The tragedy of GenAI for education

Wherein I decided to "try" to use the built in Microsoft Copilot to see how it does.

students using ChatGPT to do their homework for them

I work in IT training and certifications. If you are in the IT space, you undoubtedly know what I “own” as a product manager. But that is not what this post is about.

No, I have been following the rise of ChatGPT and its relatives, and one of the interesting phenomena is that if you chart usage trends, it is clear that a LOT of students are using it for their schoolwork. The trends are that usage is heavy from September until mid December, and then from January through early June.

It doesn’t take a rocket scientist to realize that is aligned to the academic calendar.

And, if you follow any teachers in high school or university, they tell tales of a constant cat and mouse (or is it Whac-a-Mole?) game with students. Alas, it seems that there is a trend of instructors and professors beginning to adapt their syllabi to account for the advent of Generative AI.

But, as a student of physics (my degree is a B.Sc. Physics, minor in Mathematics, as well as all the coursework for a M.Sc. in Physics), I wanted to test it for myself.

One of the things that was a game changer for me in uni was my third year and when we learnt about the Hamiltonian formulation of classical mechanics. As opposed to the Newtonian formulation, it provided a steppingstone to the advent of Quantum Mechanics and all that modern physics brings (semiconductors, atom bombs, etc).

So, I asked Copilot to explain the Hamiltonian formulation to me as if I was a senior in university studying physics. The section below is what it spit out:

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In the Hamiltonian formulation, we start with the Hamiltonian function, H(q,p,t), which represents the total energy of a system in terms of generalized coordinates q (positions), conjugate momenta p, and possibly time t. This approach reformulates classical mechanics using symplectic geometry, providing a framework that is particularly powerful for dealing with complex systems and for making connections to quantum mechanics.

1. Generalized Coordinates and Momenta: Unlike in Newtonian mechanics where we deal with position and velocity, in Hamiltonian mechanics, we use generalized coordinates qi and conjugate momenta pi. These pairs (qi,pi) form the phase space of the system, which provides a complete description of its state.

2. Hamilton's Equations: The equations of motion are derived from the Hamiltonian function. They are:

   \(\dot{q}_i = \frac{\partial H}{\partial p_i}, \quad \dot{p}_i = -\frac{\partial H}{\partial q_i}\)

   These first-order differential equations describe the time evolution of the system.

3. Canonical Transformations: These are transformations of the phase space coordinates (qi,pi)→(Qi,Pi) that preserve the form of Hamilton's equations. They are crucial for simplifying problems and for understanding the invariance properties of physical systems.

4. Poisson Brackets: The Poisson bracket of two functions f and g on phase space is defined as:

   \(\{f, g\} = \sum_i \left( \frac{\partial f}{\partial q_i} \frac{\partial g}{\partial p_i} - \frac{\partial f}{\partial p_i} \frac{\partial g}{\partial q_i} \right)\)

   The Poisson bracket plays a central role in the structure of Hamiltonian mechanics, analogous to the commutator in quantum mechanics.

5. Hamilton-Jacobi Equation: This approach provides a bridge to quantum mechanics and wave mechanics. The Hamilton-Jacobi equation is given by:

   \(H \left( q_i, \frac{\partial S}{\partial q_i}, t \right) + \frac{\partial S}{\partial t} = 0\)

   where S is the action, a function whose gradients with respect to the coordinates give the momenta. This method simplifies the process of finding solutions to complex mechanical problems.

6. Application to Quantum Mechanics: The Hamiltonian formulation directly leads to the development of quantum mechanics, where the Hamiltonian operator governs the time evolution of the quantum state via the Schrödinger equation.

In essence, the Hamiltonian formulation is a powerful and elegant reformulation of classical mechanics, providing deep insights into the nature of dynamical systems and paving the way for modern theoretical physics. It's a cornerstone of both classical and quantum theories, making it indispensable for advanced studies in physics.

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This is an incredibly good summary. It even had the LaTeX code for the equations (I pasted the code into Substack’s LaTeX widget to format the equations).

What I struggle with is that my journey to get to being ready to understand the Hamiltonian formulation of physics, I needed a solid understanding of the Newtonian forms, and a metric butt-load of mathematics. Calculus, Differential Equations, PDE’s, and vector calculus at a minimum to fully be able to work in this space.

Alas, I worry that using ChatGPT or Claude, or (insert th next groovy chatbot) to jump to the answer will mean that yes, you can answer the exam questions, but do you really understand the concepts?

I think not.

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I think about this a lot, and I frequently argue with one of my staff. He’s 100% on board with using the tools that are at hand, and that what matters is the answer.

But I am not so sure. It is like reading the tabs for a song, and then thinking that you can play it. Just because I can follow the notated arpeggios of an Yngwie Malmsteen solo doesn’t mean I can play it.

It is like when I was in high school in the stone age (narrator: it was the early 1980s) and calculators became ubiquitous, but before the TI-85 graphing calculator became standard equipment, the teachers in my math and science classes structured the lesson plans to not rely on calculators, and in fact make calculators counterproductive.

Indeed, when I was in college, the only class I needed my calculator for was Chemistry, where you calculate bond strengths, molarities, and activation energies. None of my physics classes needed calculators (I should add that just as I was graduating in 1988 the first PC labs appeared in my college, prior to that, we all used timeshare systems that sucked).

But it is clear that Chatbots and access to information instantly is here to stay. Will it help raise generations of smart adults? Or will it be like GPS and destroy the ability to navigate with paper maps and street atlases.

Anyone else have thoughts? Let’s discuss in the comments!

Oh, and if you understand that snippet of Physics, I salute you!

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