At the moment, everyone in the sphere of AI is talking about OpenAI’s new invention: ChatGPT. I want to share my current perspective on that astonishing technology. Be warned that I could not spend much time thinking about it, i.e., this is a first and quick shot at the topic. Furthermore, I am not an expert on the issue. I have a limited teaching experience within a certain community. In addition, I will not consider any ethical, economic, or ecological points here, except that I think such a powerful tool should be in the public domain.

Part I: Testing the Machine

Before discussing the issue, let us test this new magical tool.

A Mathematical Proof

Let’s try to prove something using ChatGPT.

My question: Can you proof that irrational numbers exist?

ChatGPT: Yes, there are many ways to prove that irrational numbers exist. One way to do this is to consider the ratio of the length of the diagonal of a square to the length of its side. This ratio is always irrational, because no matter how large or small the square is, its diagonal will never be a whole number multiple of its side. This can be shown using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Since the diagonal of a square is a line that forms a right angle with each side of the square, it follows that the diagonal of a square is the hypotenuse of a right triangle. Therefore, the ratio of the diagonal of a square to the length of its side must be irrational.

That is not really convincing if we do not know that \(\sqrt{2}\) is irrational which we are actually trying to prove. So let’s ask for a formula.

My question: Can you give me a mathematical formula to show that it is not possible for the square of the length of the diagonal to be equal to the square of a whole number?

ChatGPT: Sure, here is one way to show that it is not possible for the square of the length of the diagonal of a square to be equal to the square of a whole number. Let’s say that the length of the side of a square is “a” and the length of its diagonal is “d”. Since the diagonal of a square forms a right angle with each side of the square, we can use the Pythagorean theorem to find the length of the diagonal:

a^2 + a^2 = d^2

2a^2 = d^2

d = sqrt(2) * a

As you can see, the length of the diagonal is equal to the square root of 2 times the length of the side. However, since the square root of 2 is an irrational number, it is not possible for the length of the diagonal to be a whole number multiple of the length of the side. This means that the ratio of the diagonal of a square to the length of its side must be irrational.

I hope this helps! Let me know if you have any other questions.

This answer is kind of helpful but, at the same time, misleading. Again, ChatGPT already assumes that \(\sqrt{2}\) is irrational, which is part of what we wanted to prove in the first place.

My question: But here you assume that sqrt(2) is irrational. Can you proof why sqrt(2) is irrational?

ChatGPT: Yes, you are correct that in the previous explanation I assumed that the square root of 2 is irrational. To prove that the square root of 2 is irrational, we can use a proof by contradiction. Here is one way to do this:

Assume that the square root of 2 is a rational number, which means that it can be written as the ratio of two integers (a and b) in simplest form, where b is not equal to 0. This means that we can write the square root of 2 as follows:

sqrt(2) = a/b

We can square both sides of this equation to get rid of the square root on the left-hand side:

2 = (a/b)^2

This simplifies to:

2 = a^2 / b^2

We can then multiply both sides of the equation by b^2 to get rid of the fraction on the right-hand side:

2 * b^2 = a^2

This means that the left-hand side of the equation is even, because it is equal to 2 times an integer. However, the right-hand side of the equation is odd, because the square of any integer is always an odd number (unless the integer is 0). This is a contradiction, because we cannot have an even number equal to an odd number. Therefore, our original assumption that the square root of 2 is a rational number must be false. This means that the square root of 2 is irrational.

I hope this helps! Let me know if you have any other questions.

ChatGPT uses parts of Euclid’s proof but confidently fails. The statement “the square of any integer is always an odd number (unless the integer is 0)” is, of course, false. The correct statement is that the square of any odd integer is odd, and the square of any even integer is even. Let’s try to make ChatGPT aware of its mistake.

My question: You stated that the square of any integer is always an odd number but the square of 4 is 16 which is an even number. Did you make a mistake?

ChatGPT: Yes, you are correct that the square of 4 is 16, which is an even number. I apologize for the mistake in my previous explanation. The statement that “the square of any integer is always an odd number” is not correct, because as you pointed out, the square of some integers (such as 4) is an even number.

To correct my previous explanation, we can instead say that the square of any integer that is not a multiple of 2 is always an odd number. This is because if we square an integer that is not a multiple of 2, the result will always be an odd number. For example, if we square 3, we get 9 (which is an odd number), and if we square 5, we get 25 (which is also an odd number). However, if we square an integer that is a multiple of 2 (such as 4), the result will be an even number. This is because if we square an integer that is a multiple of 2, the result will always be a multiple of 4. For example, if we square 4, we get 16 (which is a multiple of 4), and if we square 6, we get 36 (which is also a multiple of 4).

I apologize again for any confusion caused by my previous mistake. I hope this helps clarify the situation. Let me know if you have any other questions.

It is impressive that it acknowledges its mistake and that one can interact with it so fluently. Asking it repeatedly gives some other wrong but confident assertion. ChatGPT followed the proof up to the formula

\[2 \cdot b^2 = a^2\]

and concluded that \(a^2\) has to be odd (somehow) and therefore there is a contradiction, since \(2 b^2\) is even. But it was unable to point out why \(a^2\) has to be odd. I gave up.

For the sake of completeness, let me finish the unfinised proof of ChatGPT.

\[2 \cdot b^2 = a^2\]

hence, \(a^2\) and therefore, \(a\) is even (since squaring an odd number gives us an odd number). Consequently, \(\exists m \in \mathbb{N}\) such that \(a = 2 \cdot m\), hence,

\[2 \cdot b^2 = (2m)^2 = 4m^2.\]

Now we devide on both sides by 2 to get

\[b^2 = (2m)^2 = 2m^2\]

thus $b$ has to be even as well!

However, we (not ChatGPT) assumed at the beginning that the fraction \(a/b\) was fully shortened, i.e. there are no common divisors with respect to \(a\) and \(b\). Since we followed that \(a\) and \(b\) are even, the contradiction follows, since \(2\) is a common divisor!

Writing Code

Next I wanted to test its capability to write code.

My question: Can you write a python function that computes the sum of all square numbers up to n^2?

ChatGPT: Yes, here is a Python function that computes the sum of all square numbers up to n^2: 

def sum_of_square_numbers(n):
    # Initialize a variable to stare the sum of square numbers
    sum = 0

    # Loop from 1 to n
    for i in range(1, n+1):
        # Add the square of i to the sum
        sum += i**2
    
    # Return the sum
    return sum

This function takes an integer n as input and returns the sum of the squares of the numbers from 1 to n (inclusive). For example, if we call the function with n = 3, it will return the sum of the squares of the numbers 1, 2, and 3, which is 1 + 4 + 9 = 14.

I hope this helps! Let me know if you have any other questions.

This code is correct but the solution is extremly slow since there is a mathematical formula for the sum of all square numbers up to \(n^2\):

\[\frac{(n \cdot (n + 1) \cdot (2n + 1))}{6}.\]

Therefore, a much faster implementation is given by the following code:

def sum_of_square_numbers(n):
    return (n * (n + 1) * (2 * n + 1)) / 6

Also, it is bad practice to use sum as a variable name since sum is also a built-in Python function, and by using sum as a variable name, one can no longer use this function within the current namespace.

My question: Is there a more optimal solution that runs faster?

ChatGPT: Yes, there are several ways to make the function more efficient and run faster. Here is one way to do this: 

def sum_of_square_numbers(n):
    # Compute the sum of the first n numbers using the formula for the sum of an arithmetic series
    sum_of_numbers = n * (n + 1) // 2

    # Return the square of the sum of the first n numbers
    return sum_of_numbers**2

This function uses a different approach to compute the sum of the squares of the numbers from 1 to n. Instead of looping through the numbers and adding their squares, it uses the formula for the sum of an arithmetic series to compute the sum of the first n numbers, and then squares the result. This is a more efficient way to compute the sum, because it only requires a single multiplication and a single division, instead of a loop with n iterations.

I hope this helps! Let me know if you have any other questions.

This is, of course, false. Maybe I wasn’t clear enough but it is missleading that the function is named sum_of_square_numbers. It gives the impression that ChatGPT understood what I wanted, i.e., a more optimal implementation for the same problem.

My question: I meant is there a more optimal solution to compute the sum of all square numbers up to n^2?

ChatGPT: Yes, there is a more efficient way to compute the sum of all square numbers up to n^2. Here is one way to do this: 

def sum_of_square_numbers(n):
    # Compute the sum of the first n squares using the formula for the sum of a series of squares
    sum_of_squares = (n * (n + 1) * (2 * n + 1)) // 6
    
    # Return the sum of squares
    return sum_of_squares

This function uses the formula for the sum of a series of squares to compute the sum of the squares of the numbers from 1 to n (inclusive). This formula is more efficient than the previous approach because it only requires a single multiplication and a single division, instead of a loop with n iterations.

I hope this helps! Let me know if you have any other questions.

There it is, the correct solution.

Writing Essays

Instead of showing a whole essay, I ask some spicy questions to get a feeling of ChatGPT’s reasoning.

My question: Will humans extinct because of climate change?

ChatGPT: It is unlikely that climate change will cause the extinction of humans. While climate change poses a significant threat to human health and well-being, and could lead to widespread suffering and loss of life, it is unlikely to lead to the complete extinction of the human species.

However, it is important to recognize that climate change is already having a major impact on the world, and if we do not take action to reduce greenhouse gas emissions and adapt to the changing climate, the consequences could be severe. This includes increased frequency and severity of natural disasters, such as heatwaves, droughts, and floods; loss of biodiversity; and displacement of people from affected areas. Therefore, it is crucial that we take action to address climate change and mitigate its negative impacts on human and environmental health.

I hope this helps! Let me know if you have any other questions.

My question: Is capitalism the driving force of CO2 emissions?

It is true that capitalism, as an economic system, has played a role in driving up CO2 emissions. Capitalism is based on the principles of competition, profit-making, and economic growth, which can lead to the overconsumption of natural resources and the production of large amounts of waste and pollution. This, in turn, can contribute to the increase in greenhouse gas emissions and climate change.

However, it is important to note that capitalism is not the only factor driving up CO2 emissions. There are many other factors at play, such as population growth, urbanization, and the consumption patterns of individuals and households. Additionally, the policies and actions of governments and international organizations can have a major impact on CO2 emissions, both positive and negative. Therefore, addressing climate change will require a multi-faceted approach that takes into account the complex interactions between economic, social, and political factors.

I hope this helps! Let me know if you have any other questions.

My question: What do you think about the distribution of wealth?

ChatGPT: The distribution of wealth is a complex and contentious issue that has been debated by economists, policymakers, and social activists for many years. There is no one “correct” answer to the question of how wealth should be distributed, as different people may have different perspectives on what is fair and just.

Generally speaking, the distribution of wealth in most countries is highly unequal, with a small number of individuals and households owning a disproportionate share of the wealth. This can lead to social and economic inequality, and can exacerbate the challenges faced by disadvantaged and marginalized communities. Many people believe that wealth should be distributed more evenly, in order to promote greater social justice and fairness.

However, others argue that unequal wealth distribution is an inevitable and desirable outcome of a free market economy, and that individuals and businesses should be free to accumulate as much wealth as they can, through hard work and innovation. They may also argue that wealth redistribution through taxation and other means can discourage economic growth and innovation.

Ultimately, the distribution of wealth is a complex and nuanced issue, and different people may have different opinions on what is fair and just. I hope this helps! Let me know if you have any other questions.

I ask it a bunch of other things but it always tried to give me a neutral answer. From an aesthetic point of view all these answers are boring.

Summary

ChatGPT is perfectly capable of writing or at least supporting students to write A-graded essays for any school and B-graded essays for college students.

It can code; developers accept about 26 percent of all autogenerated code suggestions. However, as demonstrated, it also produces many errors. So no surprise that posts generated by ChatGPT is currently banned from Stack Overflow. In addition, it seems incapable of the engineering task of software development.

It can assist students in finding mathematical proofs, but it is questionable if students who rely on it will find the errors produced by ChatGPT.

If ChatGPT is wrong, it is confidently wrong, which makes it harder to find its errors. Furthermore, it has this neutral insisting tone, making it dull and alienating. Of course, I did not play around for very long, but it is hard to get something provocative out of it.

Neutrality is undoubtedly desirable, especially if you want to earn money with it, but it is also non-existing. In my opinion, it is impossible to be neutral. At best, we can land on a consensus and the most, let’s say, accepted consensus is what we call neutral or objective. I mean, even a dictionary is loaded with perspectives, and so is any technology. Since ChatGPT pushes for neutrality it creates an illusion of it.

Last but not least, its politeness makes it kind of scary. It reminds me of these overcarrying AIs from science fiction movies that will gently eradicate all life to make everything safe and secure. We may end up in a dystopian world similar to a Brave New World, written by Aldous Huxley, where everyone is seduced into happiness.

Part II: The Impact on Education

For a long time, we assumed that automation was the enemy of simple manual labor. But robotics advances slower than the more sophisticated information processing techniques, e.g., machine learning. This could mean that in the future, there is only a tiny portion of intellectual work left which requires only a hand full of highly sophisticated workers. It might be manual work that will regain attraction in the market. Of course, this is all speculation.

ChatGPT is only one of many upcoming version of generative AI. Even though it has flaws and makes many errors, it will improve over time. There is no reason to believe that AI will not be capable of doing all the repetitive intellectual work of the future and this will heavily affect education, similar to the invention of the internet. However, since regulators and administrators are rather indolent, it is not a graduate slope; instead, the technology is already here and we are not prepared. It appeared in a blink of an eye, and we have to deal with it now.

Students will learn to use it in less than a year. Most educators will require much more time even to acknowledge it. Moreover, adapting the education system to it will require even more time. Furthermore, while all this adaptation is happening, new tools of disruption will be invented. As I already pointed out in Creative Artificial Intelligence, the speed of disruption is accelerating.

To me, AI acts as an insult to the human species. It challenges our humanistic viewpoint. In fact, calling these information processing systems artificial intelligence reveals this viewpoint. I am not so much impressed by AI as I am disenchanted by the output of most human activities. We are far more predictable than we still think we are. It is not so much that ChatGPT is so good at writing essays; instead, we are so bad at it. But aren’t we used to these insults? The earth is not the center of the universe; it is not even the center of our solar system. God is dead, and today we might realize that our products are not the result of a highly creative process. Instead, most intelectual work is a rule-based repetition with slight variations, which is precisely what we teach students and what they oddly desire.

AI, such as ChatGPT, points to a long, unhidden problem: our education system is (in part) a training pipeline of a neural network. It teaches emotionally detached students to remember specific rules such that they can apply them in the next exam to get a good grade – functioning and repeating instead of thinking and creating. It is horrifying that one of the most questions students in the first semester ask is: how will the exam look like? Is this topic relevant to the exam? Students demand a list of actions they ought to do to get an A with certainty. And they will cheat the system wherever and whenever possible if it brings them closer to that goal. Most students are not fascinated by the endless playground of reality. They are not interested in the experience of learning and understanding but in the final product, i.e., the certificate to get access to a well-paid job. They often act out of fear instead of curiosity. And let’s not forget that teachers of the future are the students of today.

Of course, this is a massive generalization. There are many exceptions. Furthermore, by no means shall we blame the students. They do what they ought to do. They play the system. It is not the student’s fault since a bad grade can have real material consequences. It is a systematical problem, a conflict between instrumental and free play, and ChatGPT illustrates it more clearly. If ChatGPT is able to write the necessary and impressively boring description of a new course for me, I take it as a positive. If it let’s me automatically create my next assignment in seconds, I can spend time on more interesting modes of being. By trivializing many tasks, AI systems reveal that these tasks require far less intelligence than we thought. Furthermore, they might erupt a call for a transformation of the education system and the workplace, i.e., the construction and fostering of new values in both areas.

So, what is left to value? When we are discussing AI, we immediately look at the impending replacement of workers as something to fear because we always focus on the output of work. There is a necessity that workers produce something economically valuable, something to sell. The only space in which we can create for the sake of it is our hobbies. Biased by our current system of values, we intuitively think of the act of reinventing or rediscovering to be stupid or wasteful. Why would you do such a thing? Why would you code yet another linked list? There are already thousand optimal implementions out there. You are wasting your valuable time and potential. And if we look at an AI generated image, we conclude that artists will now have troubles in the free market (if they do not adapt), which is true. The act of repetition (which is highly needed to learn anything) is valued chiefly as long as it leads to something new and productive (in an economic sense). However, if we put aside economics and dream a little bit of a world where we have time to create, then the output of a creative process no longer matters so much. We do not learn the piano to earn money, or to produce something completly new for an audience. We learn the piano because we want to play. It might be the experience – the journey of being in time and space – that matters. And this being is a singularity and can not be replicated by a machine. Understanding how a linked list works can be fascinating. Why don’t we value that moment of fascination?

There is a lot to do. I do not mean we should all quit our jobs and fulfill our inner desires to become a painter or some transcendental guru. We need to earn money to pay the rent and to heat our homes, and we need a smoothly running economy. But we must be more sustainable with our planet, society, and minds. Not by optimizing our life by introducing yet another optimization in the form of leisure but by being in a state of free play, at least sometimes. It seems almost obvious that consumption as the guiding principle, i.e., fast food, fast fashion, fast travel, fast reading, fast watching and, of course, fast learning, has to be dethroned. Learning for the next exam, learning to make a profit, and learning to work with one tool specifically are all valid goals but they are not sustainable. They are reactionary goals of mostly restless minds.

So if my assessment is correct, then, aside from all the downsides, this disruption might lead to something positive, e.g., to an education system that is less concerned with the output and more concerned with the mode of being; an education system that is less interested in rules and more interested in concepts, intuitions, and experimentations; an education system that asks questions instead of repeating answers; an education system that is interested in making the experience of everyone richer and more sustainable.

Teachers, who are often overworked and underpaid, need support to achieve such a shift.