Let’s get hypothetical, I’m a stranded time traveler in the stone age, and I need to speed run scientific progress to get back to my time period. Only problem is, I don’t have anything to measure with! No rulers, no thermometers, nothing. Just the knowledge in my head, and raw materials.
What’s the most primitive experiments I could conduct to find known natural units of measure to convert from? Boiling and freezing water for temperature are obvious, I could apply an electrical current to a quartz crystal and count 32,768 vibrations to get seconds of time, but what about distance? What about weight? What about electrical current, differential, and resistance?
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Getting that quartz to oscillate at the correct frequency is going to be a major challenge. It depends on size, shape, and the purity of the crystal. Commercial crystals are tuned by making them the correct size & shape to get the desired frequency. Trouble is, you don’t have a standard to compare them with. And you don’t have a length standard to make things the correct size.
I think you would be better off using the duration of a day as your standard. Divide by 86,400 to get 1 second. That should be good to better than four digit accuracy, unless you go too far back in time (duration of day changes). Or maybe use the length of a tropical year, that changes very little. It is very close to 365.24219 x 86400 seconds, and I don’t think it would differ by even 10 seconds if you go back 50,000 years.
There aren’t any natural units of measure, everything is relative.
For distance, that has historically been a problem. I might consider measuring the Earth’s polar diameter and calling that 12,713.5046 km. You do know how to figure the diameter by survey of a small part, right? Don’t forget to project your survey down to sea level.
Weight (mass) is almost impossible without a known standard. How about a 10 cm cube of pure water, at 4 deg C? That’s damn close to 1 kilogram. I haven’t studied how you might get good enough purity, maybe steam condensation?
Metric units have standards that could in theory, be attained even if every yardstick or measuring device on earth vanished. You start with distance. The meter has a conversion to a light year, so in theory, you could reestablish how long a meter is by measuring how far light travels in a vacuum over the equivalent time period. Once you know how long a meter is, you can figure out volume. An ml is the same as a cubic cm. A kilogram was originally the weight of a liter of water. Unfortunately, they never established at what temperature that water is, which effects the density. So at one point, they decided they needed a designated kilogram (literally a physical piece of metal weighing exactly a kilogram) to settle it and have a hard standard. They then made several offshoots with the same complex scientific methods to get the weight just right. Then one day they routinely weighed the original kilogram only to find it had lost about 50 micrograms.
So eventually they decided they needed a scientific metric to establish what a kg weighs using universal parameters, but the method is way more complicated.
Basically you just keep a record of the maximum error from your measuring device ,for any measurement.
You might mark anything built with the error known at the time
Well see, that doesn’t always mean the measuring device is limited to that accuracy. Rh the size of a clock parts might be +- 1%, but a 60 teeth gear system can count to 60 no matter what size the gears are, so they can count up seconds more accurately than 1%…
It depends on how accurately you remember stuff.
You can calibrate your time piece against the length of a day.
You can calibrate distance, with some difficulty, if you can somehow measure the angle of incidence of the sun’s rays simultaneously (or nearly so) in two distant locations. Then measure the distance with arbitrary units of some sort (a counting wheel, for example).
It would not be easy to recover modern day units. But if you had a lot of stuff memorized, you might be able to do it.
Edit: to explain, if you measure the difference in solar angle between point A and point B at a specific instant, and you are willing to ignore solar parallax (which you should, for now), you can use the circumference of the earth to calculate the distance between the two spots.
D = C / 360 * Theta
Where ‘D’ is the distance between the two spots, C is the circumference of earth in meters, and Theta is the difference in the sun’s angle at point A vs point B.
Accuracy would be an issue, but one drop of water equals one gram and one ml… Ish… Stone age remember? That’s weight and volume… Length and time could be derived by dropping something maybe knowing gravity is 9.8 m/s/s?
That’s an interesting question.
It’s very similar to a scenario where you have found a way to communicate with an alien species and somehow overcome the language barrier but now it’s time to discuss units of measure so we can discuss scientific principles with a shared vocabulary. Assuming you can’t just hand someone a meter-stick or kilo-weight then it’s very difficult to work from scratch but not completely impossible. There’s a similar principle that it’s literally impossible to explain left/right or clockwise/anticlockwise without a direct point of reference.
The Pioneer Plaque engraved on the side of the Pioneer space probes picked a baseline measurement that could be used to create a universal system of measurements. The amount of energy needed to cause the lone electron in a neutral hydrogen atom to flip it’s spin is called the Hyperfine Transition and it corresponds to a photon with the wavelength of a little over 21cm. With some rearranging equations you can also use this as a unit of energy or a unit of time and start to build up from there.
If you’re sticking with a time-travel scenario where you’re in the past without access to modern technology then it’s going to be a different story. If you’re actually on Earth not Westeros or some fantasy land you could probably get Time by building a clock that runs at an approximation of the right speed and correcting it. Let’s say you make a clock with an adjustable speed and you just kinda guess at how long a minute is, you know it’s going to be wrong but you don’t know by how much. By looking at the stars and the sunrise you can measure the length of a day on the equinox. Let’s say you clock measures 77760 seconds in a day, but you know a day should have 86400 seconds, so your clock is moving 10% too fast. If you adjust your clock you now have an accurate measurement of a second.
The time it takes a pendulum to swing from side to side depends ONLY on the length of the pendulum and the strength of gravity, which we can assume to be constant. So if you can accurately measure a second then a pendulum with a period of 1 second should have a length of 24.8cm. (Edit: Correction, a length of 1 meter. I was fairly certain it was 1 meter or possibly 10cm, so I googled it. The AI response at the top comprehensively explained the formula and calculated a value of 24.8cm but apparently that was bullshit because the correct answer is 1 meter). You can build a thermometer to measure temperature, mark the freezing and boiling points of water, divide by 100, find a climate where the room is around 25 degrees and declare victory. Standard pressure you’ll just have to eyeball. Or cheat and do your measurements barely above sea level like the Victorian scientists who defined sea level. A cube of water measuring 10x10x10cm at room temperature and pressure has a weight of exactly 1 kilogram.
Use your own height as reference for distance. Alternatively, once you have a clock you could use g=9.81 m/s^(2) to measure the length of a pendulum. Your local acceleration will vary a bit but that’s only of the order of 0.1%.
> I could apply an electrical current to a quartz crystal and count 32,768 vibrations to get seconds of time
Only if you carefully cut the crystal to have the right frequency (it’s not an accident that 32768 is a power of 2, that’s a human choice), but you need an existing clock to do that. Use the day or year as reference.
The kilogram is approximately the weight of a cubic decimeter of water.
The voltage of batteries only depends on the chemicals used, if you have the relevant numbers memorized then you can measure volts. Ampere is a bit trickier, time to electrolyze stuff can work if you remember the numbers, or you can measure the force between conductors to follow the original definition.
Geometry has you covered. You can get angle measures by cutting up a circle evenly, which can be done with the tools you used to draw the circle.
Just make a new system based on badgers.
Badgers weight, badgers width etc.
Anything that weighs more than a badger need not concern you.
You just make it up. That’s what people have always done.
You just define it, and convince everyone else to use it.
My phone is 75 macro flensips long and weighs 500 billibaubles.
It’s pretty easy to get above 90% accuracy of a unit of length just by eyeballing it, (and much closer if you work with length a lot) then that could be your new standard from which to derive the rest. Greater-than-90% is out by miles for metrology but will do the job given that you’re in a cave with no access to any measuring equipment. (And anything that this discrepancy could cause to not work is just an additional way to dial in the accuracy.)
Egyptians used the length of a pharoah’s forearm as the standard, and it worked well enough to build the pyramids. So really, its just about how accurate you need to be to get a job done. Trying to measure time in microseconds when you don’t even have electricity is needlessly difficult. your primary job is to work with stone age materials and technology but also to preserve the knowledge you have about materials so that future generations can leap back to a modern age. How would you even build a circuit board in the first place when you can’t even mine the copper with the stones and sticks at your disposal?
Start with a good time piece. You’ll probably need to reinvent clockwork to do this. Almost any material will work but bronze is probably the minimum tech for sub-second accuracy. You could teach yourself contemp metallurgy, stone carving, wood working, etc, but it would be much faster to convince local contemp artisans to do the engineering. Trade them some knowledge like the Archimedes Screw or something.
Now take your clock and:
Measure the length of a day to derive a fairly accurate second.
Measure the distance an object falls in one second to derive 4.9 meters.
Measure .001 square meter of water to derive the liter and kg.
You’d probably like this great video. It’s not exactly what you’re asking for but it’s all about starting from nothing and building up from there.
All you need to remember is how to make gunpowder and you will live like a god. No point messing around with seconds, metres and watts .
you get the seconds by observing the day at 24h. fokm the second you make a pendulum, the meter is the length of the pendulum thay swings once per second. The kilogram you get from length and water. the kelvin you get from boiling the water.
This all seems very reasonable to do in the stone age.
Distance is easy. Ask a local caveman for a US dollar bill. It’s close to 6″.
The right thing to do is to create your own arbitrary unit system using available tools — your unit of length is This Stick, your unit of mass is That Rock — and develop your engineering toolchain from there. Refine your unit definitions as you go: the Standard Stick eventually becomes a platinum rod the same length as the old stick.
Once you get to the tech level where you can measure the speed of light, or measure atomic vibrations, then you can tie in to the SI metric system. Or just not bother: you’re now technologically advanced enough that your stick-based unit system is as good as SI.
The universe is full of known standards, it depends on what you’re looking for and how much work you’re willing to do to get it. In the stone age, what value is it to know a meter or a kilogram?
You’re already jumping way too far ahead with a quartz crystal! Your first time unit would just be a sundial. Measure hours, or 15-minute increments. If you need more precision then get a pendulum. A swinging object’s period is determined only by the length of the rope, after all. Time probably wouldn’t be super necessary until later anyway.
For the purpose of anything you’ll be building in the stone age, you can probably get all the length precision you need with an arbitrary length like “the number of knots in this cord” and use Greek style geometry to ensure values and angles are correct.
Once you have glass and lenses, you can use wavelengths of light for a direct measurement, but this will be limited to quite small units and probably not very useful until later.
Weight is an important unit but another one that doesn’t really benefit much beyond standardization. If you have a set of Standard Weights and can make reasonably accurate scales, then the true kilogram doesn’t matter much. You’ll need metalworking and casting to make good weights with repeatable values – not just to make the weights themselves, but the balances and scales necessary to measure their differences.
Most electrochemical cells are natural references – if allowed to reach an equilibrium, they’ll approach a maximum value. There’s a lot to go wrong here, you’ll need alchemists to make sulfuric acid and metalworkers to get you lead plates, then potters to get you containers for it all. But once you’ve done that AND you have a robust copper wire drawing industry ready to provide circuitry, you can get something done electrically!
Boiling/freezing point of water is fairly stable, but for additional accuracy you could reach the Triple Point – which is a cosmic standard for both temperature and pressure.
If you know either the weight of a duck or a witch, you have it covered. I am wise in the ways of science.
3 ears of barley. Inch.
Forearm to middle finger cubit.
Your first priority would be survival, as you are most likely unable to feed yourself in a stone age world.
If you are lucky, the locals find you interesting enough to feed you and keep you alive. You may get away with doing some magic tricks to be kept around for entertainment. (If not lucky, or in time of shortage, you may end up as dinner instead.)
If you arrive in the time when humans did not know how to make fire and relied on keeping natural fire alive at all times, you may become popular if you are able to make fire.
Then you have to learn their language ASAP, so you can communicate. You can then expand your entertainment repertoar with storytelling.
Your goal is to make one of the local big guys interested enough in your stories about what you can make so he will sponsor you with food, material and labor. Then you can finally start on this other stuff.
Baby I’m missing the point, but wouldn’t you be better served by figuring out what you’re going to eat, and how you’re going to eat it? Vibrating a quartz crystal ain’t going to get you home and it ain’t going to fill up your belly. You’ll also be needing shelter and something to defend yourself from whatever the heck is out there that’s going to want to eat you
It depends a bit on how precise you need your units to be, but basically you’re kinda boned if you need them much closer than you could get with remembering your own body measurements.
You can get meters from using Earth’s surface gravity in various ways, probably the easiest to actually pull off more accurately than “well, I’m about so many centimeters tall” would be using a vacuum to suck relatively pure water (yes. distilled would be nice, and put your temperature measurements to good use) up an 11 meter pipe (or just filling the pipe, lifting it out of the water, and seeing how high you could get it before a bubble appeared at the top).
That “10.2 m” will be more exact (percentagewise) than your height, which can vary by a couple of centimeters. But it won’t be accurate to the millimeter, or even the centimeter (otherwise I’d have put “.197” instead of “.2” and maybe even more digits). The variation in atmospheric pressure at “sea level” is going to affect your temperature scale too. Nothing to be done about it other than trying multiple times over the span of a year and averaging them.
Time is subdivided from the length of a day, start the measurement at night using a specific star (not the sun, that’s why we’re starting at night). You won’t be precise enough to care about extra fractions of a second out of 86,164 (not without a measuring tool that already encompasses highly exact measures of all the units you’re trying to recreate). And yes, you’re going to want to roll all your daily measurements of this over a year together and average them too.
Meters, seconds, and temperature will get you most other SI units (including watts, the basis for all the electrical measurements). But not really a lot more precisely than you could do with your own body as a reference. A little closer, sure. Cause even your seconds are going to be affected by the quality of whatever tool you create to create subdivisions of time.
If the consequences of being off by a fraction of a percent is simply “I’m still in the past”, then you can just try again. Heck, trying multiple times with fractional adjustments might be faster and more convenient than taking measurements over the course of a year (or several). If being off means you explode (maybe along with the entire planet) then take your time and think seriously about just giving up if the fraction is smaller than, say, a quarter.
Exact odds of catastrophic failure are up to you to calculate based on the variation in your initial measurements, just keep in mind that the climate and sea levels changed a lot in the early Holocene (which probably matters since you said “stone age”). That means the chances are your initial measurements have a systemic error worse than your pattern of variation suggests.
If you’re speed running scientific progress, then just come up with arbitrary standards for each measure. It doesn’t matter what the standard is.
Pick a stick; that’s your standard for length. Use the stick to regularly space knots in a rope. Now you have something akin to a tape measure. You can get a right angle from it and everything.
Make a spring. The distance it deforms is pretty much proportional with respect to the weight put on it. Use your stick to mark regular distances of stretch and you now have a measure of weight (which for all practicality is also a measure of mass).
Make a pendulum and you now have a measure of time, etc.
Eratosthenes of Cyrene was able to measure the size of the Earth based on estimated heights and shadows.
If you would enjoy a fictional treatment of that kind of question, you might check out Leo Frankowski’s Conrad Stargard novels, about a 20th century engineer who gets dropped into 13th century Poland and has ten years to prepare for the Mongol invasion.
What good does it do you to know what meter is and what are the down sides to being wrong? You’re starting from scratch and units are arbitrary, the scientific value of them is in their relationships. You’d find something to be your length standard, then you can make an accurate cubic vessel and that’s how you get your weight, from that volume of pure water, then you can do energy and temperature from boiling that volume of water, etc.
Point is what do you even need it for?
1 you need metres, original was done by measuring earth, from that you can get cm, from that you can make cubic cube, fill it with destiled water you have kg. Also you can use pendulum and angles to measure seconds. It may help if you know your measures so you can use that, you probably didnt end up shorter after time travel.
Short: you cant
Long: modern world technology is so complex and multi-level-magic, Just producing the Tools to build the Tools needed to build the Tools to return would outlast your Lifetime by tenfold.
Temperature, as you say, should be relatively easy – as soon as you can build a thermometer, you can easily calibrate it to the Celsius scale.
By the time you can apply an electrical current to a quartz crystal and count the vibrations, you’re probably well past basic measurements. The obvious way to measure time would be using the length of the day, although it will of course take a while to get a good accuracy. If you have solved length, you can take a shortcut: The period of a pendulum is 2π√(L/g), where L is the length of the pendulum and g is the gravity acceleration, about 9.8. So a pendulum measuring a second per half-period (one swing) would be about 0.994 m. This was actually the original rationale for the meter, but since gravity acceleration isn’t quite the same everywhere, it was replaced by the circumference of the Earth. One neat solution would have been to travel to the place where g is exactly π^(2), but sadly that’s a little bit more than the maximum on Earth.
Mass is also relatively easy once you have length, since the kg is based on the density of water. It should be 4° water, but the difference isn’t big by stone age standards.
So really, length might be the main issue here. For okay accuracy, your best bet is probably to experiment with pendulums until you get one that swings the right number of times per day, and then use that to determine the meter. You’d want to start with a bigger pendulum that measures something like 5-10 s and can swing all day. As a side bonus, that should also act as a Foucault pendulum, and tell you when a day has passed.
Of course, there’s no reason you should replicate the metric system; you might as well take the opportunity to create something better.
Although no super exact if you have a length of rope so that a pendulum makes a swing of 2 seconds round trip (1 sec between stops) then that rope is 1 meter long, assuming you time traveled to earth’s past an not some other planet.
All measurements are relative anyways. Just invent your own system because it wouldn’t matter.
Get yourself a British monarch, measure their foot, then create a bureaucratic standards organization to promulgate the measure of “foot” to the present day. Lean into the closed loop of time travel like Bill and Ted stealing the car keys.
You just make up new units. There’s nothing special about units.
The average erect human penis is 5.17 inches in length.
I measured the distance between my thumb and pinky when I do this 🤙 at full stretch. So I always have something with me that I can use to get a relatively accurate measurement
I’m pretty sure units are not going to be your major problem. Until you’ve mastered fire, furnaces, smelting, etc approximate units like “hands full”, “arm lengths”, and “quarter turn of the sun” will be entirely sufficient. If you live long enough to start caring about seconds and grams it would be amazing.
Give https://m.youtube.com/channel/UCAL3JXZSzSm8AlZyD3nQdBA a watch with the subtitles on to see what you’d be up against.
If you can use quartz crystals for time, you can figure out something close enough to a meter using the gravitational constant G.
If you’re stranded in the Stone Age without standards…pick something, and make it your standard. That’s essentially what Britain did in the 17th century with the “Imperial Standard Yard.” The near-descendants of that were good enough to put men on the Moon three centuries later. I’m sure that you can do even better.
Most common units have been arbitrarily decided so I dont think there is much point in trying redefine them as exactly the same thing unless you intend to use a bunch of memorized values from before being transported to this situation. And honestly, given no resources to actually do anything it would be easiest to make your own standardized units for basic things like length, weight, and volume for the time being. Lets face it, you would be so busy with survival that it will take several generations for measurements to matter anywhere near past those three.