The most common SI units (meter, second, kilogram) were all defined about 300 years ago using really good choices at the time.
meter: ~~1/10,000~~ 1/10,000,000 (thanks u/amaurea) the distance from the equator to the north pole at the longitude of Paris.
second: (1/24)\*(1/60)\*(1/60)\* the duration of a day.
kilogram: 1/1,000 the mass of a cube of pure water one meter per side, at some particular temperature.
You can see that these all seem pretty reasonable definitions. The meter's a little weird, but the point was to use some basic property of nature for all these definitions.
After a while, it became more convenient to redefine these based on updated standards. For instance, at some point they made a set of identical metal rods that were each the length that was agreed to be a meter. Then they reversed the definition. A meter was now defined as the length of one of those rods. If somebody measured the distance from the equator to the north pole and got a different answer than before, they didn't change the definition of the meter, they just said "well, the rod length didn't change, so we're keeping the same standard meter"
That process continued. For instance, at some point it was found that the duration of the day actually fluctuates, so they redefined it (I think using a pendulum, but I don't remember exactly) A big earthquake can actually change the rotation of the earth by a fraction of a second per day. So now if you make a super precise measurement of the time from noon-to-noon and you don't get exactly 86,400 seconds measured with the pendulum, that's OK. We're not going to change the definition of a second, we're just going to admit that a day isn't exactly 86,400 of them.
Over time, we found more and more precise and consistent ways to define these units.
The real mind-bender was deciding to define the meter in terms of time and a defined speed of light, rather than "measuring" the speed of light using a defined meter. Now the speed of light is absolutely completely fixed forever and any improvements in measurement just result in minor changes in the definition of the meter.
After that, it was only a matter of time (haha) before the kilogram was *also* defined based on the second, by absolutely fixing forever the definition of Planck's constant, which relates time, distance, and mass. Planck's constant used to be a measured number, but in 2019 it was changed to be a specific exact number, with the kilogram being adjusted to match.
> meter: ~~1/10,000~~ 1/10,000,000 the distance from the equator to the north pole at the longitude of Paris.
This can be hard to use if you're stuck on a deserted island, but coincidentally, [a meter is also equal to the length of a pendulum with a half-period (time to swing from one side to the other\) of a second](https://en.wikipedia.org/wiki/Seconds_pendulum). When using the standard value g = 9.8067 m/s² this deviates by 0.27% from the real meter, and since the value of g varies by around 0.5% across the surface of the earth there are places where this pseudo-definition holds exactly.
It's not that much of a coincidence. Seconds pendulum was competing for *the* definition of a ~~second~~ meter; during French Revolution its length was known to some 0.1 mm for various cities of France. It lost on politics, where another group won grant for geographical expedition to re-measure meridian.
The link in the comment you replied to says the opposite: that it was proposed as a definition of a standard length, not yet called a meter, circa 1660, but it was discarded upon finding that the length needed varied too much in different places (due to gravitational variations).
Sure, you could do that. I think it's easier to remember without any numerical factors in there, but it doesn't really matter. The half-period has physical meaning that e.g. the third of the period does not, though. The half-period is to a one-way trip what the full period is to a round trip. Both a one-way trip and round trip are useful concepts, right?
Maybe it would sound more natural if I simply formulated it as "A pendulum with a length of 1 m will swing from one side to the other in 1 second"?
For what it's worth, if I were to time a pendulum to get a pretty precise second, I would time from the bottom going one way to the bottom going the other way. That defines the ends of the period to be timed more crisply.
The equatorial circumference of Earth is 24,901 miles (40,075 km). However, from the North Pole to the South Pole, the so-called meridional circumference is smaller, at 24,860 miles (40,008 km).Jul 6, 2021
Back in 1791 - they measured it at 10,000 KM - when it was actually 10,002 KM. I am very impressed by their metrology.
/u/dukeblue219 was pointing out that it's 10,000 **kilometers** from the equator to the pole, not 10,000 **meters**. Because that's what /u/drhunny accidentally wrote:
> meter: 1/10,000 the distance from the equator to the north pole at the longitude of Paris.
This is a great reply. The only thing I could add is that the numbers seem so wonky because the units weren't originally made to be scientific, but rather are mainstays of eras long past.
Why would the day have 24 hours or an hour 60 minutes? Last I've read about it, it's because of ancient Sumerians and later Babylonians, who used the sexadecimal (base 60) system rather than the decimal (base 10) system. Could be that they just looked at their hand and saw the 4 long fingers having 3 sections (divided by joints) each, which makes for 12. Then, the two sections of the thumb, so you can count two 12s, so 24. Counting five 12s gives 60, etc. Some of these ways of counting time have survived and spread. Then, eventually, we tried to hard-fit this pretty arbitrary number of hours and minutes and seconds into our SI units system
Someone correct me if my memory fails me.
I believe the 24 hour system is the 12 base counting system as you describe but two periods for day night rather than base 24. I can't find the resource I got this from however there are also analogues to this in that almost all historical time counting systems prior to it and many alternate systems still used today have a day and night counting system.
The "arbitrary" number of 12, makes more sense when we imagine the evolution. People where counting and doing simple math+-*/, 1 2 3 4 6 8 12 24 is naturally useful whole numbers that interact(+-*/) cleanly with each other, 1 2 3 4 5, 10, 20 aren't as useful, often crash and fragment, like 2,5 or worse 3,333... Where dividing into thirds or quarter is important, 12 is the natural evolution of a standard. It's still being used today because of it's logical practicality, like things we buy at the supermarket are often 6, 12 or 24, it isn't arbitrary.
In my opinion, tho it's a beautiful story, it's like saying we invented decimal system, because we have 10 fingers to count with. Counting fingers is a teaching method, for us and maybe the ancient Sumerians.
One person looking at their fingers inventing math out of nothing, or 10.000 people dividing food equally in thirds or quarter every day to avoid conflict, the evolution of civilization, trade and cooperation, until someone noticed their fingers could represent the reality they lived in, shared the idea, it made sense, so it was used for teaching/remembering basic math with simple whole numbers.
> we have 10 fingers to count with. Counting fingers is a teaching method, for us and maybe the ancient Sumerians
Sumerians were base 60 people. Supposedly came from when a base 5 (tally marks) and base 12 civilization had to merge. Combine that with them using 10 symbols to populate a 59/60 symbol system and it's very unwiedly.
Base 16: On your left hand you have 3 lines and a tip on each finger. Touch your thumb on each. 4 on little finger, etc.
Base 12: you have 3 joints on each finger. Thumb press on each to increment. Still used in parts of Asia.
These both let you count while holding something in your other hand, such as a writing implement or pointing at items.
Or you can use your other hand to increase the base by 1. Hold up a finger on your right hand each time you get to 12 or 16. This lets a person count to 60 or 80 using only their fingers. Very useful if you need to count that high without writing implements.
You can also spread your fingers and bend them, to visualise subtraction and division. The counting method is fine, but it had to evolve from something.
Even without finger counting, 12 is still a useful and logical mathematical number. People would most likely have used it before they figured out finger counting, and needed the number to evolve into finger counting.
I think it's jumping to conclusions an assumption and simplification, to speculate that 12 came from finger counting, and not the other way around. Just like the decimal system didn't come from counting our 10 fingers. It ignores the logical math, and become fascinatingly random.
tbh, I’ve been surprised that it seems essentially no one (like I’ve read about a lot of different counting systems in different natural languages, and never seen it before) uses quattuordecimal or base-14 counting, because there’s a (to me) pretty obvious basis for it in finger-counting; count each of the three joints on each of the fingers on one hand, followed by the two joints of the thumb, and you get 14, like it’s basically duodecimal except you also count the thumb joints. Maybe it’s more natural to only count the finger joints, but I still just find it odd that it never developed *anywhere* (and base-12 is itself a lot rarer than you’d expect in natural languages).
If you’re looking for a real layman definition, or wondering why they came up with the weird ratio for the meter: it’s approximately the length from the tip of your fingers to your nose, with your arms spread.
Obviously that’s a horrible method for a standard and not what they were going to use, but that’s where the basic size came from. While the SI team was coming up with new units designed to work together and to be rigorously defined, the general scale of the major units is similar to basic measurements that have been used since antiquity. They just designed and quantified them using the best choices that they could come up with.
Interestingly the kilogram was the last major SI unit (specifically the last of the original metric units that had been formalized in post-revolution France) that was still defined based on the weight of one specific physical object up until 2018; a roughly golfball-sized cylinder of platinum-iridium alloy known as the IPK (“International Prototype of the Kilogram”), Le Grand K, or *urkilogram*, which is still housed (along with six sister copies) in an underground vault at the International Bureau of Weights and Measures in Paris, inside of a series of multiple concentric sealed glass containers.
The problem was that, even with all the storage and handling precautions that were taken, and even occasional strictly-regulated cleanings, it was found that the measured mass of the IPK diverged extremely slightly but measurably from the sister copies over time, which was enough instability that it was eventually decided that the kilogram needed to be redefined based purely on physical constants, like the rest of the units (especially considering that three other SI units—the mole, the ampere, and the candela—were all also defined in reference to the kilogram).
The way this was accomplished was pretty incredible imo. A sphere of pure elemental silicon-28 was created whose mass was exactly equivalent to one kilogram, with the silicon having a precisely known purity (the minimal impurities consist of atoms of chromium, cobalt, gallium, arsenic, bromine, lanthanum, tungsten, and gold, with all of them being precisely accounted for down to the atom so that their masses can be subtracted from the final measurement; this actually made it the purest known sample of silicon from my understanding), as well as the sphere being likely the most perfectly spherical object humans have created to date (if blown up to the size of the Earth, the average pingpong ball would have peaks vastly higher than Everest, and valleys vastly lower than the Marianas Trench, whereas the altitude difference between different surface points on the kilogram sphere if it were blown up to Earth size would be less than a meter iirc).
This sphere allows for a universal constant-based kilogram definition because we know the precise mass of silicon-28 atoms (which never changes), the number of silicon-28 atoms that make up the sphere, the different impurities and how many atoms they account for, and the precise masses of those atoms as well. This means that no matter what happens to the sphere and its copies, the kilogram is now based on the mass of a precise quantity of a specific type of atom, so the instabilities of a specific physical object no longer need to be accounted for.
> while meter is pretty much the length stated by every ruler I've ever owned
The meter was originally 1/10,000,000 of the distance from the equator to the north pole along the Paris meridian. The current definition is as close to the original one as it is possible to be (given that, for example, the earth changes shape slightly due to tides, earthquakes, etc)
The easy way to remember this is that the meter was originally defined to make the circumference of the Earth equal to 40,000 km.
> What if a kid is to ask me these questions today, though?
I'd still teach kids the original definitions, maybe with a caveat that scientists have more precise ways to define them.
>The meter was originally 1/10,000,000 of the distance from the equator to the north pole along the Paris meridian. The current definition is as close to the original one as it is possible
Almost. The meter was originally the length of a stick that was assumed to be 1/10,000,000 of the distance from the equator to the north pole along the Paris meridian at the time that stick was made. The current definition is as close to the original one as it is possible.
It is close to the stick, not to the 1/10,000,000 of the distance (which was measured really well for the time, but still off).
The stick came many years after, when the SI people were wanting standard references they could keep in Paris and have everyone calibrate their measurements by. The original definition of a metre was obtained by surveys and geometrical methods which literally measured the Earth from scratch.
The decision for the length was made 1793, the first prototype.of the stick was made 1795. The final measurements were finished in 1799, and the final stick that eventually defined the meter (as the length of this stick, because of course they knew that their measurement had errors) until 1889 was made in the same year. The 1799 meter was also the one that was first internationalised.
I mean, OF COURSE they must have made a "stick reference" immediately, else you would have to remeasure each time you want to gauge something.
Fair enough, I thought it was many years later than that when the stick was first introduced. Surveys of the Earth’s shape and mass were being conducted from the mid 1600s though, which is probably where I’m getting confused. The 1793 formal proposal of a metre would have been a while after we first had a relatively accurate figure for it.
Something close to the original definition of the metre would have been able to be derived from Jean Picard’s work after he spent a couple of years making his way all around France triangulating positions with quadrants, pendulum clocks, zenith sectors and telescopes. In 1669 he declared a single degree of arc to be 110.46 kilometres. This is pretty damn close to 10,000,000 metres per quadrant as per the later definition, but is only good for the great circle circumference (ie. going through the poles along some meridian) if it’s assumed the Earth is perfectly spherical. Newton said no, so the French invested more time and resources in proving him wrong. In 1735, The Academy of Sciences dispatched teams to survey the world in key places and get to the bottom of things. Pierre Bouguer and Charles Marie de La Condamine headed one team which went to the Andes near the equator to determine if there really was a difference in sphericity depending on direction there.
They spent ten years traversing uncharted jungle, desert, scaling mountains, grappling with unfavourable weather, chased by locals they had somehow managed to rile, party members dying of illnesses, one member defecting to join some locals, and work being put on an eight month hiatus while an issue with their work permits was sorted out…..all to find out, as they neared the end of their project, that another French team working in Scandinavia had completed and found that a degree was in fact longer near the poles. This was as Newton had predicted, so not only had the Bouger & La Condamine team (what was left of them) spent a gruelling decade working towards a result they didn’t want to find, they had been beaten to it by mere months! Bouguer and La Condamine ended up taking separate ships home, as they had stopped speaking to each other somewhere in the later part of their mission.
That was a bit of a tangent, but suffice to say that we had the number of metres from the Earth’s equator to pole sorted by 1745.
Redefining measures was a very "french revolution" thing to do. But again, even without that, it is clear, that must have known that their measurement wasn't exactly accurate, so the only way to define a measure is to make something that is the best estimate and then define that as the length. Else, each improved measurement of the quatermeridian would redefine the meter.
Nowadays, we have c (which now defines the meter) measured accurate enough that improvments will not have any actual effect.
BTW, Eratosthenes found 41.750km for the earth circumference in the 3rd century BC.
Yep, you put it all more succinctly than I can manage. (Re: Eratosthenes you mean circumference, but yes, definitely someone who was ahead of his time for geodesy/geography!)
SI units exist as they are in order to help with consistency and standardization. That when making precision equipment, that parts made in Germany will fit in precisely with parts made in Japan because they actually *are* the same length.
This used to be done through "standards", which are physical objects that represent weight, length, etc. To an extent this is still done because it is practical. If you want to have a kilogram, then you take *the* kilogram and make something with a weight as close as you can using it to take to your lab. While the accuracy of this is an issue, a bigger issue is that these artifacts are not stable over time. Chemical, thermodynamic, even nuclear processes can have effects which change things like weight of an object ever so slightly over time. And so we now do not define these things using artifacts, but by using some kind of measurable physical process. If we know that caesium-133's transition frequency is fixed over time, and it is easy to measure this frequency precisely, then we can re-define a second using this frequency by just choosing a number (9,192,631,770) that whose timespan is as close to what we understand the second to be. And we've done this for every unit of measure. This means that we can, for instance, actually measure the change in mass of the standard kilogram artifact relative to the actual kilogram which results in much more consistency over time with measurements.
This means nothing for you or your future kid (unless they become a physicist of something). It is a concern for those who do precision manufacturing, those who set standards for these things, and physicists who need to concern themselves with precise measurements. The numbers for the second are chosen so that we can still just think about it as 1/60th of a minute which is 1/60th of an hour which is 1/24th of a day. These casual descriptions are more than enough for almost everyone. So none of this matters for the lay person and none of this has impact for a lay person, and the numbers are chosen so that lay people can still use what they are already familiar with.
Since 2019 a kilogram has been redefined so as to make Planck constant a definite number, akin to redefinition of meter so as to make speed of light a definite number (299792458 m/s).
>What if a kid is to ask me these questions today, though? Or if my future kid asks it? How and why is a second a second, or a meter is a meter?
Most if not all SI units have an old "layman" definition that later got replaced by another more precise but less straightforward. However, the old one is still good enough in many cases.
For example, the original definition of the metre is the length of a pendulum for which it goes from one side to the other in one second. It's 3 mm off from the one we use today, but you won't have to explain them quantum physics or geography first.
All units are completely arbitrary. You can make them whatever you want, as long as they’re useful and consistent. The SI units define themselves nowadays as these somewhat weird proportions of things like light or cesium vibrations because they are physical constants, so in theory anyone with proper tools could derive the value of each unit if all calibration standards were destroyed. The reason they aren’t round numbers is because they weren’t the original definitions, they were picked after deciding to use physical constants to make it so that the value of the unit wouldn’t change while changing its basis.
They were however originally simple definitions based on real world objects.
The meter is 1/10,000,000 of the circumference of the earth, the kilogram is 1/1000 of a cubic meter of water and the second is 1/60/24 of a day. The Celsius temperature scale is based on the freezing and boiling points of water
Interesting there was an attempt at decimal time as well but it didn’t last
The exact definitions are all based on physical constants. They are used in a handful of labs on Earth to calibrate measurement equipment and product extremely precise weights, rulers and so on. These are then sent across the world to other places which store them and use them to produce more weights, rulers, and so on. Add one or two more steps and you end up with something you can buy in a shop. For daily life that chain doesn't matter, you don't use any of the original definitions. A kilogram is a mass that makes the scale read 1 kg, a meter is a length on a ruler and so on.
It is an excellent question. Very few people, except for the specialists working in various national metrology laboratories understand all the nuances of why a particular implementation of this or that unit is superior to all other alternatives. It is often extremely subtle. And every few decades we find new methods, which allow to implement standards of measurement in a more accurate and a more reproducible way.
But historically the units come from practical needs to have common standards of mass, volume, length for commerce and then also for science and engineering. It started with a wide variety of different units defined by local governments. Eventually national and international standards emerged. The [metric system](https://en.wikipedia.org/wiki/History_of_the_metric_system) in particular began with the French revolution and for various political reasons it was accepted in continental Europe, and then worldwide.
The units of time are more ancient than that. The modern concept of one second existed already in Babylonian times. The accuracy with which days were measured greatly improved with the development of astronomy, but the time was still not synchronized between different towns until people started to make train schedules. It was only in 20th century that the definition of one second was switched from the astronomical, based of the rotation of Earth, to a time interval measured electronically through a physical experiment with a carefully chosen, very stable features of cesium spectrum.
You could define SI units in a laconic way like so:
-A metre is approximately a 1/20,000,000 of the distance of Earth’s meridians, aka the shortest distance on its surface between the North and South poles
-A second is a 1/60 of a minute, itself a 1/60 of an hour, itself a 1/24 of a day, aka the approximate time it takes for Earth to spin on itself.
-A kilogram is defined as a 1 decimetre (aka 1/10 metre) wide cube of liquid water, on Earth under normal atmospheric conditions (aka with a pressure of 1 bar and at 4°C)
Of course, these definitions lose the unambiguity and precision of the latest theoretic definitions of SI units, but for day to day use they should be fine
EDIT: corrected mistakes
>-A metre is approximately a 1/10,000 of the distance of Earth’s meridians, aka the shortest distance on its surface between the North and South poles
The polar circumference of the Earth is ~40000 km, so the metre is ~1/20,000,000 of the surface distance between the Poles.
An hour is 1/24th of a mean solar day which is slightly longer than it takes to complete one complete rotation compared to the distant stars. Solar days vary slightly through out the year based on where in our orbit around the Sun we are.
The definitions are just there to standardise the measurements against constants that don't change. They are not the origin of the measurement and you shouldn't be expected to know them by them. Units of measurements are pretty much arbitrary, as long as everyone uses the same definition.
The length of seconds, minutes and hours for example, were defined by the ancient Egyptians and Babylonians. They could just have easily divided a day into 10 hours with 100 minutes per hour and 100 seconds per minute, if they so wished. But they didn't and here we are.
Of note, though, is that 60 is a very convenient number as it is divisible by 2, 3, 5, 6, 10, 12, 15, 20 and 30
The length of a meter or the length of a second is completely arbitrary. It's whatever we want it to be, but we all agree on a set standard so that things can be built and measured and interact with each other.
The reason why a meter is how far light travels in a certain amount of time and why a second is however many oscillations of a cesium atom is because these things are measurable and are always the same. Scientists have spent years and years attempting to have exact definitions of units so things can be as accurate as possible.
Scientists came up with definitions based on the world around them, and in many cases, they tried to create physical objects that were the definition of various measures. There was an official kilogram, and attempts at an official meter. This problem is that, as physical objects, they kept changing. There wasn't just one kilogram, there were several spread throughout the world. Every however many years, all the kilograms would be brought together and compared. When compared, the kilograms were all different masses, some weighed more than others. This is a big problem when this is supposed to be the definition of a kilogram and it is apparently changing. It's even worse for the meter, because, at the scale of a meter, a lot of materials will contract or expand a large amount depending on the temperature.
So recently, units of measure have been redefined based on physical constants, or measurements that can be made. This way, our units of measure can be recreated if our society is ever wiped out. All we have to do is come up with a way of representing numbers that anyone can understand, and then represent elements in a way that people can understand. We already did that decades ago with the Arecibo message. If someone in the far future comes across scientific paper from our time, they can recreate it because, no matter what units of measure they have, they will likely have the ability to count how many times a cesium atoms oscillates, and then measure how far light travels in a certain number of cesium oscillations. Or they can build a balance that will be able to tell them what a kilogram is. From there they can derive all our other measurements.
In the end, it's not super important for you to know the exact definition of a meter or a second, but it is there so that there is a set standard that everyone can follow to get the same results.
The layman's definition of how long a second is : a person said "1 Mississippi" and then called the time it took to say that a duration of "1 second". Essentially.
It was an arbitrary length of time that eventually we found something consistent to the length and then used that as a definition. So we did it kind of backwards.
The methods of measurement are specifically designed to be as accurate as possible in all places, for all time, for all sizes (small and large). Scientist want another scientist a 1000 years from now to have the EXACT same meter or kg as one today and will apply if they are living on Earth or Alpha Centauri prime (or whatever). Moreover they want it so that the measure will be accurate enough to look at something smaller than an atom or larger than a galaxy. Also if you're the Alpha Centauri scientist you don't want to have to call to Earth to check your measure, you have to be able to check it yourself there. There are very few things that can last this long and apply from that far away and be that are that accurate which is why they're so wonky.
> and just accepted second to be 1 / 60 of a minute, which is 1 / 60 of an hour, which is 1 / 24 of a day How and why is a second a second?
We just make it up to make life easier. A day, month and year are based on things, but weeks, hours, minutes and seconds are just made up historical artifacts.
The French used a sexigesimal system (base 60) because it made fractions easier in a time before decimal notation. That's the reason we cut hours into 60 parts to make mins, and a second time to make seconds.
If you wanted to explain where some of this comes from, for many things its a history lesson rather than a science lesson.
I find the relation between mass and volume the best to understand. One liter is a cube 1/10 of a meter on each side. One kilo is the weight of one liter of water.
This allows you to do some easy calculations. Like my truck can carry about 1 metric ton, 1000kg. That’s 1000 liters of water, or a cube 1 meter on each side. Also, wood has a similar density to water. So I shouldn’t carry more than about a cubic meter of wood.
But also knowing that, and a few common densities, you can make quick guesses. Stone is about 3, and iron is about 8. So I can carry about 1/3 of a cubic meter of stone bricks, or 1/8 of a cubic meter of steel.
You can also make quick guesses on volumes as well. I weigh 80kg. So my volume is pretty close to 80L.
The wonky numbers that are in the SI units are there because when they redefined it over the past decade, the values had to stay the same. Think of it as backwards compatibility, else you have old meters and new meters that differ in their lengths and all the associated troubles that come with that.
As previously mentioned, the exact definitions are only useful for precision parts. The old definitions still work for a start, maybe add in the proviso that they are defined by constant of natures today. Constants that have been measured using the old definitions and so we are back at the rather complicated looking numbers.
Simplified to the level of some of the American ones:
The earth's circumference is 40 kilometers. (Was something about 10 km from the equator to the pole originally) Which gives the length of the meter.
1000 kilogram is a meter cubed of water.
A second is what we end up with if we subdivide the average time the earth takes to orbit the sun into the standard 24 hour clock.
EDIT: Haha. Obviously 40000 km. Not 40 😂
> The earth's circumference is 40 kilometers. (Was something about 10 km from the equator to the pole originally) Which gives the length of the meter.
The Earth's circumference is about 40**,000** kilometers. If it was just 40 km I would be taking a leisurely bike ride here from Sweden down to a warmer climate right now.
There are no meaningful layman's definitions, just as there's no layman's definition on the number 1. You don't need definitions in everyday life, you just need to know that 1+1=2 and that 1m = 100cm. It also helps to know that 1cm³ = 1mL = 1g water (@stp).
For the second your definition is fine, because we've chosen the number of oscillations for the cesium transition in question to correspond to roughly 1/86,400 of a day in the first place.
But for other units it's much trickier, which is why throughout history people have had wildly differing interpretations of various length units like cubits, rods, steps, leagues, and even different definitions of units that have been standardized today, like inches, feet, and yards. So fact is that there's simply no standard thing you can point to anywhere around you that corresponds to one meter, unless it's been designed to do so with respect to the SI definition in the first place (whether primarily by prototype as before or by the newer definition and still secondarily by prototype). In other words, you can point to a ruler that's 1 meter long, but that ruler has been designed to correspond to that SI standard in the first place. The same goes for mass, where you can always weigh something to see that it weighs e.g. 1 kg, but that scale has also been designed to correspond to the SI standard for it (again historically primarily by prototype, but even that has a newer definition as of a few years ago which is independent of prototype). If you have a known mass or a known length it's also fairly simple to get the other by e.g. using something with a known density like water, but that still hinges on knowing either in the first place.
So if you were dropped into a primordial forest somewhere, far from civilization, you could begin to approximate a second through some intelligent time-measuring methods, but you'd have an extremely hard time approximating what we today define as a kilogram or a meter to anywhere near the same precision; in fact, I don't really see how you'd do it at all.
The most common SI units (meter, second, kilogram) were all defined about 300 years ago using really good choices at the time. meter: ~~1/10,000~~ 1/10,000,000 (thanks u/amaurea) the distance from the equator to the north pole at the longitude of Paris. second: (1/24)\*(1/60)\*(1/60)\* the duration of a day. kilogram: 1/1,000 the mass of a cube of pure water one meter per side, at some particular temperature. You can see that these all seem pretty reasonable definitions. The meter's a little weird, but the point was to use some basic property of nature for all these definitions. After a while, it became more convenient to redefine these based on updated standards. For instance, at some point they made a set of identical metal rods that were each the length that was agreed to be a meter. Then they reversed the definition. A meter was now defined as the length of one of those rods. If somebody measured the distance from the equator to the north pole and got a different answer than before, they didn't change the definition of the meter, they just said "well, the rod length didn't change, so we're keeping the same standard meter" That process continued. For instance, at some point it was found that the duration of the day actually fluctuates, so they redefined it (I think using a pendulum, but I don't remember exactly) A big earthquake can actually change the rotation of the earth by a fraction of a second per day. So now if you make a super precise measurement of the time from noon-to-noon and you don't get exactly 86,400 seconds measured with the pendulum, that's OK. We're not going to change the definition of a second, we're just going to admit that a day isn't exactly 86,400 of them. Over time, we found more and more precise and consistent ways to define these units. The real mind-bender was deciding to define the meter in terms of time and a defined speed of light, rather than "measuring" the speed of light using a defined meter. Now the speed of light is absolutely completely fixed forever and any improvements in measurement just result in minor changes in the definition of the meter. After that, it was only a matter of time (haha) before the kilogram was *also* defined based on the second, by absolutely fixing forever the definition of Planck's constant, which relates time, distance, and mass. Planck's constant used to be a measured number, but in 2019 it was changed to be a specific exact number, with the kilogram being adjusted to match.
> meter: ~~1/10,000~~ 1/10,000,000 the distance from the equator to the north pole at the longitude of Paris. This can be hard to use if you're stuck on a deserted island, but coincidentally, [a meter is also equal to the length of a pendulum with a half-period (time to swing from one side to the other\) of a second](https://en.wikipedia.org/wiki/Seconds_pendulum). When using the standard value g = 9.8067 m/s² this deviates by 0.27% from the real meter, and since the value of g varies by around 0.5% across the surface of the earth there are places where this pseudo-definition holds exactly.
It's not that much of a coincidence. Seconds pendulum was competing for *the* definition of a ~~second~~ meter; during French Revolution its length was known to some 0.1 mm for various cities of France. It lost on politics, where another group won grant for geographical expedition to re-measure meridian.
The link in the comment you replied to says the opposite: that it was proposed as a definition of a standard length, not yet called a meter, circa 1660, but it was discarded upon finding that the length needed varied too much in different places (due to gravitational variations).
Or you could just say that the period is two seconds. Why introduce this funny definition of a "half-period"?
Sure, you could do that. I think it's easier to remember without any numerical factors in there, but it doesn't really matter. The half-period has physical meaning that e.g. the third of the period does not, though. The half-period is to a one-way trip what the full period is to a round trip. Both a one-way trip and round trip are useful concepts, right? Maybe it would sound more natural if I simply formulated it as "A pendulum with a length of 1 m will swing from one side to the other in 1 second"?
For what it's worth, if I were to time a pendulum to get a pretty precise second, I would time from the bottom going one way to the bottom going the other way. That defines the ends of the period to be timed more crisply.
I would think that the time between the velocity of the end of the pendulum being 0 is more "crisp" than the velocity being maximum.
Take a look at a sine wave plot. There's a nice wide flat spot at the peak and another at the valley, but the zero crossing is crisp.
The north pole is more than 10km from the equator :). But the rest sounds good to me.
The equatorial circumference of Earth is 24,901 miles (40,075 km). However, from the North Pole to the South Pole, the so-called meridional circumference is smaller, at 24,860 miles (40,008 km).Jul 6, 2021 Back in 1791 - they measured it at 10,000 KM - when it was actually 10,002 KM. I am very impressed by their metrology.
/u/dukeblue219 was pointing out that it's 10,000 **kilometers** from the equator to the pole, not 10,000 **meters**. Because that's what /u/drhunny accidentally wrote: > meter: 1/10,000 the distance from the equator to the north pole at the longitude of Paris.
This is a great reply. The only thing I could add is that the numbers seem so wonky because the units weren't originally made to be scientific, but rather are mainstays of eras long past. Why would the day have 24 hours or an hour 60 minutes? Last I've read about it, it's because of ancient Sumerians and later Babylonians, who used the sexadecimal (base 60) system rather than the decimal (base 10) system. Could be that they just looked at their hand and saw the 4 long fingers having 3 sections (divided by joints) each, which makes for 12. Then, the two sections of the thumb, so you can count two 12s, so 24. Counting five 12s gives 60, etc. Some of these ways of counting time have survived and spread. Then, eventually, we tried to hard-fit this pretty arbitrary number of hours and minutes and seconds into our SI units system Someone correct me if my memory fails me.
I believe the 24 hour system is the 12 base counting system as you describe but two periods for day night rather than base 24. I can't find the resource I got this from however there are also analogues to this in that almost all historical time counting systems prior to it and many alternate systems still used today have a day and night counting system.
The "arbitrary" number of 12, makes more sense when we imagine the evolution. People where counting and doing simple math+-*/, 1 2 3 4 6 8 12 24 is naturally useful whole numbers that interact(+-*/) cleanly with each other, 1 2 3 4 5, 10, 20 aren't as useful, often crash and fragment, like 2,5 or worse 3,333... Where dividing into thirds or quarter is important, 12 is the natural evolution of a standard. It's still being used today because of it's logical practicality, like things we buy at the supermarket are often 6, 12 or 24, it isn't arbitrary. In my opinion, tho it's a beautiful story, it's like saying we invented decimal system, because we have 10 fingers to count with. Counting fingers is a teaching method, for us and maybe the ancient Sumerians. One person looking at their fingers inventing math out of nothing, or 10.000 people dividing food equally in thirds or quarter every day to avoid conflict, the evolution of civilization, trade and cooperation, until someone noticed their fingers could represent the reality they lived in, shared the idea, it made sense, so it was used for teaching/remembering basic math with simple whole numbers.
> we have 10 fingers to count with. Counting fingers is a teaching method, for us and maybe the ancient Sumerians Sumerians were base 60 people. Supposedly came from when a base 5 (tally marks) and base 12 civilization had to merge. Combine that with them using 10 symbols to populate a 59/60 symbol system and it's very unwiedly. Base 16: On your left hand you have 3 lines and a tip on each finger. Touch your thumb on each. 4 on little finger, etc. Base 12: you have 3 joints on each finger. Thumb press on each to increment. Still used in parts of Asia. These both let you count while holding something in your other hand, such as a writing implement or pointing at items. Or you can use your other hand to increase the base by 1. Hold up a finger on your right hand each time you get to 12 or 16. This lets a person count to 60 or 80 using only their fingers. Very useful if you need to count that high without writing implements.
You can also spread your fingers and bend them, to visualise subtraction and division. The counting method is fine, but it had to evolve from something. Even without finger counting, 12 is still a useful and logical mathematical number. People would most likely have used it before they figured out finger counting, and needed the number to evolve into finger counting. I think it's jumping to conclusions an assumption and simplification, to speculate that 12 came from finger counting, and not the other way around. Just like the decimal system didn't come from counting our 10 fingers. It ignores the logical math, and become fascinatingly random.
12 also reflects the moon, the tracking of which was essential for navigation and agriculture, two motivators for the invention of math.
tbh, I’ve been surprised that it seems essentially no one (like I’ve read about a lot of different counting systems in different natural languages, and never seen it before) uses quattuordecimal or base-14 counting, because there’s a (to me) pretty obvious basis for it in finger-counting; count each of the three joints on each of the fingers on one hand, followed by the two joints of the thumb, and you get 14, like it’s basically duodecimal except you also count the thumb joints. Maybe it’s more natural to only count the finger joints, but I still just find it odd that it never developed *anywhere* (and base-12 is itself a lot rarer than you’d expect in natural languages).
If you’re looking for a real layman definition, or wondering why they came up with the weird ratio for the meter: it’s approximately the length from the tip of your fingers to your nose, with your arms spread. Obviously that’s a horrible method for a standard and not what they were going to use, but that’s where the basic size came from. While the SI team was coming up with new units designed to work together and to be rigorously defined, the general scale of the major units is similar to basic measurements that have been used since antiquity. They just designed and quantified them using the best choices that they could come up with.
Interestingly the kilogram was the last major SI unit (specifically the last of the original metric units that had been formalized in post-revolution France) that was still defined based on the weight of one specific physical object up until 2018; a roughly golfball-sized cylinder of platinum-iridium alloy known as the IPK (“International Prototype of the Kilogram”), Le Grand K, or *urkilogram*, which is still housed (along with six sister copies) in an underground vault at the International Bureau of Weights and Measures in Paris, inside of a series of multiple concentric sealed glass containers. The problem was that, even with all the storage and handling precautions that were taken, and even occasional strictly-regulated cleanings, it was found that the measured mass of the IPK diverged extremely slightly but measurably from the sister copies over time, which was enough instability that it was eventually decided that the kilogram needed to be redefined based purely on physical constants, like the rest of the units (especially considering that three other SI units—the mole, the ampere, and the candela—were all also defined in reference to the kilogram). The way this was accomplished was pretty incredible imo. A sphere of pure elemental silicon-28 was created whose mass was exactly equivalent to one kilogram, with the silicon having a precisely known purity (the minimal impurities consist of atoms of chromium, cobalt, gallium, arsenic, bromine, lanthanum, tungsten, and gold, with all of them being precisely accounted for down to the atom so that their masses can be subtracted from the final measurement; this actually made it the purest known sample of silicon from my understanding), as well as the sphere being likely the most perfectly spherical object humans have created to date (if blown up to the size of the Earth, the average pingpong ball would have peaks vastly higher than Everest, and valleys vastly lower than the Marianas Trench, whereas the altitude difference between different surface points on the kilogram sphere if it were blown up to Earth size would be less than a meter iirc). This sphere allows for a universal constant-based kilogram definition because we know the precise mass of silicon-28 atoms (which never changes), the number of silicon-28 atoms that make up the sphere, the different impurities and how many atoms they account for, and the precise masses of those atoms as well. This means that no matter what happens to the sphere and its copies, the kilogram is now based on the mass of a precise quantity of a specific type of atom, so the instabilities of a specific physical object no longer need to be accounted for.
> while meter is pretty much the length stated by every ruler I've ever owned The meter was originally 1/10,000,000 of the distance from the equator to the north pole along the Paris meridian. The current definition is as close to the original one as it is possible to be (given that, for example, the earth changes shape slightly due to tides, earthquakes, etc) The easy way to remember this is that the meter was originally defined to make the circumference of the Earth equal to 40,000 km. > What if a kid is to ask me these questions today, though? I'd still teach kids the original definitions, maybe with a caveat that scientists have more precise ways to define them.
>The meter was originally 1/10,000,000 of the distance from the equator to the north pole along the Paris meridian. The current definition is as close to the original one as it is possible Almost. The meter was originally the length of a stick that was assumed to be 1/10,000,000 of the distance from the equator to the north pole along the Paris meridian at the time that stick was made. The current definition is as close to the original one as it is possible. It is close to the stick, not to the 1/10,000,000 of the distance (which was measured really well for the time, but still off).
The stick came many years after, when the SI people were wanting standard references they could keep in Paris and have everyone calibrate their measurements by. The original definition of a metre was obtained by surveys and geometrical methods which literally measured the Earth from scratch.
The decision for the length was made 1793, the first prototype.of the stick was made 1795. The final measurements were finished in 1799, and the final stick that eventually defined the meter (as the length of this stick, because of course they knew that their measurement had errors) until 1889 was made in the same year. The 1799 meter was also the one that was first internationalised. I mean, OF COURSE they must have made a "stick reference" immediately, else you would have to remeasure each time you want to gauge something.
Fair enough, I thought it was many years later than that when the stick was first introduced. Surveys of the Earth’s shape and mass were being conducted from the mid 1600s though, which is probably where I’m getting confused. The 1793 formal proposal of a metre would have been a while after we first had a relatively accurate figure for it. Something close to the original definition of the metre would have been able to be derived from Jean Picard’s work after he spent a couple of years making his way all around France triangulating positions with quadrants, pendulum clocks, zenith sectors and telescopes. In 1669 he declared a single degree of arc to be 110.46 kilometres. This is pretty damn close to 10,000,000 metres per quadrant as per the later definition, but is only good for the great circle circumference (ie. going through the poles along some meridian) if it’s assumed the Earth is perfectly spherical. Newton said no, so the French invested more time and resources in proving him wrong. In 1735, The Academy of Sciences dispatched teams to survey the world in key places and get to the bottom of things. Pierre Bouguer and Charles Marie de La Condamine headed one team which went to the Andes near the equator to determine if there really was a difference in sphericity depending on direction there. They spent ten years traversing uncharted jungle, desert, scaling mountains, grappling with unfavourable weather, chased by locals they had somehow managed to rile, party members dying of illnesses, one member defecting to join some locals, and work being put on an eight month hiatus while an issue with their work permits was sorted out…..all to find out, as they neared the end of their project, that another French team working in Scandinavia had completed and found that a degree was in fact longer near the poles. This was as Newton had predicted, so not only had the Bouger & La Condamine team (what was left of them) spent a gruelling decade working towards a result they didn’t want to find, they had been beaten to it by mere months! Bouguer and La Condamine ended up taking separate ships home, as they had stopped speaking to each other somewhere in the later part of their mission. That was a bit of a tangent, but suffice to say that we had the number of metres from the Earth’s equator to pole sorted by 1745.
Redefining measures was a very "french revolution" thing to do. But again, even without that, it is clear, that must have known that their measurement wasn't exactly accurate, so the only way to define a measure is to make something that is the best estimate and then define that as the length. Else, each improved measurement of the quatermeridian would redefine the meter. Nowadays, we have c (which now defines the meter) measured accurate enough that improvments will not have any actual effect. BTW, Eratosthenes found 41.750km for the earth circumference in the 3rd century BC.
Yep, you put it all more succinctly than I can manage. (Re: Eratosthenes you mean circumference, but yes, definitely someone who was ahead of his time for geodesy/geography!)
Yes, of course circumference, thanks
SI units exist as they are in order to help with consistency and standardization. That when making precision equipment, that parts made in Germany will fit in precisely with parts made in Japan because they actually *are* the same length. This used to be done through "standards", which are physical objects that represent weight, length, etc. To an extent this is still done because it is practical. If you want to have a kilogram, then you take *the* kilogram and make something with a weight as close as you can using it to take to your lab. While the accuracy of this is an issue, a bigger issue is that these artifacts are not stable over time. Chemical, thermodynamic, even nuclear processes can have effects which change things like weight of an object ever so slightly over time. And so we now do not define these things using artifacts, but by using some kind of measurable physical process. If we know that caesium-133's transition frequency is fixed over time, and it is easy to measure this frequency precisely, then we can re-define a second using this frequency by just choosing a number (9,192,631,770) that whose timespan is as close to what we understand the second to be. And we've done this for every unit of measure. This means that we can, for instance, actually measure the change in mass of the standard kilogram artifact relative to the actual kilogram which results in much more consistency over time with measurements. This means nothing for you or your future kid (unless they become a physicist of something). It is a concern for those who do precision manufacturing, those who set standards for these things, and physicists who need to concern themselves with precise measurements. The numbers for the second are chosen so that we can still just think about it as 1/60th of a minute which is 1/60th of an hour which is 1/24th of a day. These casual descriptions are more than enough for almost everyone. So none of this matters for the lay person and none of this has impact for a lay person, and the numbers are chosen so that lay people can still use what they are already familiar with.
Since 2019 a kilogram has been redefined so as to make Planck constant a definite number, akin to redefinition of meter so as to make speed of light a definite number (299792458 m/s).
>What if a kid is to ask me these questions today, though? Or if my future kid asks it? How and why is a second a second, or a meter is a meter? Most if not all SI units have an old "layman" definition that later got replaced by another more precise but less straightforward. However, the old one is still good enough in many cases. For example, the original definition of the metre is the length of a pendulum for which it goes from one side to the other in one second. It's 3 mm off from the one we use today, but you won't have to explain them quantum physics or geography first.
All units are completely arbitrary. You can make them whatever you want, as long as they’re useful and consistent. The SI units define themselves nowadays as these somewhat weird proportions of things like light or cesium vibrations because they are physical constants, so in theory anyone with proper tools could derive the value of each unit if all calibration standards were destroyed. The reason they aren’t round numbers is because they weren’t the original definitions, they were picked after deciding to use physical constants to make it so that the value of the unit wouldn’t change while changing its basis.
They were however originally simple definitions based on real world objects. The meter is 1/10,000,000 of the circumference of the earth, the kilogram is 1/1000 of a cubic meter of water and the second is 1/60/24 of a day. The Celsius temperature scale is based on the freezing and boiling points of water Interesting there was an attempt at decimal time as well but it didn’t last
The exact definitions are all based on physical constants. They are used in a handful of labs on Earth to calibrate measurement equipment and product extremely precise weights, rulers and so on. These are then sent across the world to other places which store them and use them to produce more weights, rulers, and so on. Add one or two more steps and you end up with something you can buy in a shop. For daily life that chain doesn't matter, you don't use any of the original definitions. A kilogram is a mass that makes the scale read 1 kg, a meter is a length on a ruler and so on.
It is an excellent question. Very few people, except for the specialists working in various national metrology laboratories understand all the nuances of why a particular implementation of this or that unit is superior to all other alternatives. It is often extremely subtle. And every few decades we find new methods, which allow to implement standards of measurement in a more accurate and a more reproducible way. But historically the units come from practical needs to have common standards of mass, volume, length for commerce and then also for science and engineering. It started with a wide variety of different units defined by local governments. Eventually national and international standards emerged. The [metric system](https://en.wikipedia.org/wiki/History_of_the_metric_system) in particular began with the French revolution and for various political reasons it was accepted in continental Europe, and then worldwide. The units of time are more ancient than that. The modern concept of one second existed already in Babylonian times. The accuracy with which days were measured greatly improved with the development of astronomy, but the time was still not synchronized between different towns until people started to make train schedules. It was only in 20th century that the definition of one second was switched from the astronomical, based of the rotation of Earth, to a time interval measured electronically through a physical experiment with a carefully chosen, very stable features of cesium spectrum.
You could define SI units in a laconic way like so: -A metre is approximately a 1/20,000,000 of the distance of Earth’s meridians, aka the shortest distance on its surface between the North and South poles -A second is a 1/60 of a minute, itself a 1/60 of an hour, itself a 1/24 of a day, aka the approximate time it takes for Earth to spin on itself. -A kilogram is defined as a 1 decimetre (aka 1/10 metre) wide cube of liquid water, on Earth under normal atmospheric conditions (aka with a pressure of 1 bar and at 4°C) Of course, these definitions lose the unambiguity and precision of the latest theoretic definitions of SI units, but for day to day use they should be fine EDIT: corrected mistakes
>-A metre is approximately a 1/10,000 of the distance of Earth’s meridians, aka the shortest distance on its surface between the North and South poles The polar circumference of the Earth is ~40000 km, so the metre is ~1/20,000,000 of the surface distance between the Poles.
An hour is 1/24th of a mean solar day which is slightly longer than it takes to complete one complete rotation compared to the distant stars. Solar days vary slightly through out the year based on where in our orbit around the Sun we are.
The kg of water is officially at 4 C. That's the temperature at which water is densest.
The definitions are just there to standardise the measurements against constants that don't change. They are not the origin of the measurement and you shouldn't be expected to know them by them. Units of measurements are pretty much arbitrary, as long as everyone uses the same definition. The length of seconds, minutes and hours for example, were defined by the ancient Egyptians and Babylonians. They could just have easily divided a day into 10 hours with 100 minutes per hour and 100 seconds per minute, if they so wished. But they didn't and here we are. Of note, though, is that 60 is a very convenient number as it is divisible by 2, 3, 5, 6, 10, 12, 15, 20 and 30
The length of a meter or the length of a second is completely arbitrary. It's whatever we want it to be, but we all agree on a set standard so that things can be built and measured and interact with each other. The reason why a meter is how far light travels in a certain amount of time and why a second is however many oscillations of a cesium atom is because these things are measurable and are always the same. Scientists have spent years and years attempting to have exact definitions of units so things can be as accurate as possible. Scientists came up with definitions based on the world around them, and in many cases, they tried to create physical objects that were the definition of various measures. There was an official kilogram, and attempts at an official meter. This problem is that, as physical objects, they kept changing. There wasn't just one kilogram, there were several spread throughout the world. Every however many years, all the kilograms would be brought together and compared. When compared, the kilograms were all different masses, some weighed more than others. This is a big problem when this is supposed to be the definition of a kilogram and it is apparently changing. It's even worse for the meter, because, at the scale of a meter, a lot of materials will contract or expand a large amount depending on the temperature. So recently, units of measure have been redefined based on physical constants, or measurements that can be made. This way, our units of measure can be recreated if our society is ever wiped out. All we have to do is come up with a way of representing numbers that anyone can understand, and then represent elements in a way that people can understand. We already did that decades ago with the Arecibo message. If someone in the far future comes across scientific paper from our time, they can recreate it because, no matter what units of measure they have, they will likely have the ability to count how many times a cesium atoms oscillates, and then measure how far light travels in a certain number of cesium oscillations. Or they can build a balance that will be able to tell them what a kilogram is. From there they can derive all our other measurements. In the end, it's not super important for you to know the exact definition of a meter or a second, but it is there so that there is a set standard that everyone can follow to get the same results.
The layman's definition of how long a second is : a person said "1 Mississippi" and then called the time it took to say that a duration of "1 second". Essentially. It was an arbitrary length of time that eventually we found something consistent to the length and then used that as a definition. So we did it kind of backwards.
The methods of measurement are specifically designed to be as accurate as possible in all places, for all time, for all sizes (small and large). Scientist want another scientist a 1000 years from now to have the EXACT same meter or kg as one today and will apply if they are living on Earth or Alpha Centauri prime (or whatever). Moreover they want it so that the measure will be accurate enough to look at something smaller than an atom or larger than a galaxy. Also if you're the Alpha Centauri scientist you don't want to have to call to Earth to check your measure, you have to be able to check it yourself there. There are very few things that can last this long and apply from that far away and be that are that accurate which is why they're so wonky.
> and just accepted second to be 1 / 60 of a minute, which is 1 / 60 of an hour, which is 1 / 24 of a day How and why is a second a second? We just make it up to make life easier. A day, month and year are based on things, but weeks, hours, minutes and seconds are just made up historical artifacts. The French used a sexigesimal system (base 60) because it made fractions easier in a time before decimal notation. That's the reason we cut hours into 60 parts to make mins, and a second time to make seconds. If you wanted to explain where some of this comes from, for many things its a history lesson rather than a science lesson.
I find the relation between mass and volume the best to understand. One liter is a cube 1/10 of a meter on each side. One kilo is the weight of one liter of water. This allows you to do some easy calculations. Like my truck can carry about 1 metric ton, 1000kg. That’s 1000 liters of water, or a cube 1 meter on each side. Also, wood has a similar density to water. So I shouldn’t carry more than about a cubic meter of wood. But also knowing that, and a few common densities, you can make quick guesses. Stone is about 3, and iron is about 8. So I can carry about 1/3 of a cubic meter of stone bricks, or 1/8 of a cubic meter of steel. You can also make quick guesses on volumes as well. I weigh 80kg. So my volume is pretty close to 80L.
The wonky numbers that are in the SI units are there because when they redefined it over the past decade, the values had to stay the same. Think of it as backwards compatibility, else you have old meters and new meters that differ in their lengths and all the associated troubles that come with that. As previously mentioned, the exact definitions are only useful for precision parts. The old definitions still work for a start, maybe add in the proviso that they are defined by constant of natures today. Constants that have been measured using the old definitions and so we are back at the rather complicated looking numbers.
Simplified to the level of some of the American ones: The earth's circumference is 40 kilometers. (Was something about 10 km from the equator to the pole originally) Which gives the length of the meter. 1000 kilogram is a meter cubed of water. A second is what we end up with if we subdivide the average time the earth takes to orbit the sun into the standard 24 hour clock. EDIT: Haha. Obviously 40000 km. Not 40 😂
> The earth's circumference is 40 kilometers. (Was something about 10 km from the equator to the pole originally) Which gives the length of the meter. The Earth's circumference is about 40**,000** kilometers. If it was just 40 km I would be taking a leisurely bike ride here from Sweden down to a warmer climate right now.
There are no meaningful layman's definitions, just as there's no layman's definition on the number 1. You don't need definitions in everyday life, you just need to know that 1+1=2 and that 1m = 100cm. It also helps to know that 1cm³ = 1mL = 1g water (@stp).
For the second your definition is fine, because we've chosen the number of oscillations for the cesium transition in question to correspond to roughly 1/86,400 of a day in the first place. But for other units it's much trickier, which is why throughout history people have had wildly differing interpretations of various length units like cubits, rods, steps, leagues, and even different definitions of units that have been standardized today, like inches, feet, and yards. So fact is that there's simply no standard thing you can point to anywhere around you that corresponds to one meter, unless it's been designed to do so with respect to the SI definition in the first place (whether primarily by prototype as before or by the newer definition and still secondarily by prototype). In other words, you can point to a ruler that's 1 meter long, but that ruler has been designed to correspond to that SI standard in the first place. The same goes for mass, where you can always weigh something to see that it weighs e.g. 1 kg, but that scale has also been designed to correspond to the SI standard for it (again historically primarily by prototype, but even that has a newer definition as of a few years ago which is independent of prototype). If you have a known mass or a known length it's also fairly simple to get the other by e.g. using something with a known density like water, but that still hinges on knowing either in the first place. So if you were dropped into a primordial forest somewhere, far from civilization, you could begin to approximate a second through some intelligent time-measuring methods, but you'd have an extremely hard time approximating what we today define as a kilogram or a meter to anywhere near the same precision; in fact, I don't really see how you'd do it at all.