Mag World

It’s a Mag World

If life is going to exist in a Universe of this size, then the one thing it cannot afford to have is a sense of proportion.

– Douglas Adams (Hitchhikers Guide to the Galaxy)

The universe is very large, but it is not infinite. All quantities in the universe (distance, time, energy, mass, etc) exist within 50 to 100 orders of magnitude.

The human species interacts with only 25 of these magnitudes. Humans before the year 1900 only knew about 15 of them.

When we go about our daily lives, we have to focus on a single magnitude, and this linear perspective might include a couple of magnitudes higher and lower. The rest of the magnitudes get blurred out as either “too small to care about” or “too big to care about”.

However, there is a way to zoom out and get a larger perspective. This is particularly useful when dealing with quantities of widely different magnitudes, like the past 50 years of computer memory, or wealth distribution, or any kind of napkin estimation.

The Mag Scale is Universal

You can put every quantity in the world on a scale from -10 to +10, where ↑0 is human-scale, and every number higher means 10x more (and every number lower means 1/10th as much). Then, every level of the scale has an appreciably different feel.

For instance, on the mag scale of size, ↑0 is a human, ↑1 is a single family home, ↑2 is a city block, ↑3 is a neighborhood, ↑4 is a city, ↑5 is a small state or country, ↑6 is a large state or country, ↑7 is Earth, ↑8 is Jupiter, and ↑9 is the Sun. It doesn’t get much bigger than that unless you’re doing astrophysics.

Then on the smaller side of the scale, since ↑0 is a human, ↑-1 is a book, ↑-2 is a coin, ↑-3 is a flea, ↑-6 is a red blood cell and ↑-10 is a Hydrogen atom. It doesn’t get much smaller than that unless you’re doing nuclear physics.

Magnitude Notation

Currently, scientists and engineers communicate with each other using Scientific Notation.

multiply two numbers in scientific notation

Scientific notation was never really designed, and the notation it in turn it’arose out of and is unnecessarily complicated. The magnitude is the most important part of any number, and yet in scientific notation, it’s obscured by a bunch of numeric clutter. It’s tucked away at the very end in a smaller font, like a footnote. On top of that, it’s difficult to type and speak and read and copy-paste (try it: 3.1 × 10⁹).

But there is a way to make everything simpler: magnitude notation. If we assume the base is 10 (which it always is anyway), and allow the coefficient to become a fractional magnitude, then we’re left with just one number: the magnitude, also called the common logarithm, or log base 10 (log₁₀).

We use ^ or ↑ as a sigil to indicate the following number is a magnitude. For example:

number	scientific notation	mag notation
100,000	1.0 × 10⁵	↑5
10 million	1.0 × 10⁷	↑7
3,600 (seconds in an hour)	3.6 × 10³	↑3.5
31,557,600 (seconds in a year)	3.1 × 10⁷	↑7.5
299,792,458 m/s (speed of light)	3.0 × 10⁸	↑8.5

This notation makes common operations much simpler. To multiply two numbers in Mag World, you add them together. So if light speed is ↑8.5 meters per second and a year is ↑7.5 seconds, how far is a light-year? ↑8.5 ↑7.5 = ↑16 meters. We can add more precision if we want (a light-year is actually ↑15.976 meters), but for almost all intents and purposes, it’s completely unnecessary. We don’t need it unless we’re trying to get to the Moon, in which case, we have computers.

Each Mag Level Feels Different

In Mag World, numbers are usually rounded to the nearest integer or half integer. Rounding makes it easier to remember basic numeric facts and do math with them in your head. But also, it makes the differences between magnitudes clearer. For thinking and talking and writing about big ideas, this is often more important.

For instance, on our scale above, the Moon is ↑6 size, the rocky planets are ↑7, the gas giants are ↑8, and the Sun is ↑9. These different configurations of matter are essentially correlated to their size: Earth can’t be the size of Jupiter; rocky planets don’t come that big. And Jupiter can’t be the size of Earth; gas planets don’t come that small.

Mag Firefox Plugin

Now you can install a Firefox plugin that automatically converts numbers and units on webpages into Mag World numbers and units. For instance, “10 million kWh” becomes “↑13.6” (hover for original text).

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