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Calculating Reality With Non-Existent Variables

Author: Dan Kruglov

Editors: Talia McDaniel and Max Herbreteau

Artist: Kyra Wang

Isn’t it cool that researchers and AI used alternative mathematical pathways but also form the same solution. The AI was tasked with solving a double pendulum problem with a known solution and was allowed to find its own algorithm for the desired answer, but how did it happen?

When we tackle such problems, we use primitive parameters, such as angular velocity (length and speed) or intuitive definitions (kinetic and potential energy) in order to understand the process visually, and we assign our physical framework of the world to each of them. For mass, we imagine how “heavy” an object is; for velocity, we imagine how “fast” something is, and so on. Upon dissecting the AI, researchers found that the algorithm used four variables. Two of these variables closely corresponded to the angles of the arms, but the other two variables were not identified. Researchers tried correlating these variables with ones we know, such as energy, velocity, and angular momentum, but nothing matched. The conclusion derived from this research is that instead of reinventing the wheel, AI came up with its own math - and some variables that AI used do not have a “physical sense” from the perspective of our human mind.

This might seem like a digression from common sense, but surprisingly, this pathway might lead the scientific community to new discoveries that were previously unimaginable. In 1926, Erwin Schrödinger invented a variable called the quantum wave function. Formally, it gives a mathematical description of the quantum state of a particle as a function, but what is particularly interesting is that this variable does not have any physical sense. By manipulating this function, we can find useful information about the quantum particle, like the probability density of finding a particle. Still, the wave function has no physical interpretation we can understand. The function is denoted with Greek letter Psi, Ψ(x), and the square of its amplitude is denoted as |Ψ(x)|^2.

To tell the truth, some variables that we use today do not always make complete sense. We frequently use the term energy in our lexicons, even though we can barely imagine it. Energy is “the quantitative property transferred to a body or a physical system, recognizable in work performance.” We say that energy can do “work,” yet we do not know what energy is. But by saying that something or someone is “energetic,” we immediately understand the point. In the quantum world, there are many conundrums such as this, where we don’t know for certain the physical interpretation of some variables, and even some variables that we think we understand can suddenly appear challenging to comprehend.

Our brain does not register the physical implication of the “wave function,” but we can still compute this variable and derive results from it that can speak about reality. When mathematics and physics were developed, people invented variables that seemed intuitive to understand and correlate with other known intuitive variables. To characterize electric current, people invented definitions such as “amperage,” which identifies the strength of the current, and “resistance,” as a measure of opposition to that current. It might not seem obvious, but this need to create physically logical variables is where our consciousness could give us flaws in understanding the universe. AI could be key in overcoming this barrier, inventing variables that only make mathematical sense but still lead us to the truth. Besides the double pendulum, researchers also fed AI a video of a lava lamp and a fireplace, and the program returned eight and 24 variables, respectively.

To illustrate the usefulness of such an algorithm, we’ve covered an example with quantum mechanics; researchers also add that this AI can be used in many subject areas, from biology to cosmology. While Artificial Intelligence might seem like a wild beast to tame, we can already see how its computational potential can maneuver the intuitive constraints of the human mind and calculate precise outcomes nonetheless, pushing science above and beyond!



Chen, Boyuan, et al. “Automated Discovery of Fundamental Variables Hidden in

Experimental Data.” Nature News, Nature Publishing Group, 25 July 2022,

Evart, Holly. “Roboticists Discover Alternative Physics.” Phys.Org,, 26 July 2022,

“Wave Function.” Wikipedia, Wikipedia Foundation, 16 Aug. 2023,

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