In statistical physics, temperature corresponds to the average thermal energy per particle: $$ K_B T \sim E $$ So the temperature formula in the paper is just: $$ T \sim \epsilon \, \frac{E_\text{Ry}}{k_B} $$ William H. Press (b. 1948) is a physicist best known for work in astrophysics and computational science (co-author of the classic Numerical Recipes). He earned his PhD under Nobel laureate William Fowler at Caltech, later held professorships at Harvard and UT Austin, was deputy director of Los Alamos, and served on the U.S. President’s Council of Advisors on Science and Technology.  The author argues that intelligent life requires - (i) complex chemistry - (ii) substantial atmosphere - (iii) bodies strong enough to resist gravity. From these premises, he derives the density of life-forms, environmental temperature, planetary mass and radius, and finally the characteristic size and lifespan of intelligent beings. The only free parameter is the effective bond energy, ε ≈ 0.003 Ry (hydrogen bonds), with size depending weakly on ε (∝ ε^¼) and lifespan strongly (∝ ε$^{–2.75}$). His conclusion: intelligent creatures across the universe should be roughly Earth-sized and live on Earth-like planets, though their characteristic timescales may differ greatly with stellar environment. The Rydberg energy is the binding energy of the electron in the hydrogen atom’s ground state The Bohr radius is a fundamental length scale in atomic physics, it’s the typical size of the hydrogen atom in its ground state, according to the Bohr model. We want to estimate the condition for a planet to retain a nontrivial atmosphere. Press first sets the ambient temperature by the chemistry scale: #### Thermal velocity \[ k_B T \sim \epsilon \, E_{\rm Ry} \] For hydrogen atoms (mass $m_p$) in a gas at temperature $T$, the typical kinetic energy per particle is of order the thermal energy, \[ E_{\rm kin} \sim E_{\rm thermal} \sim k_B T. \] Using $E_{\rm kin} \sim \tfrac{1}{2} m_p v_{\rm th}^2$, we get \[ \tfrac{1}{2} m_p v_{\rm th}^2 \sim k_B T \quad \Rightarrow \quad v_{\rm th}^2 \sim \frac{2 k_B T}{m_p}. \] Since this is an order-of-magnitude argument, factors of order unity are dropped, so we write \[ v_{\rm th}^2 \sim \frac{k_B T}{m_p}. \] Substituting, \[ v_{\rm th}^2 \sim \frac{\epsilon \, E_{\rm Ry}}{m_p}. \] #### Escape velocity For a planet of mass $M_\oplus$ and radius $R_\oplus$, the surface escape speed is \[ v_{\rm esc}^2 \sim \frac{G M_\oplus}{R_\oplus}, \] again omitting the factor of 2 as we keep only leading scalings. #### Retention condition To avoid losing the atmosphere, we require $v_{\rm esc} \gtrsim v_{\rm th}$. Equating the scales gives \[ \frac{G M_\oplus}{R_\oplus} \sim \frac{\epsilon \, E_{\rm Ry}}{m_p}, \] which is Press’s Eq. (5). Intelligent life elsewhere should be roughly our size (meters tall) and live on Earth-like planets (mass and radius close to Earth’s), since size of creatures depends weakly on 𝜖. Howver their characteristic timescales (metabolism, reaction speeds, lifespans) could differ drastically, since they depend sensitively on the fraction 𝜖 of the Rydberg that local chemistry actually uses. So aliens might be our size, but experience time very differently: “slow” or “fast” compared to us. The anthropic principle is the idea that the universe’s laws and constants must allow for the existence of observers like us, otherwise we wouldn’t be here to notice them. There are a couple of standard formulations: - Weak anthropic principle (WAP): Our observations of the universe are necessarily biased by the fact that we exist. For example, we shouldn’t be surprised to find ourselves on a planet with liquid water, because only such planets can support beings asking the question. - Strong anthropic principle (SAP): The universe (or multiverse) must have properties that inevitably give rise to life and observers at some stage. This is more controversial, because it sounds like the universe is “designed” for life, though in physics it’s often interpreted in terms of selection effects across many possible universes. Physicists sometimes use the principle in a very practical sense: to explain why certain physical constants (like the strength of gravity or the fine-structure constant) take the values they do if they were even slightly different, stable stars, chemistry, or life might not exist.