Split Thread Conspiracy theories about unconventional usage of notation

[LondonJohn]

PS: how would one annotate, using primes, a distance of 3 yards, 2 feet and 10 inches? (question for Vixen)

 

[jimbob]

Then you've had a pretty sheltered life. The notation is used (see my earlier reference to John Cage) by many. The salient point is that most people who do use it are actually familiar enough with it to get it right, and honest enough to admit when they get it wrong.

/Thread.

My issue was with using prime notation in a way that was out by a factor of 60.

There's a reason why people tend to use hh:mm:ss.x

 

[jimbob]

Apropos of nothing, this is the current XKCD.

 

[Andy_Ross]

Imagine the confusion in a navigation manual or log if time and angles used the same notation!

 

[JayUtah]

Question 1. Using Base-60 ONLY, show how you would annotate a value of zero using primes.

0.

Or 0º 0′ 0″ 0‴ 0⁗… if you want to get pedantic in the original notation.

Or 0₆₀ in modern mathematical notation.

I wrote a whole lengthy post in this thread about what º means. But see also below where we see why º (or anything else) is a poor universal notation for the first division of a natural unit. We can omit trailing elements that are either zero or beyond our precision, so 0 means zero in base 60, in primes notation, and in doling out intelligence rankings.

The option to omit leading elements that are zero, without loss of rigor, is what makes the primes system work. When you think you have to write out "one hour and two minutes" to clarify what you meant by 1′ 02″ you might as well just hand in your exam paper and leave the room in shame, because that's all the evidence the instructor needs that you missed the whole point. The notation was invented to be unambiguous, and the only reason you think there can or should be any ambiguity (to be guessed at by "context") is to save face over a small error you could have admitted to years ago with little consequence.

In addition, you're also conflating the history of why we divide some units into 60 parts with the scripta of how we notate those divisions, whatever the divisor may be. ′ does not always mean "the sixtieth part of a thing," nor does ″ always mean "a further sixtieth part." For distance measurements, ′ means the third part (of a yard) and ″ means the twelfth part of a foot. ‴ means the twelfth part of an inch, a ligne. Base 60 has nothing at all to do with any of it.

Historically 12 is just as common a divisor as 60, if not more so. The words "inch" and "ounce" themselves come from uncia (Lat. "the twelfth part"). Something divided into twelve parts can be evenly meted out to two or three parties. But since few Englishmen were French watchmakers, the common subdivision of the inch was the Barley-corn, three lengthwise or four by thickness. The lengthwise barleycorn is still used in commerce for shoe sizes.

The reference to base 60 for time measurement is appropriate, but trying to connect it inexorably to primes notation in general is not.

Question 2. Most posters were only aware that primes were used in denoting time durations in primes as a short hand. - for example, in jotting down race times on sports day -

No, you're not an unsung genius who got it right while everyone else either got it wrong or didn't know about it at all. You got it wrong from the start, proceeded to get it even more wrong by improperly decimalizing a value, and simply refused to correct yourself or be corrected. Anyone reading this thread can see the absurd, childish lengths you went to—and are still going to—in order to try to save face.

when composer John Gage's 4'33" was pointed out. Task: taking care to take note of the above in Question 1, , describe how John Cage might have annotated zero hours in his title.

0h 4′ 33″.

No different than measuring the length of my dog as 0 yd 2′ 3″. The only quibble is where spaces should go. The modern preference is that a space should intervene between the digit and the unit abbreviation, although this is commonly violated.

Imagine the confusion in a navigation manual or log if time and angles used the same notation!

Which is why the proposal to use º for hours was rejected and allegedly persisted only for a time in medicine. Similarly we are now moving away from primes notation in navigation because we need accuracy beyond the second cut. If you're going to decimalize seconds of arc then you can decimalize the whole thing from degrees. Besides, astronomers and navigators differ on what the ‴rd cut of a degree should be—the twelfth part or a further sixtieth part. In order to avoid the specter of "ounces of arc," we decimalize.

Let me know how you get on.

Far better than you. The questions you're trying to position as "gotchas!" have simple, straightforward answers to those who actually know the notation. You are clearly not a "numbers person" or a triple-niner.

 

[jimbob]

Far better than you. The questions you're trying to position as "gotchas!" have simple, straightforward answers to those who actually know the notation.

That is consistent over multiple domains

 

[JayUtah]

PS: how would one annotate, using primes, a distance of 3 yards, 2 feet and 10 inches? (question for Vixen)

I'm sorry. I gave this away in my answer before I read your challenge.

 

[JayUtah]

In order to avoid the specter of "ounces of arc," we decimalize.

BTW, there were "ounces of time."

Back in the Olden Dayes, an hour (from the Greek, ώρα) was simply the twelfth part of the time between observed sunrise and observed sunset. Again, there's that connection to a natural unit. And again, there's that useful divisor—12, thanks to the Romans. But obviously as the seasons change, the actual elapsed time for an hour differed. This is perhaps why the ancient word for "season" migrated to the word for "hour," rather than using some derivation of uncia. Or a better explanation might be that "ounces" were reserved for something else.

Each hour was divided into four "points" (Lat. puncta). If that seems weird, ask yourself why church clocks still chime on the quarter hour. Each point was divided into ten "moments" (Lat. momenta). If that seems weird, ask yourself why we say, "Just a moment," when we ask someone to wait for a short period of time. And finally, each moment was divided into twelve "ounces," which serve the same purpose as seconds in the modern system.

So John Gage could just as easily have written his piece as "Four moments and thirty-three ounces," which could be written in primes notation as—wait for it!—

4′ 33″​

This illustrates the ongoing tension between notation (as opposed to "annotation"—not a mistake a numbers person would make) and actual systems of weights and measures that must ultimately relate to something objectively replicable and physical. Still, a momentum would never be mistaken for a punctum or an uncia. The only "context" in this system is the observation of sunrise and sunset, which made sense because time was being reckoned on a sundial.

And for completeness, the zero value for an hour could appropriately be written

0ω 4′ 33″ 0‴​

where ‴ indicates atoms (Gr. άτομα, "indivisibles"), the 47th part of an ounce. And appropriately the piece would be shorter when performed in the winter than in the summer. But those symbols were never used in the systema secondum compotistas that I've been able to find. While Bacon is the authority for these divisions (and the chaotic mess of similar compositoria), he does not explain where 47 came from other than from the voluntate magis, nor does he use primes notation to identify the parts. As expected, 'h' notated hours (not the omega that I facetiously introduced), 'p' for points, 'm' for moments, and 'a' for atoms. And now I'm off to brunch, to experience a far more desirable form of bacon.

 

[Vixen]

1) 0
2) 0h4'33''

Let me know how you get on assimilating the answers.

It was a trick question. There is no 'zero'. In addition, there is no such thing as 'Zero' O'Clock.

the Babylonian numeral system, credited as the first positional numeral system, was base-60. However, it lacked a real zero. Initially inferred only from context, later, by about 700 BC, zero came to be indicated by a "space" or a "punctuation symbol" (such as two slanted wedges) between numerals.<a href="https://en.wikipedia.org/wiki/Positional_notation#cite_note-multiref1-1"><span>[</span>1<span>]</span></a> It was a placeholder rather than a true zero because it was not used alone or at the end of a number. https://en.wikipedia.org/wiki/Positional_notation

 

[Vixen]

PS: how would one annotate, using primes, a distance of 3 yards, 2 feet and 10 inches? (question for Vixen)

What base? One realises that for the non-mathematician, things need to be spelt out with proper names, such as 'yards' and what have you*. Don't worry about it. However, it shouldn't be assumed that the limits of one's own knowledge are the limits of human understanding universally.

*This reminds me of a colleague who insisted I was not allowed to denote 'October' (date) as 'X'.

 

[Steve]

What base? One realises that for the non-mathematician, things need to be spelt out with proper names, such as 'yards' and what have you*. Don't worry about it. However, it shouldn't be assumed that the limits of one's own knowledge are the limits of human understanding universally.

*This reminds me of a colleague who insisted I was not allowed to denote 'October' (date) as 'X'.

"not allowed" . You can do whatever you like. If you care at all that people understand you (do you?) it helps a lot to learn and follow well established conventions.

 

[Jack by the hedge]

... Each hour was divided into four "points" (Lat. puncta). If that seems weird, ask yourself why church clocks still chime on the quarter hour.

This makes everything better. From now on, each time I'm a few minutes late for a Teams meeting I can comfort myself that's still punctual.

 

[JesseCuster]

It was a trick question. There is no 'zero'. In addition, there is no such thing as 'Zero' O'Clock.

"There is no zero"? Uh, what? Yes there is.

Also, there certainly is a "zero o'clock" even though it's not called that. Have you never used a 24 hour clock? Also an irrelevant thing to say, who mentioned anything about Zero o'clock?

 

[Jack by the hedge]

It was a trick question. There is no 'zero'.

It was a poorly worded trick, then. There was no zero in ancient Babylon but that wasn't what you asked.

You asked "How would you..." and not "How would the ancient Babylonians ..." etc.

 

[Thermal]

It warms the cockles of my heart that this discussion is in Conspiracy Theories.

 

[Vixen]

"not allowed" . You can do whatever you like. If you care at all that people understand you (do you?) it helps a lot to learn and follow well established conventions.

Have a look at Turku Cathedral clock and tell us what you see.

 

[MarkCorrigan]

How are you still repeating this gibberish Vixen?

 

[Jack by the hedge]

Have a look at Turku Cathedral clock and tell us what you see.

I see it's not winter.

Sunshine at half past six.

 

[JayUtah]

It was a trick question. There is no 'zero'. In addition, there is no such thing as 'Zero' O'Clock.

According to whom?

What base?

Primes notation does not require a "base." You're confusing the notion of a base with the notion of modular arithmetic.

One realises that for the non-mathematician, things need to be spelt out with proper names, such as 'yards' and what have you*. Don't worry about it. However, it shouldn't be assumed that the limits of one's own knowledge are the limits of human understanding universally.

You are not a mathematician. You are not a "numbers person." You are not a genius. You are not the teacher. You've stepped in something you clearly don't understand and can't let go.

Have a look at Turku Cathedral clock and tell us what you see.

Probably yet another frantic attempt to save face. And not the clock face.

 

[JayUtah]

I can post pictures of clocks too.