There are modalities of thinking that don't involve language, but our vocabulary consists of concepts we arrange and rearrange while trying to navigate the world. We know language is the basis for communicating with others, but the dual role of words is often overlooked. When exploring a "thought-space," if we encounter something truly new, we need to create a word for it, to act as a map to find our way back. And to tell others. The language of large numbers is no exception.

In the 20th Century, Anthropologists began in earnest to understand different societies. Rather than finding a universal translation for all human languages, they did find important conceptual differences. These reflected the adapted needs of societies to their environments. If you have heard "Eskimos have 50 words for snow" then you are acquainted with the "Linguistic Relativism" hypothesis.

An example that stood out for me was the repeated discovery of the "one...two...many" counting system of several tribes around the world. It indicates that (our) math is not incorporated into universal human language, although perhaps it should be. The Pirahã tribe in the Amazon utilize "one..two..many" counting. It serves them, because they are reported to lead extremely minimalist lives, and live entirely in the present. Anthropologists found that tasks requiring large quantity recognition were beyond them. Much like a non-Inuit trying to survive in the Arctic.

 

 

Our OTMBTQ Community

Our society has its own language adaptation to modern conditions. It has been inherent in our counting system for some time, and scientists have been the earliest adopters. This adaptation is a set of methods for dealing with larger and larger quantities. Americans would write 1,000 to represent one thousand, Europeans write 1.000, and scientific notation for the same quantity is 10³, pronounced "ten to the third."

Outside of numeric notation, we also use names to further condense giant quantities: OTMBTQ:

• One - 10⁰: 1
  
• Thousand- 10³: 1,000
  
• Million- 10⁶: 1,000,000
  
• Billion- 10⁹: 1,000,000,000
  
• Trillion- 10¹²: 1,000,000,000,000
  
• Quadrillion- 10¹⁵: 1,000,000,000,000,000
  

Money is what has made us familiar with these terms: We buy single-dollar items, we earn thousands, we aspire to accumulate millions, and we hear of freakish "billionaires." The largest companies are now worth a trillion dollars, and government spending occupies those same strata. "Quadrillion" is not yet in the common vocabulary but the trend indicates it will be all too soon.

Order of Magnitude

"Decimate" means to reduce by 10%, and "Order of Magnitude" means to increase 10 times. The terms are often used incorrectly, but even when the meaning is spot on, our intuition is not aligned. The "Speed of Life" is to demonstrate what these types of increases mean and how far they can objectively go. I am going to anchor on a single common metric, miles per hour (mph), and guide a tour across reality. The examples are not always exact, but the order of magnitude is accurate. I selected 7 because it's an easy value to remember, so don't look for cosmic significance there.

Fastest Bacteria - 0.007 mph

Bacteria were the first life forms on Earth, and if life is an inevitable consequence of chemistry, it will be bacterial life, not "little green men." Cellular Biologists like to measure bacterial movement in terms relative to body length, and speed is hard to measure. But we can still posit the James Bond of bacterial velocity maxes out at .007 mph. This is where we will begin; our journey through "Orders of Magnitude" speed-increase launches from here.

Fastest Snail - 0.07 mph

Snails exemplify slowness. And there have even been races to determine the fastest of the slow. Given their size and multicellular advantage, it's disappointing to learn they are just 10 times faster than the humble bacteria. But hey, they do proceed "at a snail's pace."

Ant Running - 0.7 mph

Ants are impressively industrious. Their pace over a snail's is obvious and they clearly "have places to go and things to do." Multiple articulated limbs are a big advantage over flagella or a single mucus-exuding foot.

Human Running - 7 mph

There are several theories about human advantage; traits that allowed humans to dominate the environment: Big brains, language, opposable thumbs, tool use, and bipedalism. One trait is the ability to run long distances at a moderate pace. Pursued game eventually reaches exhaustion and is taken easily. 7 mph is an 8:30 pace. Slower than 10 minutes a mile is considered jogging, while world record marathons are just under a 5-minute pace. But no amount of effort would allow a human to outrun a cheetah.

Cheetah Running - 70 mph

That humans are an order of magnitude faster than ants is not surprising. Tiny insects scurrying about versus a large mammal that chases down prey. The order of magnitude jump from humans to cheetahs, however, is a testament to specialized evolution. Cheetahs also chase down prey but accomplish it with an all-out, brief sprint. It seems imaginable then, that one day, with enough training, genetics, drugs, etc. a human sprinter could cross an order-of-magnitude barrier and keep up with a cheetah. But it won't happen. Our intuition about orders of magnitude is critically flawed. If a cheetah could run 10 times faster, it would break the sound barrier.

Sound Barrier - 700 mph

Widely considered impossible by experts, in 1947 Chuck Yaeger rocketed the Bell X-1 past the speed of sound. Earlier attempts had caused catastrophic failure to aircraft attempting to surpass "Mach 1." Rather quickly though, new designs allowed a safe passage through the "sound barrier." Comfortable travel at supersonic speed (up to Mach 2) was achieved by the commercial airliner Concorde in the 1970s. Nevertheless, attempts to reach multiple Mach speeds ended at 6.7, in 1967, short of reaching an order of magnitude increase. No cheetahs were harmed in the process.

Orbital Speed - 7,000 mph

7,000 miles above Earth is the MEO - Medium Earth Orbit. The MEO has a pretty broad range. Closer than 1,200 miles is Low Earth Orbit, which requires higher speeds to maintain orbit for the International Space Station, as an example. Above MEO is GSO, where geosynchronous satellites orbit. At the boundary of MEO and GSO (2,223 miles), a satellite will make a rotation around the earth every 24 hours, and require a speed of...7,000 mph.

Interplanetary Travel - 70,000 mph

Man-made probes pioneer the way for interplanetary exploration. They are safer and less expensive than sending humans directly at this point, but manned missions to other planets are in the planning stages. In 1999 the Stardust Probe was sent out for multiple trips around the Sun at 70,000 mph, almost triple the speed of the Voyager missions 20 years prior. In 1997 the Cassini probe was sent on a mission to survey Saturn, which ended with a 70,000 mph impact into the planet itself.

Speed of Light < 700,000,000 mph

No man-made objects have made the next order of magnitude jump. In fact, there are only three 10x jumps left. The fourth would be to 700,000,000 mph, faster than the speed of light. This is a Hard Stop. The Parker Solar Probe has almost reached half of the first 10x, but nothing remotely suggests a path to the next Order of Magnitude. I almost used an icon of the Starship Enterprise to represent Interplanetary Travel but thought better of it. "Jump beyond lightspeed" is science fiction, and finding the Boundaries of Objectivity means anchoring to physical reality. The purpose of this exploration of speed is to develop an intuition of Orders of Magnitude.

 

 

Count the Zeros

Speed of Light tops out below the 10⁹ range, which we represent verbally as a "Billion." Since we started at fractional speed for the bacteria (10^-3) we add those zeros and can say the Boundary for the Speed of Life occurs within 10¹² or as we say, "Trillion." That's it.

In terms of money, entire global wealth is estimated at $500 trillion, or half a "Quadrillion." You could play at changing dollars to pennies or pesos to get a verbal number shift, but it would not affect the reality of assets behind the wealth. Likewise you could start with slower and slower bacteria to expand my "Speed of Life" range, but the categories would seem artificial. Instead, the big takeaway tells us a lot about the effect of our language advance over "one..two..many" counting. The single letter jump from "Million" to "Billion" belies Orders of Magnitude, and is yet the equivalent jump from Ant speed to a Supersonic jet.

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