One Knot (could have been) Equal about 1.5 Degrees

Finished reading Cognition in the Wild by Edwin Hutchins. He mentions how the invention of the chip log represents an important shift in how navigation at sea was done.

Been looking around for similar things and came across this article:

The angle can then be measured by counting the number of knots from the teeth to the card,

When held at arm’s length, the width of a finger measures an angle that remains fairly similar from person to person. This was widely used (and still is today) for rough angle measurements, an angle known as issabah إصبع in Arabic or a zhi 指 in Chinese (both meaning ‘finger’). By modern measure, this is about 1 degree, 36 minutes, and 25 seconds, or just over 1.5 degrees.

Capt Doug once told me that to steer about “a finger off” a point of land when were were navigating the Inside Passage.

From the Wikipedia article:

was thus the earliest step towards the use of quantitative methods in navigation.


I now have a new killer scrabble word: zhi. 15 points. Not bad.


Hutchins refers to devices like this as analog-to-digital devices, don’t recall seeing that outside the context of electrical / electronic devices.

From Cognition in the Wild: A lot of OCR errors in the PDF document.


I think Hutchins got carried away here. A better way to say to describe early nav instruments would have been analog-to-numerical converters, or proportional-to-numerical. “Digital” refers to storing information in binary code. To say chip logs and sextants convert anything to digital code is incorrect.

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If you see someone looking at his wristwatch and, after some seconds, you ask him what time it is, he will most probably have to look at his watch again.

His brain worked analogously:
My train parts when the clock hand is up… it still is not… hence, I have plenty of time…
This is analog to analog.

His second look at the watch was to transform analog to digital, and return the time in digits.


Sure, that’s what analog-to-digital means in electronics, but what does it mean in cognitive science?

IDK that answer but Hutchins makes it clear what he means in the book.

Here’s link to the pdf version:

An alt-F search for “analog” tells the story. Hutchins says an analog to digital conversion is made when something is measured.


When mooring if the vessel speed looks too fast by eye that’s analog, if the Doppler log is used that’s digital.

From the book here’s an example of an analog-to-digital conversion…


Here a chart is described as a (non-mechanical) analog computer.


When the bearing (digital) is plotted on the chart it’s a digital-to-analog conversion. If the course is computed using the chart and then converted to a number (analog-to digital) the gyro can then be used to convert that number to analog by sighting down that bearing out the window (digital-to-analog).

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Hutchins has his own way of looking at the world.

To my my taste, a more accurate statment would be analog-to-fractional-to-digital. The chip log divides the hour fractionally into units of speed. A 32-point compass (which was the norm for most of the history of Western seafaring) divides the compass rose fractionally based on four cardinal points.

Today we accept mathematics as the language of understanding the world. But mariners of yesteryear were mostly simple men, and tended to think fractionally, i.e. in terms of ratios. Not an exclusive thing. They certainly used mathematics, too. But the ratio of one thing to another was the fundamental Greek way of interpreting the sciences, and the Greeks held sway over the sciences even after the Arabs invented the decimal point. We eventually got to a digital (mathematical) way of looking at the world, but we had a geometrical (ratio-based, or fractional) way of looking at it for far longer.

To my taste Hutchins overstates his thesis. He claims, “The navigation chart is an analog computer. Clearly, all problems that are solved on charts could be represented as equations and solved by symbol processing techniques.” Which is true. But you could also say that the English language is a code, and the code can be rendered into binary code and read using digital technology. That statement is true also, but It is a very narrow specialist view of the English language. It tells you nothing about the roots of the English language, or how it developed, or the reason why it persists. Not to say anything bad about Hutchins. He’s not talking about history I guess.

To my mind, charts were invented as a roughly proportional representation of geography, which after many centuries were crafted to be analyzed using exact geometric and fractional methods. Which is what Hutchins means as a chart being an analog computer. But the sticking point for me comes down to the single word “digital”.

In Figure 1.2 before Hutchins shows the view through an alidade, showing how information is transposed from analog to digital. But if you had used a similar instrument in 1821 it is likely the bearing would have been in points rather than degrees. Navigation had not advanced sufficently for degrees to be universally used to divide a circle. Are points --a fraction of a 32-point compass system–digital information? A matter of semantics, I suppose.

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This is an interesting example of how society has moved from a fractional way of interpreting phenomenon to a mathematical (digital) way. If you asked someone prior to the 1970s what the time was, you would most likely hear the response given not as an exact number but as, fractions;

  • Half past eleven.
  • A quarter to.
  • Three o’clock, straight up.

For everyday use, that was as exact as people got, until they were a quarter hour from a given event.

If someone on the street told you the time was “8:23” you’d get a strange look. I remember as a young person wearing the first of the digital watches. When someone asked me the time, I simply read the digital readout. Old people were perplexed at my exactitude. They were not used to it. Some thought me rude. They had simply expected a normal, civil, “half past” or “quarter-to” answer, not a passive-aggresive lecture, which is how some interpreted it.


This is because the electronic world was looking for a word to mean non-digital and they hijacked the word analog. Dates back to 1946 according to the intertubes.

The original meaning of analog:

“an analogous thing,” from French analogue (adj. and n.), from Latin analogus (adj.), from Greek analogos “proportionate, according to due proportion,” from ana “throughout; according to” (see ana-) + logos “ratio, proportion,” a specialized use (see Logos).

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That’s it exactly–the slipperiness of words. Describing mathematics with words is always a problem. The first dictionary definition for “digital" comes up as:

of signals or data) expressed as series of the digits 0 and 1, typically represented by values of a physical quantity such as voltage or magnetic polarization. Often contrasted with analog

Which is not what Hutchins means. To my mind he means “mathematical”, or possibly some other word.

So, to further revise my original statement, a truer way of expressing Hutchins statement would be “analog to mathematical” or "fractional to mathematical”.

Just a matter of semantics.

Sure, but Hutchins isn’t trying to prove that the result of a measurement is digital or that a chart is an analog computer. He’s defining them as such as a way to frame his argument that navigation is an example of distributed cognition.

Here’s another link wrt navigation Hutchins - Technology of Team Navigation

One of the themes in Hutchins’ book is the how the “Western” instrument form of navigation diverged from the non-instrument Micronesian navigation.

The contrast is seen wrt to the chip log. Prior to the use of the chip log the distance between ports was given as so many days sail (in a “fair wind”). This would require local knowledge to navigate between ports. Such local knowledge would have only be acquired by a few. In fact this was the case with Micronesians navigations.

Perhaps the distance of a “day’s sail” was thought of as being analogous to the sun’s journey across the sky. As the sun’s journey is half done at noon so is the ship’s day’s sail.

The chip log changes all that. Now the key to navigating the entire globe is the manipulation of formulas such as r * t = d.

Yes, likewise when using an hourly DR plot on a chart; at the time when the clock’s minute hand is 2/3rds the way around the face of the clock the ship’s DR position will also be 2/3rds the distance between the two hourly DRs.

Decades ago, some car manufacturers replaced the round speedometers with “band speedometers” that looked futuristic at the time. Some even went so far as to replace the “ancient” analog instruments with purely numerical instruments.

Today, all the cars I know have a large round speedometer with a fat hand again.
A glimpse will tell you whether your speed is what you want it to be, while you have to really read other types of instruments.

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The justification for the term analog-to-digital is that it’s part of a larger metaphor.

From the introduction:


Introducing Navy life and work on the bridge, Hutchins makes a clear distinction between the cognitive properties of an individual and the cognitive properties of a system. In striking contrast to the usual laboratory tasks of research in cognitive science, he applies the principal metaphor of cognitive science—cognition as computation (adopting David Marr’s paradigm)—to the navigation task. After comparing modern Western navigation with the method practiced in Micronesia, Hutchins explores the computational and cognitive properties of systems that are larger than an individual.

There is a growing interest in Polynesian navigation in New Zealand where the knowledge had been lost over the centuries. Why move on when you have arrived at a decent chunk of land where no one else was. Most of the methods used were preserved in Micronesia and from there passed to Hawaii and to Māori here.
I have read a lot of what’s available and those in charge of navigation were of priestly status. The knowledge required to years to acquire and a prodigious memory of the movement of the heavens.
But from my understanding this ability wasn’t transportable and it worked in their patch, the Pacific.
It was a bit like a blind person moving with confidence around their own house then being dumped in a strange house.
Captain Cook knew where he was on the globe of the earth he just didn’t know what was on that globe until he got there.


I also have been skeptical on that topic wrt early Micronesian navigation. I assumed views held were mostly the result of people’s overly romantic views of (so-called) primitive societies, the old “Noble Salvage” trope.

Reading this book has changed my opinion. Capt. Cook is held in high esteem for good reason. His accomplishments however take nothing away from Micronesian culture or the accomplishments and skills of their navigators.

I’d be a mistake to overattribute the use of tools and techniques (sextants, use of astronomical tables, survey and mapping methods etc.) to an individual.

With regards to the use of navigation tools I think Homer Simpson had it right.

But every time I learn something new, it pushes out something old. Remember that time I took a home wine-making course and forgot how to drive?


Digit means number but it means finger and we use fingers to count to ten. But analog displays digits too.

The author is using analog / digital as a metaphor so no need to debate the exact correct definition. The world is not really a stage and we are not actually actors upon it.

We perceive the real world as analog and navigation team uses instruments to convert information to numbers.

I posted something similar about a year ago:

This is wrt maneuvering in traffic and not navigation plotting but the principle is the same.