Beyond the token:
why AI needs geometry and physics to understand the world

1. The original sin of LLMs: the tyranny of probabilities

The tech industry sells us artificial intelligence as an omniscient revolution. Yet if you look under the bonnet, current architectures (Transformers, large language models) rest on one fundamental principle: statistics.

An LLM "understands" nothing in the physical sense of the word. It computes probabilities in a high dimensional vector space to determine which word is statistically most likely to follow the previous one. That is brilliant for generating text, but it is a conceptual dead end as soon as you have to interact with the real world.

At engineering school or in preparatory classes we are taught a golden rule: faced with a complex equation, getting bogged down in raw algebraic calculation or guessing the result leads to failure. You switch to geometry. You solve problems through invariants, through sums and integrals, because geometry is exact. The result falls into place by itself.

2. The missing link: the analogue-to-digital connector

The criticism voiced by some of the heavyweights of research (notably on the absence of a "world model" in AI systems) is right on the diagnosis, but often misses the target on the means.

For a system to develop a real awareness of its environment, stacking layers of artificial neural networks is not enough. It needs a physical body.

The real world is analogue: it is made of continuous flows, voltage variations, electromagnetic waves, raw signals and inertia.

The computing world is discrete: it handles zeros and ones, logical states frozen in time.

The real bridge, the one current AI architectures so badly lack, is what we have handled in signal processing for decades: the analogue-to-digital converter (ADC/DAC) coupled to a geometric topology.

Until an AI system is plugged into a closed loop of physical feedback (as in advanced robotics or the spectral analysis of a network signal in real time), it stays confined in a textual and abstract matrix. It does not live its environment, it comments on it.

3. Applying geometry to data: towards an engineer's AI

If we want AI to become a real tool of sovereignty and defence for our infrastructure (networks, firewalls, Linux systems), we have to drop the logic of "probabilistic blur" and return to the rigour of the engineer:

Multidimensional analysis through geometry: treat data flows not as sequences of textual logs to parse, but as a field of vectors and waves. A cyber attack (a DDoS, an intrusion) is never anything but a shock wave or an interference in a dynamic system.

Mathematical certainty: use geometric models to set impassable limits, guaranteeing that the system reacts with the certainty of a mathematical integral and not with the uncertainty of a statistical "maybe".

Conclusion

There is no strict need for revolutionary tools. With tools like n8n and some Python code, we can already simulate geometric and analogue-to-digital behaviours that will make all the difference, for example in connected home management systems, where fine interpretation of the real world matters more than plain binary code.

— Hosman