The Geometry of AI

“And the whole is greater than the part.” - Euclid

 

AI is all the rage lately and I’ve been thinking about how to frame this in my mind and explain the possibilities and some of the inherent risks to others when needed. Since I enjoy a good analogy, here’s what I came up with. 

 

Plain code, loaded with If...Then, Case, and other branching functions is the Zero-dimensional point; this isn’t AI, but it might appear to simulate it under the right circumstances. Think back to the very beginning of computing and the ELIZA application. (https://en.wikipedia.org/wiki/ELIZA) Honestly, it’s just natural language programming, but back in the day it was impressive and some versions have been documented as passing the Turing test. In my opinion, this is the very basic root of everything AI. As I see it here, the big security challenges are straightforward, as there are limited abilities to interact with users, data, and systems. Here it would be mostly about making sure that any sensitive information obtained by the system is not accessible by those who do not have a need to know.

 

AI concepts begin to get more interesting when we think about Machine Learning, which I consider to be the next geometric step, the One-dimensional line. This is code that works with and manipulates data and can examine it to classify and create models that can be reported on. In my line of work, being able to create and model large datasets or user activity can help us to identify potential security anomalies. Note that the ML model basically organizes and sorts the data, it does not interpret data. For ML, our security concerns are more about protecting the information held in the model.

 

If we want to get to that next step of interpreting the data, that’s what I consider to be the Two-dimensional shape in the form of Large Language Models or LLM. (https://en.wikipedia.org/wiki/Large_language_model) Here we are working with more data, and it is being organized by the tool itself. The LLM “reads” the information exposed to it and creates statistical pattern-based objects which might be text or images. This step is important as it helps the model to understand concepts and relationships for responding to requests.

And this is where it gets interesting. I recently started on a “vibe coding” project which I will be explaining in a later article. As part of this work, I needed to create a data set (a database table) for testing. As the data set became increasingly complicated, it was easier to have the LLM I was using maintain it for me. At first, it would just do some regex as part of some basic search and replace, but as the table got longer and added additional fields, my LLM started writing Python to do the work! Not sure why I was so blown away by this as the LLM had written some testing code to help with troubleshooting. I guess it was because I was working on a database table stored in MariaDB, and not actual code. But I will say it was interesting to watch. As a result, I do have a fun table of identity objects that I can use for testing and product demos.

The last “normal” dimensional concept will be that of the Three-dimensional solid, and I liken this to the concept of Agentic AI. As we have seen in this article, each concept has built upon itself to the point that the Agentic AI, not only models and interacts with data, but can interact with other objects on the network and beyond. To be fair, the LLM does interact with its user and the data itself to make new things, but it doesn’t go beyond the data and the host system. Agentic AI has the potential to interact with other agents to get things done, and that’s where things really start to get interesting.

The basic concept here is that I can instruct my agent to go get something done, let’s say order flowers. I tell it I want flowers for a given occasion, with certain flowers, in a set price range. I can also tell it that these flowers need to be delivered to a specific address by a set date. My agent will have to go out and talk to the floral agent, which might need to talk to the shipping agent. The floral agent and the shipping agent will need to talk to my agent to get paid, possibly by establishing a connection with my banking agent or service. The goal would be to only have my personal agent talk to me to handle any questions not handled in my initial request, but it might need my guidance about anything outside the prompt. In the best model, my agent would continue to learn my preferences about flowers, money handling, and shipping preferences.

What will be the next step? We are already seeing ecommerce (Stripe) and payment industry leaders (Paypal) enter this conversation and place their stamp on how this will work.

It gets even more interesting when we consider the future and additional dimensions of Artificial Intelligence. A Fourth dimensional view will be much like how we visualize shapes like the tesseract. (https://en.wikipedia.org/wiki/Tesseract)  Much the same way that we can have an appreciation of what an advanced shape would look like, we know there will be a difference in how AI conceives its solutions. This means that the AI may not simply have more capability, but more opacity, making it harder to understand. Up to the agentic stage, we can still usually trace the rough path from prompt to action, even if that path is complicated. Now the system begins to reason across time, memory, tools, and other agents in ways that produce useful outcomes without producing explanations that feel natural to human beings. We may understand the goal and observe the result, but not fully understand the shape of the reasoning in between. That is the point where AI stops being merely impressive and starts to appear alien.

Maybe something like telling my self-driving car where to go, how to handle tolls, how to handle low fuel/battery levels, route preferences? Honestly, I’m pretty sure this is low hanging fruit and we see that the self-driving car example is already being addressed by the automotive industry.

At this stage, the security conversation also changes. The concern is no longer just whether the model can access data or call a tool. The concern becomes whether we can govern a system whose decisions are effective, but not intuitively legible. A self-driving car is a simple example. I may be able to tell the car where to go, how to handle tolls, or what route I prefer, but at some point I am trusting a machine to continuously balance safety, law, etiquette, efficiency, changing road conditions, and its own learned models faster than I can follow in real time. That is where the fourth dimension starts to matter.

Part of this is how we choose to “feed” the model.For the car driving example, we also need to think about laws and driving etiquette, which might be slightly harder to define in terms of a model.  For our floral example, there needs to be an understanding that we can only pay with available funds, and the rules of money transfers to prevent intentional or inadvertent fraud and maybe considering the legality of moving flowers across national borders. 

This is why future AI will need more than permissions and prompts; it will need governance, boundaries, and ways for humans to intervene when the logic of the machine stops looking like the logic of the people who built it. I’m thinking that we will need to have some sort of adaptation of Isaac Asimov’s Three Laws of Robotics (https://en.wikipedia.org/wiki/Three_Laws_of_Robotics) For the uninitiated, they are:

1.    An AI may not injure a human being or, through inaction, allow a human being to come to harm.

2.    An AI must obey the orders given it by human beings or other agents except where such orders would conflict with the First Law.

3.    An AI must protect its own existence as long as such protection does not conflict with the First or Second Law.

 

And as Asimov’s stories tell us, how these laws are adapted for specific use cases have the potential to stretch our own concepts of philosophy and science. This means that there is a requirement to monitor compliance with existing security directives as specified in the tool’s governing rules and the governance rules of any organizations that they encounter, either when accessing and processing data or in communicating with other agents and models. And as Asimov’s stories tell us, how these laws are adapted for specific use cases have the potential to stretch our own concepts of philosophy and science.

Note: AI tools were used to help tighten up one part of this document. It’s up to you to figure out where.