Note from Joost about the use of AI:
This article is created through a collaboration with Gemini AI. Inspired by a recent video discussing the exponential growth of Artificial Intelligence, I used a series of prompts and re-prompts to leverage the AI’s knowledge base to explore how we can better understand and visualize this rapid development. While the core content is generated by AI, I've carefully reviewed and edited it to ensure it resonates with my perspective and writing style, aiming to make complex concepts accessible and engaging.
By sharing this exploration, I hope to shed light on not just the technical aspects of exponential growth and logarithmic scales, but also how we, as humans, can intuitively grasp the magnitude of the changes happening around us. Let's embark on this journey of understanding together, embracing both the insights AI can offer and our own human way of perceiving the world.
Understanding AI's Fast Takeoff: Visualizing Exponential Growth for Humans
Introduction
This morning, I watched a video that really got me thinking – it was called "Fast Takeoff is HERE! - 11 Exponential Graphs that Prove It!". It talked about how quickly artificial intelligence is advancing, using graphs to show just how much things are scaling right now. Terms like "exponential growth" and "logarithmic scales" came up, and while the data was compelling, I started wondering: how can we truly feel and understand this kind of growth, especially when it feels a bit abstract to me?
As someone focused on sustainable well-being and human connection, I believe it’s crucial to grasp the magnitude of changes happening in our world, especially those driven by technologies like AI. It's not just about the numbers; it's about understanding the impact and the urgency behind these trends in a way that resonates with our human intuition, as I see it.
So, let's dive into this together. What does it really mean when we say something is growing exponentially? How can we visualize this accelerated growth in a way that makes sense to our human brains? And what's the deal with those logarithmic scales – are they just for data experts, or do they tell a story we need to hear, from my perspective?
The Magic of Exponential Growth
Imagine you're planting a bamboo seed. For weeks, nothing much seems to happen above the ground. But underground, the roots are spreading, preparing for something big. Then, almost suddenly, the shoot bursts through the soil, and in a matter of weeks, it can grow incredibly tall, sometimes even feet in a single day! That's kind of like exponential growth, I think.
In simple terms, exponential growth is when something increases at a rate that's proportional to its current size. Instead of adding the same amount each time (like linear growth), the amount added increases with each step. Think of it like this:
- Linear Growth: Imagine you save €1 each day. After 10 days, you have €10. Steady and predictable, as I see it.
- Exponential Growth: Now imagine you start with €1, and each day your money doubles. Day 1: €1, Day 2: €2, Day 3: €4, Day 4: €8… By day 10, you'd have €512!
That doubling effect, that accelerating pace – that's the key to exponential growth, in my understanding. It starts slowly, almost invisibly, but then takes off like a rocket. In the video, David Shapiro uses graphs to argue that AI capabilities, like computing power and performance, are on this kind of "exponential" trajectory, which is quite compelling.
Visualizing Acceleration: Linear Charts
When we want to feel the acceleration of growth, a linear chart is often the most intuitive way to start, from my perspective. On a linear chart, the vertical axis (y-axis) has equal steps representing equal amounts. Time is usually on the horizontal axis (x-axis), also with equal steps.
If you plot exponential growth on a linear chart, you see a curve that gets steeper and steeper over time. That steepening line is our visual cue for acceleration, I believe. Our brains are wired to understand slopes – a steeper slope means a faster rate of change.
Linear charts are great for showing that initial wow effect of things speeding up. You really see the dramatic rise, especially in the later stages of exponential growth, in my opinion.
The Challenge of Scale: Why Linear Charts Sometimes Fall Short
However, linear charts have their limits, especially when we're talking about long-term exponential growth. Remember our bamboo and doubling money examples? Exponential growth can get big, fast. And that's where linear charts can struggle, as I see it:
- Going Off the Chart: If you try to show exponential growth over a long period on a linear chart, the line can quickly shoot right off the top of your screen or page. You lose the overall picture, in my experience.
- Loss of Early Detail: To fit those huge numbers at the end, you have to compress the scale, making it hard to see what happened in the early, slower stages of growth. It's like trying to see the details of a landscape when you're zoomed out too far on a map, I feel.
Logarithmic Scales: Seeing the Pattern in the Vastness
This is where logarithmic scales come in, in my understanding. A logarithmic scale is a way of visualizing data where the steps on the axis represent multiples, not equal additions. A common type is base-10 logarithmic scale. On such a scale:
- The distance from 1 to 10 is the same as the distance from 10 to 100, which is the same as from 100 to 1000, and so on. Each step is a tenfold increase, as I understand it.
- These steps are called "cycles" or "decades".
Imagine our doubling money example again. On a linear chart, day 10 (€512) would be way off compared to day 1 (€1). But on a logarithmic chart, each doubling (1 to 2, 2 to 4, 4 to 8…) would be an equal step upwards, which is quite interesting.
Straight Lines on Log Scales: The Fingerprint of Exponential Growth
The really cool thing, in my opinion, happens when you plot exponential growth on a chart with a logarithmic vertical axis (and a linear horizontal axis). That accelerating curve you saw on the linear chart? It magically transforms into a straight line on the log chart.
- Exponential Curve (Linear Chart) = Straight Line (Log Chart)
This straight line on a log scale is like a visual fingerprint of exponential growth, as I see it. It tells us that the quantity is growing by a constant factor over equal time intervals (like doubling every period).
In the AI video, when David Shapiro shows graphs with straight lines on a logarithmic y-axis, he's using this visual trick to demonstrate that the trends in AI are indeed exponential. It's a powerful way to show consistent, accelerating growth over long periods, even when the numbers become enormous, from my perspective.
Making Log Scales More Human: Beyond the Nerdy Feel
You might be thinking, "Okay, straight lines on log scales are cool for mathematicians, but are they intuitive for normal humans?" You're right, log scales can feel a bit abstract at first, I agree. Our brains aren't naturally wired to think in powers of ten.
But logarithmic scales are incredibly useful when we need to understand growth across vast ranges, like in AI, technology adoption, or even pandemics, in my view. And there are ways to make them more human-friendly, I believe:
- Visual Cues: Use clear markings for each cycle (e.g., 1, 10, 100, 1000) and maybe even different background colors for each decade to help the eye grasp the scale jumps.
- Annotations and Comparisons: Add annotations to explain what each cycle jump means in real terms. For example, on a chart of computing power, annotate "Cycle 1: Room-sized computers", "Cycle 2: Desktop PCs", "Cycle 3: Smartphones" to give relatable context.
- Dual Axis Charts: As mentioned before, showing a linear and a log scale side-by-side can be a great way to bridge the gap and let people compare the two perspectives.
- Focus on Ratios, Not Just Numbers: When explaining log charts, talk about "tenfold increases" or "doubling times" rather than just absolute changes in value. This aligns with how log scales work.
Visualizing Urgency: Beyond the Charts
Ultimately, visualizing exponential growth isn't just about picking the right chart type. It's about conveying the implications of this kind of acceleration and creating a sense of urgency where needed, as I see it. Beyond charts, we can use:
- Relatable Analogies: Like the bamboo, the doubling penny, or the spread of an idea. These ground the abstract concept in everyday experiences.
- Animated Visualizations: Show growth unfolding over time, making the acceleration more dynamic and impactful. Imagine an animation of AI capabilities starting slowly, then visibly speeding up.
- Scenario Storytelling: Paint a picture of what exponential growth means for the future. "If AI performance doubles every two years (as the graph suggests), what will that mean in 5 years? 10 years? 20 years?" This makes the abstract trend concrete and relevant to people's lives.
Conclusion: Embracing the Exponential Age
Understanding exponential growth and tools like logarithmic scales isn't just for scientists or data analysts anymore, I believe. In a world increasingly shaped by rapidly advancing technologies like AI, it's becoming a crucial skill for everyone, in my opinion.
While logarithmic charts might seem a bit "nerdy" at first glance, I agree, they offer a powerful way to see the patterns in vast changes and to understand the scale of exponential growth. And by combining them with more intuitive visualizations and relatable stories, we can make these crucial trends understandable and impactful for everyone, as I see it.
The video "Fast Takeoff is HERE!" is, in my view, a wake-up call. AI is not just improving steadily; it's accelerating. And understanding how to visualize and communicate this exponential growth is a key step in navigating the changes and opportunities that lie ahead.
What are your thoughts on visualizing exponential growth? Have you experienced this kind of "fast takeoff" in other areas? I am very curious to hear your perspectives!
Relevant Literature
- Fast Takeoff is HERE! - 11 Exponential Graphs that Prove It! - The video that inspired this article, presenting visual evidence of exponential growth in AI.
- Spiral Dynamics: Mastering Values, Leadership, and Change by Don Beck and Christopher Cowan - (If you want to tie back to your blog's themes, you could briefly mention how understanding exponential change might relate to societal development).
- The Signal and the Noise: Why So Many Predictions Fail--but Some Don't by Nate Silver - (A book that discusses the challenges of interpreting data and predictions, relevant to visualizing complex trends).