These Mathematicians Don’t Believe Large Numbers Exist. I’m Serious.

The Pervasive Problem of Infinities in Physics

• ⚠️ Infinities are a common feature in current physics, appearing in concepts such as the infinite universe, Big Bang curvature, black hole tidal forces, and various quantum physics calculations.
• 💡 Physicists frequently employ "mathematical gymnastics" to eliminate these infinities, suggesting they are not physically real entities.
• 🌌 The cosmological constant is even considered by some to be a lingering issue stemming from problems with infinity.
• 🔬 The concept of the infinitely small also presents challenges, with space, time, and Hilbert space in quantum physics often conceptualized as containing infinitely many points of size zero.

Physicists Challenging Infinite Concepts

• 🧠 Several physicists are questioning the reliance on infinities; for example, George Ellis suggests their careless use led to the belief in the multiverse.
• 🔑 Nicolola Jiza argues against using real numbers because their infinite digits demand an impossible infinite precision.
• ⚡ Tim Palmer proposes that issues in quantum mechanics arise from the use of Hilbert space's continuum, advocating for discretization and finite steps.
• 🚧 Most physicists, however, view infinities as innocent mathematical tools or approximations, believing their removal would not alter fundamental results.

Introducing Ultra-finitism

• 🎯 Ultra-finitism is a philosophical movement that seeks to remove not only infinities but also extremely large numbers (like 10^100) from mathematics and physics.
• 💬 According to Joe Humpkins, a math professor at the University of Notre Dame, ultrafinitism posits that these large numbers do not actually exist.
• 💡 This approach involves mathematicians exploring how to define mathematics using only small numbers, focusing on consistent ultra-finitist logic and bounded arithmetic.

Potential Impact on Physics

• 🚀 Ultra-finitism could potentially explain existing puzzles, such as why entropy has a maximum bound or the persistent presence of infinities in quantum theory.
• 🛠️ It might provide a crucial tool for quantizing gravity by resolving the infinities that current theories repeatedly encounter.
• 📈 A recent conference in April highlighted the growing interest and the developing mathematical backbone supporting this philosophical perspective.

The Speaker's Perspective

• 🤔 The speaker expresses difficulty in comprehending how a number like 10^100 can "not exist" when it can be readily written and computed.
• 💡 While acknowledging that physical quantities might be finite, the speaker finds denying the existence of numbers to be a "different level of denialism."
• 💬 Despite personal skepticism, the speaker emphasizes the importance of open-mindedness and informing the audience about such potentially paradigm-shifting ideas.