The Universe Syndrome (7)

A practical lingo for how big and small it is with some fun facts

Black hole rendition, looking at you quizzically like an eye, as though wondering whether you know of its big number plans for you.

Complaints

We complain: the universe is small and big beyond our instinctive understanding. The large and small worlds can overwhelm us with their uncanny magnitudes. They can cause us vertigo.

Therefore, an exponential representation, as hinted at early even in Sumerian culture and at least in my preceding posts, can help stabilizing us against the vertigo. In its powers of ten notation, it sounds a little cumbersome when spelled out fully. Take Avogadro’s number as six time ten to the twenty third. I would expect that aliens hearing about our tongue twisters will have some forgiving understanding of our early stage of development. To get us on a better footing with them, I will below further develop some shorthand for everyday use with examples. One interim solution was the prefix. But wait a minute, what was it for Avogadro’s number? Well, the yotta would come in handy as ten to the power 24. Now it is 0.6yotta particles, or 600 zetta. You knew that of course, I have to admit I didn’t.

Even with exponential short hands, the universe will stay overwhelming, don’t you fret. This overwhelming is here referred to as a Science or “Universe Syndrome”. It can be similarly enveloping and carrying us away as other syndromes such as the Florence Syndrome with its overwhelming Renaissance art that sends, year in year out, culturally exhausted to the emergency room. There is also India Syndrome based on India’s passive philosophy that can persuade tourists to give up on Western values altogether and stay for good. They would then buy a walking stick, bells, bracelets and rings for ear, toe, nose, and finger, and exhaust their financial resources over the long haul for the new mind draw of subsistence living.

Solutions

But we want to overcome this uncertain drowning in awe of the “Universe Syndrome”, exemplified eg with Carl Sagan’s “billions of billions” (or Emily Dickinson’s Rugged Billion). In other words, to avoid similar emergency treatment or subsistence poverty, hinted at above, we will first resort, at least as an anchor, to powers of ten counted in numbers rather than prefixes. It is so much simpler and less controversial. The quadrillion (English system) is denoted as ten to the power 15 or p15. It can alternatively be written as 15 being underlined (which this format can’t do). This, similarly, also holds for the syllable Peta (eg Petabyte, and no it’s not petfood. If you feel energetic enough, you might even check the power notation for the Domegemegrottebyte and then wish you hadn’t, or it would have been given numerically at the outset). Now almost miraculously the dimensions of the universe in meters have reduced to the manageable range of p62, or 62 orders of magnitude in meters, from the smallest Planck dimensions at p-35m to its outer range at p27m (p-35 can alternatively be written as n35). It is still awesome, as they say, especially within the usual limits of the mega-micron worlds of p12, but now more graspable so.

And you can calculate, on your own and even without calculator, such exquisite data as how many years per living person the time to the Bounce corresponds to. As the Bounce happened 1.4p10 years ago, and as there are soon to be p10 people on earth, then it will be 1.4 year per person. See, now we can do business. Of this majestic time from the Bang on, everybody presently on earth owns more than a year. It suddenly isn’t so large anymore. And you have your own stake in it now that you suddenly own a year and some. What will you make of that year? Will this year of your choice be one tumultuous one after the Big Bounce or a tranquil one of the Ediacaran period? Will it be one of ancient Alexandria’s or the year of the CRISPR discovery by Emmanuelle Charpentier and Jenifer Doudna?

Involve yourself numerically in this way and that will not only make the math less cumbersome, but it will foster a better intuitive understanding of the orders of magnitude in question. It reduces redundancy and avoids the mnemotechnically trying magnitudes that have no common-use prefixes. It also circumvents the inconsistencies within cultural spheres such as the use of billion (anglophone, so-called short form) vs milliard (European long form), both as p9. Yet, the European billion is p12, which is the anglophone trillion (the counting is here per million rather than thousand). In other words, in the anglophone world a cancer patient dies when amassing a trillion cancer cells, while in the mainland European world this ominous number would be deceptively called a billion. Death, being an internationalist, wouldn’t be fooled though, and arrive at comparable times anyway. But you may bring it up at parties that we live in a time when basic agreement is not yet reached even on such basic issues. Repeatedly mistakes are made on cumbersome translating that could have been avoided using numbers. These mistakes have caused accidental death. On the lighter side, just think of mixed-up exponential notation in time travel.

But if you are forsworn on the whole word salad of ten to the power etc, then don’t worry either. A switch to something simpler won’t come soon. Some people will object that no specification is given about the base of this exponential. It could be any number after all. In fact, the number two is a popular choice and people will point out how often it appears on your body, with two eyes or nasal openings. Your holding up your ten fingers won’t cut the mustard with people of conviction. So perhaps just give it some time and simplify on the side.

𓆤    (please welcome here my new Egyptian bee hieroglyph as a thought connector and ameliorator of potential rough feelings created in the above)

Billions

I want now to exercise this principle on the more graspable billion and trillion, and search for some fun facts. 14 billion years is a number worth remembering as the beginning of our practically accessible historical time after the Big Bounce. But how to remember, and how big is that? Well, our billion (and Sagan’s) is p9 and the trillion is p12 (note again that the Europeans’ is different). The time to the Big Bounce then is 1.4p10. This allows us ready comparisons with other large numbers. As an example, 1.4p10 happens to be also in the ballpark of “letters” in strands of DNA of living things. This is a letter per year from the Big Bounce, creating your material basis. Now bare facts start to become memorable: years to the BB roughly correspond to people on earth and letters in some DNA.

The amoeba dubia holds a dubious record concerning letters in the DNA, with about 670p9, while we have only 3p9 letters. For our purpose, we assumed something in between. The number of cells in a detectable cancer of one cubic centimeter is 1p9. There are 3p9 heartbeats in a life. You will have too few heartbeats to have one for everybody on earth, but it almost would work out (McDonald had a famous sign, boasting of more than 99 billion burgers served and you can’t equal that with heartbeats even over all your life). A lightning bolt has p9watt, or a gigawatt. There are more than 100 billion (p11) stars in the Milky Way, which is about comparable to the number of neurons in a brain or the number of atoms in a molecule of DNA. In this analogy the brain is a metaphorical galaxy of neurons. There may be up to p9 black holes in the Milky Way and 100p9 planets. This is the realm of the billion: from banging beginnings to burgers to bases in DNA, galaxies of neurons, lightning bolts and number of humans and their heartbeats. Let us now play: a billion is big but a trillion is bigger.

Trillions and going

The number of galaxies in the universe is 2000 billion and it is more expedient to count here in trillions (p12), which in this case makes 2p12. A trillion cancer cells kill, even as the body sports almost one hundred times as many healthy ones (p12 cancer cells corresponds to about 1 liter). There are 20p12 of red blood cells or erythrocytes in a person. The number of atoms in one of those cells is about a trillion (you can best Sagan here by speaking of hundred times trillions of trillions of cells in your body). The US budget is in the trillions of dollars, ten brains of neurons so to speak. 1% of US citizen own $30p12. In total wealth this has passed 50% and is predicted by 2022 as going towards 70%. Somehow, we can still wrap our mind around the trillion. And this serves us well, as the number of our cells per liter or kg is roughly a trillion. At 100 liter, a person has then a hundred trillion cells, and if their entire cells’ DNA is lined up straight then that makes 200p12 meters. A light year is about p16 meters, so this distance makes 0.02 light years. So, this “beanstalk of lined up” DNA is not yet reaching the closest star beyond the sun. But take about 200 people’s DNA and it does. This is the realm of the trillion: from the thrill of a total of galaxies to the kill of cancer.

🐝

The next measure in counting per thousand is the quadrillion as p15. An example would be 1 quadrillion hour as slightly more than the age of the universe. Or, according to Randall Munroe*, as of 2011 the total economic production of humanity so far has been 2 quadrillion dollars. So, in dollars per hour of the universe existing we have earned $2 each of us including our ancestors.

A quintillion (p18) liter or roughly kg of water is in the Earth’s oceans and interestingly a similar if somewhat larger number, namely 5 quadrillion kg, is in the Earth’s atmosphere. A quintillion second is about 32 billion years, about twice the age of the universe.

Avogadro’s number is roughly 600septillion (600p21; now you can shine). Or the current estimate of the number of stars in the observable universe is 0.3septillion (0.3p21), which happens to be roughly the size of the universe in km. Earth weighs 6 septillion kilograms. The average human body has about seven octillion (p27) atoms. The sun weighs about 2 nonillion kilograms (p31). The particles in Earth’s atmosphere are at p44 a little over hundred times as many in the oceans (as p46 and Avogadro’s number at 6p23 are off by a factor of 2 in exponent, 18 gram of your urine, mixed in the oceans, will have one molecule of your original water in another sample of 18g ocean water collected). Earth is itself made of about 89 quindecillion (p48) molecules. Yet, the number of atoms in the observable universe has been estimated to be approximately p78, still on the low side of a googol (p100, getting its name in 1938, when nine-year-old Milton Sirotta came up with it and suggested it to his uncle, mathematician Edward Kasner).

One wonders why Tibetan Buddhism hasn’t reached beyond this western grand scaling. It would have been there for the grabbing. But its vast system of p59 universes, that together are called a Buddha Field, falls short of a googol. It could so easily have been defined as a googol of a googol. Can't you just confabulate it, for Buddha’s sake?

For something yet more enigmatic sounding, consider: The quartic hypervolume of the observable universe from the Big Bang to 3.8 septillion years in the future is about a centillion quartic Planck units. A centillion (p303) is the largest -illion with an official name in US English, although in some other places it would be different. In the competition of the giants, it wins over the googol but loses to the googolplex (a googol of a googol). The Burj Khalifa is the tallest building on earth at 830m and 163 floors. If you let each meter of it correspond to a power of ten, then you see that the number of molecules on earth or even in the observable universe is only a small percentage of it but that the googolplex (p100^p100) would bury it.

But don’t forget the small world, the pico and the tera or the femto and the further elaborations and you see that the simple power notation comes in as a blessing, allowing you to forget the arbitrarily constructed prefixes and spare yourself the wows about things big or small. Forget about the tiny weeny. Let yourself not be ridiculed by extraterrestrials, do it for them in numbers they can understand!

Small worlds

For examples, let us indeed go briefly into the small world. A human egg is n4m, which is 100micrometer diameter, with the micrometer at n6m. This happens to be a monstrously large cell at a tenth of a millimeter, and just visible. Cells generally are of order n5m and ranging down some (one cubic millimeter with a million cancer cells is just detectable with some imaging). A water-based aerosol, effective in transporting flu or corona virus over room distances, has about n6m diameter, invisible but infective as drifting in air like smoke. The size of that virus is under n7m, just below the wavelength of blue light at 4n7m, and can therefore not be seen with a light microscope. The size of hydrogen atom is n10m, its nucleus n15m. The size of the smallest length, the Planck length, is 1.6n35m.

𓆤

I summarize that it is easy to quantify especially large and small numbers with exponential writing since almost the time of Sumer, no prefixes and tongue breakers needed. This way one can avoid words like humongous or “ginormous”, or Sagan's billions of billions. The latter is simply p18; I don’t know about the former two.