Entries by Brian Powell

A Poor Man’s CMB Primer: Quantum Seeds

  The CMB establishes a record of ancient acoustic oscillations in the baryon-photon plasma. We’ve been studying how these primordial sound waves evolve, and how to analyze the last scattering surface to learn about them. Now it’s time to confront their origin: what process composed the cosmic symphony? A few different proposals have been advanced […]

A Poor Man’s CMB Primer: Cosmic Acoustics

  Before decoupling, photons and charged particles were in good thermal contact: though the primordial plasma might have varied in temperature from place to place, the photons and baryons were in local thermal equilibrium and shared a common temperature. If some physical process caused the baryons to heat up in some place, this change in […]

Scientific Inference: Balancing Predictive Success with Falsifiability

  Bayes’ Theorem: Balancing predictive success with falsifiability Despite its murky logical pedigree, confirmation is a key part of learning. After all, some of the greatest achievements of science are unabashed confirmations, from the discovery of acquired immunity to the gauge theory of particle physics. But because we cannot isolate a unique hypothesis from the […]

Scientific Inference: Do We Really Need Induction?

  Part 2. “We don’t need no stinkin’ induction” — Sir Karl Popper The traditional scientific method supposedly employs induction both in the course of forming hypotheses and empirically confirming them. The examples of inductive inference from the previous note—whether the sun will rise tomorrow, or whether the sequence 1,3,5,7,9,… anticipates all odd numbers—were discussed […]

Scientific Inference: Logical induction ain’t logical

  Three million years ago, the grandfathers of our genus used sharpened stones to chop wood and cut bone. Today, surgeons use fiber optic-guided lasers to clear microblockages in the heart. Within our own lives, we’ve gone from burning our mouths on hot soup as children to cautiously blowing on the first spoonful as adults. […]

Perfect Secrecy and the Unbreakable Cipher

Is it possible to design an unbreakable cipher? Do methods of encryption exist that guarantee privacy from even the most capable and highly-resourced of prying eyes? This question is especially relevant today, as individual privacy and national security increasingly find themselves at opposite ends of the arbitration table. Powerful nation-states with unparalleled mathematical know-how and […]

The Monographic Substitution Cipher: From Julius Caesar to the KGB

A monographic substitution cipher works by replacing individual characters of plaintext with corresponding characters of ciphertext. It is perhaps the simplest encryption scheme ever devised: early monographic substitution ciphers were employed by Julius Caesar to secure private correspondence. These ciphers were low-tech, required virtually no mathematics, and encryption and decryption could be accomplished by finger […]

A Poor Man’s CMB Primer: Bumps on a Blackbody

  Astronomers Arno Penzias and Robert Wilson discovered the cosmic microwave background in 1965. They were not looking for it. They were using the comically distorted Holmdel Horn Antenna at Bell Labs, New Jersey, to study the reflection of radio waves off NASA balloon satellites. Despite all efforts to remove interference while calibrating the instrument […]

A Poor Man’s CMB Primer: The Birth of a Cosmic Background Radiation

  The early universe was hot. So hot, in fact, that nuclei boiled. The great thermal energy of the universe overwhelmed the confining efforts of the nuclear and electromagnetic forces, and droves of fundamental particles—quarks, gluons, leptons, photons—bounced and jostled in a tightly-coupled plasma. The universe, however, has a built-in cooling mechanism: expansion. Matter particles […]

A Poor Man’s CMB Primer: Orientation of the Universe

  This is a picture of the cosmic microwave background: Fig 1. The cosmic microwave background as seen by the European Space Agency’s Planck satellite, 2013. If the universe is an 80-year-old man, here it is as a zygote only a tenth of a second old. It is the oldest light ever observed, and it tells […]

Inflationary Misconceptions and the Basics of Cosmological Horizons

It is a common saying that during inflation “space expanded faster than the speed of light.”  This statement is meant to articulate the extreme rates of expansion seen during inflation, and this it does successfully. Unfortunately, it is at least a little wrong, and what little there is right about it is not unique to […]