Metricise...

[Boerseun]

In the old days, the ancient Greeks and their pals in and around the Med played around with maths and geometry. And they hit upon the bright idea that the Earth is round. And they decided to assign 360 days to the year, due to the crudeness of their instruments and observations. Sounds crude - they were off by more than five days, but for the time it was remarkably accurate.

 

But here's my problem:

 

Circles are today still assigned 360 degrees because of this ancient observational error.

 

Today, using the metric standard where everything is interlinked, in other words one liter of water weighs one kilogram (volume to weight) and one kilogram/liter of water equals one cubic decimeter etc. etc. etc., what would be the benefits if a circle was metricised as well? For instance, if we assign 100 degrees to a circle, would we be able to somehow plug that into the rest of the system? And minutes and seconds of arcs can be metricised as well. Also, time can be metricised so that we have 100 units per day due to the Earth also being a big circle. We can then also change the year into 100 units, as we travel around the circle of our orbit. Okay, not a perfect circle, but close enough for this proposal.

 

So that a circle consists of 100 degrees, and every degree consists of 100 minutes which would consist of 100 seconds and so forth.

 

Your watch might read something like 72:13:89 if you get my idea.

 

Cumbersome at first, but would there be benefits to this?

[Turtle]

So that a circle consists of 100 degrees, and every degree consists of 100 minutes which would consist of 100 seconds and so forth.

 

Your watch might read something like 72:13:89 if you get my idea.

 

Cumbersome at first, but would there be benefits to this?

 

Yes, you can "metricise" to any amount you please. It may prove cumbersome in some areas, particularly in the public arena with a watch as you say. However, under certain circumstances it is worth the effort. In some math applications, metricizing to radians simplifies the calculations for example. The simplest metric for the circle is 1; 1 circle :hihi:

[Jay-qu]

I was going to suggest like turtle did that radians are somewhat metricised, they are dimensionless numbers, pi = 360 degrees, they have many properties that help with the linking you mention boerseun.

[C1ay]

Why should the measure of a circle be based on time? That there was an error in the length of a year really has nothing to do with the division of a circle.

[Boerseun]

Why should the measure of a circle be based on time? That there was an error in the length of a year really has nothing to do with the division of a circle.

I think you misunderstood me there, C1ay. Whether there was an error in the initial measurement of a year or not, fact is circles are cut up into 360 degrees because of the original measurement of the amount of days that went into a year. And we're still stuck with it, which I think might be improved upon. Why else would we have an arbitrary figure like 360 asigned to the amount of degrees in a full circle?

 

With the International Standard system, things like volume and weight and length etc. can be understood in terms of each other. I'm wondering if time can somehow be brought into the System as well - and to metricise it as explained above might just achieve something to that end.

[ughaibu]

360 is a convenient number, it divides by all integers up to 10, except 7.

[Mercedes Benzene]

360 is a convenient number, it divides by all integers up to 10, except 7.

 

That's true... I suppose.

I'm a huge fan of the metric system. I wish the U.S. would "metricise" their measurements.

[Turtle]

That's true... I suppose.

I'm a huge fan of the metric system. I wish the U.S. would "metricise" their measurements.

 

The US is metricised. In linear measure, to the nearest 1/64th inch is standard. It is in fact a misnomer to consider "metric" a 10-fold article only. Any division you choose, is a metric. Knots, chains, miles, kilometers, yards, etc..

[Mercedes Benzene]

The US is metricised. In linear measure, to the nearest 1/64th inch is standard. It is in fact a misnomer to consider "metric" a 10-fold article only. Any division you choose, is a metric. Knots, chains, miles, kilometers, yards, etc..

 

I meant THE metric system. As in the SI metric system, which IS exclusively based on the meter and the gram. Increments of 10. In that case, the US is not based on the metric system I was refering to.

We are one of 3 countries that do not use the metric system.

[Qfwfq]

Are you sure Boerseun that the Greeks got the number of days in a year wrong?

 

:)

 

People had been observing solstices and equinoxes since ancient times, though maybe this was less important to the Greeks than to the Scandinavians, all seafaring peoples had been noticing the constellations etc...

 

As Ughaibu says, 360 is a quite convenient number and, supposing the terrestrial obit quasi-circular, it means the arc for each day is approximately 1 degree but I'm not sure this was quite enough to determine the choice. They mainly wanted it to be easy to split their pies into equal slices. I think the Sumerians used sexagesimal a lot and they wanted the degree to be reasonably small.

 

Quiz: Why do we say 'minute' and 'second' when talking about time?

[Boerseun]

I've been thinking about this for a few days now.

 

Consider:

 

One Joule is the amount of energy taken to raise the temperature of one milliliter of water by one degree Celcius. So here we have a link between energy, volume and temperature. Can't we include time in a system like this?

For instance, saying one "metric second"* will be the time taken to raise one milliliter of water by one degree Celcius?

 

Obviously, the shape of the container will dictate the energy flow, but that can be standardised as well. Like saying one "metric second" will be the time taken to raise the temperature of one milliliter of water by one degree Celcius where the container is a cube one centimeter to each side - which will make up one milliliter? And the energy is flowing equally from all six sides of the cube?

 

In doing this, we've established a link between energy, volume, temperature and time...

 

Would there be any benefits to such a scheme?

 

* For want of a better name...:hihi:

[Turtle]

I've been thinking about this for a few days now.

 

Consider:

 

In doing this, we've established a link between energy, volume, temperature and time...

 

Would there be any benefits to such a scheme?

 

* For want of a better name...:hihi:

Since I last responded I have encountered a metric here at Hypog that may fit the further elucidation of your thinking. (How's that;) ) You're such a bright young man Boerseun. :rainbow: For want of a better name, shall we do as Frank has & call them Euclidean Natural Units ?

[FrankM]

That is one of the peculiarities of the metric system, it devised a system where everything could be tens multiples or divisions, but they left the time unit in its medieval form as well as the divisions of a circle. The French attempted to impose a decimal time system, but they couldn't make that stick.

 

There were European efforts to use other than 360 for describing the divisions of a circle, 400 was one such division, this giving 100 divisions per quarter circle. It would be more logical to have a decimal based circle system, it would definitely simply calculations. 1000 would be a good circle division, as it gives 250 a quarter, which makes sense numerically. It doesn't make any difference for radians, as radians are a definition relative Pi.

 

When working with angles with my calculator, I convert them to their decimal equivalent, manipulate them and then convert them back to deg. min. sec.; bother, bother.

 

Yes, you can "metricise" to any amount you please. It may prove cumbersome in some areas, particularly in the public arena with a watch as you say. However, under certain circumstances it is worth the effort. In some math applications, metricizing to radians simplifies the calculations for example. The simplest metric for the circle is 1; 1 circle :hihi:

That could be the Euclidean Natural Unit for a circle, and its divisions could be multiples of ten, a 1000 would be good.

 

This is why I recommend that there be a different system for scientific use, and let the common folk and commercial people use their archaic but familiar system. The SI was created using more politics than scientific logic.

[ughaibu]

"A different system for scientific use, and let the common folk and commercial people use their archaic but familiar system", this proposal would appear to further mystify various branches of knowledge, this trend is divisive, exclusivist and elitist, it in no way helps the propagation and promotion of logical solutions to problems posed by reality.

[CraigD]

Apologies for the off-topic excursion.

I meant THE metric system. As in the SI metric system, which IS exclusively based on the meter and the gram. Increments of 10. In that case, the US is not based on the metric system I was refering to.

We are one of 3 countries that do not use the metric system.

Actually, in as much as the government of the US is permitted to declare any system of measurement “the official standard”, the US has been officially a SI system country since 1975.

 

The legal history of the SI system in the US is interesting, and reasonably well summarized at the USMA’s ”Metric system laws” page. It was “authorized” – meaning that no court, etc, could refuse to recognize speech or a document using it - in 1866. It was required to be included on some labeling in 1967, and more in 1994. Federal government agencies and the military has been required to use it more-or-less exclusively since 1975.

 

The US has flirted with requiring auto speedometers to have both English (MPH) and SI (km/hr) scales – most people over 20 should recall US cars with dual-scale speedometers.

 

Why English system of measurement has persisted in common usage in the US, even as it faded from the common usage in England, is an interesting question. My guess is that it has to do with the US’s form of government, which lacks the authority to compel the use of any system of measurement over another, and is historically very reluctant to grant itself such authority. For similar reasons, I believe, the US also lacks an official language – one can legally introduce a bill in Congress or argue a case before a US court in any language one likes, though obviously interpreters would be required for you to be understood. Although the UK, also lacks an official language, I believe it still has a stronger tradition of government dictating common usage to the public than does the US.

[C1ay]

I think you misunderstood me there, C1ay. Whether there was an error in the initial measurement of a year or not, fact is circles are cut up into 360 degrees because of the original measurement of the amount of days that went into a year. And we're still stuck with it, which I think might be improved upon. Why else would we have an arbitrary figure like 360 asigned to the amount of degrees in a full circle?

It's actually a result of the Babylonian base 60 number system. The circle is also easily divided into 6 parts by striking off divisions equal to the radius with a compass. Closing these divisions with chords makes 6 equilateral triangles.

 

There is a system where the circle is divided into 400 parts called gradians used by surveyors. My calculator actually has modes for gradians as well as radians and degrees. I use radians quite often myself.

[CraigD]

A truly die-hard fan of the original Star Trek series (1966-1969) would be able to relate that the United Federation of Planets used a unit of angular measurement called “divisions” with 400 in a full circle, but that this “Metrisization” disappeared in ST: The Next Generation (1987-1994). According to my lovingly retained copy of Franz Josephs’s 1975 Star Fleet Technical Manual, the bearing from the center of the galaxy to the center of the UFP (which, coincidentally, is centered on good ‘ole Sol) is [math]000^D00^{CD}00^{MD}[/math].

 

A nautical history buff would note that the points of the compass are actually a binary system of angular measurement, with 4 major points (N, S, E, W) and 32 principle points.

 

Personally, I’m partial to binary systems – there’s something elegant about the-base-system-none-can-be-lesser-than. So, I propose that the ideal angular measurement is the “cycle”, and that the cycle is best represented in base 2. Here’s an equivalence table:

Cycle (base 2)  Degrees (base 10)
1               360
0.1             180
0.01             90
0.001            45
0.0001001001...  30

Hum… An annoying repeating binary for the ever-popular 30°, arcsin(1/2). Even in base 10, it’s an equally annoying 0.08333...

 

So perhaps its best to use a base system with a factor of 2 and 3 in it:

Cycle (base 6)  Degrees (base 10)
1               360
0.3             180
0.13             90
0.043            45
0.03             30

Definitely nicer!

 

So my vote’s for cycles, in base 6 :thumbs_up (seriously)

 

It's actually a result of the Babylonian base 60 number system. …

Damn! Those ancient Babylonians appear to have beaten me to my brilliant suggestion by a few millennia ;)

There is a system where the circle is divided into 400 parts called gradians used by surveyors.

Double damn! Those cursed surveyors appear to have gotten the drop on the Franz Josephs, too. :)