AI does not hallucinate because it is broken. It hallucinates because we built finite machines on top of mathematical architectures with no legitimate place for silence, exhaustion, or the cost of verification.

My new essay explores hallucination as a thermodynamic and architectural problem — connecting local AI, finite mathematics, Bayesian updating, Coq-verified VOID Theory, and the strange possibility that honesty in machines may require a completely different notion of computation.

The Cloud promised infinite intelligence. But maybe the future lies where descendants of apes belong and feel more at place: not the fucking sky.

Comments URL: https://news.ycombinator.com/item?id=48186335

Points: 2

# Comments: 1

Core ideas:

Every operation costs "budget" — network dies before seeing everything Confidence is Ratio(n,d), not float — division only for human display Rare symptoms weighted higher (entropy from information theory) 500 lines of Rust, formal spec in Coq (44 files)

Emerged from a critique of Pascal's Wager: what if observation itself has finite cost?

Oh, and it runs on CPU, not GPU. And it runs fast as hell. How? That's a bit of a mystery for me too...

However, what's most important is that it is inherently capable of saying "well, I dunno...".

no binary dictate of YES or NO. there is always an option to chose UNCERTAINTY. and there is nothing more natural than uncertainty in real life.

well, in there repository, you will not only find the network but also a hefty collection of coq files that define the ontology of finitiary math I have written with ai during my long stay in hospital bed with cancer. cancer is receding, code is compiling, and the network is learning. try it out.

Comments URL: https://news.ycombinator.com/item?id=46852043

Points: 1

# Comments: 0

Comments URL: https://news.ycombinator.com/item?id=44818472

Points: 3

# Comments: 1

Comments URL: https://news.ycombinator.com/item?id=43122430

Points: 1

# Comments: 3

About:

At its core, finite mathematics is about bounded capacity and discrete structures. It’s a system where:

1. Numbers Are Finite: • No irrational numbers, no infinities—just finite fractions like \(\tfrac{k}{N}\), where defines the granularity. • Instead of approximating values with floating points, we work with exact, bounded representations.

2. Probabilities Are Granular: • All probabilities are stored as discrete increments, like \(\tfrac{3}{10}\), ensuring that systems remain exact and free of floating-point errors. • Probabilistic systems reflect real-world uncertainty, not theoretical abstractions.

3. Geometry Is Combinatorial: • Distances and spaces are not infinite or continuous but finite and relational, built from distinguishable patterns and connections.

4. Capacity Is Central: • Every observer or system has a capacity, which determines how finely it can represent or compute distinctions. Capacity can grow, but it’s always finite.

5. Updates Are Stepwise: • All changes happen in finite steps—no limits, no infinitesimal changes, no unbounded loops. This makes systems more predictable and efficient.

Why Should IT Professionals Care?

Finite mathematics aligns directly with the challenges and realities of modern IT systems:

1. Precision Without Floating-Point Errors • Floating-point arithmetic introduces rounding errors, precision loss, and bugs. Finite mathematics stores numbers exactly, ensuring precision and eliminating common pitfalls in calculations.

2. Scalable Probabilities for AI: • AI and machine learning models often rely on continuous probabilities, which are computationally expensive and prone to precision issues. Finite mathematics offers discrete probabilistic models that are faster, simpler, and more robust.

3. Optimized Resource Usage: • Systems with finite capacity—like networks, databases, or hardware—can be modeled more effectively using finite math, ensuring that resources are used efficiently without overcommitment or overflow.

4. Discrete-Time Modeling: • Finite mathematics mirrors how systems evolve in discrete time steps, making it ideal for modeling distributed systems, event-based simulations, or even neural networks.

5. Closer to Reality: • Unlike traditional math, which assumes infinite sets and continuous variables, finite mathematics is grounded in real-world constraints, making it a better tool for understanding and building systems that actually exist.

Applications in IT

Finite mathematics isn’t just theoretical—it has direct applications across IT:

1. Probabilistic Systems: • Store probabilities as discrete fractions for use in decision-making, risk modeling, or probabilistic AI. • Example: Lumps-coded probability systems where every outcome has a finite, exact representation.

2. Neural Networks and Machine Learning: • Replace floating-point weights with bounded, discrete increments to eliminate rounding errors and optimize computation. • Example: Adaptive capacity in finite neural networks.

3. Quantum-Inspired Computation: • Finite systems can approximate quantum probabilities and behaviors without relying on infinite Hilbert spaces. • Example: Finite lattices to simulate quantum systems.

4. Distributed Systems: • Model systems as finite-state machines with bounded capacity, ensuring predictable behavior and efficient resource usage. • Example: Finite graphs for network optimization.

5. Game Development and Graphics: • Use finite geometry for more accurate physics engines or rendering systems, avoiding floating-point inaccuracies in calculations. • Example: Discrete distances and adjacency in game worlds.

Comments URL: https://news.ycombinator.com/item?id=43087490

Points: 1

# Comments: 0

Comments URL: https://news.ycombinator.com/item?id=43070507

Points: 3

# Comments: 0

Comments URL: https://news.ycombinator.com/item?id=43052500

Points: 1

# Comments: 1

What do you think happens when we finally confront the illusion of infinity in everything we build?

https://voids.blog/2025/02/14/breaking-infinitys-grip-the-fi... https://github.com/probabilistic-minds-consortium/finite-cap...

Comments URL: https://news.ycombinator.com/item?id=43048365

Points: 1

# Comments: 0

However, the drama thing… if you’ll find time to read that one text below, you’ll see that maybe it’s not a matter of choice. To drama or not to drama - that isn’t even a question!

https://drive.google.com/file/d/1ZtiEvB79aohVhWE1vGdNCuamqwz...

best, k.

Comments URL: https://news.ycombinator.com/item?id=41977725

Points: 2

# Comments: 5