Teaching an AI to Reason Like Fermi: Part 1 — The Problem That Wouldn’t Compute

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Posted on February 7, 2026 by matteomycarta

How many piano tuners are in Chicago?

That’s one of the famous questions Enrico Fermi posed to his physics students. Not because he cared about piano tuners, but because he wanted to teach them how to reason through problems with limited information. You don’t need to know the exact answer – you need to know how to think about it.

Let’s break it down: Chicago has maybe 3 million people. Perhaps 1 in 20 households has a piano – certainly not as common as TVs (nearly everyone), but more common than harps (quite rare). That’s roughly 150,000 pianos. Each piano needs tuning once a year. A tuner can probably do 4 pianos a day – more than 1 (they’d barely make a living), fewer than 10 (each tuning takes a couple hours) – so maybe 1,000 per year. That means you need about 150 tuners.

NASA even uses it to teach estimation. You got a reasonable answer using nothing but logical decomposition and bounded guesses.

This is Fermi estimation. And I tried to teach an AI to do it.

Why this matters

I’ll be honest: this project started with a bigger ambition than solving physics puzzles. I wanted to know if AI could become a partner in thinking critically about numbers – not just as a calculator, but as a collaborator in quantitative reasoning. One inspiration was Carl Bergstrom and Jevin West’s book Calling Bullshit. They describe what they call the “new bullshit”: using data, statistics, and visualizations to construct the appearance of scientific rigor – giving false authority to misleading claims. It’s sophisticated deception dressed up as analysis. The book teaches a skill: detecting and dismantling this kind of numerical misdirection. Fermi estimation is a different but complementary skill – it exercises similar muscles: decomposing claims, questioning assumptions, sanity-checking results. The dream was an AI partner for this kind of thinking. Not an oracle that gives you answers, but a collaborator that helps you interrogate whether answers are reasonable. It was Bergstrom and West’s YouTube lectures that first introduced me to Weinstein’s Guesstimation books – which became the methodological backbone of this project.

The frustration

Let me take you back to 2023. I was excited – maybe naively so – about using LLMs for Fermi estimation. These models had access to vast amounts of physics knowledge, and they were supposedly good at reasoning.

But here’s the thing: they were terrible at arithmetic. Not just GPT-3.0 – the problem persisted through 3.5 and even 4.0. I documented one session where GPT-4 attempted to multiply 836 x 1923 eight times. It got the correct answer exactly once – then regressed to different wrong answers on subsequent attempts. It could describe the long multiplication algorithm perfectly while executing it incorrectly. Each attempt produced a different error. There was no stable learning, just occasional lucky generations.

The arithmetic failures made it impossible to even evaluate whether the models could do Fermi estimation. Was the model struggling with decomposition? With bounding? With proceeding under uncertainty? I couldn’t tell – every attempt would derail on basic multiplication or unit conversion long before I could assess the reasoning quality.

The model would freeze when faced with uncertainty. It would apologize profusely for not having exact values. When it did proceed, it would present numbers with no reasoning, no bounds, no indication that this was a guess rather than a fact. Where did that number come from? Is it reasonable? You have no way to know. But I couldn’t systematically address any of this while arithmetic kept breaking.

I started drafting what would become the framework – ideas about decomposition, bounding, proceeding with uncertainty. But I couldn’t finalize anything. The arithmetic problem had to be solved first.

Note: Modern models with carefully designed custom instructions handle arithmetic more reliably. I know it for a fact (I tested it on ChatGPT 4.5, adapting my instruction from Jeremy Howard’s recommendations in A Hackers’ Guide to Language Models, and got the same results on the tricky questions he works through). But the judgment problem remains unsolved.

The Wolfram plugin: the turning point

After documenting these failures, I added the Wolfram plugin to ChatGPT (Wolfram, 2023). That’s when things changed enough to really push on the Fermi idea.

Wolfram fixed the arithmetic: unit consistency improved, scientific notation became reliable, basic math errors disappeared. The model could finally compute accurately and consistently.

And that’s when I could finally see what remained.

The model could compute, but it couldn’t estimate. It still wouldn’t commit to bounded guesses. It still hedged or refused when faced with uncertainty. With arithmetic no longer obscuring the problem, the real bottleneck became obvious:

The model could calculate, but it couldn’t reason like Fermi.

This led to a crucial realization. There were two different problems requiring two different solutions:
1. Arithmetic reliability -> Wolfram plugin solved this
2. Estimation judgment -> Required something else entirely

The bottleneck wasn’t calculation. It was the model’s inability to proceed confidently with explicit uncertainty – to say “I don’t know this exactly, but I can bound it” and then move forward.

Only then could I finalize the framework.

Drafting the Laws: permission to estimate

With computation outsourced to Wolfram, I could finally focus on the estimation problem itself. I drafted what I called “the Laws” – giving the model permission and methodology to reason under uncertainty.

The framework I drafted wasn’t pulled from thin air. The methodology itself comes from Enrico Fermi – this is how he trained his physics students to reason and experiment in their heads. Lawrence Weinstein took that foundational approach and built something substantial: a rich, modern pedagogical method with brilliant and often humorous worked examples in his Guesstimation books (Weinstein & Adam, 2008; Weinstein, 2012). My Laws were an attempt to translate Weinstein’s approach into something an AI could follow – to adapt it from human pedagogy to human-AI partnership.

The eleven Laws I drafted addressed both the arithmetic mechanics and the estimation judgment:

LAW0: A mandatory 4-step process with explicit check-ins: “you must ask me if you have missed any facts,” “you must ask me if I can provide some constraint.” The collaborative DNA was there from the start – I knew the model needed human input. It just wouldn’t ask for it, even when told.

LAW1-LAW9: Scientific notation rules, arithmetic procedures, and unit handling – establishing a procedure the model could reliably follow, making the reasoning transparent and auditable. With Wolfram handling the computation, these laws ensured consistency and transparency in how calculations were performed and reported. LAW8-LAW9 specifically addressed unit conversions and ensuring final answers were always in SI units.

LAW10: “Read all examples before solving.” I was observing my own learning process – how I improved as I worked through more of Weinstein’s examples, how I absorbed his thinking patterns, how my decomposition and bounding strategies refined with practice. I replicated that learning process for the AI by providing worked examples.

LAW11: “Don’t reprint my prompt” – fighting the model’s tendency to waste tokens repeating instructions back to me.

The framework combined reliable computation (Wolfram) with structured methodology (the Laws). It helped – but the results were inconsistent. The model would follow some Laws, ignore others, and systematic improvement remained elusive.

The real breakthrough would have to wait for better models and a rebuilt framework.

Building something better

Fast forward to late 2025. Better models, more experience, and lessons learned from that 2023 framework. I rebuilt it from scratch – not to compensate for failure, but to enable even greater success.

The new framework has 17 Laws: 12 mechanical (arithmetic, units, notation) and 5 focused specifically on estimation judgment. It includes 14 worked examples demonstrating complete reasoning patterns. The core shift was from defensive rules to empowering principles (“bound uncertain quantities with explicit reasoning,” “classify every estimate as KNOWN, BOUNDED, or ASK”).

The 2023 framework worked – it just wasn’t refined enough. The late 2025 version is more systematic, more explicit about judgment, and designed from the ground up for modern models that can reliably compute but still struggle with metacognition.

I tested it with Claude Sonnet 4.5. Here’s a before/after on that drag coefficient:

Before framework:
Model writes: “The drag coefficient for an F1 car is 0.9”

Where did 0.9 come from? Is that reasonable? We have no way to know.

After framework:
Model writes: “Lower bound: more than 0.5 (very streamlined). Upper bound: less than 2 (very blunt). Geometric mean ~ 1.”

Now we see the thinking. We know what the bounds are. Even if you don’t know fluid dynamics, you can think: “is an F1 car closer to streamlined or blunt?” You can disagree intelligently.

The framework doesn’t make the model know more. It makes the model show its uncertainty instead of hiding it behind assertions that sound confident but can’t be audited.

The results: does the framework actually help?

To find out, we ran a controlled comparison. Same eight problems, same model (Sonnet 4.5), same system-wide preferences. The only difference: one condition got the full framework (17 Laws, 14 worked examples, explicit KNOWN/BOUND/ASK classification requirements), while the other got only basic Fermi methodology – “decompose problems, bound uncertain quantities with upper and lower limits, take geometric means, show your work.”

The results:

Minimal prompting: 7.9/10
Full framework: 8.5/10

That’s a modest lift – 0.6 points – and with only eight problems and a single evaluator, it’s a directional finding, not a statistically significant one. The model can do reasonable Fermi estimation with just basic methodology concepts. Modern LLMs have improved dramatically since 2023.

But the numbers don’t capture everything. Reading the solutions side by side, the framework-trained answers show their reasoning differently. Instead of “drag coefficient ~ 1,” you get explicit bounds with justification. The answers are more auditable, more teachable, more useful for collaboration.

We also tested whether providing reference tables (order-of-magnitude values for common quantities) would help. Score: identical. But the model cited its sources explicitly – “air density: 1.2 kg/m^3 (from reference tables)” – instead of just labeling values as “KNOWN.” Same accuracy, better transparency.

I also ran an earlier exploratory test on eleven different problems from Weinstein’s books. That diagnostic helped shape the framework, revealing where the model needed more guidance. The patterns were consistent: decomposition excellent, bounding inconsistent, asking for help essentially never.

The framework’s value isn’t dramatic capability lift. It’s structure that enables auditing, teaching, and targeted improvement.

What works excellently:

Decomposition: Perfect. Every single problem was broken down cleanly.
Forward progress: The model proceeds confidently with bounded estimates.
Numerical accuracy: Usually within an order of magnitude of Weinstein’s solutions.
Comparisons: Good contextualization of answers.

What works when tested explicitly:

Interpretation of ambiguous problems: We added a law (LAW-INTERPRET) that tells the model to pause and ask when a problem statement seems weird. We tested it with an absurd prompt – an F1 car at “5% of walking speed.” The model correctly recognized the absurdity, stated its interpretation, and asked for clarification. This works.

What’s inconsistent:

Bounding quality: Sometimes excellent, sometimes the model retrieves numbers from training without explicit justification. The model doesn’t know when it’s doing bounding well versus when it’s pulling data without reasoning. The numbers are often correct, but the reasoning isn’t transparent – you can’t audit the thinking or learn from the process.

What almost never triggers:

Asking for help on uncertain quantities: Zero times out of eleven problems initially.

As I noted in my evaluation:

“Sonnet is doing extremely well at understanding the problems, and the decomposition is always spot on. The answers are very reasonable, often close to Weinstein’s. However, its bounding is weak. Sometimes it gets it excellently, but more often than not, it gets maybe one bound but completely misses another. And it does not know it does, so it just pulls data out of nowhere, rather than asking.”

That last part is crucial: it doesn’t know that it doesn’t know.

The attempted fix

We tried to solve this. We added a law (LAW-FLAG) requiring the model to classify every estimate:

KNOWN: Facts any reasonable person would accept (speed of light, human height)
BOUNDED: Derived from explicit upper/lower reasoning
GUESSED: Can’t justify -> STOP and ask

Our first version failed. On a neutron star problem, the model classified “neutron star mass ~ 1.4 solar masses” as KNOWN. Technically it’s in the training data, but could you justify that to a skeptic who isn’t an astrophysicist?

We tightened the language: “KNOWN applies only to quantities you could justify to a skeptical non-specialist.”

This worked… once. On a Yellowstone supervolcano problem, the model stopped and asked for the mass of magma. Progress! But on an astrophysics problem (what would kill us first if the Sun went supernova), it plowed ahead with “KNOWN from supernova theory” and “KNOWN from particle physics.”

Three tests, one success. The fix isn’t reliable.

The evolution summarized

Capability	GPT-3.0 (2023)	Sonnet 4.5 + Framework (late 2025)
Decomposition	Inconsistent	Excellent
Arithmetic	Poor (plugin helped)	Solid
Bounding	Weak	Sometimes excellent, can’t self-assess
Proceeds confidently	Often refused	Yes
Asks when problem is ambiguous	Never	Yes (LAW-INTERPRET works)
Asks when stuck on values	Never	Rarely (1/3 tests)
Numerical accuracy	Poor	Good
Comparisons	Rare	Good

The gap has narrowed significantly. What remains is the hardest part: metacognition about its own uncertainty. And I’ll be honest-bounding is at least as important as decomposition in Fermi’s approach. Without reliable bounding and self-awareness, the model gets good answers but can’t teach you how it got them or give you confidence about why they’re reasonable.

Where this fits in the research

More recently, I found out that researchers at Allen AI found that fine-tuned LLMs were off by two orders of magnitude on average when solving Fermi problems (Kalyan et al., 2021). Our framework shows similar patterns: decomposition is now essentially solved (perfect scores), and numerical accuracy is much improved (most answers within 10x).

But the deeper problem remains unsolved. The model doesn’t know what it doesn’t know. It produces bounds when it has familiar anchors (everyday quantities, mathematical relationships), but pulls numbers from nowhere when facing exotic physics – and doesn’t recognize the difference. It never asks for help, even when it should. Recent work on LLM calibration confirms this: models are systematically overconfident, with nominal 99% confidence intervals covering truth only 65% of the time (Epstein et al., 2025).

We’ve made progress on the methodology of Fermi estimation. The metacognition gap – knowing when you’re guessing-remains open.

Is the framework worth it?

That depends on what you want. If you just need a rough estimate, modern Sonnet can produce decent answers with minimal prompting (7.9/10). But if you want Fermi-style reasoning – methodical, transparent, bounded estimation – then yes, the structure matters.

Yet the framework alone isn’t the full solution. Throughout this project, reflection was the critical ingredient: challenging unjustified assertions, asking “could you defend that bound to a skeptic?” Catching when the model should have asked for help but didn’t.

The framework makes reasoning visible. Reflection makes it rigorous.

And that reflection layer – currently human, potentially multi-agent in the future – is what Part 3 will explore.

What’s coming next

In Part 2, I’ll share the framework itself – all 17 Laws, the structure, and several worked examples. I’ll show you what works reliably and what we tried to fix.

But I’ll also share what I eventually realized. Throughout this whole project, there was already a “reflection agent” catching assertions without reasoning and challenging unjustified claims. Asking “could you really justify that to a skeptic?” Flagging when the model should have asked for help.

It was me. The human in the loop, with enlisted help from Claude.

In Part 3, we’ll explore what that means. If the model can’t reliably judge its own uncertainty, maybe the solution isn’t better prompting – it’s separating the tasks. One agent estimates. Another agent reflects. That’s the architecture I was already using before I figured it was a “thing”.

Andrew Ng's X post on Agents — Agent vs. Agentic reasoning

A confession

While drafting this post, I asked Sonnet (different instance) to help write an opening example – a bullet fired from Los Angeles, could it reach you in San Diego? Sonnet wrote “the bullet stops in about 2 kilometers” without showing any derivation.

When I pushed back, it admitted: “I just did what we’re critiquing – presented a number without showing the work.”

Then we tried to verify it together. Constant deceleration gives roughly 600 meters – I verified this with ballistic calculators. Where did that 2 km come from? We still don’t know.

That’s why I replaced the bullet problem with the piano tuner question – something we could verify. And that’s why this work matters.

Stay tuned.

References

Bergstrom, C. T., & West, J. D. (2020). Calling Bullshit: The Art of Skepticism in a Data-Driven World. Random House.

Epstein, E. L., Winnicki, J., Sornwanee, T., & Dwaraknath, R. (2025). LLMs are Overconfident: Evaluating Confidence Interval Calibration with FermiEval. arXiv preprint arXiv:2510.26995.

Kalyan, A., Kumar, A., Chandrasekaran, A., Sabharwal, A., & Clark, P. (2021). How Much Coffee Was Consumed During EMNLP 2019? Fermi Problems: A New Reasoning Challenge for AI. arXiv preprint arXiv:2110.14207.

Weinstein, L. (2012). Guesstimation 2.0: Solving Today’s Problems on the Back of a Napkin. Princeton University Press.

Weinstein, L., & Adam, J. A. (2008). Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin. Princeton University Press.

Wolfram, S. (2023). ChatGPT Gets Its “Wolfram Superpowers”! Stephen Wolfram Writings. Retrieved from https://writings.stephenwolfram.com/2023/03/chatgpt-gets-its-wolfram-superpowers/

Picobot Revisited: Optimizing a Tiny Robot’s Rules, Ten Years Later

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Posted on January 31, 2026 by matteomycarta

A decade-old folder, handwritten notes, and a deceptively simple robot.

Introduction

Wrapping up a third personal fun project in two months? Check!! And this is the longest-standing one, and possibly one of my favourite ever. It goes back to when I was barely past the first steps into my exploration of both Python, and Computer Science. This project was fun because it had to do with solving puzzles. I am happy to share it with you, my readers, today.

If you’ve ever watched a Roomba bump into a wall, spin around, and trundle off in a seemingly random direction, you’ve witnessed a real-world version of the problem I’m about to describe. How does a robot that can only sense what’s immediately around it — no map, no memory of where it’s been, no grand plan — manage to cover every square inch of a room?

In January 2015, I was working through Harvey Mudd College’s “CS for All” materials on my own — no live instruction, no solutions to check against — and I encountered Picobot: a simulated robot even simpler than a Roomba. Picobot became one of my favourite puzzles. I scribbled diagrams, wrote copious amounts of notes, tested rules, and eventually optimized my solutions down to what I believed were the minimum number of rules needed to cover the whole room. I kept everything into a well-worn file folder. This was my very first serious dab into CS, and I loved it!

That folder has survived multiple reorganizations over the years – every once in a while I’d open it, think about writing it up properly, and close it again. But, after positive experience wrapping up projects collaboratively with Claude — the colormap app, the Mill’s Methods post — Picobot was next in line.

With the help of Claude Opus (v 4.5) I verified those old solutions, built a Python simulator, and finally documented the work properly.

This post is about the optimization journey. The reasoning. The moments when things click.

What is Picobot?

Picobot is a pedagogical robot created for Harvey Mudd’s introductory computer science course. It lives in a grid world and has one job: visit every empty cell. The catch? Picobot is nearly blind.

The Constraints

Picobot can only sense its four immediate neighbours: North, East, West, and South. For each direction, it knows one thing: is there a wall, or is it empty? That’s it. No memory of where it’s been. No coordinates. No global view.

Here’s an example of what Picobot “sees”:

    N
  W ● E    ←  Picobot sees: N=empty, E=wall, W=empty, S=empty
    S

We encode this as a 4-character string: xExx

x means empty (nothing there)
N, E, W, or S means wall in that direction
Position order is always: North, East, West, South

So xExx means “wall to the East, everything else empty.”

The Rules

Picobot follows rules that say: “If I’m in this state and I see this pattern, then move this direction and switch to this state.”

The format is:

STATE  SURROUNDINGS -> MOVE  NEW_STATE

For example:

0 Nx** -> E 1

This means: “In State 0, if there’s a wall to the North and East is empty, move East and switch to State 1.”

The wildcard * matches anything:

0 x*** -> N 0

“In State 0, if North is empty (don’t care about the rest), move North and stay in State 0.”

There’s also a special move: X (stay put). The robot doesn’t move but can change state. This seems useless at first. It’s not.

The Goal

Write the smallest set of rules that makes Picobot visit every empty cell in a room, regardless of where it starts.

The Harvey Mudd Picobot lab posed two main challenges, below, and several optional one.

Empty Room: A rectangular room with walls only on the boundary
Maze: A maze with single-cell-wide corridors

The lab simulator is actually still live at https://www.cs.hmc.edu/picobot/

Give it a shot, it’s fun!

Back to the story.

The Empty Room: From 7 to 6 Rules

The Strategy: Boustrophedon

The word comes from Greek: “ox-turning.” It’s how you plow a field — go one direction, turn around at the end, come back the other way. Mow a lawn. a line of text, then the next (if you are Etruscan).

For Picobot, the boustrophedon pattern looks like this:

The robot sweeps East, drops down, sweeps West, drops down, repeats. But first, it needs to get to the top of the room — so it goes North until it hits the wall.

My Initial Solution: January 6, 2015

I have an email I sent to myself at 12:44 AM on January 6, 2015 — working late (on a Tuesday night!!!) on this puzzle. It shows my first experiments:

First experiment: go to origin:
# go to origin
0 **** -> X 3
3 ***x -> S 3
3 ***S -> W 2 
2 **x* -> W 2
2 **W* -> X 0

And then my first complete solution:

Final solution program 1
0 x*** -> N 0     # (initial) state 0 with nothing N: go N
0 Nx** -> E 1     # state 0 with a wall N but none E: go E, AND

1 *x** -> E 1     # state 1 with nothing E: go E
# OR, instead of previous 2. This is if initially by E wall
0 NE** -> W 2     # state 0 with a wall N and one E: go W

# once it reaches east wall
1 *E** -> W 2     # state 1 with a wall E: go W
2 **x* -> W 2     # state 2 with nothing W: go W
2 **W* -> S 1     # state 2 with a wall W: go S

That’s 7 rules. The comments show my thinking — I was handling the case where Picobot starts by the East wall separately.

The Harvey Mudd lecture slides posed an extra challenge: “how FEW rules can you use? The current record is six rules” The solution wasn’t shown — just the target. That became the question that hooked me: how do you get there? I was one rule away

The Insight: “C and F Are the Same”

My handwritten notes show positions labelled A through F, representing different situations Picobot might encounter. The breakthrough came when I realized:

Position C (just finished going North, need to decide: East or West?) and Position F (at a wall during the sweep, need to decide direction) were being handled by separate rules — but they didn’t need to be.

The key insight: after going North and hitting the wall, I don’t need a separate rule to check East. I can use the X move (stay put) to transition to State 1, and let State 1’s existing rules handle it.

This is counter-intuitive. The X move looks like wasted time — the robot just sits there! But it’s not wasted. It’s a state transition without movement that lets me reuse existing rules instead of duplicating logic.

The Final Solution: January 24, 2015

Eighteen days later, I emailed myself the optimized solution — Saturday, January 24, 2015 at 5:05 PM (weekend fun work):

# Optimized EMPTY ROOM program:
0 x*** -> N 0
0 N*** -> X 1
1 *x** -> E 1
1 *E** -> W 2
2 **x* -> W 2
2 **W* -> S 1

Six rules. Let me walk through why this works:

State 0 handles “going North.” When Picobot hits the North wall, it executes X 1 — stays put but switches to State 1. Now State 1 takes over.

State 1 is dual-purpose:

If East is empty → go East (continuing the sweep)
If East is wall → start going West (end of row)

Because Picobot stays put when transitioning from State 0 to State 1, it’s in the exact same position, and State 1 correctly determines whether to go East or start heading West.

State 2 sweeps West. When it hits the West wall, it goes South and switches back to State 1. Again, State 1 determines: East or end of row?

The elegance is that State 1 does double duty. It handles both “continue going East” and “decide what to do at the end of a row.” The X move is what makes this possible.

Verified

I tested this against all 529 possible starting positions in a 25×25 room. Every single one reaches 100% coverage. Maximum steps: 1,013. The solution works.

The Maze: From 16 to 12 Rules

The maze challenge is different. Corridors are one cell wide. There are dead ends, branches, and loops. The boustrophedon strategy won’t work here.

The Strategy: Right-Hand Wall Following

The classic maze-solving algorithm: keep your right hand on the wall and walk. You’ll eventually visit everywhere (in a simply-connected maze).

For Picobot, “right hand on wall” translates to:

If you can turn right, turn right
Otherwise, if you can go forward, go forward
Otherwise, if you can turn left, turn left
Otherwise, turn around (dead end)

With four directions (North, East, West, South) and the “right-hand” rule relative to each, we need four states — one for each direction Picobot is “facing.”

State 0: Going North (right hand on East wall)

State 1: Going East (right hand on South wall)

State 2: Going West (right hand on North wall)

State 3: Going South (right hand on West wall)

Initial Solution: 16 Rules

The straightforward implementation uses 4 rules per state:

# State 0: Facing North (right hand = East)
0 *x** -> E 1      # Can turn right → turn right (now facing East)
0 *Ex* -> N 0      # Can't turn right, but forward is open → go North
0 *EW* -> W 3      # Can't go forward → turn left (face West)  
0 *EWS -> S 2      # Dead end → turn around (face South)

# ... and similarly for States 1, 2, 3

16 rules total. It works. But can we do better?

Two-Phase Optimization

My maze notes show two distinct approaches:

Phase 1: Working from principles. The small diagram in my notes shows me reasoning about the state transitions theoretically. What’s the minimum information needed at each decision point? Where is there redundancy?

Phase 2: Empirical debugging. The large diagram shows positions A through K — specific spots in a maze where I tested rules. When the principled approach hit edge cases, I sketched the situation, walked through it (“what would I do here?”), and translated my intuition into rules.

The note “Key is G” appears on the page. Position G was where the solution got validated — when it handled G correctly, the logic was proven.

The Iteration: A Failed Attempt

That same January 24 email shows me trying to adapt the empty room optimization for the maze — and failing:

This, optimized for maze, does not work. At dead ends it turns around but then it goes to the other end and enters an infinite loop...

The attempt that followed didn’t handle dead ends properly. The robot would turn around, walk to the other end, and loop forever.

The Final Solution

Then, in the same email:

This works!!
0 *x** -> E 1
0 xE** -> N 0
0 NE** -> X 2
1 ***x -> S 3
1 *x*S -> E 1
1 *E*S -> X 0
2 x*** -> N 0
2 N*x* -> W 2
2 N*W* -> X 3
3 **x* -> W 2
3 **Wx -> S 3
3 **WS -> X 1

12 rules: 3 per state instead of 4. A 25% reduction.

The key insight: each state now handles only three cases:

Right is open → turn right
Forward is open → go forward
Both blocked → stay put, rotate to next state (which will check left/behind)

The X move chains states together. If right and forward are blocked, we stay put and try the next state. That state checks its right (our left). If that’s blocked too, it chains again. The sequence continues until we find a way forward.

Verified

Tested against all 287 reachable positions in a 25×25 maze, and all 280 cells in the actual Harvey Mudd lab maze. 100% coverage every time. Here’s one simulation:

The right-hand rule doesn’t just guarantee coverage — it collapses the state space. The rules are ordered to check “right side open” first. In State 0 (facing North), rule 1 asks: is East open? If yes, go East — Picobot never evaluates what’s ahead. That’s how rule ordering implements “keep your hand on the wall.” Different physical positions with the same wall-relationship become equivalent, and that’s what makes 4 states and 12 rules possible. Take a look at the simulations below of the two equivalent positions sketched in my handwritten notes, shown earlier:

Making It Explicit: Starting State Matters

Here’s something worth highlighting — something that’s in the Harvey Mudd lab instructions but easy to overlook.

The 6-rule empty room solution requires Picobot to start in State 0.

The Harvey Mudd simulator always starts in State 0, and the lab materials mention this. Whether I consciously accounted for this in 2015, I don’t remember — I didn’t document it in my notes. But when I built my own simulator in 2025, I could test explicitly: what happens if Picobot starts in State 1 or State 2?

Start State	Initial Direction	Coverage
0	North	100% ✓
1	East	~50% ✗
2	West	~45% ✗

Starting in State 1 or 2, Picobot gets stuck. It begins the East-West sweep from wherever it starts — never going North to reach the top first. The rows above its starting position never get visited.

This isn’t a bug in the solution. It’s a constraint: the boustrophedon pattern assumes you start by going North. The 6-rule minimum only works because State 0 guarantees that first trip to the top wall.

A truly state-agnostic solution — one that works regardless of starting state — would need more rules. The elegance of 6 rules comes from working within the standard initial conditions.

What I Learned

The X move is not wasted time. It’s a state transition that enables rule reuse. This is the key to minimizing rule count.
Different problems, different methods. The empty room yielded to analytical insight (“C and F are the same”). The maze required two phases: principled derivation, then empirical debugging.
Implicit assumptions matter. The starting state requirement was in the lab materials all along, but easy to overlook. Building my own tools made it explicit.
Old projects are worth revisiting. With fresh eyes — and some help — I found new ways to understand and share work I already knew.
How I approached it. Looking back at my notes, I see a pattern that’s familiar from my day-to-day work: diagrams everywhere, positions A-K labeled, “me walking in the maze.” Try something → watch where it fails → sketch that spot → ask “what would I do here?” → translate to rules → repeat. “C and F are the same” collapsed the problem by seeing equivalence the formal notation obscured. The notes weren’t just records — they were how I thought. And 18 days between 7 rules and 6 rules: no rushing, no giving up. This is field scientist methodology applied to computer science. Maybe that’s why I loved it.
There is no free lunch in AI collaboration. This project — both the technical verification and this blog post — would not have been possible without deep understanding of the subject matter. That understanding came from me (the 2015 work, the insights, the diagrams), from the extensive documentation I’d kept, and from all the iterative work we did together. This isn’t “vanilla coding” where you prompt an AI and get a finished product. It’s genuine collaboration: human insight plus AI execution. The AI didn’t optimize Picobot — I did, in 2015. The AI helped me verify, document, and communicate that work in 2025.

Try It Yourself

The full Python implementation is on GitHub: https://github.com/mycarta/picobot-optimizer

Itncludes:

picobot_simulator.py — The core engine
picobot_rooms.py — Empty room and maze generators
picobot_visualizer.py — GIF animation creator
optimized_solutions.py — The 6-rule and 12-rule solutions
test_solutions.py — Exhaustive verification

All documented and ready to explore.

What’s Next

Part 2: How I revisited this project with AI assistance — and what that collaboration actually looked like.

Part 3: Educational materials. Exercises, concept checks, and scaffolded challenges for those learning to code.

The Picobot simulator was created for Harvey Mudd College’s “CS for All” course. My optimization work is from January 2015. Verification, documentation, and visualization were completed in January 2025 with AI assistance.

AI/HI (Human Intelligence) Transparency Statement

Modified from Brewin

Has any text been generated using HI?	Yes
Has any text been generated using AI?	Yes
Has any text been improved or corrected using HI?	Yes
Have any methods of analysis been suggested using HI?	Yes
Have any methods of analysis been suggested using AI?	Yes
Do any analyses utilize AI technologies, such as Large Language Models, for tasks like analyzing, summarizing, or retrieving information from data?	Yes

Additional context:

The Picobot optimization work described in this post — the solutions, the insights, the handwritten diagrams, the reasoning behind “C and F are the same” and “Key is G” — was done entirely by me in January 2015, working alone through Harvey Mudd’s CS for All materials with no live instruction and no solutions to check against. The emails quoted in this post are timestamped records from that work.

In January 2025, I revisited this project with Claude AI (Anthropic). Claude built the Python simulator, ran exhaustive verification tests, created the GIF visualizations, and helped document the reasoning. The explicit testing of starting states emerged from our joint exploration — I asked the question, Claude ran the tests.

This post was drafted collaboratively. I provided the source materials (my 2015 notes, emails, the verified solutions, our session transcripts), direction, and editorial judgment throughout. Claude drafted based on these inputs and our discussion of structure and framing. I reviewed, revised, and made all final decisions about what went to publication.

A note on AI collaboration: This kind of work is not “vanilla coding” — prompting an AI and receiving a polished output. It required deep domain knowledge (mine), extensive primary documentation (my 2015 notes and emails), iterative correction (many rounds), and genuine intellectual engagement from both sides. The AI contributed too — not the original insights, but meta-insights: recognizing patterns in my notes, naming things I’d done but hadn’t articulated (like “C and F are the same” as a key moment), and seeing that I’d used different methodologies for the empty room versus the maze. The AI did not and could not have done this alone. Neither could I have done the verification, visualization, and documentation at this scale without AI assistance. That’s what real collaboration looks like.

The intellectual work is mine. The documentation, verification, and articulation is collaborative.

Modernizing Python Code in the AI Era: A Different Kind of Learning

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Posted on January 24, 2026 by matteomycarta

A few years ago I wrote about advancing my Python coding skills after working through a couple of chapters from Daniel Chen’s excellent book Pandas for Everyone. In that post I showed how I improved code I’d written in 2018 for the SEG Machine Learning contest. The original code used unique() to get lists of well names, then looped through with list comprehensions to calculate flagged samples and proportions. The 2020 version replaced all that with groupby() and apply(), making it much more compact and Pythonic. For example, where I’d written a list comprehension like [result_a.loc[result_a.zone==z,'flag'].sum() for z in zones_a], I could now write simply result_a.groupby('zone', sort=False).flag.sum().values. The runtime also improved – from 86ms down to 52ms. I remember being quite happy with how much cleaner and more readable the code turned out, and how the learning from those two chapters made an immediate practical difference.

Recently, I had to modernize the Busting bad colormaps Panel app, which I built back in 2020 to demonstrate colormap distortion artifacts (something that – as you know – I care a lot about). The app had been deliberately frozen in time – I’d pinned specific library versions in the environment file because I knew things would eventually become obsolete, and I wanted it to stay functional for as long as possible without having to constantly fix compatibility issues.

But some of those issues had finally caught up with me, and the app had ben down for soem time. Last fall, working with Github copilot, I fixed some matplotlib 3.7+ compatibility problems – replace the deprecated cm.register_cmap() with plt.colormaps.register(), fix anrgb2gray error, and resolve a ValueError in the plotting functions.

But the deployment was also broken. In 2021, mybinder.org had switched to JupyterLab as the default interface, changing how apps needed to be deployed. Panel developers had to adapt their code to work with this new setup. The old Panel server URL pattern no longer worked. I tried to figure out the new URL pattern by browsing through the Binder documentation, but I couldn’t make sense of it and failed miserably. It was a short-lived effort that pushed me toward trying something different: full-on coding with Claude Opus 4.5 using Copilot in VSCode.

That’s what allowed me, this month, to complete the modernization process (though honestly, we still haven’t fully sorted out a Binder timeout issue).

A step back to 2020: Building the app from scratch

When I originally built the colormap app, I coded everything myself, experimenting with Panel features I’d never used before, figuring out the supporting functions and visualizations. I also got very good advice from the Panel Discourse channel when I got stuck.

One issue I worked on was getting the colormap collection switching to behave properly. After the first collection switch, the Colormaps dropdown would update correctly, but the Collections dropdown would become non-responsive. With help from experts on the Discourse channel, I figured out how to fix it using Panel’s param.Parameterized class structure.

2026: Working with Claude

The second, and hardest part of the modernization was done almost entirely by Claude Opus. Here’s what that looked like in practice:

Binder deployment: Claude independently figured out the new JupyterLab URL pattern (?urlpath=lab/tree/NotebookName.ipynb instead of the old ?urlpath=%2Fpanel%2FNotebookName). Only later, when fact-checking for this post, did we discover the history of Binder’s 2021 switch to JupyterLab and how Panel had to adapt. This helped, though we’re still working through some timeout issues.

Environment upgrade: Claude upgraded to Python 3.12 and Panel 1.8.5, bringing everything up to modern versions. The key packages are now Panel 1.8.5, param 2.3.1, and bokeh 3.8.1.

Code modernization: Claude spotted and fixed deprecated API calls – the style parameter for Panel widgets became styles.

Collection switching – Claude’s breakthrough: This was Claude’s biggest solo contribution. The collection switching broke during the update, and Claude independently diagnosed that the class-based param.Parameterized approach that had worked in Panel 0.x wasn’t reliable in Panel 1.x. Without me having to guide the solution, Claude figured out how to rewrite it using explicit widgets with param.watch callbacks.

The comparison shows the change:

The new approach uses explicit widget objects with callback functions, which works more reliably in Panel 1.x than the class-based parameterized approach.

New features: Claude integrated two new colormap collections I’d been wanting to add for years – Fabio Crameri’s scientific colormaps (cmcrameri) and Kristen Thyng’s cmocean colormaps. That brought the total from 3 to 5 colormap collections.

Here are examples of the app showing each of the new collections:

The app testing of **cmocean deep** colormap

The app testing of Crameri’s **batlow** colormap

Documentation: Claude updated the README with detailed step-by-step Binder instructions, added a troubleshooting section, and created a table documenting all five colormap collections.

I provided the requirements and guidance throughout, but I almost never looked at the implementation details – what I’ve taken to calling the “bits and bobs” of the code. I focused on what I needed to happen, Claude figured out how to make it happen.

What changed (and what didn’t)

I still understand what the code does conceptually. I can read it, review it, check that it’s correct. I know why we needed to move from Parameterized classes to explicit widgets, and I understand the reactive programming model. But I didn’t write those lines myself.

The work happens at a different level now. I bring the domain expertise (what makes a good colormap visualization), the requirements (needs to deploy on Binder, needs these specific colormap collections), and the quality judgment (that widget behavior isn’t quite right). Claude brings the implementation knowledge, awareness of modern best practices, and the ability to quickly adapt code patterns to new frameworks.

This is really different from my 2020 experience. Back then, working through those Pandas patterns taught me techniques I could apply to other projects. Now, I’m learning what becomes possible when you can clearly articulate requirements and delegate the implementation.

The honest trade-off

There’s a trade-off here, and I’m trying to be honest about it. In 2020, working through the Panel widget patterns taught me things that stuck. In 2026, I got working, modernized code in a fraction of the time, but with less hands-on knowledge of Panel 1.x internals.

For this particular project, that trade-off made sense. I needed a working app deployed and accessible, not deep expertise in Panel migration patterns. But I’m conscious that I’m optimizing for different outcomes now: shipping features fast versus building deep technical understanding through hands-on work.

What this means going forward

After years of writing code line by line, this new way of working feels both efficient and different. I got more done in a couple of hours than I might have accomplished in several weeks working solo. The app is modernized, deployed, working better than ever, and even has new features I’d been wanting to add for years.

This has been a gamechanger for how I work. I still do the work that matters most to me: seeing the tool gap, coming up with the vision, iteratively prototyping to flesh out what I actually need. That’s substantial work, and it’s mine. But after that initial phase? A lot of the implementation will be done with Claude. The app is done and it’s great, and I know this is the path forward for me.

References

Chen, D.Y. (2018). Pandas for Everyone: Python Data Analysis. Addison-Wesley Professional.

Crameri, F. (2018). Geodynamic diagnostics, scientific visualisation and StagLab 3.0. Geoscientific Model Development, 11, 2541-2562. https://www.fabiocrameri.ch/colourmaps/

Niccoli, M. (2020). Keep advancing your Python coding skills. MyCarta Blog. https://mycartablog.com/2020/10/22/keep-advancing-your-python-coding-skills/

Thyng, K.M., Greene, C.A., Hetland, R.D., Zimmerle, H.M., and DiMarco, S.F. (2016). True colors of oceanography: Guidelines for effective and accurate colormap selection. Oceanography, 29(3), 9-13. https://matplotlib.org/cmocean/

Try the app yourself: The modernized colormap distortion app is available on GitHub and you can run it in Binder without installing anything.

The value of intellectual play: Mill, machine learning, and a drilling problem I couldn’t stop thinking about

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Posted on January 20, 2026 by matteomycarta

A few years back, I watched a CSEG talk by Lee Hunt (then at Jupiter Resources) called Value thinking: from the classical to the hyper-modern. One case study in particular stuck with me—so much so that I ended up exploring it in a Jupyter Lab notebook, bringing it up in a job interview, and eventually testing whether an AI could reason through it on its own.

This post is about that journey. It’s also about what happens when you let yourself get genuinely curious about someone else’s problem. And—fair warning—it involves a 19th-century philosopher, a seven-well dataset, and a neural network that learned to distrust AVO attributes.

The problem

Jupiter Resources had a history of occasionally encountering drilling trouble in the Wilrich reservoir—specifically, loss of circulation when encountering large systems of open fractures. Mud loss. The kind of problem that can cost you a well.

They had done extensive geophysical work with multiple seismic attributes that, in theory, should correlate with fractures: Curvature, Coherence, AVAz (amplitude variation with azimuth), VVAZ (velocity variation with azimuth), and Diffraction imaging. But they lacked direct calibration data for the drilling problem, and some of the attributes were giving conflicting results.

Lee Hunt, who led the team and the geophysical work, suspected from the start that the AVO-based attributes might be compromised. He had seen evidence as far back as 2014 that AVAz and VVAZ responses in the Wilrich were dominated by an overlying coal, not the fractures themselves—the attributes were measuring a different geological signal entirely. Diffraction imaging was planned early as a complementary measure, precisely because it might not be affected by the coals in the same way (personal communication).

Seven wells. Five attributes. Four of the wells had experienced drilling problems; three had not. Here’s the data:

The question: which attribute—or combination—could reliably predict drilling problems, so that future wells could be flagged ahead of time?

Mill’s Methods: 19th-century philosophy meets drilling risk

Rather than accept uncertainty and provide no geophysical guidance at all, the team at Jupiter tried something different: Mill’s Methods of Induction. Their goal was to find a pattern that could help them advise the operations team—flag high-risk well locations ahead of time so contingency plans could be in place. Mill’s Methods are a set of logical procedures for identifying causal relationships, laid out by philosopher John Stuart Mill in 1843. They’re often illustrated with a food poisoning example (who ate what, who got sick), but they work just as well here.

This approach was characteristic of Lee Hunt’s attitude toward quantitative geophysics—an attitude I had come to admire through his other work. A few years earlier, he had published a CSEG Recorder column called “Many correlation coefficients, null hypotheses, and high value,” a tutorial on statistics for geophysicists that included synthetic production data and an explicit invitation: “You can do it, too. Write in to tell us how.”

I took him up on it. I worked through his examples in Jupyter notebooks, built visualizations, explored prediction intervals, learned a good deal of scientific computing along the way. I reached out to him about the work. I even wrote up some of that exploration in a blog post on distance correlation and variable clustering—the kind of technical deep-dive where you’re learning as much about the tools as about the data. That extended engagement gave me a feel for his way of thinking: understand the statistics, accept the uncertainty, improve your techniques if you can—but don’t just throw up your hands when the data is messy.

Method of Agreement: Look at all the problem wells (A, B, F, G). What do they have in common? Curvature is TRUE for all four. So is Diffraction imaging. The other attributes vary.

Method of Difference: Compare problem wells to non-problem wells (C, D, E). Neither Curvature nor Diffraction alone perfectly discriminates—Well E has Curvature TRUE but no problem; Well D has Diffraction TRUE but no problem.

Joint Method: But here’s the key insight—Curvature AND Diffraction together form a perfect discriminator. Every well where both are TRUE had problems. Every well where at least one is FALSE did not.

This wasn’t a claim about causation. It was a decision rule: when the next well location shows both high curvature and diffraction anomalies, flag it as elevated risk and ensure contingency protocols are in place.

The logic is sound because of asymmetric costs. Preparing for mud loss (having lost circulation material on site, adjusting mud weight plans) is a minor expense. Not preparing when you should have—that’s where you lose time, money, sometimes the well. You don’t need certainty to justify preparation. You need a defensible signal.

What a neural network learned

I wanted to see if a data-driven approach would arrive at the same answer. Looking at the table myself, and spending some time applying Mill’s Methods, I had already seen the pattern—Curvature and Diffraction together were the key predictors. But I was curious: what would a simple neural network learn on its own?

I trained a two-layer network (no hidden layer)—mathematically equivalent to logistic regression—on the same seven wells. (Yes, seven wells. I know. But stay with me.)

The network classified all seven wells correctly. But the real insight came from the weights it learned:

Attribute	Weight
Curvature	+14.6
Diffraction	+9.7
Coherence	~0
AVAz	−4.9
VVAZ	−14.5

Curvature and Diffraction were strongly positive—predictive of problems. Coherence contributed almost nothing. But AVAz and VVAZ were negative—the network learned to suppress them.

A way to think about negative weights: imagine training a network to identify ducks from a set of photos that includes birds, ducks, and people in duck suits. The network will learn to weight “duck features” positively, but also to weight “human features” negatively—to avoid being fooled by the costumes. In the Wilrich case, the AVAz and VVAZ attributes were like duck suits: they looked like fracture indicators, but they were actually measuring something else.

This was interesting. All five attributes have theoretical justification for detecting fractures. Why would the network actively discount two of them?

When I mentioned this result to Lee Hunt, he confirmed what he had long suspected (personal communication): the AVAz and VVAZ responses in the Wilrich were dominated by an overlying coal, not the fractures themselves. He had measured this effect and documented it in a 2014 paper, where multiple attributes—including AVAz—showed statistically significant correlations to coal thickness rather than to reservoir properties. The neural network had learned, from just seven data points, to suppress exactly the attributes that Lee’s domain knowledge had already flagged as problematic.

This is Mill’s Method of Residues in action: if you know something else causes an observation, subtract it out. And it’s a reminder that domain knowledge and data-driven methods can converge on the same answer when both are applied honestly. I found this deeply satisfying.

What the AI got right—and what it missed

More recently, I revisited this problem using ChatGPT with the Wolfram plugin. I wanted to see if an AI, given just the table and a prompt about Mill’s Methods, could reason its way to the same conclusions.

It did—mechanically. It correctly identified Curvature and Diffraction as the consistent factors among problem wells. It noted that neither attribute alone was a perfect discriminator. It even offered to run logistic regression.

But it missed the interpretive leap. It hedged with phrases like “although there are exceptions” when in fact there were no exceptions to the conjunction rule. And it didn’t articulate the pragmatic framing: that the goal wasn’t to find the true cause, but to build a defensible decision rule under uncertainty.

That framing—the shift from epistemology to operations—required domain knowledge and judgment. The AI could apply Mill’s Methods. It couldn’t tell me why that application was useful here.

Drafting this post, I worked with a different AI—Claude—and found the collaboration more useful in a different way: not for solving the problem, but for reflection. Having to explain the context, the history, the why of my interest helped me articulate what I’d been carrying around in my head for years. Sometimes the value of a thinking partner isn’t in the answers, but in the questions that force you to be clearer.

Why this stuck with me

I’ll be honest: I kept thinking about this problem for years. It became part of a longer arc of engagement with Lee’s work—first the statistics tutorial, then the Wilrich case study, each building on the last.

When I interviewed for a geophysics position (Lee was retiring, and I was a candidate for his role), I mentioned this case study. I pulled out a pen and paper and wrote the entire seven-well table from memory. They seemed impressed—not because memorizing a table is hard, but because it signaled that I’d actually enjoyed thinking about it. That kind of retention only happens when curiosity is real.

I didn’t get the job. The other candidate had more operational experience, and that was the right call. But the process was energizing, and I’m sure that enthusiasm carried into my next opportunity, where I landed happily and stayed for over six years.

I tell this not to brag, but to make a point: intellectual play compounds. You don’t always see the payoff immediately. Sometimes you explore a problem just because it’s interesting—because someone like Lee writes “You can do it, too” and you decide to take him seriously—and it pays dividends in ways you didn’t expect.

The convergence

Three very different approaches—19th-century inductive logic, a simple neural network, and (later) an AI assistant—all pointed to the same answer: Curvature and Diffraction predict drilling problems in this dataset. The AVO attributes are noise, or worse, misleading.

When three methods converge, you can trust the signal. And you can make decisions accordingly.

That’s the real lesson here: rigorous reasoning under uncertainty isn’t about finding the One True Cause. It’s about building defensible heuristics, being honest about what you don’t know, and updating as new data comes in. Mill understood this in 1843. A neural network can learn it from seven wells. And sometimes, so can an AI—with a little help.

I hope you enjoyed this as much as I enjoyed putting it together.

The original case study was presented by Lee Hunt in his CSEG talk “Value thinking: from the classical to the hyper-modern.” The neural network analysis is in my Geoscience_ML_notebook_4. Lee documented the coal correlation issue in Hunt et al., “Precise 3D seismic steering and production rates in the Wilrich tight gas sands of West Central Alberta” (SEG Interpretation, May 2014), and later reflected on confirmation bias as an obstacle to recognizing such issues in “Useful Mistakes, Cognitive Biases and Seismic” (CSEG Recorder, April 2021). My thanks to Lee for the original inspiration, for confirming the geological context, and for sharing the original presentation materials.

References and Links

Hunt, L., 2013, Many correlation coefficients, null hypotheses, and high value: CSEG Recorder, December 2013. Link
Hunt, L., S. Hadley, S. Reynolds, R. Gilbert, J. Rule, M. Kinzikeev, 2014, Precise 3D seismic steering and production rates in the Wilrich tight gas sands of West Central Alberta: SEG Interpretation, May 2014.
Hunt, L., 2021, Useful Mistakes, Cognitive Biases and Seismic: CSEG Recorder, April 2021.
My neural network analysis: Geoscience_ML_notebook_4
My earlier exploration of Lee’s production data: Data exploration in Python: distance correlation and variable clustering
ChatGPT + Wolfram session on Mill’s Methods: Gist

AI/HI Transparency Statement Modified from Brewin http://www.theguardian.com/books/2024/apr/04/why-i-wrote-an-ai-transparency-statement-for-my-book-and-think-other-authors-should-too

Has any text been generated using AI?	Yes
Has any text been improved or corrected using HI?	Yes

Additional context: This post emerged from a conversation with Claude AI (Anthropic). I provided the source materials (a ChatGPT + Wolfram session, a Jupyter notebook, personal history with the problem), direction, and editorial judgment throughout. Claude drafted the post based on these inputs and our discussion of structure, voice, and framing. I reviewed multiple draft, revised as needed, rewrote some key sections, and made all final decisions about what went to publication. The core analysis—Mill’s Methods, the neural network, the interpretation—was done by me years before this collaboration; the AI’s role was in helping articulate and structure that work for a blog audience.

ChatGPT as an essay-writing assistant – Part III

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Posted on January 11, 2026 by matteomycarta

The Challenge of a Satisfying Conclusion

When I published Part II of this series back in February 2025, I had a plan for Part III. Show the prompts I used, analyze the time investment, evaluate the result against Part I’s GPT-3.5 baseline, maybe try one more iteration with even newer tools. Straightforward. Methodical.

But I never finished it. To be honest, I lost interest. Another marginally better AI-generated essay wasn’t going to cut it—not for me, and probably not for you readers either. Another iteration showing GPT-4.5 writes slightly better than GPT-4? That’s predictable, uninspiring… so I dropped it.

But the unfinished series sat there in the back of my mind. I wasn’t actively working on it, but I also couldn’t quite let it go. It created a kind of block—I found myself not writing about anything at all, partly because this felt incomplete, partly because my interests had genuinely shifted elsewhere.

Recently though, I came back to this question. Not because I wanted to complete the series for completeness sake, but because I wanted to understand what would actually make Part III worthwhile.

So I asked for help. I brainstormed with Claude (Anthropic’s AI) about what Part III should actually be about—what would make it worth writing and worth reading. And something clicked.

What Was the Question Really Asking For?

Looking back now, with decades between me and that moment in Professoressa Carbone’s classroom, I think I understand what she was asking for. She wasn’t looking for recitation of Plato’s philosophy mechanically applied to medieval warfare. She wanted to see if I could reason using philosophical frameworks in unfamiliar territory. Synthesis, not facts. Thinking, not performing memorization.

At 15, I wasn’t ready for that. I had volunteered for the oral examination thinking I could rely on prepared material about Plato’s recent lessons. Instead, she cut through my preparation with a single question that required genuine philosophical thinking: “What would Plato have thought about the Hundred Years’ War?”

It was a brilliant pedagogical move. It required understanding Plato’s ideas deeply enough to apply them to a completely different context—a context Plato never encountered, in a historical period he never knew. It required the kind of intellectual flexibility and reasoning that, honestly, I didn’t have yet.

The humiliation I felt wasn’t really about not knowing facts. It was about being exposed as someone trying to get by on memorization rather than understanding. And I think she knew it. She saw through my bluff.

So What Would Satisfy?

This brings me back to the problem of Part III. Showing that AI can now generate a more sophisticated-sounding essay than my 15-year-old self could produce doesn’t prove anything interesting. AI is very good at generating sophisticated-sounding content. That’s almost the problem.

What would actually satisfy—both as closure for this series and as something worth your time reading—is demonstrating the kind of reasoning Professoressa Carbone was asking for. Can I, now, with the benefit of intellectual maturity and AI assistance, actually think through what Plato might have thought about prolonged warfare between nations? Not just string together plausible-sounding paragraphs with proper citations, but engage in genuine philosophical reasoning?

What Would That Actually Look Like?

If I were to actually write that essay—the one demonstrating real philosophical reasoning rather than AI-generated content—what would it need?

Looking back at the GPT-4 essay from Part II, it has proper citations and coherent structure, but it’s superficial. It lists Platonic concepts (philosopher-kings, guardians, ideal states) and applies them mechanically to medieval warfare. That’s exactly the kind of recitation Professoressa Carbone was testing me against.

Real reasoning would require:

Connecting Plato’s specific ideas to specific events or decisions during the Hundred Years’ War—not just general principles applied generally
Exploring how Plato’s concepts might actually illuminate something about prolonged conflict between nations that we wouldn’t see otherwise
Considering contemporary interpretations or modern applications—what do we learn about conflict, governance, or political philosophy from this exercise?
Drawing genuine insights about both Plato and warfare, not just restating both

That’s the essay I’d want to write someday. Not as an academic exercise, but as personal closure—proving to myself I can do the kind of thinking she was asking for.

Closure for Now

But that’s not this post. This post is about giving you, the readers, closure on this series. About acknowledging honestly what I learned about AI as a writing assistant, and why simple iteration wasn’t the answer.

Here’s what I’ve learned:

AI is excellent at generating plausible content. GPT-4 produced an essay that looks credible—proper structure, citations, coherent arguments. For many purposes, that’s enough.

But AI doesn’t reason, it recognizes patterns. The essay from Part II strings together familiar ideas in familiar ways. It’s sophisticated pattern matching, not thinking. It can’t do what Professoressa Carbone was asking for: genuine synthesis that produces new insight.

The real value of AI as a writing assistant isn’t in replacing thinking—it’s in supporting it. AI can help with research, organization, articulation. It can reduce cognitive load so you can focus on the hard part: the actual reasoning. But you still have to do the reasoning.

Writing with AI requires clarity about what you’re trying to accomplish. If you want content generation, AI does that well. If you want thinking support, you need to know what thinking you’re trying to do. The tool can’t figure that out for you.

This series started with a simple question: can AI help me write an essay? The answer turned out to be more nuanced than I expected. It depends entirely on what kind of essay, and what role you want AI to play. For the essay I’d need to write to truly answer Professoressa Carbone’s question—the one that demonstrates reasoning rather than recitation—AI could help, but it couldn’t do the essential work.

Maybe someday I’ll write that essay. For now, I’m moving on to other projects where I’m excited about what AI can do: document extraction in geoscience, agentic workflows, problems where AI’s strengths align better with what I’m trying to accomplish.

Thank you for following this journey with me. Even if it didn’t end where I originally planned, I learned something worth sharing.

A Final Thought: Rigor Without Brutality

I started this series partly because of concerns about AI in education—concerns rooted in my own experience.

ChatGPT has educators calling for more in-class writing and oral examinations. I agree we need assessment that can’t be faked by AI. But I’m deeply opposed to the brutality that often came with those older systems.

Here’s the thing: the brutality was never necessary for the educational value. Professoressa Carbone’s question was pedagogically brilliant. The public humiliation didn’t make it more effective; it just made it traumatic.

We need assessment methods that demand genuine reasoning, in environments that support both students and teachers. It’s possible to have rigorous evaluation without breaking people in the process.

AI forces us to confront what we actually value in education: not the appearance of learning, but the development of genuine understanding and reasoning. The question is whether we can build systems that nurture that without the cruelty.

AI/HI Transparency Statement Modified from Brewin http://www.theguardian.com/books/2024/apr/04/why-i-wrote-an-ai-transparency-statement-for-my-book-and-think-other-authors-should-too


Has any text been generated using AI?	Yes
Has any text been improved or corrected using HI?	Yes

Additional context: This post was collaboratively written through an iterative conversation with Claude (Anthropic). The human author provided the direction, constraints, personal context, and decisions about what to include/exclude. The AI assistant drafted text, which was then reviewed and revised based on feedback. Sections were rewritten multiple times to match the author’s voice and intentions. The final editorial decisions, including what content made it to publication, were made by the human author.

10-year anniversary

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Posted on July 15, 2022 by matteomycarta

July 15th, 2022

Dear readers:

I started writing this blog 10 years ago and it is to date one of the things I am the most proud of.

This is a big milestone for me, so I would like to begin with thanking all the people that encouraged me at the beginning, and in particular, for their valiant support and feedback: Matt Hall, Evan Bianco, Oliver Kuhn, Steve Lynch, and last but not least my life partner Rebecca.

A lot of the work I did in the first couple of years was on furthering my understanding, and sharing that with others, of the use of colours in scientific visualization, and how to use better colormaps, for example Perceptual rainbow palette, part a and part b.

I am grateful I achieved those knowledge-sharing goals:

The material is referenced in the matplotlib documentation
The blog has often been used as reference in talks and other publications on colormaps, beginning with this classic matplotlib talk given by Kristen Thyng at scipy 2014
I was thrilled to have received positive feedback on my work by Bernice Rogovitz, someone I hold in very high esteem
Some of that work on the blog resulted in being invited by Matt Hall to write a tutorial for The Leading Edge (SEG). The tutorial came with a Jupyter notebook demonstrating how to evaluate default colour maps and favour more perceptual alternatives
I am particularly proud to see that the article is still ranking in the top 20 most downloaded papers from The Leading Edge (between 2010-2020)
Additionally, the two blog post are to date top results for the #google search “perceptual rainbow” and “perceptual palette images”

Ultimately, I am very happy to have created a space for sharing and exchanging ideas freely.

So, to celebrate these 10 years of MyCarta, I treated it to a new domain, mycartablog.com (but the old domain, and links still work) and a brand new look (it took me a while to get there but I like it a lot) with a theme that should now be responsive for all devices (welcome to the new era Matteo!).

I will also soon publish a short series of short but sweet new posts on colormaps and visualization (and republish on linkedin).

Thank you all for sharing this journey!

Be a geoscience and data science detective

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Posted on September 16, 2020 by matteomycarta

September 16, 2020

Introduction

These days everyone talks about data science. But here’s a question: if you are a geoscientist, and like me you have some interest in data science (that is, doing more quantitative and statistical analyses with data), why choose between the two? Do both… always! Your domain knowledge is an indispensable condition, and so is an attitude of active curiosity (for me, an even more important condition). So, my advice for aspiring geoscientists and data scientists is: “yes, do some course work, read some articles, maybe a book, get the basics of Python or R, if you do not know a programming language” but then jump right ahead into doing! But – please! – skip the Titanic, Iris, Cars datasets, or any other data from your MOOC or that many have already looked at! Get some data that is interesting to you as geoscientist, or put it together yourself.

Today I will walk you through a couple of examples; the first one, I presented as a lightning talk at the Transform 2020 virtual conference organized by Software Underground. This project had in fact begun at the 2018 Geophysics Sprint (organized by Agile Scientific ahead of the Annual SEG conference) culminating with this error flag demo notebook. Later on, inspired by watching the Stanford University webinar How to be a statistical detective, I decided to resume it, to focus on a more rigorous approach. And that leads to my last bit of advice, before getting into the details of the statistical analysis: keep on improving your geo-computing projects (if you want more advice on this aspect, take a look at my chapter from the upcoming Software Underground book, 52 things you should know about geocomputing): it will help you not only showcase your skills, but also your passion and motivation for deeper and broader understanding.

First example: evaluate the quality of seismic inversion from a published article

In this first example, the one presented at Transform 2020, I wanted to evaluate the quality of seismic inversion from a published article in the November 2009 CSEG Recorder Inversion Driven Processing. In the article, the evaluation was done by the authors at a blind well location, but only qualitatively, as illustrated in Figure 5, shown below for reference. In the top panel (a) the evaluation is for the inversion without additional processing (SPNA, Signal Protected Noise Attenuation); in the bottom panel (b) the evaluation is for the inversion with SPNA. On the right side of each panel the inverted seismic trace is plotted against the upscaled impedance well log (calculated by multiplying the well density log and the well velocity log from compressional sonic); on the right, the upscaled impedance log is inserted in a seismic impedance section as a colored trace (at the location of the well) using the same color scale and range used for the impedance section.

Figure 5 caption: Acoustic impedance results at the blind well for data without (a) and with (b) SPNA. The figure shows a 200 ms window of inverted seismic data with well B, the blind well, in the middle on the left, along with acoustic impedance curves for the well (red) and inverted seismic (blue) on the right. The data with SPNA shows a better fit to the well, particularly over the low frequencies.

What the authors reported in the figure caption is the extent to which the evaluation was discussed in the paper; unfortunately it is not backed up in any quantitative way, for example comparing a score, such as R^2, for the two methods. Please notice that I am not picking on this paper in particular, which in fact I rather quite liked, but I am critical of the lack of supporting statistics, and wanted to supplement the paper with my own.

In order to do that, I hand-digitized from the figure above the logs and inversion traces , then interpolated to regularly-sampled time intervals (by the way: if you are interested in a free tool to digitize plots, check use WebPlotDigitizer).

My plan was to split my evaluation in an upper and lower zone, but rather than using the seismically-picked horizon, I decided to add a fake top at 1.715 seconds, where I see a sharp increase in impedance in Figure 5. This was an arbitrary choice on my part of a more geological horizon, separating the yellow-red band from the green blue band in the impedance sections. The figure below shows all the data in a Matplotlib figure:

The first thing I did then, was to look at the Root Mean Square Error in the upper and lower zone obtained using the fake top. They are summarized in the table below:

Based on the RMSE , it looks like case b, the inversion with Signal Protected Noise Attenuated applied on the data, is a better result for the Upper zone, but not for the Lower one. This result is in agreement with my visual comparison of the two methods.

But lets’ dig a bit deeper. After looking at RMSE, I used the updated version of the error_flag function, which I first wrote at the 2018 Geophysics Sprint, listed below:

def error_flag(pred, actual, stat, dev = 1.0, method = 1):
    """Calculate the difference between a predicted and an actual curve 
    and return a curve flagging large differences based on a user-defined distance 
    (in deviation units) from either the mean difference or the median difference
    
Matteo Niccoli, October 2018. Updated in May 2020.
    
    Parameters:
        predicted : array
            predicted log array           
        actual : array
            original log array            
        stat : {‘mean’, ‘median’}
            The statistics to use. The following options are available:
                - mean: uses numpy.mean for the statistic, 
                and np.std for dev calculation
                - median: uses numpy.median for the statistic, 
                and scipy.stats.median_absolute_deviation (MAD) for dev calculation        
        dev : float, optional
            the standard deviations to use. The default is 1.0           
        method : int {1, 2, 3}, optional
            The error method to use. The following options are available
            (default is 1):
                1: difference between curves larger than mean difference plus dev
                2: curve slopes have opposite sign (after a 3-sample window smoothing)
                3: curve slopes of opposite sign OR difference larger than mean plus dev  
    Returns:
        flag : array
        The error flag array
    """   
    
    flag = np.zeros(len(pred))
    err = np.abs(pred-actual)
    
    if stat == 'mean':
        err_stat = np.mean(err)
        err_dev = np.std(err)
    elif stat == 'median':
        err_stat = np.median(err)
        err_dev = sp.stats.median_absolute_deviation(err)
        
    pred_sm = pd.Series(np.convolve(pred, np.ones(3), 'same'))
    actual_sm = pd.Series(np.convolve(actual, np.ones(3), 'same'))
    ss = np.sign(pred_sm.diff().fillna(pred_sm))
    ls = np.sign(actual_sm.diff().fillna(actual_sm))
                  
    if method == 1:
        flag[np.where(err>(err_stat + (dev*err_dev)))] = 1
    elif method == 2:      
        flag[np.where((ss + ls)==0 )]= 1
    elif method == 3:
        flag[np.where(np.logical_or(err>(err_stat + (dev*err_dev)), (ss+ls)==0 ))]= 1
    return flag

I believe this new version is greatly improved because:

Users now can choose between mean/standard deviation and median/median absolute deviation as a statistic for the error. The latter is more robust in the presence of outliers
I added a convolutional smoother prior to the slope calculation, so as to make it less sensitive to noisy samples
I expanded and improved the doctstring

The figure below uses the flag returned by the function to highlight areas of poorer inversion results, which I assigned based on passed to the function very restrictive parameters:

using median and a median absolute deviation of 0.5 to trigger flag
combining the above with checking for the slope sign

I also wrote short routines to count the number and percentage of samples that have been flagged, for each result, which are summarized in the table below:

The error flag method is in agreement with the RMS result: case b, the inversion on Signal Protected Noise Attenuated data is a better result for the Upper zone, but for the Lower zone the inversion without SPNA is the better one. Very cool!

But I was not satisfied yet. I was inspired to probe even deeper after a number of conversations with my friend Thomas Speidel, and reading the chapter on Estimation from Computational and Inferential Thinking (UC Berkeley). Specifically, I was left with the question in mind: “Can we be confident about those two “is better“ in the same way?

This question can be answered with a bootstrapped Confidence Interval for the proportions of flagged samples, which I do below using the code in the book, with some modifications and some other tools from the datascience library. The results are shown below. The two plots, one for the Upper and one for the Lower zone, show the distribution of bootstrap flagged proportions for the two inversion results, with SPNA in yellow, and without SPNA in blue, respectively, and the Confidence Intervals in cyan and brown, respectively (the CI upper and lower bounds are also added to the table, for convenience).

By comparing the amount (or paucity) of overlap between the distributions (and between the confidence intervals) in the two plots, I believe I can be more confident in the conclusion drawn for the Lower zone, which is that the inversion on data without SPNA is better (less proportion of flagged errors), as there is far less overlap.

I am very pleased with these results. Of course, there are some caveats to keep in mind, mainly that:

I may have introduced small, but perhaps significant errors with hand digitizing
I chose a statistical measure (the median and median absolute deviation) over a number of possible ones
I chose an arbitrary geologic reference horizon without a better understanding of the reservoir and the data, just the knowledge from the figure in the paper

However, I am satisfied with this work, because it points to a methodology that I can use in the future. And I am happy to share it! The Jupyter notebook is available on GitHub.

Second example: evaluate regression results from a published article

My second, more recent example, is shorter but no less interesting, in my opinion. It is a case study correlating inversion data to petrophysical estimates of porosity-height in the Doig and Montney Formations in Western Canada (from the paper Tight gas geophysics: AVO inversion for reservoir characterization, Close et al. CSEG Recorder, May 2010, an article which I enjoyed very much reading).

The authors indicated that Vp/Vs and/or Poisson’s ratio maps from seismic inversion are good indicators of porosity in the Lower Doig and Upper Montney reservoirs in the wells used in their study, so it was reasonable to try to predict Phi-H from Vp/Vs via regression. The figure below, from the article, shows one such Vp/Vs ratio map and the Vp/Vs vs. Phi-H cross-plot for 8 wells.

Figure 7 caption: Figure 7. a) Map of median Vp/Vs ratio value and porosity-height from 8 wells through the Lower Doig and Upper Montney. The red arrows highlight wells with very small porosity-height values and correspond in general to areas of higher Vp/Vs ratio. The blue arrow highlights a well at the edge of the seismic data where the inversion is adversely affected by decreased fold. The yellow line is the approximate location of a horizontal well where micro-seismic data were recorded during stimulation. b) Cross-plot of porosity-height values as shown in (a) against Vp/Vs extracted from the map. The correlation co-efficient of all data points (blue line) of 0.7 is improved to 0.9 (red line) by removing the data point marked by the blue arrow which again corresponds to the well near the edge of the survey (a).

They also show in the figure that by removing one of the data points, corresponding to a well near the edge of the survey (where the seismic inversion result is presumably not as reliable, due to lower offset and azimuth coverage), the correlation co-efficient is improved from 0.7 to 0.9 (red line).

So, the first thing I set out to do was to reproduce the crossplot. I again hand-digitized the porosity-height and Vp/Vs pairs in the cross-plot using again WebPlotDigitizer. However, switched around the axes, which seems more natural to me since the objectives of regression efforts would be to predict as the dependent variable Phi-h, at the location of yet to drill wells, given Vp/Vs from seismic inversion. I also labelled the wells using their row index, after having loaded them in a Pandas DataFrame. And I used Ordinary Least Square Regression from the statsmodels library twice: once with all data points, the second time after removal of the well labelled as 5 in my plot above.

So, I am able to reproduced the analysis from the figure. I think removing an outlier with insight from domain knowledge (the observation that poorer inversion result at this location is reasonable for the deviation from trend) is a legitimate choice. However, I would like to dig a bit deeper, to back up the decision with other analyses and tests, and to show how one might do it with their own data.

The first thing to look at is an Influence plot, which is a plot of the residuals, scaled by their standard deviation, against the leverage, for each observation. Influence plots are useful to distinguish between high leverage observations from outliers and are one of statsmodel ‘s standard Regression plots, so we get the next figure almost for free, with minor modifications to the default example). Here it is below, together with the OLS regression result, with all data points.

From the Influence plot it is very obvious that the point labelled as zero has high leverage (but not high normalized residual). This is not a concern because points with high leverage are important but do not alter much the regression model. On the other hand, the point labelled as 5 has very high normalized residual. This point is an outlier and it will influence the regression line, reducing the R^2 and correlation coefficient. This analysis is a robust way to legitimize removing that data point.

Next I run some inferential tests. As I’ve written in an earlier notebook on Data loading, visualization, significance testing, I find the critical r very useful in the context of bivariate analysis. The critical r is the value of the correlation coefficient at which you can rule out chance as an explanation for the relationship between variables observed in the sample, and I look at it in combination with the confidence interval of the correlation coefficient.

The two plots below display, in dark blue and light blue respectively, the upper and lower confidence interval bounds, as the correlation coefficient r varies between 0 and 1 (x axis). These two bounds will change with different number of wells (they will get closer with more wells, and farther apart with less wells). The lower bound intersects the x axis (y=0) axis at a value equal to the critical r (white dot). The green dots highlight the actual confidence interval for a specific correlation coefficient chosen, in this case 0.73 with 9 wells, and 0.9 with 8 wells.

By the way: these plots are screen captures from the interactive tool I built taking advantage of the Jupyter interactive functionality (ipywidgets). You can try the tool by running the Jupyter notebook.

With 9 wells, and cc=0.73, the resulting critical r = 0.67 tells us that for a 95% confidence level (0.05 alpha) we need at least a correlation coefficient of 0.67 in the sample (the 9 wells drilled) to be able to confidently say that there is correlation in the population (e.g. any well, future wells). However, the confidence interval is quite broad, ranging between 0.13 and 0.94 (you can get these numbers by running confInt(0.73, 9) in a cell.

With 8 wells (having removed the outlier), CC=0.9, the critical r is now 0.71, meaning that the requirement for rejecting the the null hypothesis (there is no association between Vp/Vs and Phi-H) is now a bit higher. However, a CC increased to 0.9, and only one less well, also results in a confidence interval ranging from 0.53 to 0.98, hence our confidence is greatly increased.

This second analysis also corroborates the choice of removing the outlier data point. One thing worth mentioning before moving on to the next test is that these confidence interval bounds are the expected population ones, based on the sample correlation coefficient and the number of observations; the data itself was not used. Of course, I could also have calculated, and shown you, the OLS regression confidence intervals, as I have done in this notebook (with a different dataset).

My final test involved using the distance correlation (dcor.distance_correlation) and p-value (dcor.independence.distance_covariance_test) from the dcor library. I have written before in a blog post how much I like the distance correlation, because it does not assume a linear relationship between variables, and because a distance correlation of zero does mean that there is no dependence between those two variables (contrary to Pearson and Spearman). In this case the relationship seems to be linear, but it is still a valuable test to compare DC and p-value before and after removing the outlier. Below is a summary of the test:

All data points:
D.C. =  0.745
p-value =  0.03939

Data without outlier:
D.C. =  0.917
p-value =  0.0012

The distance correlation values are very similar to the correlation coefficients from OLS, again going up once removed the outlier. But, more interestingly, with all data points, a p-value of 0.04079 is very close to the alpha of 0.05, whereas once we removed the outlier, the p-value goes down by a factor of 20, to 0.0018. This again backs up the decision to remove the outlier data point.

Data exploration in Python: distance correlation and variable clustering

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Posted on April 10, 2019 by matteomycarta

April 10, 2019

In my last post I wrote about visual data exploration with a focus on correlation, confidence, and spuriousness. As a reminder to aficionados, but mostly for new readers’ benefit: I am using a very small toy dataset (only 21 observations) from the paper Many correlation coefficients, null hypotheses, and high value (Hunt, 2013).

The dependent/target variable is oil production (measured in tens of barrels of oil per day) from a marine barrier sand. The independent variables are: Gross pay, in meters; Phi-h, porosity multiplied by thickness, with a 3% porosity cut-off; Position within the reservoir (a ranked variable, with 1.0 representing the uppermost geological facies, 2.0 the middle one, 3.0 the lowest one); Pressure draw-down in MPa. Three additional ‘special’ variables are: Random 1 and Random 2, which are range bound and random, and were included in the paper, and Gross pay transform, which I created specifically for this exercise to be highly correlated to Gross pay, by passing Gross pay to a logarithmic function, and then adding a bit of normally distributed random noise.

Correlation matrix with ellipses

I am very pleased with having been able to put together, by the end of it, a good looking scatter matrix that incorporated:

bivariate scatter-plots in the upper triangle, annotated with rank correlation coefficient, confidence interval, and probability of spurious correlation
contours in the lower triangle
shape of the bivariate distributions (KDE) on the diagonal

In a comment to the post, Matt Hall got me thinking about other ways to visualize the correlation coefficient. I did not end up using a colourmap for the facecolour of the plot (although this would probably be relatively easy, in an earlier attempt using hex-bin plots, the colourmap scaling of each plot independently – to account for outliers – proved challenging). But after some digging I found the Biokit library, which comes with a lot of useful visualizations, among which corrplot is exactly what I was looking for. With only a bit of tinkering I was able to produce, shown in Figure 1, a correlation matrix with:

correlation coefficient in upper triangle (colour and intensity indicate whether positive or negative correlation, and its strength, respectively)
bivariate ellipses in the lower triangle (ellipse direction and colour indicates whether positive or negative correlation; ellipticity and colour intensity are proportional to the correlation coefficient)

Figure 1. Correlation matrix using the Biokit library

Also notice that – quite conveniently – the correlation matrix of Figure 1 is reordered with strongly correlated variables adjacent to one another, which facilitates interpretation. This is done using the rank correlation coefficient, with pandas.DataFrame.corr, and Biokit’s corrplot:

corr = data.corr(method='spearman')
c = corrplot.Corrplot(corr)
c.plot(method='ellipse', cmap='PRGn_r', shrink=1, rotation=45, upper='text', lower='ellipse')
fig = plt.gcf()
fig.set_size_inches(10, 8);

The insightful take-away is that with this reordering, the more ‘interesting’ variables, because of strong correlation (as defined in this case by the rank correlation coefficient), are close together and reposition along the diagonal, so we can immediately appreciate that Production, Phi-h, and Gross Pay, plus to a lesser extent position (albeit this one with negative correlation to production) are related to one another. This is a great intuition, and supports up our hypothesis (in an inferential test), backed by physical expectation, that production should be related to those other quantities.

But I think it is time to move away from either Pearson or Spearman correlation coefficient.

Correlation matrix with distance correlation and its p-value

I learned about distance correlation from Thomas when we were starting to work on our 2018 CSEG/CASP Geoconvention talk Data science tools for petroleum exploration and production“. What I immediately liked about distance correlation is that it does not assume a linear relationship between variables, and even more importantly, whereas with Pearson and Spearman a correlation value of zero does not prove independence between any two variables, a distance correlation of zero does mean that there is no dependence between those two variables.

Working on the R side, Thomas used the Energy inferential statistic package. With thedcor function he calculated the distance correlation, and with the dcov.test function the p-value via bootstrapping.

For Python, I used the dcor and dcor.independence.distance_covariance_test from the dcor library (with many thanks to Carlos Ramos Carreño, author of the Python library, who was kind enough to point me to the table of energy-dcor equivalents). So, for example, for one variable pair, we can do this:

print ("distance correlation = {:.2f}".format(dcor.distance_correlation(data['Production'], 
                                                                        data['Gross pay'])))
print("p-value = {:.7f}".format(dcor.independence.distance_covariance_test(data['Production'], 
                                                                           data['Gross pay'], 
                                                                           exponent=1.0, 
                                                                           num_resamples=2000)[0]))
>>> distance correlation  = 0.91
>>> p-value = 0.0004998

So, wanting to apply these tests in a pairwise fashion to all variables, I modified the dist_corr function and corrfunc function from the existing notebook

def dist_corr(X, Y, pval=True, nruns=2000):
""" Distance correlation with p-value from bootstrapping
"""
dc = dcor.distance_correlation(X, Y)
pv = dcor.independence.distance_covariance_test(X, Y, exponent=1.0, num_resamples=nruns)[0]
if pval:
    return (dc, pv)
else:
    return dc

def corrfunc(x, y, **kws):
d, p = dist_corr(x,y) 
#print("{:.4f}".format(d), "{:.4f}".format(p))
if p > 0.1:
    pclr = 'Darkgray'
else:
    pclr= 'Darkblue'
ax = plt.gca()
ax.annotate("DC = {:.2f}".format(d), xy=(.1, 0.99), xycoords=ax.transAxes, color = pclr, fontsize = 14)

so that I can then just do:

g = sns.PairGrid(data, diag_sharey=False)
axes = g.axes
g.map_upper(plt.scatter, linewidths=1, edgecolor="w", s=90, alpha = 0.5)
g.map_upper(corrfunc)
g.map_diag(sns.kdeplot, lw = 4, legend=False)
g.map_lower(sns.kdeplot, cmap="Blues_d")
plt.show();

Figure 2. Revised Seaborn pairgrid matrix with distance correlation colored by p-value (gray if p > 0.10, blue if p <= 0.10)

Clustering using distance correlation

I really like the result in Figure 2. However, I want to have more control on how the pairwise plots are arranged; a bit like in Figure 1, but using my metric of choice, which would be again the distance correlation. To do that, I will first show how to create a square matrix of distance correlation values, then I will look at clustering of the variables; but rather than passing the raw data to the algorithm, I will pass the distance correlation matrix. Get ready for a ride!

For the first part, making the square matrix of distance correlation values, I adapted the code from this brilliant SO answer on Euclidean distance (I recommend you read the whole answer):

# Create the distance method using distance_correlation
distcorr = lambda column1, column2: dcor.distance_correlation(column1, column2) 
# Apply the distance method pairwise to every column
rslt = data.apply(lambda col1: data.apply(lambda col2: distcorr(col1, col2)))
# check output
pd.options.display.float_format = '{:,.2f}'.format
rslt

Table I. Distance correlation matrix.

The matrix in Table I looks like what I wanted, but let’s calculate a couple of values directly, to be sure:

print ("distance correlation = {:.2f}".format(dcor.distance_correlation(data['Production'], 
data['Phi-h'])))
print ("distance correlation = {:.2f}".format(dcor.distance_correlation(data['Production'], 
data['Position'])))

>>> distance correlation = 0.88
>>> distance correlation = 0.45

Excellent, it checks!

Now I am going to take a bit of a detour, and use that matrix, rather than the raw data, to cluster the variables, and then display the result with a heat-map and accompanying dendrograms. That can be done with Biokit’s heatmap:

data.rename(index=str, columns={"Gross pay transform": "Gross pay tr"}, inplace=True)
distcorr = lambda column1, column2: dcor.distance_correlation(column1, column2)
rslt = data.apply(lambda col1: data.apply(lambda col2: distcorr(col1, col2)))
h = heatmap.Heatmap(rslt)
h.plot(vmin=0.0, vmax=1.1, cmap='cubehelix')
fig = plt.gcf()
fig.set_size_inches(22, 18)
plt.gcf().get_axes()[1].invert_xaxis();

Figure 3. Biokit heatmap with dendrograms, using correlation distance matrix

That’s very nice, but please notice how much ‘massaging’ it took: first, I had to flip the axis for the dendrogram for the rows (on the left) because it would be incorrectly reversed by default; and then, I had to shorten the name of Gross-pay transform so that its row label would not end up under the colorbar (also, the diagonal is flipped upside down, and I could not reverse it or else the colum labels would go under the top dendrogram). I suppose the latter too could be done on the Matplotlib side, but why bother when we can get it all done much more easily with Seaborn? Plus, you will see below that I actually have to… but I’m putting the cart before the horses…. here’s the Seaborn code:

g = sns.clustermap(rslt, cmap="mako",  standard_scale =1)
fig = plt.gcf()
fig.set_size_inches(18, 18);

and the result in Figure 4. We really get everything for free!

Figure 4. Seaborn clustermap, using correlation distance matrix

Before moving to the final fireworks, a bit of interpretation: again what comes up is that Production, Phi-h, Gross Pay, and Gross pay transform group together, as in Figure 1, but now the observation is based on a much more robust metric. Position is not as ‘close’, it is ends up in a different cluster, although its distance correlation from Production is 0.45, and the p-value is <0.10, hence it is still a relevant variable.

I think this is as far as I would go with interpretation. It does also show me that Gross pay, and Gross pay transform are very much related to one another, with high dependence, but it does still not tell me, in the context of variable selection for predicting Production, which one I should drop: I only know it should be Gross pay transform because I created it myself. For proper variable selection I will look at techniques like Least Absolute Shrinkage and Selection Operator (LASSO, which Thomas has showcased in his R notebook) and Recursive Feature Elimination (I’ll be testing Sebastan Raschka‘s Sequential Feature Selector from the mlxtend library).

Correlation matrix with distance correlation, p-value, and plots rearranged by clustering

I started this whole dash by saying I wanted to control how the pairwise plots were arranged in the scatter matrix, and that to do so required use of Seaborn. Indeed, it turns out the reordered row/column indices (in our case they are the same) can be easily accessed :

a = (g.dendrogram_col.reordered_ind)
print(a)
>>> [1, 6, 2, 7, 0, 5, 3, 4]

and if this is the order of variables in the original DataFrame:

b = list(data)
print (b)
>>> [Position', 'Gross pay', 'Phi-h', 'Pressure', 'Random 1', 'Random 2', 'Gross pay transform', 'Production']

we can rearrange them with those reordered column indices:

data = data[[b[i] for i in a]]
print(list(data))
>>> ['Gross pay', 'Gross pay transform', 'Phi-h', 'Production', 'Position', 'Random 2', 'Pressure', 'Random 1']

after which we can simply re-run the code below!!!

g = sns.PairGrid(data, diag_sharey=False)
axes = g.axes
g.map_upper(plt.scatter, linewidths=1, edgecolor="w", s=90, alpha = 0.5)
g.map_upper(corrfunc)
g.map_diag(sns.kdeplot, lw = 4, legend=False)
g.map_lower(sns.kdeplot, cmap="Blues_d")
plt.show()

Figure 5. Revised Seaborn pairgrid matrix with distance correlation colored by p-value (gray if p > 0.10, blue if p <= 0.10), and plots rearranged by clustering results

UPDATE: I just uploaded the notebook on GitHub.

ChatGPT as an essay-writing assistant – Part II

Posted on February 10, 2025 by matteomycarta

The blog post below was produced entirely by GPT-4.0, following a series of iterative prompts I provided, from the Introduction to the References and Footnotes, included. Please refer to my AI (Artificial Intelligence) and HI (Human Intelligence) Table in the last section. In the next post, I will include the full listing of my prompts, text evaluation, and time investment versus return analysis. I will also attempt prompting for some further improvements beyond this initial analysis.

Plato’s Perspective on the Hundred Years’ War

Introduction

The Hundred Years’ War, a prolonged and devastating conflict between England and France (1337-1453), was a historical event unknown to the ancient Greek philosopher Plato. Nonetheless, by examining his philosophical ideas, primarily in “The Republic” and “Laws,” we may speculate on his potential views regarding such a conflict.

The Philosopher King and the Ideal State

The Philosopher-King and the Ideal State In his magnum opus, “The Republic,” Plato presents the concept of a philosopher-king, an individual embodying wisdom and justice, who governs the ideal state (Plato, Republic, Stephanus 473c-d, Book V)¹. This enlightened ruler, possessing both knowledge and moral integrity, would guide society toward harmony and justice.

War as Necessary Evil

In the “Laws,” Plato acknowledges that war might be a necessary recourse, particularly when defending the state against injustice (Plato, Laws, Stephanus 625c, Book I)². However, he also emphasizes the importance of striving for peace and pursuing diplomacy whenever possible.

Striving for Peace

Plato contends that an ideal state should always seek to cultivate peace with other nations, fostering a spirit of friendship and cooperation (Plato, Republic, Stephanus 470a-b, Book V)³. This suggests that, had he been aware of the Hundred Years’ War, Plato would likely have advocated for diplomatic efforts to resolve the conflict.

The Guardians as Defenders of the State

The Guardians: Defenders of the State In “The Republic,” Plato introduces the guardians, a class of citizens specifically trained to defend the state and uphold its values (Plato, Republic, Stephanus 414a-b, Book III)⁴. These individuals, educated in both martial and intellectual pursuits, would protect the state from external threats, such as those posed during the Hundred Years’ War.

Governance in Times of War

Though Plato acknowledges the potential necessity of war, he cautions against allowing it to dominate the state’s agenda (Plato, Republic, Stephanus 468a-b, Book V)⁵. Instead, he argues that governance should remain focused on promoting the well-being of citizens and maintaining social harmony.

Plato maintains that an ideal state should strive to cultivate virtue among its citizens, promoting wisdom, courage, moderation, and justice (Plato, Republic, Stephanus 427e-428a, Book IV)⁶. In this context, the prolonged conflict of the Hundred Years’ War might be seen as a distraction from the state’s primary goal of fostering a harmonious and virtuous society.

Conclusion

Though Plato lived centuries before the Hundred Years’ War, his philosophical ideas can provide valuable insights into how he might have viewed such a conflict. By examining his writings, particularly “The Republic” and “Laws,” we can speculate that Plato would have recognized the potential necessity of war in certain circumstances but would have strongly advocated for peace, diplomacy, and the pursuit of justice and virtue in governance.

References

Title	Author	Date Written	Chicago citation
The Republic	Plato	380 BCE	Plato. The Republic. Translated by G.M.A. Grube. Indianapolis: Hackett Publishing Company, 1992.
Laws	Plato	348 BCE	Plato. Laws. Translated by A.E. Taylor. London: Dent, 1934.

Footnotes

Plato, Republic, 473c-d. Perseus Digital Library | The Internet Encyclopedia of Philosophy
Plato, Laws, 628a-630d. Perseus Digital Library | The Internet Encyclopedia of Philosophy
Plato, Republic, 470a-471c. Perseus Digital Library | The Internet Encyclopedia of Philosophy
Plato, Republic, 433b-c. Perseus Digital Library | The Internet Encyclopedia of Philosophy
Plato, Republic, 414b-415d. Perseus Digital Library | The Internet Encyclopedia of Philosophy
Plato, Laws, 348, 663a-b. Perseus Digital Library | The Internet Encyclopedia of Philosophy

AI (Artificial Intelligence) and HI (Human Intelligence) Statement

Modified from Brewin http://www.theguardian.com/books/2024/apr/04/why-i-wrote-an-ai-transparency-statement-for-my-book-and-think-other-authors-should-too

Has any text been generated using AI?	Yes
Has any text been improved or corrected using HI?	No
Has any methods of analysis been suggested using HI?	Yes
Has any methods of analysis been suggested using AI?	No
Do any analyses utilize AI technologies, such as Large Language Models, for tasks like analyzing, summarizing, or retrieving information from data?	Yes

ChatGPT as an essay-writing assistant – Part I

Posted on May 2, 2023 by matteomycarta

Outline

Introduction and background
My first prompt
ChatGPT-3.5 result
Time investment and return
Evaluation

Introduction and background

In this multi-part series of articles, I will document my efforts in writing a high school Philosophy paper using ChatGPT. The paper shall answer in writing a question I was asked at an impromptu oral assessment in Philosophy class in my 3rd year of high school.

Let me take a step back to give you some context. I was enrolled in Classical High School in Rome, Italy. This type of school has a strong 5-year emphasis on History and Philosophy, as well as Latin, Greek, and Italian literature and grammar, with a bit of Science and Math. Students are typically evaluated on weekly written assignments, a minimum of 3 scheduled written tests each semester, and a minimum of 2 oral assessments per semester. During the latter ones, the teacher would (usually) pick two names at random from the attendance list once a week and gauge their knowledge on both the weekly lesson, in detail, but also on anything covered in the year up to that point; this could last between 30-60 minutes, and would happen in front of an audience of (often roaring) classmates. Seriously: brutal!

Only occasionally were students allowed to give a presentation on a prepared topic or volunteer for a full oral evaluation. This was the case for me during a block on Plato. And so it was that the teacher, the famously feared Professoressa Carbone (who taught both History and Philosophy), probed into my soul with her terrifying eyes and asked with a sinister smile, “Tell me, Niccoli, what would Plato have thought about the Hundred Years’ War?“

My first prompt

When I heard about OpenAI ChatGPT being available, it seemed very fit to try this question in my first investigation. So I went ahead and asked the question “What would Plato have thought about the Hundred Years’ War?“, with only the minor modification to add citations and break down the response in steps.

GPT-3.5 result

Below is the result from the default GPT-3.5 model:

Time investment and return

Time investment: the whole investigatyion took about 30 minutes, including a very light read on prompts from a reputalbe source, and reading the answer (becaue the citations really did not come as full references, there was really nothing else to do other than that).
Return: was this worth 30 minutes of my time? The answer is, as often, it depends! On the one hand, this is a really poor answer in my view (see next section for a more detailed evaluation). So, as an essay (l imagine myself as a student looking for a quick free lunch), this would not do it; not even close. For me… but then again, even at 13 in my first year of high school I would’ve known this was not going to cut it… or in Junior high, for what matters. On the other hand, I was deliberate in providing a very simple, not engineered or iteratively refined prompt. As such, the response will come useful as a benchamrk against wich I will compare other efforts (for example using a better model, GPT4, and improving the prompt).

Evaluation

Is the answer grammatically correct? yes; is it written in a uniform style, appropriate for a school essay? yes; Does it contain any hallucination? I would say no, everything sounds reasonable. However I must admit that without reference to specific passages to Plato’s work, it is hard to say for sure. From what I remember of Plato’s Philosophy it’s reasonable, and that’s all.

On the other hand, had I been handed in this as a teacher, I would not be impressed. IF this were the output of an in-class exam, I probably would have marked it as a D- (a D for the very mediocre text and a minus for the ridiculousness of the citations). Had it instead been handed for an at home written assignement (in which cse the student would have had access to their notes and books) this would definitely be certainly worth an F (Fail). Now I sound like Professoressa Carbone.

You may reasonably wonder at the end of this article: how did I fare in that evaluation in 1986? Fair question. And I am not ashamed to confess it was a disaster. At 15 I was still very immature, intelligent but unengaged in school work, and also unable to do a real analysis. By that I mean interpret information rather than just accumulate facts and connect them. I honestly do not recall the mark I got (we had different levels of Failure that went progressively deeper, not too dissimilarly from the Circles in Dante’s Inferno) but I rememberr that an F definitely it was.

P.S. The model did a perfectly fine job in proofreading my first draft for this post. THat was definitely worth a lot, given I type very slowly, and I make lots of typos.

How many piano tuners are in Chicago?

Why this matters

The frustration

The Wolfram plugin: the turning point

Drafting the Laws: permission to estimate

Building something better

The results: does the framework actually help?

The attempted fix

The evolution summarized

Where this fits in the research

Is the framework worth it?

What’s coming next

A confession

References

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Introduction

What is Picobot?

The Constraints

The Rules

The Goal

The Empty Room: From 7 to 6 Rules

The Strategy: Boustrophedon

My Initial Solution: January 6, 2015

The Insight: “C and F Are the Same”

The Final Solution: January 24, 2015

Verified

The Maze: From 16 to 12 Rules

The Strategy: Right-Hand Wall Following

Initial Solution: 16 Rules

Two-Phase Optimization

The Iteration: A Failed Attempt

The Final Solution

Verified

Making It Explicit: Starting State Matters

What I Learned

Try It Yourself

What’s Next

AI/HI (Human Intelligence) Transparency Statement

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A step back to 2020: Building the app from scratch

2026: Working with Claude

What changed (and what didn’t)

The honest trade-off

What this means going forward

References

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The problem

Mill’s Methods: 19th-century philosophy meets drilling risk

What a neural network learned

What the AI got right—and what it missed

Why this stuck with me

The convergence

References and Links

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The Challenge of a Satisfying Conclusion

What Was the Question Really Asking For?

So What Would Satisfy?

What Would That Actually Look Like?

Closure for Now

A Final Thought: Rigor Without Brutality

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Introduction

First example: evaluate the quality of seismic inversion from a published article

Second example: evaluate regression results from a published article

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Correlation matrix with ellipses

Correlation matrix with distance correlation and its p-value

Clustering using distance correlation

Correlation matrix with distance correlation, p-value, and plots rearranged by clustering

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Plato’s Perspective on the Hundred Years’ War