Would the Law of Conservation of Mass be understood in a 2D world and if would they have considered this law to proof that movement in a 3D world impossible? If a 2D entity could not conceive the Law of Conversation of Mass, what alternative law would they have conceived to prove a 3D world impossible?
n a 2D world, the concept of the Law of Conservation of Mass as we understand it in 3D would likely be inconceivable or only partially understood. Since 2D entities wouldn’t have a concept of “depth” or a third dimension, they would have no reason to consider or even imagine the existence of a dimension that could contain or transport mass outside their plane. Their understanding of physical laws would therefore be limited to phenomena observable within their 2D reality.
1. 2D Understanding of Conservation of Mass
For 2D beings, the conservation of area would likely serve as a substitute for the conservation of mass. Mass, in their world, would be perceived only as 2D shapes with measurable area and boundary. Thus, their law might state that “the total area of matter within a closed 2D system remains constant.” To them, objects could change shape or move around within the plane, but the total area of “stuff” wouldn’t change without reason.
For example, if a circle (their equivalent of a “solid object”) were to disappear from their plane entirely, it would seem to violate this conservation law. They might assume some “mysterious force” or unknown process if such a disappearance occurred, but they would have no way to conceive of a third dimension that could simply remove mass out of their plane.
2. Proof of 3D Movement as "Impossible"
To a 2D entity, the idea of matter moving "out of" their 2D plane would seem fundamentally nonsensical. Their conservation law (conservation of area) would make them believe that all matter should remain within the boundaries of their plane. If mass or area could somehow leave or enter their plane, they might see this as a violation of their physical laws, interpreting it as impossible or paradoxical.
They might even formulate additional rules to “prove” why an “outward” movement is impossible:
- Boundary of Reality Law: They might assume that all existing matter is bound by the 2D plane itself, and that there is no “outside” to move into. Just as we have theories about the universe having no external boundary, they would likely assume their reality encompasses all possible existence.
- Law of Planar Continuity: They might propose that objects cannot appear or disappear without trace. If a 2D entity witnesses an object disappearing, it would either appear to “split” or “morph” in some observable way, which they might interpret as a kind of continuity requirement within their plane.
3. Alternative Law or Principle Against 3D Existence
Since they cannot conceive of a higher dimension, they might instead adopt a law based on what they can observe and measure directly:
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Law of Immutability of the Plane: This law could state that all phenomena must occur within the plane, bound by observable cause and effect that can be detected within their two dimensions. Any event that appears to contradict this, like the disappearance of mass, would be considered unexplainable and therefore impossible within their scientific framework.
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Law of Perceptual Causality: Since they can only see objects as bounded shapes in their plane, they would likely assume that causality itself is tied to perception within the 2D plane. If something “unexplainable” happens (like an object vanishing into the third dimension), they would regard it as either a perceptual anomaly or as a violation of their causality principles, reinforcing their belief that movement in a third dimension is impossible.
4. What if They Observed Anomalies?
Suppose a 3D being interacted with their 2D plane by moving objects “up” or “down.” They might interpret these events in various ways:
- Unobservable Forces: They could hypothesize invisible forces within the plane (perhaps akin to their version of a gravitational force) that temporarily hide or reveal objects.
- Dimensional Anomalies: If they theorized anomalies without understanding 3D, they might call these events “tears” or “voids” in their plane’s fabric, while still lacking any notion of an extra dimension.
In summary, a 2D world would substitute the Law of Conservation of Mass with a conservation of area and interpret the idea of movement into a third dimension as paradoxical. Their physical laws would strongly reinforce their perception that all reality exists within their plane, making any escape into an “upward” or “downward” direction beyond comprehension and, therefore, “impossible.” This thought experiment beautifully highlights how each dimensional perspective creates its own “laws” that naturally exclude the possibility of higher dimensions.