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# a ? in regards to current si units

08/29/2009 12:36 AM

I like to know if any of the seven base units that we use in the si unit system have any direct natual measument before the fact.

For example when mesuring length we measure something and then define the unit. Then latter we set a standard and make everyone follow that standard by making rullers.

I like to know, if someone were stuck somewhere on a island without a ruller, and for some reason he/she would have to build a thing from that which used the meter as its measurment. How would i know what lenght i would have to cut my stick to match someone elses measurment? How would he or she know what length a meter would be?

When i say natural measurement I want a measurment that can be recreated anywhere without any kind of exsiting ruller or calculating device, pen & paper ok.

I was thinking that there must be somthing that can be referenced or derived geometricly from something to set a length or any of the other base measurements. I was looking for a mathmatical constant that is universal. A constant that is both found in math and found in nature physically. Pi comes to mind but that is a ratio.

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#1

### Re: a ? in regards to current si units

08/29/2009 4:36 AM

I think a meter was originally one pace of a ruler (king). Rather natural!! Why do you think a ruler is called a ruler?

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#7

### Re: a ? in regards to current si units

08/30/2009 3:34 PM

A ruler is a person who governs, a rule is a guideline.

So, if you want company, take a ruler, if you want to measure, take a rule

Tony

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#11

### Re: a ? in regards to current si units

08/31/2009 9:33 AM

Bugga...........you stole my thunder.

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#17

### Re: a ? in regards to current si units

09/01/2009 1:40 AM

In the SA English I know we measure with a ruler.

But I will accept, after all Oxford (with 1 000 007 words) is better than any local rule (expired school dictionary).

When I grew up the saying were "England waves the rules" or was it "rule the waves"?

I actually looked it up in the Pharos dictionary of my grandson :-

both ruler and rule are translated as "liniaal" "duimstok"

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#2

### Re: a ? in regards to current si units

08/29/2009 5:34 PM

Interesting question, I don't know of any naturally occurring objects that could be used reliably as a standardized ruler, at least not any that are big enough to be practical, but there are some cheats you can use for approximations: A grown mans thumb is ~1" wide for example... here are a bunch of examples of 'anthropic' measurements: http://en.wikipedia.org/wiki/Cubit. I have measured many of mine and can tell you for example that my cubit is 18", my span is 9", my thumb is 1" wide at the knuckle... I use this knowledge to great effect and recommend anyone who deals with measurements should take some of themselves for future use.

If you only use a single anthropic unit (cubit, palm, span...) then you can build something using another persons same unit and you will get good results that are scaled to you... not quiet the same as what we think of as a ruler (as soon as you start adding sub-units things start to get really wacky), but pretty useful for deserted island applications none-the-less.

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#3

### Re: a ? in regards to current si units

08/29/2009 5:56 PM

I gave you the wrong link for anthropic measurements... the correct link is:

http://en.wikipedia.org/wiki/Anthropic_units

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#4

### Re: a ? in regards to current si units

08/30/2009 12:26 AM

The metre was originally 1/10,000,000 of the distance from the north pole to the equator (if you drew the line through Paris). Not a very accurate description now since the earth isn't really round etc etc. Now it's defined in terms of wavelengths of laser light - 1,579,800.298728 wavelengths of helium-neon laser in a vacuum (or thereabouts - still some uncertainty obviously).

So pack your laser and you should be fine on the desert island.

The kilogram is a hunk of metal in Paris - mass being a really tricky one to define in absolute terms. Best to pack a 1kg mass in your trunk.

The newton is the amount of force required to accelerate one kg at 1m/s2. You've got your kg in your trunk, so the newton should be easy enough once you have your second defined.

The second used to be defined as a fraction of the year (1/31,556,925.9747 of the - length of the day on Jan01,1900 I think). Now it's defined in periods of radition of caesium atom. (So take a jar of caesium, and look up the number before you go).

The ampere is defined as the hypothetical amount of current required to produce a given force in Newtons between two infinitely long parallel conductors (so pack your infinitely long wire).

For Kelvin, take a reading of water and ice mixed up (that's your zero Celsius) and another at boiling (there's your 100 Celsius). Civide this by 100 to get one degree C, which is the same as 1K. That gives you relative K. To get absolute K, work backwards using the ideal gas equation for different gases - you'll see all the lines converge on the point -273.15 ... and there's your zero K point.

Mol - that's just clever old Avogadro.

Candela - let's face it you won't need it.

I've probably missed one, but the rest of the SI system falls out of this basic group. All fits together beautifully.

If you were stuck on the island without a lab, you would have to start from scratch again - devising a number of hours in a day etc.

Your best bet for standardising between other desert island groups might be using something based on angles between the fixed stars, or angle subtended by the disk of the sun or something.

Your mass would be ok if you defined a container based purely on these angles and then said the weight of water that would fill the container was your unit of mass.

Let us know how you get on once your island has developed the internet.

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#5

### Re: a ? in regards to current si units

08/30/2009 5:04 AM

The Newton is not a base unit! Anyway, good answer.

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#6

### Re: a ? in regards to current si units

08/30/2009 9:03 AM

Perhaps not now... but on MY desert island the Newton is THE base unit. In fact it's the only unit. We do everything based on Newtons - you can even buy stuff with em. And I'm working on a giant Newton-powered death ray with which I'm going to destroy your puny candela powered world. Fools! Mwooahh ha ha ha! (damn, giving too much away again.)

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#9

### Re: a ? in regards to current si units

08/30/2009 6:17 PM

but good point - thanks.

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#13

### Re: a ? in regards to current si units

08/31/2009 10:05 AM

A Newton is the unit of force, and is defined as.........the force required to give a mass of 1kg at an acceleration of 1m/sec2 Symbol N

f = m x g (N) f = force, m = mass, g = FORCE due to gravity, (9.81m/sec2)

May I ask what units use for force.

I hope that you are not confusing this with pressure or stress where the preferred unit is stupid.......the Pascal (Pa) which is defined as ...a force of 1N applied over an area of 1m2 .......an incredibly small unit, it is more common to use MPa (Mega-Pascals) or 1N/mm2 The bar or kg/cm2 can also be used for pressure

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#16

### Re: a ? in regards to current si units

08/31/2009 11:23 PM

Sure - Newtons are the unit of force, it's just (as SG80 reminded me) they are a derived unit, not a base unit.

That is, (as you just did) you can derive Newtons by using the base units of time, length and mass.

Base units can't be derived, they have to be defined, and the fewer base units you have the more powerful and universal your system becomes.

So the SI system has been pared down to seven base units, everything else (units of force, velocity, acceleration, pressure etc) may be defined in terms of them.

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#18

### Re: a ? in regards to current si units

09/01/2009 6:37 AM

Oh shit!..........What was I thinking.

No!.................I was not thinking..........sorry for that error.

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#19

### Re: a ? in regards to current si units

09/01/2009 7:10 AM

Yeah, well I did the same thing just up the page, so don't feel bad! And you were dead right about the stupid Pascal... never have to switch exponents so much as dealing with pressure.

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#15

### Re: a ? in regards to current si units

08/31/2009 11:43 AM

Before thefrench revolution (1789) every seigneuries had the privilege to define their own measurement system. After the revolution, some lord heads in the basket and the abolition of privileges the young republic had to define a new measurement system. through the idealism of this period they look for a universal and eternal reference and they choose to define the meter as part of a earth meridian. So, two scientifics had in charge to really measure the distance between Dunkerque (north of France and Barcelona (north of spain) that took several years, one of them became fool, but the meter was defined and the metric system was born and is now adopted by all the countries .... except one or two...... and the NASA.

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#20

### Re: a ? in regards to current si units

09/01/2009 5:33 PM

Comprehensive answer but I think we're missing the point here. All of this equipment is a far stretch from the pen & paper given to us in the question! And a lot of reference to Paris which I would mightily prefer to the desert island, but I need to build an airport first :-)

Basic astronomy will give us time and, ultimately also, distance.

Time will give us distance more portably if we use, as I suggested, a pendulum.

Distance will give us an accurate volume, which when filled with distilled water (boiled seawater) will give us a unit mass.

Force comes from mass, distance and time so again we are covered.

Force allows us to define the amp.

Temperature from the properties of aforementioned distilled water.

I remember a UK TV programme where they did just this; put boffins on a remote island and ask them to do some wonderful things with basic equipment, like make a map of the island. They had to invent ways to make ink, pen and paper, and make surveying instruments from tree-bark etc.

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#21

### Re: a ? in regards to current si units

09/01/2009 9:59 PM

hey - no fair... sure I started with units that required lab equipment to measure, but pared it back to basic astronomy, fixed angles, distance, and even unit mass using volume of water based on distances. Maybe my post was too long winded to read through to the end.

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#22

### Re: a ? in regards to current si units

09/01/2009 10:12 PM

On reflection mea culpa, I did read the whole post but then forgot your correct ending as I wrote mine as I was trying to wreck my brains thinking of the name of that programme .

And still can't.

I've been trying to think of other bases for length than astronomy e.g. parallel slits with sunlight, vibrations in a string, etc. I seem to remember the plague on Voyager Probe (or was it Pioneer) was designed by Carl Sagan and had a method to define a unit length, but again I think it was precision physics.

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#8

### Re: a ? in regards to current si units

08/30/2009 4:27 PM

And by the way, I don't think as much as people drink I do.

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#10

### Re: a ? in regards to current si units

08/30/2009 9:22 PM

What an elegant and interesting question. I'll give much greater thought to this tonight when meddlesome work does not intervene

My initial thought would be time. Or rather the measure of. Astronomical observation (from our own day to the transition of moons on planets) will give access to a universal clock. A simple Chinese water clock (i.e. drip, drip) would allow you to break the day into more useful units (sound familiar?), and from this a simple pendulum can swing in synch to give a standard length, viz:

T ≈ 2∏√(L/g)

Would I be right in saying that local variations in g due to height would be cancelled out by this method also??

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#12

### Re: a ? in regards to current si units

08/31/2009 9:37 AM

I don't think you would cancel out variations in g by synchronising with the water clock (if that's what you meant), since both the pendulum and the water clock are dependent on g as their force. A droplet of water breaks off when the surface tension force is overcome by the weight force, and the weight force is m*g. So in very low gravity the droplet could be enormous by the time the forces were in equilibrium, and consequently the time between drips would be much greater. (Or maybe I misunderstood you). Nice idea though.

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#14

### Re: a ? in regards to current si units

08/31/2009 10:42 AM

........Pi comes to mind..........

We could have 2Pi (radians).......or 3600

Oh!........What the hell.............just devise a new system of weights and measures.

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#23

### Re: a ? in regards to current si units

09/01/2009 11:42 PM

http://en.wikipedia.org/wiki/Physical_constant

I remember in my physics class learning physics at a cc it drove me insane. Yet here i am on this site posting questions about something that has been bugging me .

The reason i asked the above question in base units and what is a natural unit has something to do with this really cool equation

1/x = 1-x to solve you must put in quadratic form

http://en.wikipedia.org/wiki/Golden_ratio

While reading about the golden ratio and how its related to the Fibonacci sequence and that the "Fine structure constant" has a ratio 1/137. I then wondered if there was some way of using it as a base measurement.

http://en.wikipedia.org/wiki/Fine-structure_constant

On following site it explains all the ways the golden ratio is expressed in several mathematical concepts.

http://goldennumber.net/math.htm

Somehow there is got to be a way to use this ratio or any of the known ratios in math such as pi,phi, sqrt of 2, sqrt 3 etc. as a kind of fixed universal and beyond type of measurement.

http://en.wikipedia.org/wiki/Mathematical_constant

I was thinking if you could get a fixed measurement from a geometric object that represents one of those ratios and derive and use as a measument reference.

I found this link, apparently i am not alone in my thinking
http://math.ucr.edu/home/baez/constants.html

here's other stuf

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#24

### Re: a ? in regards to current si units

09/02/2009 4:06 AM

Ok.... you are in a desert island and you need to use a SI unit like a meter? Using only things you're finding on the island is not possible and only paper&pen is not enough! Measurement units are not mathematical entities but physical ones. The power of the SI units is that you don't need to go in Paris for the unit models, but in theory you can built the unit model in any lab with enough stuff... You are in a desert island and you need a measurement unit i.e. to measure the length? You are free to use everything you want... Just define the length unit as the length of your paper sheet, and the time unit as the time need to the pen to fall down from a height=paper length... and so on. The point is that a measurement unit is nothing of absolute or divine is just a convention between people. About the ratios (pi, golden ratio...) and use them as measurement unit I don't think that's possible... because they are ratios, they are adimensional entities: You can't use them to compare other physical entity.

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