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Measurements, Part Two: Electric Boogaloo

Channelknight Fadran


To those whom it may concern:

I wasn't planning on making a sequel to this post. Frankly, I didn't think there was much else to say.

But then I was reading What If? 2 by Randall Munroe. This is not a paid promotion or an advertisement, but GO FRIGGIN READ IT. And the first one, for that matter. In one of the sections, he brings up in a footnote that the distance light travels in one nanosecond is roughly 11.8 inches: a distance, he notes, that is "frustratingly close to a foot," and then jokingly proposes we redefine the foot to exactly one light nanosecond.

So of course I'm going to do that right here and now.

First up, we need the speed of light. 299,792,458 m / s: a frighteningly strange number. In most science classes you'll round it to 300,000,000; or 2.99e8 if you aren't a casual.

Next, we need to convert that to feet. I totally did this completely be hand and didn't use google converters to get 983,571,056.43045, which I'm going to round to 983,571,056 to give the future generations something to complain about.

There we have the speed of light per second in feet; but we need to crunch it down to one nanosecond. To do that all you need to do is shift the decimal up nine slots, giving us about 0.9835... feet. I used another handy-dandy calculator series of hand calculations to get roughly 11.802 inches.

Wonderful! We've successfully proven that Mr. Munroe was correct. Now we can move along to the cooler bits.

So what happens if we redefine the foot to exactly one light-nanosecond?

Well, my friends.

The foot would go from how we know it today

to just about almost as big as we know it today.

In other words, I need a visual. Unfortunately, most paper isn't quite a foot on the long edge, so I found a 6-inch notecard instead (and completely on accident, too. I was planning on scaling one foot down to an inch but got lucky).

So here's six inches:


Compared to how long six inches should be:



So what happens to our other units when we make this conversion?

Well, everything (in the imperial system) becomes approximately 0.0165% smaller. If we kept the mile as 5280 feet (which is the worst number), then the length of it would change to about 5192 Old Feet (si).

I looked up the new feet-to-meter conversion, hoping it would be a bit closer to a 3:1. Now instead of 3 feet making up 0.9144 meters, 3 feet makes up 0.899 meters; which is so close to just flat-out 0.9. This actually comes out surprisingly close to simply 35.5 New Inches (si) (it's roughly 35.406). For all intents and purposes, we could simply say a meter is "three feet minus half an inch," which is way better than "so, like... three feet? But... wait. Is it more or less? *Looks up conversion* okay, so... one meter is 39.37 inches. So like... three feet plus three point three inches, I guess? Or maybe three point four... I dunno."

So we did it, right?




No, there are more units in the Imperial System that we use all the time.

Okay, but, for the record, I won't be going into all of them. If you want to, go ahead and multiply them by 0.9835. By all means, go redefine the "chain" and the "furlong" or whatever the heck a "twip" is. It's a bit more complicated to convert units of area and volume, so I'm going to go into those next.

First up: the acre.

This is defined as 4840 square yards, which is just about as unhelpful a number as it gets. It isn't even a perfect square: it's roughly 69 (nice) point 5701 yards across, assuming we have a perfectly square acre. That makes 208.71 Old Feet (si), or 2504.52 Old Inches (si) on edge, which are both numbers we can plug our handy-dandy converter onto. We get a brand-new acre side of 205.2666 Old Feet (si), or 68.4222 Old Yards (si). Squaring that, we get 4681.597 square yards for one acre.

I was wrong. That number is just about unhelpful as it gets.

But we'll get to fixing that later. Next up we have our primary unit of volume in imperial: Fluid Ounces. These are how we define pints, quarts, and gallons... and also "gills," apparently. A fl oz is roughly 1.7339 cubic inches, which is awful. Fortunately, it's still just math, and -


We can't just change the definition of a fluid ounce that easily!

Why's that?

Because it's defined by one 160th of a gallon, or how much space ten gallons of water takes up! If you changed the fluid ounce, you'd have to change literal friggin water: another near constant of the universe!

Hrm. You're right of course, me.

Of course I am.

And beautiful.

Oh, shut up. *Blushes*

So now we've stumbled upon a new dynamic: fixing other imperial units of measurement. We've completely redone single-dimension units, but from what we've seen so far it's probably for the best that we do two and three-dimensional measurements individually as well.

Let's go back to the acre real quick. It's a unit of area, which means it can be defined in terms of squares. That means that we should probably find a perfect square that's pretty close to current definition and go from there. Currently it's 4640 square yards, so we want to be in the high-ish 4000s ballpark. I looked up a list of perfect squares and apparently there's a perfectly good 4624 that we can use, or 68 * 68.

I was curious as to how this stacked up in terms of Old Feet - y'know, to know how much the farmers have to re-measure their fields or whatever. 4640 Old Yards squared is... well, 4640 Old Yards squared. I don't really know how to visualize that. The same goes for 4624 New Yards squared, which comes out to roughly 4472.66688 Old Yards squared.

That's quite a way's off, isn't it? Nearly two hundred (old) yards squared.

So I went to the next perfect square. 4761. If we make the New Acre 4761 New square Yards, then it comes out to about 4605.183 Old Yards squared. Now we're only off by about 35 Old Yards squared, which I personally think is a great improvement

But that's not all.

Because you see




69 * 69






So now we have to worry about gallons and pints and quarts and scud. Now, many of you should argue that we should just stick to metric units of volume instead of imperial. After all, one cubic millimeter of water (or "millileter") equates to EXACTLY one gram.

Here's why you're wrong.

One gram is not some magic number. It, as much as anything else, is a contrived unit. Now you might argue that one mole of a given element gives you its atomic weight in grams, and therefore the unit is still superior: but you're wrong AGAIN. You FOOL. I mean, look at Avagadro's Constant! 6.02214076×10^23? Do you call that clean? No! It, as much as anything else, is completely contrived. The gram is not magically equal to "exactly" something of something.

Basically what I'm saying is that you can't hate on gallons for being "ten pounds of water," because a pound is just as arbitrary a number as a kilogram is. Are the numbers associated with it worse? Yes. Is the metric system still way more useful in every situation ever? Of course! But that's as far as the superiority goes: both systems are still completely arbitrary.

'Course, the gallon was defined back in the 1800s. It needs some fixing, most likely.

For y'alls information, the gallon was defined first in 1824 as the volume ten pounds of room temperature water takes up (room temperature so that it hasn't expanded or contracted; ten because that's a good number). It was then quartered into - you guessed it - a quart, which was in turn halved into a pint. A fluid ounce is 1/20th of a pint (and a gill is 1/4 of a pint). A gallon is 160 pints. 

What this means is that we probably shouldn't change it, on second thought. It's based almost entirely on constants outside of the rest of the imperial system: and good constants at that.

But I was curious, so I started by figuring out how many New cubic Inches an Old Gallon would be. Wikipedia tells me a gallon is 277.42 cubic inches (correct to five significant figures). That means 6.519768931 inches on edge. Plug in our converter and BAM: 6.41436427437 inches on edge, or 263.913 cubic inches. Personally I think that "almost 264" is better than "277 and a half-ish." Still... it isn't that great a number.

It was then that I realized there was something else we could change in order to make ourselves a cleaner gallon:

The definition of a pound

because hoo boy is this one stupid.

Take a good look at this:

  • Currently, a pound is officially known as an "avoirdupois pound."
  • It is equal to 0.45359237 kg.
  • It's also equal to 16 avoirdupois ounces. What is an avoirdupouis ounce? Arbitrary, is what it is.

We can do better. But where to start?

I decided to reverse-engineer this one. There isn't jack scud we can do about water's density (and believe me; people have tried), so let's use that. A gallon is roughly equivalent to 4.54609 Liters. That's pretty close to a better number: let's go from there.

Let's redefine a gallon to 4.5 Liters. That's a good number.

Next up we take how much water can fit in that (4.5 kilograms) and divide that by ten.

A pound is now 0.45 kilograms.

Math is fun!

The New Gallon (si) is 274.607 Old Inches, or ~270.1 (270.0759845) New Inches. Much cleaner!

Let's review:

  • The Foot has been redefined to "1 Light Nanosecond."
  • All one-dimensional units of measurement are reduced by 0.0165%, or to 0.9835 times their original size.
  • We overhauled the Acre, making it 4761 New Yards squared.
  • The gallon has been redefined to 4.5 liters. The pound has been redefined alongside it to 0.45 kilograms.

Everything is better.





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i'm making my own system of measurement now

because this disgusts me

in a good way

edit: turns out our good friend Max Planck already did what I was about to do. Define all measurements based only on universal constants. 
We have a single unit of Planck time, and ofc the infamous Planck length.
Just scale both of those up by some number, and derive measurements of speed/volume/temperature from that
you're welcome universe


clarifying that when i said 'this disgusts me" i was referring to the fact that units of measurements are gross. not 'this' meaning 'this post'. this post is great. 10/10. good job fadran.

Edited by dannnnnnex
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Changing the distance of a mile would cause too many problems for my runner brain. Instead we should increase the speed of light until it travels a full foot in a nanosecond.

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