Chat with AI about definition of intelligence itself.

Nickle: What's your definition of intelligence? Please think step by step and tell me using mathematical language.

ChatGPT4: Defining intelligence using mathematical language can be challenging, as intelligence is a complex and multifaceted concept that encompasses various cognitive abilities and problem-solving skills. However, one way to express intelligence mathematically is through the lens of information theory and decision-making.

In this context, intelligence can be viewed as the ability to process and utilize information to make optimal decisions, which can be represented mathematically as follows:

Information representation: Let S represent a set of possible states in the environment, and A represent a set of possible actions an agent can take. The agent receives observations O from the environment and maintains a belief state B, which is a probability distribution over S.

B(s) = P(s | O)

where s ∈ S and B(s) represents the probability of state s given the observations O.

Decision-making: The agent makes decisions based on its belief state B and a utility function U that quantifies the desirability of each state. The goal is to choose an action a ∈ A that maximizes the expected utility:

1. a* = argmax_a ∑_{s ∈ S} B(s) * U(s, a)
2. The utility function U(s, a) quantifies the desirability of taking action a in state s, and the agent selects the action that maximizes the expected utility given its belief state.

Learning and adaptation: An intelligent agent should be able to learn from experience and adapt its behavior to improve decision-making. This can be modeled as updating the belief state B and utility function U based on new observations and feedback.

One approach to learning is using Bayesian updating to refine the belief state:

B'(s) = P(s | O, o) = P(o | s) * P(s | O) / P(o | O)

where o is a new observation, B'(s) is the updated belief state, and P(o | s), P(s | O), and P(o | O) are probabilities related to the new observation, previous belief state, and overall observation likelihood, respectively.

Learning can also involve updating the utility function U based on feedback, such as adjusting weights in a neural network or updating coefficients in a linear regression model.

This mathematical framework captures some aspects of intelligence, such as information processing, decision-making, and learning from experience. However, it is important to note that this is only one way to represent intelligence mathematically, and there are many other perspectives and theories that attempt to model and define intelligence from different angles.

Nickle: what's the difference between intelligence and wisdom?

ChatGPT4: Intelligence and wisdom are related but distinct concepts, often used to describe different aspects of an individual's cognitive abilities and understanding. Here are some key differences between the two:

Intelligence:

1. Intelligence generally refers to the capacity to learn, reason, problem-solve, and adapt to new situations.
2. It is associated with the ability to process information quickly, recognize patterns, and think analytically or critically.
3. Intelligence can be measured to some extent through standardized tests, such as IQ tests, which assess logical, verbal, and mathematical skills.
4. It often pertains to the acquisition and application of knowledge, allowing individuals to find solutions to specific problems or challenges.

Wisdom:

1. Wisdom, on the other hand, encompasses a deeper understanding of life, human nature, and the complexities of the world.
2. It involves the ability to make sound judgments and decisions based on personal experiences, insight, and empathy.
3. Wisdom is not easily quantifiable, as it represents a combination of knowledge, experience, and emotional intelligence.
4. It relates to the ability to see the bigger picture, understanding the consequences of actions, and recognizing the underlying principles and values that guide decision-making.

In essence, intelligence is about the ability to learn, process, and apply knowledge to solve problems, while wisdom is about the ability to make sound judgments and decisions based on a broader understanding of life and human experience. Intelligence is more focused on the cognitive aspects of problem-solving, whereas wisdom encompasses a deeper, more holistic understanding that incorporates emotional intelligence and life experience.

Nickle: To achieve one given goal, say add 1 + 100 using two computers, or machines, how can you measure which is more intelligent? How can you measure intelligence? In information theory, you have entropy to measure how much info. Here, how can you measure how much intelligence each computer has?

ChatGPT4: In the context of a specific task like adding 1 + 100, measuring intelligence can be challenging since it is a simple and well-defined problem that does not require much intelligence to solve. However, one can compare the efficiency, adaptability, and generalizability of the two machines to get some idea of their relative intelligence. Here are some factors to consider when comparing the intelligence of the two machines in this context:

1. Speed: You can measure how quickly each machine computes the sum. The faster machine might be considered more intelligent if it can solve the problem in a shorter amount of time without sacrificing accuracy.
2. Resource utilization: You can measure the computational resources each machine uses to solve the problem. A more intelligent machine might use fewer resources, such as memory or processing power, to arrive at the correct solution.
3. Adaptability: You can test each machine's ability to adapt to different input formats or variations of the problem. For example, how well does each machine handle adding larger numbers, negative numbers, or decimals? A more intelligent machine would be able to adapt to these variations more effectively.
4. Generalizability: You can test the machines on a broader range of arithmetic problems or other types of mathematical operations. A more intelligent machine would be able to generalize its knowledge and apply it to a wider variety of tasks.
5. Robustness: You can test each machine's ability to handle erroneous inputs or unexpected situations, such as missing or malformed data. A more intelligent machine would be more robust in handling these situations and provide meaningful output or error messages.
6. Learning capability: If the machines are capable of learning, you can measure their ability to improve their performance on the task over time or with additional training data. A more intelligent machine would show more significant improvements or faster learning rates.

It is important to note that these factors only provide a limited and task-specific view of the machines' intelligence. Measuring intelligence in a more comprehensive way would require evaluating the machines across a broad range of tasks, considering their adaptability, learning capabilities, and ability to solve complex problems. There isn't a single metric like entropy in information theory to measure intelligence directly, as intelligence is a complex and multifaceted concept.

Nickle's final comment:

Next time, I will ask him to measure intelligence in his own term he just define at the front of the article. Let's see. But right now, I am pretty sure, we can use it as a thinking assistant. Hope this can inspire people to think more about the key questions we have to have answers before it is too late.