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Repeating the same experiment but one year later. GPT 5.6 Pro cannot be used vanilla for this prompt because it immediately fires the right CAS command to compute the Galois group. So instead I used a very restrictive prompt. One year has passed since GPT 5 Pro premiere, GPT...

70,809 Aufrufe • vor 2 Tagen •via X (Twitter)

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GPT-5.6 vs GPT-5.5 on my custom spaceship prompt. I gave both models the exact same custom prompt. This is also the same prompt I previously gave to Fable 5. For context, GPT-5.6 Pro worked for 87 minutes, while GPT-5.5 Extra High worked for 34 minutes and 42 seconds. As I’ve said before, based on great authority GPT-5.6 will be an incremental/soldi improvement over GPT-5.5, not a “Fable killer.” My rough expectation has been that it would trade blows with Fable 5 on some benchmarks, maybe win around half depending on the category, but not clearly surpass it overall. And again fable five will have bigger model smell, but this was expected. After testing this coding output, that view feels pretty accurate. GPT-5.6 is clearly better than GPT-5.5 in several visual areas. The lighting, shading, chairs, object details, and exterior of the spaceship looked noticeably stronger. The scene was also easier to test. I do want to give GPT-5.5 credit though. It built out the rooms much much better and the planets looked better than GPT-5.6’s. It was also interesting that both GPT-5.5 and GPT-5.6 produced better-looking planets than Fable 5 in this specific test. The downside with GPT-5.5 was stability. The game was much glitchier and harder to test compared to GPT-5.6. But when it comes to the core of the demo, which is the spaceship itself, Fable 5 still beat both models pretty comfortably. GPT-5.6 is impressive, but from this test, it looks exactly like what I expected which was a meaningful incremental improvement over GPT-5.5, at least for indie game demos, but not something that replaces Fable 5. In collaboration with Chetaslua

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Quantum mechanics has a reputation for being mystical mainly because people skip the rules and jump to interpretations. In this lecture series, we’re doing the opposite. We start from the rules, follow the algebra, and let the picture be the calculation. Classical Probability Theory combines alternatives by adding their probabilities. Quantum Theory combines them one step earlier…add complex amplitudes first, then square at the end. That swap in order is everything. Expand |a₁ + a₂|² and you don’t just get |a₁|² + |a₂|²…you get a cross-term, 2 Re(a₁ a₂*). Its sign is set by phase, so the same two contributions can reinforce or cancel. Interference is just the algebra of squaring a sum. In the 3D render, the surface height is proportional to |a(x)| (so peaks become bright bands after squaring), while the surface skin is colored by the local phase arg(a(x)). As the phase knob φ(t) is swept on path 2, the cross-term oscillates, and you literally watch the interference ridges slide across the screen. We model a detector screen with coordinates x in R² (think x = (x,y)). A quantum state assigns a complex amplitude a(x). The rule for outcomes is p(x) = |a(x)|² Now the key situation: two coherent alternatives contribute to the same outcome x. Let their amplitudes be a₁(x) and a₂(x). Quantum says a(x) = a₁(x) + a₂(x) So the probability density becomes p(x) = |a₁(x) + a₂(x)|² Expand it (this is the whole episode): p(x) = (a₁ + a₂)(a₁* + a₂*) = |a₁|² + |a₂|² + a₁ a₂* + a₁* a₂ = |a₁|² + |a₂|² + 2 Re(a₁ a₂*) That last term is the interference term. It can be positive or negative. To see phase explicitly, write each contribution in polar form: a₁(x) = r₁(x) exp(i θ₁(x)) a₂(x) = r₂(x) exp(i θ₂(x)) Then a₁ a₂* = r₁ r₂ exp(i(θ₁ − θ₂)) So the cross-term is 2 Re(a₁ a₂*) = 2 r₁ r₂ cos(θ₁(x) − θ₂(x)) That’s the fringe engine: p(x) = r₁² + r₂² + 2 r₁ r₂ cos(Δθ(x)) Now the phase knob we animate: Add a controllable phase shift φ to path 2: a₂(x) → a₂(x) exp(i φ) Then Δθ(x) → Δθ(x) − φ, so p(x; φ) = r₁² + r₂² + 2 r₁ r₂ cos(Δθ(x) − φ) As φ changes smoothly, the bright/dark pattern slides continuously. Same setup, same geometry, same magnitudes r₁,r₂, only phase changed. #QuantumMechanics #WaveInterference #ComplexAmplitudes #DoubleSlit #Physics #Mathematics

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Do you actually know what convex optimization is in the geometric, guarantee-theoretic sense or have you only met it through solvers and loss curves? Convexity is rare comfort in optimization...there are no spurious local minima, no surprise traps, and inequalities you can use like tools instead of prayers. So, what is this convexity? Let x = (x₁, x₂) and let f(x) be convex. Plot the surface z = f(x). Pick a contact point x₀. The local slope is the gradient p = ∇f(x₀). That p is exactly the data that defines the supporting plane: z = f(x₀) + p · (x − x₀). Thus, f is said to be convex because for every x, f(x) ≥ f(x₀) + p · (x − x₀). So the plane at x₀ can slide under the surface, but it never slices through it. Not near the point...everywhere. Now for here is the interesting part: The slope becomes a coordinate system! Rewrite the same plane as z = p · x − b, where b is the offset. Because the plane passes through (x₀, f(x₀)), the offset is forced to be b = p · x₀ − f(x₀). And that number isn’t just geometry trivia. It’s the convex conjugate: f*(p) = sup over x ( p · x − f(x) ). At a differentiable contact point, the supporting plane touches f tightly enough that the supremum is achieved at x₀, giving the identity f*(p) = p · x₀ − f(x₀) when p = ∇f(x₀). So one moving contact point gives two linked readouts: primal position x₀ dual position (slope) p = ∇f(x₀) dual offset f*(p) One surface. Two worlds. #ConvexOptimization #Optimization #MachineLearning #SignalProcessing #AppliedMath #Engineering

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GPT-5 is live in Cline. We've been working with OpenAI to get this model ready, and here's our take: it's disciplined, persistent, & highly competent. It's collaborative in planning & and a diligent operator while acting. It plans thoroughly, asks optioned follow-ups when needed, & then gets out of the way and ships code. On long tasks it keeps going before pausing to check in. It follows instructions to the letter. And most importantly -- it writes good code. GPT-5 is like "The Wolf" from Pulp Fiction. Comes in, assesses the situation, then executes. Here's what you can expect from GPT-5 in Cline: > verbose while planning; terse while executing > asks a lot of good clarification questions, & frequently provides options when appropriate > strong context retention and persistence over long horizons (256k context window) > good at diff-style edits and multi-file changes (we'll monitor as more usage data comes in) > quiet in Act mode -- writes code without yapping Metaprompting is another strength. We tested early with OpenAI and used GPT-5 to tune our own prompt for GPT-5. Here's a pattern we like: “Answer from your own perspective: what changes or additions would help you better follow this prompt? Here is the prompt (or snippet): [snippet]. Users have complained about X and Y. What minimal edits would you make while keeping the rest intact?” Do you need to change any of your existing patterns in Cline? No -- it's good out of the box. Give a clear goal and constraints, let it plan, then let it cook. Expect more clarifying questions than most models. Pricing: $1.25/M input tokens (+90% cache), $10/M output. Roughly half of Sonnet 4 ($3/$15). Want to try GPT-5? Use it in Cline today for pure, unfiltered inference via the OpenAI, Cline, or OpenRouter providers. (fyi -- GPT-5 one-shotted this browser DAW below on the prompt "build something impressive to show me what you're capable of")

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