In Judaism, time is an artificial construct, made “real” by our own declarations. Remarkably, the Torah teaches us a similar lesson with regard to space!
The key unit of length in the Torah is an “amah.” How long is an amah?
The Torah does not tell us. We understand that an amah is the length of a forearm, but whose forearm, exactly? And where on the wrist or hand does the forearm end? Nobody can be sure.
Indeed, there are no objectively knowable measurements in the Torah at all. On the contrary – the only measurement we have that connects an amah to any one person is to the giant, Og, the king of Bashan. His arm, surely, was larger than most, and yet the Torah sees fit to tell us about the size of his bed: “Nine amahs was its length, and four amahs its breadth, according to the amah of that man.”
This leads us to an intriguing conclusion: the Torah is deliberately vague about this (and all) measurements. Precise measurements seem to be unimportant, and if Og can be the model of an amah’s length (since his is the only “sample” amah given in the Torah), then we can legitimately use any forearm in the world to build something described in the Torah.
In other words, the Torah does not give us an absolute calibration point on any length or volumetric measurement at all!
But then why does the Torah have measurements in the first place? Why say that something needs to have a height of X amahs, if the underlying unit of measure can be entirely subjective? Wouldn’t a vague measurement be almost entirely useless? And if that is so, then why does the Torah give us measurements in the first place?
The answer lies in the realization that there are (almost) no standalone measurements in the Torah! Every single measurement is given as a proportion, in relation to something else. X amahs long and Y amahs wide, or one “hin” of this, for a measure of that. Always there is a proportion given, a ratio.
Is there a broader lesson here that we can learn from? Before we can answer this, we first have to look at what the Torah is actually measuring when it uses units of measure.
To start with the Torah only gives measurements in Amahs when it describes enclosing something that is alive! Noach’s Ark is measured in Amahs. So is the Mishkan. The Torah also uses the amah (amah) to give the dimensions around a city, and for Og’s bed. All contain living things.
But the Amah itself is not based on anything that is merely physical. The measurement uses the arm of a man, the agent of Hashem in this world. The Torah tells us that mankind, not a stick or a rock or the sun or the moon, is supposed to be the measure of everything in the world. Man is the measure of all things having to do with housing the divine spirit whether inside people (as in the Ark), or for the Shechinah itself (in the Mishkan).
So why is an amah such a vague metric? The Torah uses the amah because such a metric tells us that there no “perfect” or “ideal” man. Indeed, the metric of an amah tells us that each and every person is capable of being the reference yardstick around which mankind can serve Hashem. We don’t need to use Moshe’s amah, or Avrahom’s amah. If Og’s amah can be used as a measuring stick, then so can the arm for any person on the earth. This is a profoundly egalitarian vision.
But if the amah is such a variable and individualistic measurement, then why does the Torah give so very many measurements? The answer can be found by realizing that, in almost every case, the Torah gives no measurements using only a single dimension. Each measurement is in two dimensions, not one: It is never “X amahs.” Instead, the measurements are “X amahs by Y amahs.”418
Every one of these measurements was information given to mankind concerning a place for life. So we can conclude that man’s forearm is the measurement for all enclosures for Hashem and man. These measurements are fundamentally about man’s creation of a house or dwelling or bed: a single stick is not a building, but once we take a piece of (functionally) one-‐dimensional wood or thread and build it with others into two dimensions, we have an actual product of human creativity. Working in two dimensions creates complexity from what had been a simple stick or thread beforehand. We use amahs to build things that emulate Hashem’s creation. Just as Hashem made the world to house life, so, too, we take from the natural world, and build houses and arks and the Mishkan that defines the space around a living soul.
Except for in the case of the flood, where the waters went fifteen amahs higher than anything else. Nechama Cox suggests this further reinforces the need for proportion in our lives. The Torah is giving us these guidelines to teach us the need for proportion, and brings the counter proof – when there is no proportionality, it leads to death and destruction.
Note that while people make houses that are in fact three-‐dimensional, the Torah never gives a volumetric measurement of something built with amahs. Even when a volume can be computed, such as in the example of the length times the width times the height of Noach’s Ark, the Torah does not do so.
But the Torah does indeed have volumetric measurements! They are named as the hin for fluids, and the ephah and the omer for dry goods. But note what is actually measured: with the arguable exception of the manna, in every case the thing quantified by the Torah is a processed food product: olive oil, wine, grain and flour.
Why these products?
The things that are measured in each of the three dimensions are all used as offerings to Hashem. We are meant to make our sacrifices complete, as well-‐rounded as possible, and that means using even measurements that are in three dimensions. Note too, that each of these things (oil/wine/grain) are themselves also perishable, so they could be said to be measured in the dimension of time as well (a possible fourth dimension). Lastly, and perhaps more importantly, they are all products of both the natural world and mankind’s effort, meaning that they are candidates for holiness – combining the efforts of Hashem and man, and offered to Hashem as part of a sacrifice.
Just as we do with other commandments, we measure things in the Torah for the purpose of elevating nature. We use natural components solely when we connect the world below to the world above, specifically in an offering to Hashem in His home. Nothing offered to Hashem is measured in amahs (a man-‐centered metric), for it would be an egregious misunderstanding of our relationship with Hashem to think that we, the agents who bring about holiness in this world, are ourselves supposed to form part of an offering. Man connects the world below to the world above, but we are not supposed to consider ourselves part of that offering to Hashem. Instead of being the sacrifice, we are the middle-men who bring the two together. And those offerings are measured using three dimensional, volumetric measurements.
But our buildings are all based on the amah – which is a measurement of a person’s arm. No animal or plant is the metric: “Man is the Measure.” Nature is then measured not by its own metric, but by mankind’s constructions, using man’s own arm as the reference point. Hashem does not give us any length measurements in the Torah which are based on anything in the natural world at all. 419 And so domiciles (whether Noach’s Ark, the Mishkan for Hashem, or Og’s bed) are all measured by amahs.
So the Torah is telling us that when we use our arms to build, we are making homes fit for men, kings (even one such as Og), and Hashem Himself. None of these things are meant to be offered up to Hashem; they are meant for improving the world in which we live. In this, we are emulating Hashem. That is why the Torah gives us no linear measurements using
Thus there is no reference in the Torah itself to any natural-‐world yardstick except Og’s amah.
We build according to the metric of man, not the metric of nature. Our buildings are reflections of our own will, not reflections of the natural world. Which means that it is mankind’s job to make his imprint on nature, not the other way around. The connection between the earth and Hashem is made through man; everything is measured by the metric of a man. We do not elevate nature using natural forces but through artificial (literally “manmade”) efforts.
Which leaves us with one substantial – and unanswered question: why does the Torah give us indefinite measurements, but entirely specific relative measurements? We may not know how long a amah is, but we know the curtains for the Mishkan were specifically twenty-‐eight by four amahs. Measurements may not be precise. But the relationships between those measurements are precise. The absolute dimensions of the Mishkan may be impossible for us to know, but the relative dimensions are fixed. In this respect the Torah does not discriminate between offerings and buildings, the work of nature or the work of man: precise proportions are given in every situation.
Chana Cox adds:
Relativity is true of any measure of space or time. We cannot have an absolute measure, and any number assigned to the measure is entirely dependent on the “yardstick” chosen. The measurement of the room I am sitting in is not absolute. It depends on my choice of measuring device. Imagine, if you will, that thing Newtonians called true and absolute space. Imagine a triangle in that space. Would there be any way of determining if the sides of the triangle were 5 feet or 5 miles? Not without putting something else into the picture. In a sense, then, no measurement is real in any absolute sense (Newton notwithstanding). But: ratios can be real. Virtually all the laws of physics are equations which express a ratio. The empirical work is always about determining precisely what that ratio is – what the constant or coefficient is. Whether the numbers are in meters or in yards is simply a matter of arithmetical convenience. The seemingly absolute number is totally arbitrary, but the ratio is not.
What is different about the Torah measurements is that they seem to be keyed to the forearm of a man – any man. They are not geared to a meter-‐stick in a vault in Paris. Historically, the measures we use are always decided by convenience. Perhaps, like my example of the triangle, it doesn’t much matter how big the triangle is. That is not what establishes its true geometric qualities. It matters what the ratios are. Alternatively, it is likely that in any particular community of builders, someone decides whose forearm to work from. To us it seems inconvenient but it need not be. Everybody in the “building business” probably knew they would have to agree on a measure before the job began.
Finally, to measure anything or to count anything is, in a very real sense, to treat it as an object and therefore not as a person. We do not count people. I think, in a real sense, the Torah is reluctant to even assign a number to a part of a person such as a forearm.