Measuring without intruments

Assume a person who winds up in some other version of Earth. All the physical constants are the same, but no measuring instruments exist. How would you go about recreating standard units of length, weight, time, temperature, etc — and instruments for measuring them? Assume that string and pegs are available, everything else has to be made. Basic hand tool (saw, hammer and the like) are available.

This entry was posted in advice requested. Bookmark the permalink.

10 Responses to Measuring without intruments

  1. Lyle says:

    It seems to me you’ve answered your own question, for the most part. If all the physical constants are the same (and where are they not?) then there’s your basis for increments. The Celsius temperature scale starts with the freezing and boiling points of water (at a specified pressure, but that could be re-affirmed for your new environ) and divides the difference by 100, for example, to arrive at a “degree”. The meter, IIRC, is now defined as a specific number of wavelengths of a particular spectral emission of a particular atom as it jumps from one specific state to another (which won’t change according to your location), but it could just as well be defined as half the height of your father. The gram is derived from the meter, as one CC of water, and so on. Water is a good basis for units, being as we can’t live without it, and so if there’s no water around, there are no people to worry about creating increments of measurement.

    Many cultures over the millennia have come up with their own units, and most of them would still be useful, but the current international scientific units (we usually refer to as the “metric system”) are fairly universally applicable. Since the math works very well within that system, it’s what I’d prefer to “take along” to the greatest extent possible (in my head). Given that you’ve taken away all of my instruments, I’d have to find ways to improvise instruments, using the same system to the extent possible. That would be extremely challenging, and would likely take generations to rebuild, but there are more or less “hard” baselines from which to work. For an agrarian or hunter/gatherer/subsistence society, the need for a sophisticated system as in, say, space travel or electronics, would not exist, so the wonderful system of scientific units we use today would be largely irrelevant.

    You’d have to define the situation, I’d think, being that our units have always been taken from our environment and designed to accommodate our common experiences in trade. What is the environment, and what are we trading? Right there is the basis for primative units.

    The bar and the G as units of pressure and gravitational force, respectively, and any other unit for that matter, can always be taken with you, no matter where you go. Your new planet may have a different atmo, and a different gravity, but the old units are still just as useful.

    I’m curious as to why you ask.

  2. ET Bryan says:

    Until you can get to the point where you can measure stuff like the wavelength of a particular emission of the Cesium atom you’ll just have to designate your own set of units arbitrarily. Usually as a function of what ever measuring equipment you can put together. An analytical balance, for example would be far less accurate if made from rough wood and you wouldn’t have a calibration weight anyway. So you chose some nice looking rock and call your measure “Rock”, make it your “Standard” and work back from there.

  3. Glenn says:

    I would probably start with the average length of the human foot.

  4. Ray says:

    All units of measure are arbitrary so start wherever you wish. “Universal standard” simply does not occur in nature. It is a human construct allowing standardization of manufactured goods, and standardization of taxation to the benefit a centralized authority. That’s why it was created by kings and not serfs. It is completely unneeded for anything else.

  5. Historian says:

    If you have a saw, you have a measuring instrument, using the teeth as a gage.

    Once you have an yardstick and other length measurements, you have volume measurements, and once you have that, using water and the known density thereof, (62.4 lb per cubic ft) you have weights and then mass.

    Tedious and time consuming, but not technically challenging.

  6. Eric Wilner says:

    The units, as Ray notes, are arbitrary, but the relationships among them need not be.
    What makes SI units so handy to calculate with is not the specific length of a meter, nor the decimal subdivisions (duodecimal is handier for trade!), but the definition of derived units in terms of the fundamental units – e.g., a Newton being a kilogram meter per second squared, rather than some independent unit of force with a non-obvious relation to the units of mass, distance, and time.
    But, then, there’s a reason legacy units have confusing units like pounds, and it’s the same reason people mistake the kilogram for a unit of weight: weight, despite being neither a fundamental unit nor an inherent property of an object, is more intuitive than mass.
    So, really, it comes down to what you want the units for. If you have a shelf full of science & engineering handbooks, you’ll want to approximate the units used in those books. If not, and you have no prospect of re-establishing contact with Earth Prime, then any ad hoc units that your people and their trading partners can agree on will do as well as any others.
    As Lyle points out, the Celsius temperature scale is easily defined in terms of an available reference material. As others have elaborated elsewhere, though, the range isn’t really handy for typical human purposes; Fahrenheit, though poorly calibrated in terms of the original definition, is handy for everyday use – and you can always calibrate your thermometers using water, as you would for Celsius, but divide the range into 180 degrees instead of 100, and start counting at 32: ’tis arbitrary.

  7. sprithitler says:

    The carat will be the same if it is the same earth, just lacking any crafted tools of measurement. This gives you a standard of weight, if you can find the tree. I would not use one of them as a weight, but 5000 should be so close to one kilogram that the difference is irrelevant for most practical purposes. If you wanted to use a metric system for weight and distance you could compute the distance from the weight. one liter of lead for example weighs 11.35 kilogrammes, which is equal to 56750 Carat Seeds.
    Having weighed one kilo of lead you form it into a cube and thus have a measure of 10 centimeters.

    The temperature is defined in the celcius scale with 0 as freezing point at sea level and 100 as boiling point at sea level (or rather at a specific pressure, but at sea level is close enough for most purposes.

    Whatever units of measure you choose though, the relevant thing is consistence. to get an extremely accurate standard of length or weight you should create a “standard unit” in a durable and stable material, study the old standard meter and standard kilo for examples.

    Measuring time is easier, as well as more dificult.
    Between noon and noon you have 24 hours, figure out noon (when the sun is the highest) and then create a sun dial, it has been done for millenia. From then on it is mostly a matter of mechanics.

  8. Paul Koning says:

    This sounds like a great science fiction story in the making.

    “Physical constants are the same” — you mean things like the speed of light and Planck’s constant? Or do you mean the rotation time of the planet and the acceleration of gravity on the surface? I’ll assume only the former. So, for example, the day is a different length, and weight has changed.

    You’re aiming to create a system of units. Does it have to match one we use here? Or does it just have to be a useable set? If the latter, it would make sense to create a copy of the SI (metric) system, but with whatever is at hand picked as the base units. Measure your foot, times three; call it “my meter”. Make a pendulum that length, call its half-period a second. Make a cube 1/10th meter in size, fill with water, call it a kilogram. They won’t match the Earth ones but that’s not particularly important. As Lyle said, you can replicate the Celsius scale, though it won’t actually match unless air pressure is the same. But again, that doesn’t matter, the system’s structure will be sound if you copy how SI is put together. Current — just use the SI definition.

    If at some point you want to replicate the actual SI units, you’ll need to build a whole bunch of fairly hairy physics devices first. I’d probably use the next to last definition of the meter (the 86Kr lamp), that’s easier to work with than speed of light. That gives you the liter, which gives you a pretty good though not exact kilogram (kg is problematic because it is defined by a unique object, which by hypothesis you don’t have with you). The rest is straightforward once you have the technology.

  9. Jeff Dege says:

    Do you know your resting heart rate?

    Do you know your pace count?

    You can reconstruct time and distance to a couple of decimal places just from that.

    (Anyone who’s done serious land nav knows his pace count – how many paces does it take you to walk 100 meters.)

  10. Paul Koning says:

    Jeff’s comment makes me realize that the original question was ambiguous. What is the requirement?
    – Construct a useable system of units, so you can do engineering, science, etc. ?
    – Reconstruct an Earth system of units ?

    I was answering the former. If you want the latter, the answer would be entirely different. The question then is how you can most accurately reconstruct some Earth system (SI, Imperial, doesn’t matter) without having any external standards with you.

    I can see two approaches. One assumes you can’t build complex devices; the other assumes that you can.

    Case 1: I think the most accurate standard you have with you is your height. Measure it and make a yard / meter stick. Now measure a cubic decimeter (“liter”) of water, that’s a kilogram. The second is harder: Jeff’s idea sounds like a good one. (If the planet’s gravity is high, or oxygen pressure low, your resting heart rate might be affected, though.) And many people can count off a one second cadence fairly accurately. Those three will get you going on engineering; the other SI base units can wait. If by “another version of Earth” you meant a place with the same acceleration of gravity, then a good way to get a second is with a pendulum.

    Case 2: Build a cesium standard to give you the second. Measure speed of light for the meter, or (easier) use the previous definition using a krypton lamp wavelength. Kilogram is a unique artifact in Sèvres so the best you can do without it (or a copy) is a liter of water, which will be quite close given an accurate meter.

Comments are closed.