The AI Inflection Point
Navigating the Exponential Frontiers of Factorial Growth
The general public has no idea what’s happening.
Even the nerds and geeks who are locked-in to their areas are failing to see the big picture.
We are not simply witnessing a technological shift; we are living through an inflection point of historical significance. Artificial general intelligence represents a fundamental paradigm shift, akin to the advent of the printing press, the internal combustion engine, or the internet – but with a crucial difference: the rate of change is unprecedentedly constantly growing… at an accelerating rate.
We are inside the singularity right now.
This isn't a linear progression; it's an exponential explosion, and understanding this distinction is the key to unlocking unparalleled opportunities for both individuals and businesses. We may go faster than exponential.
For decades as a technologist and investor I've observed the cyclical nature of technological adoption.
There's the initial hype, followed by the trough of disillusionment, and then, for the truly transformative technologies, the slow, steady climb to widespread adoption. But AI is defying this traditional curve. Its ascent is not slow and steady; it's a rocket launch. And the fuel powering this rocket is exponential growth.
The Linear Mind vs. The Exponential Reality
The persistent underestimation of AI's potential isn't due to a lack of data; it's rooted in a fundamental cognitive bias.
Humans are inherently linear thinkers. We project the future based on our past experiences, extrapolating in a straight line. This works reasonably well in stable environments, but it completely breaks down when confronted with exponential phenomena.
Consider this familiar analogy: Imagine you're standing on a chessboard, and on the first square, there's a single grain of rice. On the second square, there are two grains, on the third, four, and so on, doubling with each square. A linear thinker might look at the first few squares and conclude, "This is manageable; it's just a few grains of rice." But by the time you reach the 64th square, you're dealing with more rice than exists on the entire planet. This is the power of exponential growth, and it's precisely what we're seeing with AI.
Another helpful analogy might be compound interest. Most people understand the concept of gaining, lets say, 6% interest. It doesn't seem like a lot. 6%? That's fine, nothing crazy. But when you understand that that 6% compounds on itself year after year and your actual returns will be much, much higher, you can see why "Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it", as Einstein supposedly said.
The initial iterations of AI – the early chatbots, the rudimentary image generators – were like those first few grains of rice. They seemed underwhelming, easily dismissed. But each iteration wasn't just a small step forward; it was a multiplication of the previous capabilities. And this multiplicative effect is accelerating.
The Recurring Pattern of Dismissal
Let's revisit five now-familiar examples, but this time, frame them within the context of investment and technological foresight:
2022 - ChatGPT (Early Versions): The prevailing sentiment was, "It's a glorified autocomplete, incapable of true understanding."
Missed Opportunity: Failing to recognize the underlying architecture – the transformer model – and its potential for revolutionizing natural language processing. Investors who understood this saw the potential for massive disruption in search, customer service, content creation, and countless other fields.
2022 - Image Models (Stable Diffusion, etc.): "It's creating distorted, dreamlike images; it's a novelty, not a tool for professionals."
Missed Opportunity: Underestimating the speed at which these models would improve and the transformative impact they would have on graphic design, advertising, visual effects, and the very concept of visual content creation.
2023 - Realistic People in Images: "The uncanny valley is insurmountable; AI-generated humans will always be detectable."
Missed Opportunity: Ignoring the rapid advancements in generative adversarial networks (GANs) and the potential for creating photorealistic virtual beings for gaming, entertainment, virtual assistants, and even personalized education.
2024 - AI-Generated Video (Sora, etc.): "The motion is jerky, the physics are unrealistic; it's years away from being usable."
Missed Opportunity: Failing to grasp the exponential trajectory and the potential for AI to democratize filmmaking, create hyper-personalized video content, and revolutionize fields like training and simulation.
2025 - AI in Game Development: "It'll lead to generic, uninspired games; AI can't replicate human creativity."
Missed Opportunity: Underestimating the ability of AI to assist with asset creation, level design, character behavior, and even the generation of entirely new game mechanics, leading to more immersive and personalized gaming experiences.
In each case, the "experts" focused on the present limitations rather than the future potential.
They were looking at the chessboard and seeing a handful of rice grains, completely oblivious to the mountain of rice that was about to materialize. This is not just a matter of academic interest; it's a matter of trillions of dollars in missed investment opportunities and squandered competitive advantage.
From Exponential to Factorial
This is a concept that borders on the incomprehensible but we must explore it to understand AI's trajectory.
What if AI is able to improve its own architecture?
What if AI is able to build its own training data?
What if AI drives breakthroughs in hardware design for chips, cooling and more?
While exponential growth is already challenging for our linear minds to grasp, there's a possibility (which I believe is inevitable) that AI development will eventually transition to an even more radical growth pattern: factorial growth.
What is Factorial Growth?
Factorial growth is much faster than exponential growth in the long run. While exponential growth is rapid, factorial growth is explosively rapid.
Exponential Growth: A quantity doubles at regular intervals (e.g., 2, 4, 8, 16, 32).
Factorial Growth: A quantity is multiplied by successively increasing integers (e.g., 1, 2, 6, 24, 120, 720).
Exponents have a constant multiplier… but factorial growth isn’t constrained to “only grow” at the same multiple… in fact, factorials grow at a constantly increasing rate.
In this case as an example imagine each step you multiply by a number that's one larger than the previous multiplier.
Think of it this way:
Exponential: Repeatedly doubling (or tripling, etc.) is fast.
Factorial: Repeatedly multiplying by a bigger and bigger number is much faster.
The Staggering Difference: An Example
Let's compare exponential and factorial growth over just ten steps.
Exponential growth gets you to 1,024 after 10-steps. You can see the classic doubling power coming through and gaining steam.
How much “steam” has the factorial built up after 10-steps?
3,628,800… that’s over 3,500x faster growth by the 10th step.. and every step the growth rate delta increases.
Step 1: 1
(1! = 1)
Step 2: 2
(2! = 2 * 1 = 2)
Step 3: 6
(3! = 3 * 2 * 1 = 6)
Step 4: 24
(4! = 4 * 3 * 2 * 1 = 24)
Step 5: 120
(5! = 5 * 4 * 3 * 2 * 1 = 120)
Step 6: 720
(6! = 6 * 5 * 4 * 3 * 2 * 1 = 720)
Step 7: 5,040
(7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040)
Step 8: 40,320
(8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320)
Step 9: 362,880
(9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362880)
Step 10: 3,628,800
(10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800)
As you can see, even at just step 10, the factorial growth dwarfs the exponential growth.
By step 20, the factorial is 2,432,902,008,176,640,000… while the exponential is a mere 1,048,576.
The difference is astronomical in the most accurate sense of the word.
See how the growth rate is growing at a growing rate in the Multiple column below?
The rightmost column shows the ratio of the Factorial value to the Exponential value.
This column highlights how much faster factorial growth is compared to exponential growth.
That’s the trajectory AI is accelerating toward.
How Will AI Achieve Factorial Growth?
The key lies in the concept of recursive self-improvement.
Current AI models are largely trained on existing data.
Exponential growth occurs as we get better at training models, create more efficient architectures, and gather more data.
However, several companies are building an AI that can not only learn from data but also redesign its own architecture and develop entirely new learning algorithms. This AI wouldn't just be improving its performance; it would be improving its ability to improve.
Each improvement would then be multiplied by all previous improvements, leading to a potential factorial explosion in capability.
Here's a simplified, hypothetical scenario:
AI Level 1: Can analyze data and make predictions (baseline).
AI Level 2: Can improve its prediction accuracy by optimizing its parameters (exponential improvement).
AI Level 3: Can rewrite its own code to create a more efficient learning algorithm (a new, more powerful baseline).
AI Level 4: Can design a new hardware architecture specifically tailored to its new algorithm (another, even more powerful baseline).
AI Level 5: It uses all of it's abilities at all levels to improve every level below it, and itself, at the same time.
It doesn’t even need to go “physical” at Level 4. It can focus entirely on improvements to pre-training methods, model training, data processing techniques, model architectures / designs along with dozens of other knobs and levers that control performance.
We just profiled a model that is self-rewarding. We also explored a model that can self-reason and work with tools (such as a python interpreter) to constantly improve.
Each level builds upon the previous not additively, but multiplicatively.
The Implications of Factorial Growth
If AI were to achieve even a limited form of factorial growth, the consequences would be profound and difficult to fully predict. We could see:
Deep Technological Singularity: A rapid, runaway intelligence explosion, where ASI surpasses human intelligence by an unimaginable degree.
Unprecedented Scientific Discovery: AI will solve problems that are currently intractable for humans, leading to breakthroughs in medicine, materials science, energy, and every other field.
Radical Societal Transformation: The fabric of society will be reshaped, with implications for work, governance, economics, and even the nature of consciousness.
It's crucial to emphasize that factorial growth in AI is just a possibility, not a certainty, given our technology trajectory and understanding of physics. There are significant technical hurdles to overcome, and we may never reach this point.
That being said, the trends are accelerating and we constantly discover new pathways we failed to see / appreciate previously. We have increasingly smarter tools we can use to explore these newfound pathways the moment we find them. It also enables us to connect them to other areas of research and development.
The AI revolution is not a future event; it's the present reality.
We are living through the most important period in human history.
The companies that thrive in this new era will be those that embrace the exponential nature of AI, that shed their linear thinking, and that actively integrate AI into the core of their day-to-day operations and their business model.
The people who thrive in this new era will embrace AI, too.
And while factorial growth is still a theoretical possibility, it's a possibility that underscores the sheer scale of the potential transformation. This is not just about adopting technology; it's about adopting a new mindset – a mindset of continuous learning, adaptation, a willingness to challenge assumptions, and a relentless pursuit of innovation.
The opportunity is immense.
The leverage is unprecedented.
The time to act is now.
Don't be the fool looking at the chessboard and dismissing the grains of rice doubling each step. Be the one who sees the mountain, and builds the future. And perhaps, be prepared for a future that's even more transformative than we can currently imagine.
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I started Life in the Singularity in May 2023 to track all the accelerating changes in AI/ML, robotics, quantum computing and the rest of the technologies accelerating humanity forward into the future. I’m an investor in over a dozen technology companies and I needed a canvas to unfold and examine all the acceleration and breakthroughs across science and technology.
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