligence, adapting and optimizing species for survival without conscious effort.
3. Instinct: Some animals exhibit intelligent behaviors through instinct, such as migration patterns, hunting strategies, and social organization, without the need for conscious effort.
4. Tools: Intelligence can also be present in tools and machines, such as self-driving cars or recommendation algorithms, where they make intelligent decisions and perform tasks without human effort.
5. Autopilot: In aviation, an autopilot system can maintain a flight plan, control the aircraft’s speed, altitude, and navigation without conscious effort from the pilot.

Me: It could be argued that all of these 5 points you’ve mentioned do require effort. No one will question the fact that the making of any tools and the creation of an autopilot, surely required tremendous effort. Furthermore, evolution requires an immense amount of time to produce any useful or “intelligent” changes…it takes so long, it barely can be considered an intelligent process at all. Both instinct and natural abilities would not exist without the efforts of the organisms’ ancestors, which needed to struggle (lot’s of effort) so their offspring could be born and inherit these.

ChatGPT: Yes, that’s a valid point. Effort and intelligence can be interlinked and it may be difficult to completely separate the two. However, the examples I mentioned can be seen as instances where intelligence is present in the absence of conscious effort or deliberate problem-solving. For example, the autopilot system operates automatically without the need for conscious effort, and it can still be considered intelligent as it is capable of making decisions and adjustments based on inputs. Similarly, evolution can be seen as a slow and effortless process of natural selection, yet the changes it brings about can be considered intelligent in the sense that they lead to increased adaptability and survival chances. Instinct and natural abilities can also be considered examples of innate intelligence that require little or no conscious effort.

Me: Regarding the equation I’ve presented, E x I = R, do you see any practical applications for it in robotics?

ChatGPT: The equation you’ve presented, E x I = R, as a mathematical representation of the relationship between effort, intelligence, and results, may have some practical applications in the field of robotics. In robotics, the idea of efficient and optimal performance is a constant goal, and the equation could be applied to the design of robotic systems in order to optimize the use of resources such as energy and computational power. For example, a robot that is able to achieve a task with little effort would be considered more intelligent, and the equation could be used to evaluate and compare different robotic systems based on their intelligence.

In addition, the equation could be useful in the design of robotic systems that can learn and adapt to their environment, as the equation suggests that intelligence is highest when results are obtained with little effort. This could be applied to the design of robotic systems that can improve their performance over time by learning from their past experiences, this would imply that the robot is able to learn from the results of its actions, and to adjust its effort and intelligence to optimize the results.

Me: In which ways could this same equation be employed in the improvement of artificial intelligence systems?

ChatGPT: The equation E x I = R, which represents the relationship between effort, intelligence, and results, could be employed in the improvement of artificial intelligence systems in various ways. Here are a few examples:

1. Efficiency: As the equation suggests, intelligence is highest when results are obtained with little effort. Therefore, the equation could be used to evaluate and compare different AI systems based on their intelligence, and to optimize the use of resources such as computational power and energy.
2. Learning: The equation could be used to evaluate the performance of AI systems that can learn and adapt to their environment. The AI system that can improve its performance over time by learning from its past experiences would be considered more intelligent, as it implies that the AI system is able to learn from the results of its actions and adjust its effort and intelligence to optimize the results.
3. Exploration: The equation could be used to evaluate the performance of AI systems that must explore new environments or solve new problems. An AI system that can solve a problem with little effort would be considered more intelligent, as it implies that the AI system is able to find the most efficient solution.
4. Optimization: The equation could be used to optimize the performance of AI systems by adjusting the effort and intelligence of the system to achieve the best results. For example, if the AI system is not achieving the desired results, the effort could be increased or the intelligence could be optimized to improve the performance.

It’s important to note that the equation is a simplification of the complexity of the relationship between effort, intelligence and results, and it is necessary to consider other factors such as the environment, the task, and the AI system’s capabilities in order to get a full understanding of the system’s performance. Additionally, these are just some examples of how the equation could be applied, but it would be necessary to test the equation’s validity and applicability in different scenarios and AI systems.

Me: In what other way could my equation be tested to demonstrate its usefulness in making systems more efficient?

ChatGPT: The equation E x I = R, which represents the relationship between effort, intelligence, and results, could be tested in various ways to demonstrate its usefulness in making systems more efficient. Here are a few examples:

1. Simulation: The equation could be tested by simulating different scenarios in which an AI system is trying to solve a problem with different levels of effort and intelligence, and the results could be compared to see which combination of effort and intelligence leads to the best results. This can be done through mathematical modeling, computer simulation, or even through a game like the one I described before, this is a simple way to test the equation’s validity and applicability.
2. Empirical testing: The equation could be tested by conducting experiments in which an AI system is trying to solve a problem with different levels of effort and intelligence, and the results could be measured and analyzed. This could involve collecting data from real-world scenarios, such as the performance of a robot in a specific task, or measuring the energy consumption of an AI system while solving a problem.
3. Machine Learning: The equation could be tested by using Machine Learning techniques to optimize the effort and intelligence of an AI system. For example, a Genetic Algorithm or a Neural Network could be used to optimize the effort and intelligence of an AI system.
4. Comparison with other methods: The equation could be tested by comparing it with other methods that have been proposed to optimize the performance of AI systems. This could involve comparing the results obtained using the equation with the results obtained using other methods such as Q-learning or Evolutionary algorithms.

Me: What would be an example of testing it through mathematical modeling and what kind of mathematical models can it be tested on or how would it look on a mathematical model?

ChatGPT: An example of testing the equation E x I = R through mathematical modeling would be to use mathematical equations to simulate the behavior of an AI system and to study how different levels of effort and intelligence affect the performance of the system.

One way to do this would be to use mathematical models that describe the dynamics of the AI system and its interactions with the environment. For example, a mathematical model could be used to describe the behavior of a robot moving in a specific environment, and how the robot’s effort and intelligence affect its ability to navigate the environment and find the hidden treasure.

Another way to do this would be to use optimization techniques such as nonlinear programming or dynamic programming to find the optimal values of effort and intelligence that maximize the performance of the AI system. For example, you could set up an optimization problem that minimizes the error between the results obtained by the AI system and the desired results, and use mathematical methods to solve it.

A third way would be to use mathematical models that describe the learning process of the AI system, such as Markov Decision Processes or Reinforcement Learning models. These models describe the interactions between the AI system and the environment, and how the AI system learns from the results of its actions. This can be used to study how different levels of effort and intelligence affect the learning rate and the performance of the AI system.

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Wow! Simply, wow!!! Indeed, intelligence is not as simple as it seems. Yet, those years playing the philosopher trying to solve the riddle of intelligence might have led to something more than a little fun (or funny) equation. 

Check out my original manuscript (free copy if you become a patron!) on the intelligence equation! It’s fun, funny, colorful, creative, slightly mathematical, yet filled with fun cartoons (crazy…even as a broke grad student, I managed to pay an actual artist). In all, you might find it inspirational or perhaps even insightful! Link below –> 

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