On Exponential Growth (2020-)

"Exponentially growing systems are prevalent in nature, spanning all scales from biochemical reaction networks in single cells to food webs of ecosystems. How exponential growth emerges in nonlinear systems is mathematically unclear. […] The emergence of exponential growth from a multivariable nonlinear network is not mathematically intuitive. This indicates that the network structure and the flux functions of the modeled system must be subjected to constraints to result in long-term exponential dynamics." (Wei-Hsiang Lin et al, "Origin of exponential growth in nonlinear reaction networks", PNAS 117 (45), 2020)

"With cloud data lakes you typically pay for what you use, so your costs always align with your data volumes. Since there is only a single storage layer, less data movement across different systems, availability settings, and decoupled storage versus compute, you have isolated and minimized costs for just data storage. For greater cost allocation, most cloud data lakes offer buckets, or containers (filesystems, not to be confused with application containers), to store different layers of the data (e.g., raw versus transformed data). These containers allow you to have finer-grained cost allocation for different areas of your organization. Since data sources and volumes are growing exponentially, it is extremely important to allocate and optimize costs without limiting the volume or variety of data that can be stored." (Bennie Haelen & Dan Davis, "Delta Lake: Up and Running - Modern Data Lakehouse Architectures with Delta Lake", 2023)

"In effect, AI is transforming the entire globe into a gigantic meta-brain – a vast, interconnected web of intelligence, continuously fed by humans, AI models, robots, self-driving cars, and autonomous systems of every kind. As this process accelerates, critical data density reaches unprecedented levels, driving AI into a self-reinforcing spiral of perpetual improvement, where each new insight compounds into an unstoppable force of exponential progress." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025

"When we explore the mathematics behind the natural world, we encounter a fascinating phenomenon: the principle of combinatorial complexity. This principle explains the exponential increase in possibilities that arise when we combine even a small number of elements." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"While the universe as a whole tends towards greater disorder, there are local, pinched pockets where complexity spontaneously increases. And such processes can, as we have seen, continue even over billions of years and come a very long way. We live in such a pocket, and the complexity in it is growing exponentially – and on some fronts hyperexponentially." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)