StarTalk Radio

Cosmic Queries – Understanding Infinity with Stephon Alexander

February 6, 2026

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  • Physicists often try to avoid infinities, such as those predicted in black hole singularities where density becomes infinite, viewing them as limits to the applicability of current theories like General Relativity. 
  • Quantum mechanics, while introduced to resolve classical infinities (like those in magnetic forces), introduced its own set of infinities (divergences) until theories like String Theory were developed as potentially infinity-free quantum theories that incorporate gravity. 
  • The concept of an infinite universe is complex, as one can experience an endless journey (never reaching an edge) in a finite, closed geometry (like a sphere) or an expanding universe, meaning the inability to reach an edge does not automatically prove spatial infinity. 

Segments

Introduction and Guest Welcome
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(00:01:14)
  • Key Takeaway: Neil deGrasse Tyson introduces the archived episode of StarTalk Radio focusing on ‘Infinity’ featuring Stephon Alexander.
  • Summary: Neil deGrasse Tyson welcomes listeners to an archived Cosmic Queries episode focusing on infinity. The guest is theoretical physicist, cosmologist, and musician Stephon Alexander, author of ‘The Jazz of Physics’ and ‘Fear of a Black Universe’. The episode centers on the concept of infinity, which also featured in the 2022 Netflix documentary ‘A Trip to Infinity’.
Personal Encounters with Infinity
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(00:04:44)
  • Key Takeaway: Childhood encounters with the concept of ‘Eternal Flame’ sparked early existential angst about infinity.
  • Summary: Neil deGrasse Tyson recounts his five-year-old confusion over the term ‘Eternal Flame’ at JFK’s burial, questioning how a flame could never extinguish. Negin Farsad notes her teenage angst stemmed more from existential philosophy (Sartre) than mathematical infinity. The discussion establishes that infinity is a concept that naturally provokes deep, sometimes unsettling, thought.
Infinity in Mathematics and Computing
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(00:07:27)
  • Key Takeaway: Division by zero in mathematics results in infinity, a concept that causes computer programs to crash.
  • Summary: The concept of infinity arises naturally when considering counting forever or dividing by zero in fractions (e.g., 1/0). Division by zero is mathematically linked to infinity, which is why computers are programmed to avoid this operation, resulting in a program crash. Asymptotes, where a curve approaches a line but never touches it, are related concepts that approach infinity.
Infinity as a Physicist’s Cop-Out
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(00:10:37)
  • Key Takeaway: Physicists generally try to avoid infinities in their theories, unlike mathematicians who utilize them extensively.
  • Summary: A listener question expresses frustration that ‘infinite density’ in singularities or an ‘infinite universe’ seem like labels for things physicists do not fully understand. Stephon Alexander confirms that physicists often view infinities as signs that their current theory is breaking down, contrasting this with mathematicians who actively work with the concept.
Black Hole Singularities and Theory Limits
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(00:11:22)
  • Key Takeaway: The singularity predicted at the center of a black hole, involving infinite density and curvature, signals the limit of General Relativity’s applicability.
  • Summary: Einstein’s General Relativity mathematically predicted black holes, which contain a singularity where density and forces become infinite as the radius approaches zero. While the existence of black holes is confirmed, the infinite nature of the singularity suggests that General Relativity must be replaced by a new theory (like quantum gravity) at that extreme point. Some physicists suggest nature might be ‘censoring’ these infinities from physical realization.
Taming Infinities with Quantum Physics
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(00:21:58)
  • Key Takeaway: Quantum mechanics successfully ‘de-infinitized’ infinities found in classical electromagnetism by introducing quanta like photons.
  • Summary: Classical physics predicted infinite force between magnets at zero distance, but quantum physics resolves this by describing the force as mediated by discrete particles (photons). This success leads physicists to hope that a theory of quantum gravity will similarly resolve the infinite singularity found in black holes.
String Theory and Musical Analogy
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(00:32:34)
  • Key Takeaway: String theory was developed partly because it is an infinity-free quantum theory that naturally incorporates musical analogies through vibrating strings generating notes.
  • Summary: String theory emerged as a quantum theory that successfully eliminated the infinities present in earlier quantum mechanics calculations. The theory posits that fundamental constituents are vibrating strings rather than point particles. The vibrations of these strings generate standing waves, which mathematically correspond to the notes or tones generated by vibrating musical strings.
Reconciling Research and Artistry
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(00:39:42)
  • Key Takeaway: Jazz improvisation requires embracing mistakes and breaking rules while building on foundations, mirroring how physicists must navigate nonsensical but predictive mathematical structures like infinity.
  • Summary: Stephon Alexander embraces infinities in his research, viewing them as areas where progress can still be made around the edges. In jazz, improvisation involves mastering foundations while intentionally stumbling and breaking rules to create something new, which parallels accepting mathematically difficult concepts that still yield correct predictions. The ability to appreciate complex, non-intuitive structures (like Ornette Coleman’s music) can develop over time.
Defining Space-Time and Physical Reality
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(00:43:37)
  • Key Takeaway: Loop Quantum Gravity suggests space-time is composed of discrete, linked ‘pixels’ or ‘atoms’ of gravitational fields, representing the smallest unit of space.
  • Summary: Loop Quantum Gravity attempts to resolve gravitational infinities by proposing that space-time is not a smooth continuum but is woven from linked gravitational field tubes, analogous to links in a chain. These links can be conceptualized as the smallest possible units or ‘pixels’ of space. While space-time is a medium that supports its own ripples (gravitational waves), its true nature remains difficult to grasp intuitively, relying heavily on mathematical descriptions that yield accurate predictions.