I recently ran across the research of the late Dr. Albert A. Bartlett, a physics professor who spent decades warning that our greatest human flaw is an inability to understand the exponential function. His most famous analogy involved bacteria doubling in a bottle: the bottle looks 97% empty just five minutes before it is completely full at noon.
This raises a critical question for our current era: Where will AI “fill up” the bottle, and how can we predict that point before it is too late?
The 11:55 PM of Computing Power
For decades, we viewed the growth of technology through the lens of Moore’s Law—a steady doubling of transistors every two years. However, the compute used to train the largest AI models has recently been doubling at a much faster rate, roughly every 3.4 months according to data from Epoch AI.
In Bartlett’s terms, if we are currently at “11:55 PM” in AI development, the world still looks relatively empty of “Super Intelligence.” To a linear thinker, the progress seems manageable because the bottle is 97% open space. To an exponential thinker, we are only a few doubling periods away from a total saturation of the environment.
The Finite Resources of the AI Era
Dr. Bartlett’s work focused on physical limits, specifically energy and space. AI faces the same hard walls, even if they are less visible to the average user:
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The Data Wall: Research estimates suggest that the stock of high-quality, human-generated public text data could be exhausted between 2026 and 2032. Like the bacteria running out of nutrients, AI models are reaching the limits of the “natural” information available to them.
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The Energy Limit: A single AI query consumes significantly more electricity than a traditional search. If AI energy demands continue their exponential trajectory, they will eventually collide with the physical capacity of national electrical grids and global sustainability goals.
Why We Are Historically Bad at Predicting the “Full” Point
The reason we struggle to predict the peak of AI is the same reason the “banker” in Bartlett’s story was surprised: we confuse current volume with the growth rate.
We often fall into the Linear Trap, assuming that because AI still makes basic mistakes today, the “Full Bottle” moment is decades away. However, the Exponential Reality is that the final doubling period uses as much resource—and creates as much “intelligence”—as all previous steps in history combined.
Predicting the Saturation Point
To predict where AI “fills the bottle,” we have to stop looking at how AI behaves today and start calculating the doubling time of its capabilities. If the efficiency and power of these models continue to double at the current rate, the transition from a “useful tool” to total economic and cognitive displacement won’t happen gradually. It will happen in the final “minute” of the hour.
Dr. Bartlett’s lesson is clear: by the time a problem is obvious to everyone, the time remaining to address it has already vanished. We aren’t just building faster computers; we are filling a finite bottle at an accelerating pace.
References:
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Bartlett, A. A. (1978). “Arithmetic, Population, and Energy.” American Journal of Physics.
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Villalobos, P., et al. (2022/2024). “Will we run out of data? Limits of LLM scaling based on human-generated data.” Epoch AI.
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OpenAI (2018). “AI and Compute” analysis of training trends.
