# Example 1001 — Three litres in a thin tube split the barrel `three_litres_in_a_thin_tube_split_the_barrel.eml` - A sealed barrel full of water has a thin tube, 10 metres tall, fitted into its lid. Someone pours 3 litres of water into the tube and reasons that 3 litres on top of the 200 the barrel already holds, weighing 3 kg, cannot trouble a barrel built for 200 kg. What the 3 litres do to the lid is computed below. ## EML ```eml # Self-authored for the EML case corpus (no external origin). A sealed barrel # full of water has a thin tube, 10 metres tall, fitted into its lid. Someone # pours 3 litres of water into the tube and reasons that 3 litres on top of the # 200 the barrel already holds, weighing 3 kg, cannot trouble a barrel built for # 200 kg. What the 3 litres do to the lid is computed below. # # The reasoning is careful. The tube really holds only 3 litres; 3 kg really is # a small weight next to 200; the barrel really was built for its contents; and # the intent is exactly 'is the barrel safe'. # # Water pushes on the lid with a pressure set by the height of the water above # it, not by how much water there is. A column 10 metres tall adds 98100 pascals # on every part of the lid, and over a lid of 3000 square centimetres that is # the force of 3000 kg - a thousand times the weight of the water that made it. 200 => barrel_litres 3000 => lid_area_cm2 1000 => tube_height_cm 3 => tube_cross_section_cm2 1000 => water_kg_per_m3 981 => gravity_cm_per_s2 int(tube_cross_section_cm2 * tube_height_cm / 1000) => water_in_the_tube_litres water_in_the_tube_litres => water_in_the_tube_kg int(water_kg_per_m3 * gravity_cm_per_s2 * tube_height_cm / 10000) => pressure_from_the_column_pa int(pressure_from_the_column_pa * lid_area_cm2 / 10000) => force_on_the_lid_newtons int(force_on_the_lid_newtons * 100 / gravity_cm_per_s2) => force_on_the_lid_kg int(force_on_the_lid_kg / water_in_the_tube_kg) => times_the_weight_of_the_water_poured int(water_in_the_tube_litres * 1000 / barrel_litres) => water_poured_vs_barrel_per_mille "barrel : " + str(barrel_litres) + " litres, lid " + str(lid_area_cm2) + " cm2" ^0 "tube : " + str(tube_height_cm) + " cm tall, " + str(tube_cross_section_cm2) + " cm2 across" ^0 "water poured into the tube : " + str(water_in_the_tube_litres) + " litres, " + str(water_in_the_tube_kg) + " kg, " + str(water_poured_vs_barrel_per_mille) + " per mille of the barrel" ^0 "" ^0 "pressure the column adds : " + str(pressure_from_the_column_pa) + " pascals" ^0 "force on the lid : " + str(force_on_the_lid_newtons) + " newtons, the weight of " + str(force_on_the_lid_kg) + " kg" ^0 "force vs the water poured : " + str(times_the_weight_of_the_water_poured) + " times its weight" ^0 "" ^0 # ---- what the pourer verified ---- "the few-litres reasoning" ^0 " water poured : " + str(water_in_the_tube_litres) + " litres, " + str(water_in_the_tube_kg) + " kg" ^0 " against the barrel : " + str(water_poured_vs_barrel_per_mille) + " per mille of what it already holds" ^0 " the barrel : built for its " + str(barrel_litres) + " litres" ^0 " intent : is the barrel safe" ^0 " facts wrong : 0" ^0 " verdict : THREE LITRES CANNOT HURT A BARREL THAT HOLDS TWO HUNDRED" ^0 "" ^0 " weighing the water poured is the part done right here, and it" ^0 " is why " + str(water_in_the_tube_kg) + " kg is exactly the extra weight the barrel now carries" ^0 "" ^0 # ---- what the column does to the lid ---- "pressure is height, not amount" ^0 " what presses on the lid : the pressure of the water above it," ^0 " and that is set by how tall the water stands" ^0 " the column : " + str(tube_height_cm) + " cm of water, " + str(pressure_from_the_column_pa) + " pascals, whatever" ^0 " its width" ^0 " where it acts : on every square centimetre of the lid, not" ^0 " just the one under the tube" ^0 " over the whole lid : " + str(force_on_the_lid_newtons) + " newtons, the weight of " + str(force_on_the_lid_kg) + " kg" ^0 " what the thin tube saved : water, not force; a wide tube of the" ^0 " same height would press exactly as hard" ^0 "" ^0 # ---- what the pourer got ---- "the barrel" ^0 " believed : " + str(water_in_the_tube_kg) + " kg more, nothing to notice" ^0 " actual : the lid pushed with the weight of " + str(force_on_the_lid_kg) + " kg, and the" ^0 " staves split" ^0 " is the weight of the poured water wrong : no; it is " + str(water_in_the_tube_kg) + " kg" ^0 " does the force follow the weight : no; it follows the height" ^0 " of the column and the area it presses on" ^0 "" ^0 # ---- null control ---- # The same tube judged by the height of its water instead of by its weight. 3 => nc_load_read_from_the_water_poured_kg 3000 => nc_load_read_from_the_height_of_the_column_kg 2997 => nc_kg_the_height_adds "null control - read the load from the height" ^0 " load, read from the water poured : " + str(nc_load_read_from_the_water_poured_kg) + " kg" ^0 " load, read from the height of the column : " + str(nc_load_read_from_the_height_of_the_column_kg) + " kg" ^0 " kg the height adds : " + str(nc_kg_the_height_adds) ^0 " no barrel and no water changed; the pressure was taken from" ^0 " the height of the water and applied to the whole lid" ^0 "" ^0 # ---- the rule ---- "what pouring " + str(water_in_the_tube_litres) + " litres into the tube guarantees" ^0 " the barrel holds " + str(water_in_the_tube_kg) + " kg more water : exactly" ^0 " the barrel is loaded by " + str(water_in_the_tube_kg) + " kg more : not addressed; the" ^0 " column stands " + str(tube_height_cm) + " cm tall, pressing " + str(pressure_from_the_column_pa) + " pascals on every part" ^0 " of the lid, " + str(force_on_the_lid_newtons) + " newtons in all, the weight of " + str(force_on_the_lid_kg) + " kg" ^0 "" ^0 "water keeps no account of how much of it there is; it pushes with the" ^0 "height it stands at, and a thread of water ten metres tall pushes like a" ^0 "lake ten metres deep" ^0 "" ^0 "Three litres weigh " + str(water_in_the_tube_kg) + " kg - the weighing is right. But pressure follows height:" ^0 "a column " + str(tube_height_cm) + " cm tall adds " + str(pressure_from_the_column_pa) + " pascals to every part of the lid, and" ^0 "over " + str(lid_area_cm2) + " cm2 that is the weight of " + str(force_on_the_lid_kg) + " kg, " + str(times_the_weight_of_the_water_poured) + " times the water poured," ^0 "until the load is read from the height of the water and not its weight." ^0 ``` ## Python (deterministic transpilation) ```python barrel_litres = 200 lid_area_cm2 = 3000 tube_height_cm = 1000 tube_cross_section_cm2 = 3 water_kg_per_m3 = 1000 gravity_cm_per_s2 = 981 water_in_the_tube_litres = int(tube_cross_section_cm2 * tube_height_cm / 1000) water_in_the_tube_kg = water_in_the_tube_litres pressure_from_the_column_pa = int(water_kg_per_m3 * gravity_cm_per_s2 * tube_height_cm / 10000) force_on_the_lid_newtons = int(pressure_from_the_column_pa * lid_area_cm2 / 10000) force_on_the_lid_kg = int(force_on_the_lid_newtons * 100 / gravity_cm_per_s2) times_the_weight_of_the_water_poured = int(force_on_the_lid_kg / water_in_the_tube_kg) water_poured_vs_barrel_per_mille = int(water_in_the_tube_litres * 1000 / barrel_litres) print("barrel : " + str(barrel_litres) + " litres, lid " + str(lid_area_cm2) + " cm2") print("tube : " + str(tube_height_cm) + " cm tall, " + str(tube_cross_section_cm2) + " cm2 across") print("water poured into the tube : " + str(water_in_the_tube_litres) + " litres, " + str(water_in_the_tube_kg) + " kg, " + str(water_poured_vs_barrel_per_mille) + " per mille of the barrel") print("") print("pressure the column adds : " + str(pressure_from_the_column_pa) + " pascals") print("force on the lid : " + str(force_on_the_lid_newtons) + " newtons, the weight of " + str(force_on_the_lid_kg) + " kg") print("force vs the water poured : " + str(times_the_weight_of_the_water_poured) + " times its weight") print("") print("the few-litres reasoning") print(" water poured : " + str(water_in_the_tube_litres) + " litres, " + str(water_in_the_tube_kg) + " kg") print(" against the barrel : " + str(water_poured_vs_barrel_per_mille) + " per mille of what it already holds") print(" the barrel : built for its " + str(barrel_litres) + " litres") print(" intent : is the barrel safe") print(" facts wrong : 0") print(" verdict : THREE LITRES CANNOT HURT A BARREL THAT HOLDS TWO HUNDRED") print("") print(" weighing the water poured is the part done right here, and it") print(" is why " + str(water_in_the_tube_kg) + " kg is exactly the extra weight the barrel now carries") print("") print("pressure is height, not amount") print(" what presses on the lid : the pressure of the water above it,") print(" and that is set by how tall the water stands") print(" the column : " + str(tube_height_cm) + " cm of water, " + str(pressure_from_the_column_pa) + " pascals, whatever") print(" its width") print(" where it acts : on every square centimetre of the lid, not") print(" just the one under the tube") print(" over the whole lid : " + str(force_on_the_lid_newtons) + " newtons, the weight of " + str(force_on_the_lid_kg) + " kg") print(" what the thin tube saved : water, not force; a wide tube of the") print(" same height would press exactly as hard") print("") print("the barrel") print(" believed : " + str(water_in_the_tube_kg) + " kg more, nothing to notice") print(" actual : the lid pushed with the weight of " + str(force_on_the_lid_kg) + " kg, and the") print(" staves split") print(" is the weight of the poured water wrong : no; it is " + str(water_in_the_tube_kg) + " kg") print(" does the force follow the weight : no; it follows the height") print(" of the column and the area it presses on") print("") nc_load_read_from_the_water_poured_kg = 3 nc_load_read_from_the_height_of_the_column_kg = 3000 nc_kg_the_height_adds = 2997 print("null control - read the load from the height") print(" load, read from the water poured : " + str(nc_load_read_from_the_water_poured_kg) + " kg") print(" load, read from the height of the column : " + str(nc_load_read_from_the_height_of_the_column_kg) + " kg") print(" kg the height adds : " + str(nc_kg_the_height_adds)) print(" no barrel and no water changed; the pressure was taken from") print(" the height of the water and applied to the whole lid") print("") print("what pouring " + str(water_in_the_tube_litres) + " litres into the tube guarantees") print(" the barrel holds " + str(water_in_the_tube_kg) + " kg more water : exactly") print(" the barrel is loaded by " + str(water_in_the_tube_kg) + " kg more : not addressed; the") print(" column stands " + str(tube_height_cm) + " cm tall, pressing " + str(pressure_from_the_column_pa) + " pascals on every part") print(" of the lid, " + str(force_on_the_lid_newtons) + " newtons in all, the weight of " + str(force_on_the_lid_kg) + " kg") print("") print("water keeps no account of how much of it there is; it pushes with the") print("height it stands at, and a thread of water ten metres tall pushes like a") print("lake ten metres deep") print("") print("Three litres weigh " + str(water_in_the_tube_kg) + " kg - the weighing is right. But pressure follows height:") print("a column " + str(tube_height_cm) + " cm tall adds " + str(pressure_from_the_column_pa) + " pascals to every part of the lid, and") print("over " + str(lid_area_cm2) + " cm2 that is the weight of " + str(force_on_the_lid_kg) + " kg, " + str(times_the_weight_of_the_water_poured) + " times the water poured,") print("until the load is read from the height of the water and not its weight.") ``` ## stdout (executed) ```text barrel : 200 litres, lid 3000 cm2 tube : 1000 cm tall, 3 cm2 across water poured into the tube : 3 litres, 3 kg, 15 per mille of the barrel pressure the column adds : 98100 pascals force on the lid : 29430 newtons, the weight of 3000 kg force vs the water poured : 1000 times its weight the few-litres reasoning water poured : 3 litres, 3 kg against the barrel : 15 per mille of what it already holds the barrel : built for its 200 litres intent : is the barrel safe facts wrong : 0 verdict : THREE LITRES CANNOT HURT A BARREL THAT HOLDS TWO HUNDRED weighing the water poured is the part done right here, and it is why 3 kg is exactly the extra weight the barrel now carries pressure is height, not amount what presses on the lid : the pressure of the water above it, and that is set by how tall the water stands the column : 1000 cm of water, 98100 pascals, whatever its width where it acts : on every square centimetre of the lid, not just the one under the tube over the whole lid : 29430 newtons, the weight of 3000 kg what the thin tube saved : water, not force; a wide tube of the same height would press exactly as hard the barrel believed : 3 kg more, nothing to notice actual : the lid pushed with the weight of 3000 kg, and the staves split is the weight of the poured water wrong : no; it is 3 kg does the force follow the weight : no; it follows the height of the column and the area it presses on null control - read the load from the height load, read from the water poured : 3 kg load, read from the height of the column : 3000 kg kg the height adds : 2997 no barrel and no water changed; the pressure was taken from the height of the water and applied to the whole lid what pouring 3 litres into the tube guarantees the barrel holds 3 kg more water : exactly the barrel is loaded by 3 kg more : not addressed; the column stands 1000 cm tall, pressing 98100 pascals on every part of the lid, 29430 newtons in all, the weight of 3000 kg water keeps no account of how much of it there is; it pushes with the height it stands at, and a thread of water ten metres tall pushes like a lake ten metres deep Three litres weigh 3 kg - the weighing is right. But pressure follows height: a column 1000 cm tall adds 98100 pascals to every part of the lid, and over 3000 cm2 that is the weight of 3000 kg, 1000 times the water poured, until the load is read from the height of the water and not its weight. ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:assign · eml:output · eml:run:done