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Dr Thomas Moore @drthomasmoore.bsky.social · 12/11/2025

I continue to vacillate on GenAI in teaching. This is ChatGPT on the isomorphism between the Ising and Gas Lattice models. Its explanation is the worst of both worlds: it sounds authoritative & plausible, yet is nonsensical. (We do have H[n] = H[1-n]). I worry about undergrads relying on this.

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Dr Thomas Moore @drthomasmoore.bsky.social · 03/02/2025

Update: there's still some strange fragility. If I tweak the problem slightly, the smooth reasoning stalls out, and we get nonsensical answers. I have not idea what o3 is doing here.

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Dr Thomas Moore @drthomasmoore.bsky.social · 03/02/2025

Just threw my favourite reactor engineering problem at ChatGPT's new (free) o3-mini model and it nailed it. I came up with this problem years ago. It doesn't feel solvable at first: you need a good instinct for 1st-order reactions, and I haven't seen something similar in any textbooks. Impressive.

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Dr Thomas Moore @drthomasmoore.bsky.social · 21/12/2024

Kazuo Ishiguro's novels are perfect. 💙📚 Go - go read them all. Whatever you do, don't read a review; they spoil the effect entirely. You can trust me. Start with 'The Remains of the Day'. That is all.

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/12/2024

But as you provide more parameters than data points, the interpolation gets once again. Here’s the polynomial case, showing how well the polynomial interpolates between the training data points. Note the initial decrease, the increase, the maxima around n = 14, then the decrease again.

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/12/2024

But the ML community went ahead and tried anyway. And this is what they found. When you use gradient descent to find parameters that match a 100-degree polynomial to the training data, you *don’t* get crazy polynomials; instead, they tend to interpolate quite well.

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/12/2024

So far so classical. But the deep learning community turned this idea on its head. They asked the question: what if we fit a 100 degree polynomial to just 14 data points. If you send this request to a classical least squares fitting algorithm, it won’t like you very much:

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/12/2024

The bias-variance trade-off captures these two extremes: make your model too simple, it can’t capture the signal. Make your model too expressive, it captures the noise. Bias and variance. In this case, a degree 4 polynomial is a good compromise:

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/12/2024

Variance occurs when our model is too expressive: it picks up both the underlying phenomenon and the random variation in the data. We call this overfitting. Fitting a degree 13 polynomial to 14 data points is a classic example. Notice how the model fits the data perfectly, but cannot interpolate.

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/12/2024

In classical statistics, we have something called the bias-variance trade-off. Bias and variance are the two ways a model can fail when we’re trying to fit it to data. Bias occurs when our model is too simple to capture the patterns present in the system. e.g. fitting a line through wavy data.

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/12/2024

I've spent the last little while reading the excellent (satirically titled) textbook 'Understanding Deep Learning' by Simon Prince. The field is a joy, and full of surprises. Take Double Descent: the unintuitive behaviour which is the mathematical cornerstone allowing massive LLMs to be trained. 🧵

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Dr Thomas Moore @drthomasmoore.bsky.social · 12/12/2024

I love this figure from an old Bardow-group paper which (like most of their work) has aged remarkably well. Not all uses of clean electricity have equal impact in terms of reducing lifecycle CO2 emissions! pubs.rsc.org/en/content/a...

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Dr Thomas Moore @drthomasmoore.bsky.social · 10/12/2024

With young kids, I've read The Wind in the Willows many (many) times. It's a perfect book. This scene always brings to mind the academic etiquette which forbids 'any sort of comment on the absence of one's friends from a group meeting at any time, for any reason whatsoever'. 🧪🔌💡💙📚

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Dr Thomas Moore @drthomasmoore.bsky.social · 28/11/2024

And realistic costs are likely to be far larger than those used in economic forecasting models (I do think it *may* be possible to get a little lower than $600/t, but I agree with this plot in principle)

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Dr Thomas Moore @drthomasmoore.bsky.social · 28/11/2024

On a global scale, the energy requirements are flabbergasting,

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Dr Thomas Moore @drthomasmoore.bsky.social · 28/11/2024

This paper makes a number of arguments related to energy requirements, water and land use, capital cost, scale, etc., familiar to anyone in the DAC space. For example, the dilution factor is extreme:

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Dr Thomas Moore @drthomasmoore.bsky.social · 25/11/2024

I'm a carbon capture guy after all. The word cloud doesn't lie. Courtesy @scholargoggler.bsky.social via @sylvaingigan.bsky.social

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Dr Thomas Moore @drthomasmoore.bsky.social · 23/11/2024

Finally, if Delta S is really measuring the irreversible increase in energy dispersion, it had better not decrease in an isolated system. That this is impossible is easy to prove by contradiction: if it were false, we could design a process for turning heat directly into work, as shown in the fig.

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Dr Thomas Moore @drthomasmoore.bsky.social · 23/11/2024

With our definition, the fact that S is a state function follows immediately from Kelvin’s statement of the second law: if Q could take on different values in different reversible processes, by running one forward and then the other backwards, you could turn work into heat. Here's a visual proof.

A visual proof that S is a state function.

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Dr Thomas Moore @drthomasmoore.bsky.social · 23/11/2024

Fermi takes ~40 pages, while Denbigh takes ~15, and their texts are full of scary diagrams like this:

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Dr Thomas Moore @drthomasmoore.bsky.social · 23/11/2024

Because the energies of A and B are identical, we can instead draw the complex, multi-part process above as follows, and think of Q and W as energy ‘flowing through’ the closed system. Though to be clear, strictly speaking Q is the energy *removed* from the heat bath.

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Dr Thomas Moore @drthomasmoore.bsky.social · 23/11/2024

To determine the directionality, lets design a reversible process that has exactly two effects on the universe. (I): it causes some quantity Q of heat in a reference thermal reservoir to be transformed into work (or vice versa) (II): it causes A to become B. The rest of the universe is unchanged.

A process with 2 effects on the universe.

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Dr Thomas Moore @drthomasmoore.bsky.social · 23/11/2024

Suppose you had two potential states, A and B, in an isolated system, and you wanted to determine which was more probable (or disperse) – which direction the system would tend to move. Obviously, if they can be interconverted in an isolated system, A and B must have identical energies.

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/11/2024

And we’ll end with some advice from Sadi Carnot for all Bluesky users. 6/6

Speak little of what you know, and not at all of what you do not know.

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/11/2024

Moving on. Some genuinely timeless advice for scientists here.

Yield frequently to the first inspiration.

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/11/2024

The great man then turns his shafts to the betterment of the… genetic pool.

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/11/2024

Sadi Carnot’s timeless advice for an active life.

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/11/2024

As the great man reminds us, you never can take too much bread on a walk.

carry when walking a book, and a note-book to preserve the ideas, and a piece of bread in order to prolong the walk if need be.

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Dr Thomas Moore @drthomasmoore.bsky.social · 20/11/2024

2024 marks the 200th anniversary of Carnot’s famous treatise, ‘On the Motive Power of Heat.’ One day we’ll discuss how he formulated a complete theory of reversible heat engines without understanding that heat is a form of energy. 🤯 But today, we'll look at the little-appreciated Appendix A. 🧵 🧪🔌💡

Extracts from the unpublished writings of Carnot.

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Dr Thomas Moore @drthomasmoore.bsky.social · 18/11/2024

Fair point. The original research & pilot plat demonstration doesn't explicitly acknowledge industry partnerships, but I'm sure they were involved in upscaling. The Rochelle group are one of the best industrially-connected CCS groups in the world...

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Dr Thomas Moore @drthomasmoore.bsky.social · 18/11/2024

This ‘cool-rich bypass’ was a major driver for the reducing CCS energy requirements. But they weren’t done. They also increased the temperature of the stripper from ~110C to ~150C, allowing them to generate high pressure CO2, reducing downstream compression energy two-fold 9/

Compression energy requirements as a function of stripper pressure.

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Dr Thomas Moore @drthomasmoore.bsky.social · 18/11/2024

Their process design diverted a fraction of the CO2 rich stream past the heat exchanger - just enough to make the heat loads balance, solving Prob #2. They then heated this bypassed stream using the heat in the super-low-quality steam at the top of the stripper, solving Prob #1. 8/

Cool Rich Bypass, From Lin and Rochelle's (other) paper.

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Dr Thomas Moore @drthomasmoore.bsky.social · 18/11/2024

Carbon capture processes involve 3 main units: an absorber, a stripper, and a heat exchanger connecting the two. In the absorber, a liquid absorbs CO2. In the stripper, the liquid is heated up and CO2 is released. 2/

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