Mathematical Thinking

Table of Contents
Introduction
Fermi's Piano Tuner Problem
How Old is Old?
If the Terrestrial Poles were to Melt...
Sunlight Exerts Pressure
Falling Eastward
What if an Asteroid Hit the Earth
Using a Jeep to Estimate the Energy in Gasoline
How do Police Radars really work?
How "Fast" is the Speed of Light?
How Long is a Light Year?
How Big is a Trillion?
"Seeing" the Earth, Moon, and Sun to Scale
Of Stars and Drops of Water
If I Were to Build a Model of the Cosmos...
A Number Trick
Designing a High Altitude Balloon
Pressure in the Vicinity of a Lunar Astronaut Space Suit due to Outgassing of Coolant Water
Calendar Calculations
Telling Time by the Stars - Sidereal Time
Fields, an Heuristic Approach
The Irrationality of
The Irrationality of
The Number (i)i
Estimating the Temperature of a Flat Plate in Low Earth Orbit
Proving that (p)1/n is Irrational when p is a Prime and n>1
The Transcendentality of
Ideal Gases under Constant Volume, Constant Pressure, Constant Temperature and Adiabatic Conditions
Maxwell's Equations: The Vector and Scalar Potentials
A Possible Scalar Term Describing Energy Density in the Gravitational Field
A Proposed Relativistic, Thermodynamic Four-Vector
Motivational Argument for the Expression-eix=cosx+isinx
Another Motivational Argument for the Expression-eix=cosx+isinx
Calculating the Energy from Sunlight over a 12 hour period
Calculating the Energy from Sunlight over actual full day
Perfect Numbers-A Case Study
Gravitation Inside a Uniform Hollow Sphere
Further note on Gravitation Inside a Uniform Hollow Sphere
Pythagorean Triples
Black Holes and Point Set Topology
Field Equations and Equations of Motion (General Relativity)
The observer in modern physics


How Old is Old?

How old is the universe? How old is the human race? Cosmologists believe the universe to be 15 billion years old. It began with an immense explosion called the Big Bang, the echoes of which can still be detected by radio telescopes today. It expanded from an initial singularity and passed through several developmental stages. Today, it is still expanding. Astronomical observations of distant galaxies reveal tell-tale red shifts in their spectra. The further the galaxy, the greater the red shift. From these data the rate of expansion is inferred. The rate of expansion is expressed in a number called the Hubble Constant, after Dr. Edwin Hubble, who made the first observations of these red shifts and correctly assessed their meaning. The Hubble Constant today is estimated between 50 and 100 (km/s)/Mpc.

Our solar system is believed to be 4.6 billion years old. The solar system has existed for approximately the last third of cosmic history. A scale model may be built to help comprehend these numbers. If the history of the universe were represented by a 3,000 page book (for comparison, Webster's Unabridged New International Dictionary, Second Edition, holds a total of 3,208 pages) then the entire history of the solar system would be represented by the last 920 pages.

Those 920 pages include the formation of the sun and planets, the dawn and rise of life, the great geological ages, and the entire history of the human race:

  • The last 60 pages represent time from the Devonian epoch to the present.
  • At 30 pages from the end, the Age of Dinosaurs comes into full swing.
  • And at 13 pages from the end, the Age of Dinosaurs concludes and the Age of Mammals begins.
  • At 100 words from the end of the book, the Great Ice Age begins.
  • Written human history began less than 10,000 years ago and would occupy no more than the last 1/500th of the last page of the 3,000 page book.

If an average of 500 words per page is assumed then the entire book would contain 1,500,000 (1.5 million) words. Each word would represent 10,000 years of cosmic history. The last word of the last page would represent all of recorded human history.

Surely, humanity is a newcomer to the planet!