Engineers are entirely comfortable with numbers multiplied by very large powers
of 10; that is, with many trailing (or leading if a decimal) zeros after the significant
figures. A terahertz is 1 x 1012 Hz, or 1 followed by twelve zeros,
or 1,000,000,000,000 Hz. A picosecond is 1 x 10-12 s, or eleven
zeros between the decimal point and the one, or 0.000000000001 s. The mass
of the sun is approximately 1.9885×1030 kg,
or 1,988,500,000,000,000,000,000,000,000,000 kg. The mass of an
electron is approximately 9.10938×10−31 kg,
or 0.000000000000000000000000000000910938 kg. We don't even break a sweat when
punching those kinds of numbers into a calculator. We're used to it.
When most laypeople these days hear politicians nonchalantly toss around figures
in the trillions of dollars regarding a country's deficit or planned new spending
packages, or the net worth of Amazon's
Jeff Bezos, Tesla's
Elon Musk, and
Donald Trump, they
have no concept of how big the numbers are. The largest denomination paper money
they've ever seen is the $500 bill in the Monopoly board game, and since 1969, the largest denomination
paper money circulated by the
U.S. Department of the Treasury has been the
$100 bill (worth 14¢ in 2021 after
inflation - a $500 bill in 2021 would have less purchasing power than a $100
bill in 1969).
Politicians eager to placate the yearnings by citizens (and non-citizens for
that matter) for government largess across the country and across the globe, themselves
are largely ignorant of the significance of trillion-dollar budgets, which are funded
not by an increase in real wealth or intrinsic value but by someone at the
Federal Reserve Bank clicking his/her mouse pointer on a computer screen button.
The magically created "money" is born in the form of debt to some institution, most
of which are bean counter pseudo entities created specifically to bear the "debt."
At this point, of course, nobody expects the debt to ever be paid. The government
has done a good job of purging citizens' minds of the concept of responsible spending
and honoring a debt owed. Living within one's means (aka real earnings) is clearly
discouraged as evidenced by sub-3% home mortgages and sub-1% earning on cash savings.
Meanwhile, housing prices and the cost of essential subsistence items goes up and
up and up. Not to worry, though, your elected (by hook or by crook) representative
will vote to funnel more money to feed the economy.
As a sanity check on just how large the number one trillion is, consider how
long 1,000,000,000,000 seconds of time is. If you don't know already, take a guess.
10 years? 100 years? Would it reach back to
World War II (1939-1945 AD),
World War I (1914-1918 AD),
the Civil War (1861-1865 AD),
War (1775-1783 AD)? Oh yeah, but farther back that any of those. How about
the birth of Isaac Newton
(1643), Galileo Galilei
(1564 AD), Nicolaus
Copernicus (1473 AD), Claudius
Ptolemy (100 AD), or even
Jesus Christ (0)? You'll have to go farther back than that, even.
To figure out how far back in time one trillion
seconds is, we need a little math (at the risk of exhibiting
I show my work). There are 60 seconds in a minute; 3,600 seconds in an hour; and
86,400 seconds in a year. The currently agreed-upon length of the
average sidereal year (365.256363004 days, or 365 days 6 hours 9 minutes 9.76
seconds) will be used to avoid complications of leap seconds, leap years, and the
gradual slowing of the Earth's rotation over time due to
One trillion seconds, then, represents approximately the following:
2021 AD - 31,687 years = -29,666, aka 29666 BC
That predates the birth of
Archimedes of Syracuse (287 BC),
Pythagoras of Samos (570 BC),
and Tutankhamun ("King Tut",
1342 BC) by a thousands of millennia. In fact, the 30th millennium BC
was part of the Stone Age.
Returning back to an engineer's perspective, a 1 picohertz sinewave that began
oscillating in 29666 BC would just now be completing its first cycle. You heard
it here first.
Thanks to RF Cafe visitor Bob for pointing out my subtraction
mistake, which has been fixed.
Posted April 29, 2021