Mysterious numbers: unlocking the secrets of the Universe - with Tony Padilla

The speaker begins by expressing admiration for Michael Faraday, a physicist from a humble background who overcame prejudice to make significant contributions to science. Faraday serves as an inspiration for young people entering the field of science. The speaker emphasizes the importance of numbers in physics, suggesting that numbers come to life when applied to the physical world, and announces the topic of the talk: the fantastic physics that emerges from large numbers.

The speaker recounts a personal anecdote about receiving a dictionary as a gift and becoming interested in the large numbers listed within it. The narrative highlights the excitement of discovering numbers like a trillion, quadrillion, and beyond, up to a centillion. The speaker laments not finding even larger numbers like a Google, a Googleplex, and Graham's number in the dictionary, which are the focus of the fantastic physics to be discussed. The audience is encouraged to think of the largest number they can, with infinity mentioned as an uncountable concept.

The concept of the Googleplexian universe is introduced, a hypothetical universe spanning a Googleplex meters across. The speaker humorously suggests the existence of doppelgangers in such a vast universe, including those of the speaker, the audience, and even celebrities. The idea is used to illustrate the mind-boggling scale of numbers like a Googleplex and to ponder the nature of the universe and reality itself.

The speaker delves into the Knuth's arrow notation, a system for describing very large numbers, to explain the concept of Graham's number. Starting with basic arithmetic operations, the explanation moves through exponentiation, tetration, and beyond, culminating in the description of Graham's number as an unimaginably large figure that surpasses a googolplex. The narrative emphasizes the complexity and the sheer scale of Graham's number, which is so large that it's difficult to comprehend.

The speaker humorously warns against the dangers of trying to conceptualize Graham's number, likening the attempt to a 'black hole head death,' a play on the perils of Mount Vesuvius's eruption. Entropy is introduced as a measure of missing information, with an interactive demonstration involving audience volunteers to illustrate how entropy works. The concept is further explained in the context of macroscopic objects and the loss of information that defines it.

The speaker explores the relationship between entropy and black holes, describing black holes as the 'entropic champions' of nature due to their ability to hide information. A thought experiment is conducted with audience participation to demonstrate how black holes can only have their mass, charge, and spin measured, thus hiding all other information about what they have consumed. The concept of Hawking radiation is briefly mentioned as a mechanism through which information might be released.

The speaker discusses the concept of quantum states and how they can describe different objects, such as an egg or a dinosaur, within a given volume of space. The idea of the holographic principle is introduced, suggesting that our three-dimensional universe with gravity could be equivalent to a two-dimensional universe without gravity. The principle is illustrated by comparing it to a hologram that stores information on a two-dimensional surface but can project a three-dimensional image.

The speaker touches on the concept of small numbers in physics, using a personal anecdote about a poor score on a musical test to illustrate the idea that small numbers are associated with unexpected events. The speaker then connects this to the cosmological constant problem, a significant discrepancy in theoretical physics regarding the unexpectedly small amount of vacuum energy in the universe. The emphasis is on the importance of understanding why the vacuum energy is so small, which is a fundamental question in physics.