Bob Doyle, Columnist
Last year, the book “Spectrums: Our Mind-Boggling Universe from Infinitesimal to Infinity” by David Blatner was published by Walker and Company. Its ISBN is 978-0-8027-1770-2 (hardback).
Blatner is the author of 15 books, including “The Joy of Pi,” “The Flying Book” and “Silicon Mirage: The Art and Science of Virtual Reality.”
The word spectrum is from the Latin word for vision, and consists of an assortment of characteristics or objects along a scale for comparison.
Blatner tackles the spectrums (or spectra) for numbers, sizes, light, sound, heat and time. Space limits this review to two spectra or spectrums, the great ranges in numbers and sizes.
Humans live in “the middle world” — midway between the smallest things we know and the largest things we can detect.
What is the dominant form of life on Earth? Blatner comments, “There are more insects in a single square mile of good, fertile soil than there are human beings on Earth.”
In handling very small and very large numbers, it’s best to use exponents or powers of 10 (the number 1 followed by as many zeroes as the small exponent number). There are now a little more than 7 billion or 7 x 10 to the 9 or 7,000,000,000 humans now living on Earth.
Another large number often mentioned in political discussions is the U.S. government debt of about $17 trillion or 17 x 10 to the 12 or 17,000,000,000,000 dollars.
How could this debt be paid off over the next 34 years? $17 trillion divided by 34 would require our government to pay $500 billion each year to our debtors.
This can’t be done by reducing revenues (taxes) but by increasing money flowing into the U.S. Treasury.
One reality that prevents most humans from grasping large numbers is “number numbness” (from cognitive scientist Douglas Hofstadter). One can visualize a football stadium with about 100,000 spectators. The upper boundary of our visual perception is between one and 10 million.
You can print out a poster with one million dots or units and still be able to see the individual units. But if we go to a larger number of units, most of us can’t distinguish between 5 million or 10 million.
The term “as many grains of sand as there are on Earth” is often heard. Scientists at the University of Hawaii estimate the number of sand grains in or on the Earth as 7.5 billion billion grains. (This number has 75 followed by 17 zeroes.)
The number of stars in the universe is even larger. Sky surveys estimate that there are 150 billion galaxies across the known universe. If an average galaxy has 10 billion stars, then the number of stars across the known universe would be 1.5 thousand billion billion stars or 15 followed by 20 zeroes.
When we turn our attention to size, we need units of very small distances to describe our human cells and the size of atoms. A millimeter is one thousandth of a meter or 0.001 meter. A grain of sand is about 0.5 millimeters across.
An even smaller distance unit is the micron, a millionth of a meter. The smallest thing we can see is between 100 and 200 microns, the width of dust mites and the largest human cell, a human ovum or egg. This is roughly the width of a human hair.
The next small unit is a nanometer, a billionth of a meter. Visible light has wavelengths from 400 to 700 nanometers. Objects 1000 nanometers or smaller can’t be seen due to the waves of light we use to see. Electron scanning microscopes using electric fields can detect the electron clouds of atoms that are a few tenths of a nanometer in size.
A femtometer is a millionth of a nanometer or 10 to the minus 15 meters (decimal point with 14 zeroes to the right, followed by number 1). The nucleus of an atom , containing nearly all each atom’s mass and energy is about 1 femtometer in size.
Going to the largest size, the known universe is estimated to be 46 billion light years in radius. A light year is about 6 trillion miles, the distance that light travels in a year. This means that the farthest we can see into space (the cosmic horizon) is 276 billion trillion miles.
The universe being of finite age, limits our view. We can’t see any farther than the distance that light can travel since the origin of our universe, estimated to be 13.7 billion years ago. The distance beyond 13.7 billion light years is due to the expansion of space since the time the universe started.
SKY SIGHTS AHEAD: The evening moon is now just past half full (first quarter phase) and ideal for viewing the moon’s craters and mountain ranges with telescopes or binoculars along the moon’s left edge.
The craters are concentrated in the whiter parts of the moon while the mountain ranges tend to lie on the edges of the moon’s dark plains. By next Sunday, the moon will be full and offering much less detail. owing to the lack of shadows.
Bob Doyle invites any readers comments and questions. E-mail him at firstname.lastname@example.org . He is available as a speaker on his column topics.