This post originally ran 24 October 2010.
In a 15 January Science news item, Yudhijit Bhattacharjee reported that the earliest galaxies began to form around 300 million years after the big bang. He said this was “a blink of an eye in astronomical time.”
Of course, that is just a figure of speech, but I thought we should figure that figure of speech out. Just what is “a blink of an eye”, astronomically?
Best guess of the age of the universe is about 14 billion years, maybe a little less. There’s about 365 and a quarter days per year, accounting for leap years, and 24 hours to each day. Each hour has 60 minutes, and each hour has 60 seconds. Multiplying those together tells us that 14 billion years translates to a humongous number of seconds. How many?
Write down 44 and then write 16 zeros after it: the actual number is just over 440,000,000,000,000,000 seconds. That figure is—currently—larger than our budget deficit. So it’s pretty big.
A real blink of an eye takes 300 to 400 milliseconds. Since there’s 1000 milliseconds in each second, a blink of an eye takes around 1/3 of a second.
Compared to the time span of one full second, a blink of an eye is an eternity. Thirty-three percent of that second is given over to blindness, after all. But if you’re measuring the length of the blink with respect to an hour, the disparity isn’t so dramatic.
And still less dramatic is the time of a blink weighed against the time it takes the Earth to spin once around its axis (Berkeley High School graduates: that’s one day).
These comparisons are necessary because the blink of an eye is meaningful only when it is measured against some base, or when it is contrasted with some reference.
The reference provides us with a ratio: the length of time of a blink to the length of time of the reference. Once we decide the reference, we’ll use it in calculating the ratio of the length of time for an “astronomical-blink” to the length of time the universe existed.
It works like this: We’ll know the reference time, the length of the blink, and the age of the universe. We can use those to solve for the length of the astro-blink—by applying the beloved techniques of high school algebra. So what’s the best reference?
One second is too short, as is one minute. How about a day? Does the ratio of one blink to one day feel the same as the ratio of one astro-blink to the age of the universe? It does to me.
People blink anywhere from 10 to 20 times a minute. Split the difference and say 15. Now, unless your like my crazy cousin Patrick, you don’t blink when you’re asleep. Blinking 15 times a minute in 16 waking hours translates into a whopping 14,400 daily eye flaps. Sans flirting, of course.
All that blinking sucks up about about one-and-a-third hours. And you thought you weren’t getting much done!
(An interesting side calculation would be to figure how much wind those blinks generate. After all, with each opening and closing, your eyelashes create a tiny breeze. Maybe, in the spirit of Green and to the solve the energy “crisis”, we could hook up tiny turbines over our brows. Anybody have Al Gore’s digits?)
Anyway, each day has 86,400 seconds—a number all who had college physics have memorized—and a ratio of that to 0.33333 seconds for a blink feels right for our reference. Which, by dividing, gives a ratio of 1 to 259,200.
We want that same ratio for astro-blinks to the age of the universe. Again, since we know the age, we can invoke algebra. This tells us that the length of an astro-blink is about 17 followed by eleven zeros, or 170,000,0000,000 seconds.
That number in dollars is not larger than our budget deficit, which, given the context in which it was calculated, we are truly justified in calling astronomical. Or, better, and for fans of bad puns, we could say our economy is on the blink.
Back to work: You can verify on your own that 14 billions years in seconds divided by an astro-blink is 1 to 259,200.
An astro-blink is a long time: all those seconds work out to just over 54,000 thousand years for each flutter! That means that any event that happened over a 54,000-year period would occur in the “blink” of an eye, astronomically.
Humanity’s tenure, with respect to the age of the universe, is close to a “blink.” We’re only three to four blinks old. That means, if the universe wasn’t paying attention, we could have snuck up on it. Maybe we have, too, considering our lack of visitors.
But we do know that the first galaxies did not form in the blink of an eye. It took them 300 million years. That’s about 5,600 blinks, or just over a third of an “astro-day” (a full astro-day would have about 14,400 astro-blinks).