This article is about the concept of fourth spatial dimension in addition of the three we know, length, breadth and height, don't confuse it with the four-dimensional spacetime in which time is taken as the fourth dimension. This article is about the concept of four dimensions of space itself in addition of the fifth time dimension, that is, a dimension in which mass can actually move in the regular sense.
So, why its important to think about an extra dimension in space? According to Einstein's General Theory of Relativity the spacetime is curved at points where mass is present, for example near stars and planets and this curve is the reason of gravity. It help explain why gravity is not really one of the four fundamental forces of nature because it is just due to the geometry of the spacetime rather than any exchange of particles like in other three forces. It also explains why there is no counter-force for gravity in regular sense (that is ignoring Casimir Effect) unlike other fundamental forces.
The arguement of existence of a fifth dimension in addition of the four dimensions of the spacetime is based on the perceived fact that for a n-dimensional thing to bend there need to exist a n+1-dimensional realm. So, the arguement says, there must exist a fifth dimension for the four dimensional spacetime to bend into. Its like a 2D bedsheet can bend in a 3D space but can't in a 2D surface, a shadow can't bend on itself means there can't be two layers of shadow at the same surface, a line can't bend if no 2D surface is present and so on. So, if you believe that gravity is due to curvature in spacetime, which you should as there is no better explanation then you should also believe in existence of a 5D realm we are living in.
Lets first straighten some terms to avoid confusion. A 2D environment is a surface, it can also be called plane but I prefer the term surface for easy understanding. A 3D environment is space, 4D is spacetime and for 5D there is no clear word dedicated so I use the general term "realm".
Lets see some examples of n-dimensional objects to better understand the concept:
A 0D thing can only be a point, it has no length, no breadth, no width, nothing, it is used just to locate a position in space assuming that the position is infinitely small. Also note that a 0D thing can have no shape as it has no dimensions. Infact it can be explained with zero information as there is nothing in it to explain. Also note that a point has no place to move.
A 1D object has only one direction forward-backward. It can have exactly one shape that is straight line. Since there is no second dimension to bend into a 1D object can have no other shape than straight line. Note that for the rest of this article I would be using the term "line" for straight lines and curves for any crooked kind of lines.
A 2D object knows two directions, forward-backward and right-left. It can be of an infinite number of shapes including square, rectangle, oval, circle, pentagon, hexagon etc. For our understanding of higher spatial dimensions its better to first understand a 2D Flatland and then use this understanding to imagine a 4D world. A 2D living being can only see things in 1D as we in our 3D world can only see in 2D. It is because when we see a thing from front we can only see its length and width but the width is hidden from us. Same way a 2D eye can only see a 1D object. Since all 1D objects have to be a line therefore all a 2D eye can see is lines, the only variety comes from the different lengths of the lines representing different objects in that world.
Now lets imagine a 4D world. A shadow in that realm would be 3D means like us. So, if a 4D object want to interact with us, the only way is to do so through shadows as it can't directly talk to us or hold anything of our world. Its like you being 3D can never hold in your hand your 2D shadow. Note that the other examples given of 2D objects in various books are technically incorrect, an image of you in a mirror is still 3D because the light forming the colors is 3D, the text appearing on computer screen in front of you is also 3D because the pixels of the screen are infact 3D. Infact you can't see any 2D thing because the light of our world that makes things visible to us is itself 3D. A shadow is the only 2D object but even that is not a real thing, its just an absence of light, not existence of anything. That is why I strongly criticize the story of books like FlatLand and SpaceLand because they talk about objects interacting with lower-dimensional objects which cannot happen. Infact its a very interesting point, if 2D worlds exist than an infinite number of them can be there one over another occupying no width therefore no existence in our 3D world.
A 4D living being would have a lots of superiorities over us 3D beings. For example it can see what is inside our stomach without having to do any surgeries in the same way that we can see what is inside a circle without breaking the boundaries of the circle. That is assuming if it can see, but since it cannot because for it we don't exist as we are not 4D, so it can't see.
What is this information useful for? Well, a way to travel long distance in spacetime is utilizing the curves making shortcuts. Its like a worm instead of travelling through the 2D surface of apple make a hole in the third dimension and travelling through it in short cut. Same way we can think of utilizing the naturally present curvatures in spacetime near massive celestial bodies, that may lead us to place far off in universe, say milions of light years in reasonable few tens of years. So, how to do that. One idea that come in my mind is discussed below.
Consider a room in which there is a window with a grill in it. A light source from outside cast a shadow of grill inside the room on the 2D floor of the room. The 2D shadow roll over the 2D floor as the light source moves. Then, by some special movement of the light source the shadow enter the third dimension, the wall of the room. Now think that we are this shadow but in 3D and the room is 4D. We roll over the 3D space of the room. If the room has an edge, that is, an end and we reach that end then like the shadow we ultimately enter the fourth spatial dimension, the wall. How would it feel like? Well first of all, during the transition time when part of our space ship would be in space and part curving 90 degrees in the extra dimension, the outside world for the front of ship which is in 4D would have fundamentally changed. Instead of seeing the regular things the back of the ship-mates are seeing from outside their windows the front ship-mates would be seeing a very different world. It is wrong to say that they would not be seeing anything. Like the shadow can see the 2D surface of the wall while climbing on it, the ship-mates in front of the ship too, just that it would be different than what they had ever seen before. The known 3D world at the floor of the room would ofcourse no longer be visible to the front ship-mates. The people at the back of ship still laying flat on the floor of the room would still be seeing the familiar world.
So, a 3D object can enter a 4D world by reaching the edge and continue travelling, but what the edge is? It not need be the end of universe because the 2D shadow not need to reach the end of 3D universe to climb the wall. The edge is local, limited to the room. If the shadow was laying in a flat field it would not enter the higher dimension. So, we have to find a 4D edge, it could be any 4D object, not need be a wall. If there was say a ball in the room, the object would climb on it to reach the third dimension, it not have to travel all the way to reach the wall of the room.
How would it feel to the ship while entering the extra dimension? At first the front of the ship would appear lost as the ship hit the wall, this would be a shock to the people at back of the ship and they might think they have reached the end of the world but if they continue travelling the entire ship would enter the new dimension. On their way back to the floor of the room they have to remember the co-ordinates of the point from where they entered assuming that the 4D object they climbed through would still be there. This would prove to be problematic as nothing in space can stay at one place, so when the ship go back to find the 4D object it would no longer be there.
Note that nothing in a 4D world can harm a 3D object, it would not even know about its presence, for it the 3D object do not exist. Only problematic thing would be shadows and its basically hard to imagine how a 3D void of light can affect a 3D object, may be it not affect at all because it is not anything real, just absence of a thing.
Now, the question is, why not the 2D object move under the 3D ball or wall instead of climbing on it. When a 3D object is put on another 3D object, like a wall put on ground or a ball on floor, there may still exist infinite number of 2D planes even if there is no physical 3D space between the two 3D objects. For a 2D plane or surface to exist no height is needed so the absence of space between the two 3D objects cannot stop the existence of 2D surfaces between the two 3D objects. Why then the shadow not just slip under the wall instead of laying on top of it? May be because the light source is 3D. If it would be a real 2D object it could no doubt go between the ball and floor even if no space exist between them. If that happen in our experiment then there is no other known way to enter a higher dimension.
05 August, 2009
Food Foot Print
Assuming that the diet is balanced, yields are average and land is 1k, the calculation of the area of arable land needed per person is as follows:
Notes:
(i) The figures for land is given in sq meters, there are about 4000 sq meters in one acre so the above sum is half acre.
(ii) The sum for all grains is 800 sq m (400 for wheat, 200 for barley, 100 each for rice and millet) but we should take 900 sq m because a substantial amount of grains grown goes in shell, for eg the shell of wheat removed in milling.
(iii) The grains includes barley and millet because they are nitrogen fixing crops.
(iv) Oil is vegetable oil. Since vegetable yield is 1000 kg and oil extraction rate is 25% so 250 kg is its yield.
(v) The above calculations are based on a 400 days diet per year, the extra number of days allow more-than-normal eating in feasts and parties, roughly 10% of the entire year.
(vi) For simplicity straight forward figures about crops directly eaten by humans is given first, the more complex subject of crops grown by humans but eaten by animals and then those animals and their milk consumed by humans is discussed below.
It should be known that per kg mass animals and infact insects and birds too require same number of calories as humans for same level of activities. So a cow which is lactating needs 60 calories per kg per day and which is not lactating needs 40, so average is 50. It should also be noted that for each kg gain in both animals and humans same 7,500 calories are needed. Since about 60% mass of an animals is meat (including bones), therefore 12,500 calories are needed per kg meat at minimum.
Another important point to consider is calories in hay, but first what is hay? Hay is a general term that includes all grass, straw, leaves etc eaten by animals but not all grass, straw and leaves are hay. Fresh grass which have visible moisture on its surface is only 15% dry matter and 85% moisture, fresh grass and leaves with no visible moisture contains 20% to 30% dry matter and rest is moisture, brown grass and leaves contains may be 50% dry matter. The point is, when fresh moisture level is high and when time pass and the green matter becomes brown its moisture level decreases. It should be kept in mind that the energy needed by the animals is only in the dry matter, there is no energy in moisture.
Hay is grass, straw or leaves that has atleast 80% dry matter but dry matter may rise upto 90%. For our calculations we ignore the higher proportion and assume that only 80% of hay by mass is dry matter to be safe. Each gram of dry matter contains 2.5 calories. So the hay as a whole contains 2 calories per gram.
It should be noted that all over this website the term "calorie" actually refers to "kilo calorie" which is equal to 4200 joules and has enough heat energy to raise temperature of 1 kg of water 1 degree celsius.
When grain is grown along with it an equal amount of straw is grown. This is the covering substance in which the grain is contained. Note that it is different than the shell of the grains which is still present in the cultivated crop. For example if you buy wheat (not flour) from market the covering shell is still present but the straw was removed at the time of cultivation. The straw is already hay, that is, it already contains 80% by mass dry matter and each gram of it has 2 calories.
For all grass and grass like crops grown with prominent exception of alfalfa, the same 1600 kg hay is grown per acre per year at 1k land. Note that we only are concerned with the mass of hay grown, not the mass of fresh grass etc. The trick is to store it until it lose all the moisture it can, then what is left is hay. It means that usually not more than 10 to 20 percent of moisture is left in grass and grass-like crops and not all the moisture is lost in storage.
In case of leaves, the hay yield is 600 kg per acre per year provided the land is properly covered with trees. By properly I mean the usual number of trees per acre as used to be the norm in traditional (pre-1950) agriculture. In an orchard and also in a forest, that is, in all tree lands, another 200 kg grass hay is also grown per acre per year. Note that the figure 200 came from the natural figure of 400 kg hay yield in natural pastures halved. It is halved because due to the presence of trees only half as much grass can be grown as would be in a tree less pasture. Natural pasture is a tree-less land where grass and grass-like crops are naturally grown without any farming by humans. Note that when humans do farming in a traditional way the yield is already 4 times than what is grown naturally.
Last thing to consider is that after complex calculations and data reviews I came to the conclusion that 2.56 kg hay is the minimum amount of hay needed to produce 1 kg cow milk assuming there is no meat production, but since meat production cannot be avoided as some of the food eaten by cow converts into a calf and the cow itself needed food to grow up when it was a calf and not producing any milk therefore a relation of 3.2 is the minimum practical ratio, meaning 3.2 kg hay results in 1 kg milk and along with it 1/16 kg meat. Note that in case of cows our emphasis is on milk production, not meat production. Also note that since the "meat" produced in this case would not be pure meat but would be containing bones too which are not edible by humans and since in our calculation above we only consider pure meat therefore we actually have to produce more meat-with-bone to have the desired amount of pure meat. In simple words we have to increase the ratio to 3.6. Note that if we make it 4 then milk production would be same but meat production would be 1/8 of milk production.
We want to produce 200 kg milk, half of which that is 100 kg would be drunk directly and rest half would be converted into ghee and butter. To produce 200 kg milk we need 200 x 3.6 = 720 kg hay. In above calculation we account for 110 kg grain production which means 110 kg straw-hay is produced. The straw is supposed to be stored for maximum 6 months so that food is available for our cows in autumn and winter when fresh grass-hay is not available. During storage at maximum 20% of the straw may lose its nutrients therefore we take 80% of that, 0.8 x 110 = 88 kg straw. So, we have 88 kg straw available for our cows.
We keep some land in form of pasture but that is not natural pasture. It is called pasture only because certain grass like crops would be grown on it for our cows. We keep a 1600 sq m patch of land for this purpose. Since per acre yield of grass hay is 1600 kg, therefore 1600 sq m or 0.4 acres produce 640 kg grass-hay.
We add the straw-hay and grass-hay, 88 kg + 640 kg = 728 kg. It is enough to produce 200 kg cow milk and along with it beef and beef-fats. The ratio between milk and hay is 3.6, so 200 kg x 3.6 = 720 kg. Note that about 89% of the cow food is grass or grass-like crops so unlike western industrial farming we don't feed grains to the cows which their stomach are not made for.
We also have an orchard whose size is 600 sq m. Since the per acre yield of orchard hay is 800 kg, from 600 sq m we can get 120 kg hay. Note that this is fed only to goats to have mutton and mutton-fats. Along with that there is ofcourse some opportunity to get goat-milk but we ignore that to have some flexibility. It is known that each kg of edible beef (with bones) requires atleast 12 and usually 16 kg hay to be produced and each kg of edible mutton requires 10 kg hay usually. So 120 kg hay results in 12 kg mutton. I take that as 12.5 kg mutton to get the daily figure of 31.25 grams.
While we are on this it is suitable to calculate the other crops needed per capita which are not included in food items. They are tea/coffee and cotton. Tea/coffee is considered a non-food item because it contains no calories at all. The world per person average of cotton consumption in year 2000 was 3.125 kg per year. Ofcourse non-cotton clothes items are also consumed by people included silk etc but for the purpose of this calculation we ignore all those and assume that only cotton is consumed, because we are ignoring all other clothes items we double the per capita cotton consumption estimate to 6.25 kg. In other words, it can be said that cotton is consumed as usual and an equal amount of other clothes items are also consumed. Per capita tea/coffee consumption figure is taken as 12.5 kg per year which is closed to reality.
So in addition of the 2000 sq m land needed per person shown in chart above, a 1600 sq m pasture and 100 sq m tea farm and 100 sq m cotton farm is also needed, this brings the figure to 3900 sq m. To be one acre a 100 sq m is still lacking which I leave to readers to fill in an item of their choice. It could for example be grain farm to support chicken which should result in 12.5 kg chicken meat or a pond of fresh water fish which should result in 12.5 kg fish meat or dry fruits farm which should result in 12.5 kg dry fruits.
In short, to support one person, we need on average, 1 acre of arable land, that is of category 1k meaning it either has 10 inches rain or 1 acre-ft canal water or a combination of them providing 800 cubic meter water to crops.
I stress that this is the natural arable land need per person. We can see from history that in case of subcontinent (land comprising today's india, pakistan, bangladesh, afghanistan, burma and nepal) in mughal era (1526-1739), that is, when the entire land was ruled by mughals, a population of 100 million was supported by 400 million arable acres. This give us the figure of 4 arable acres per person, how was it? Well, since by large due to absence of refrigeration a large amount of food cannot be stored so 2 arable acres were kept per person in a village, that was the norm. 2 acres so that if crop fails and half crop is grown then too the village population could be supported, usually in case of crop failure over a wide area of land the yield falls to half, not to quarter or zero. It is not to deny that locally that is in a village almost no crop is grown but due to presence of trade the risk is shared over a district so as a whole half crop is failed and half is saved. It can be seen in another way too that for example grain crops failed but the fruits and vegetables and animal products were still there. So, 2 arable acres per person in a village. In case of usual crop, twice-than-village-need crop is grown which is exported to cities. The other 2 arable acres were left for wild life, in form of forests, natural pastures, un-touched lakes etc.
Item Grams/Day Kgs/Year Yield Land
Wheat 100.00 40.00 400 400
Rice 62.50 25.00 1000 100
Millet 37.50 15.00 600 100
Barley 75.00 30.00 600 200
Veg 62.50 25.00 1000 100
Oil 31.25 12.50 250 200
Sugar 31.25 12.50 500 100
Spices 31.25 12.50 250 200
Fruits 250.00 100.00 667 600
SUM 2000
Notes:
(i) The figures for land is given in sq meters, there are about 4000 sq meters in one acre so the above sum is half acre.
(ii) The sum for all grains is 800 sq m (400 for wheat, 200 for barley, 100 each for rice and millet) but we should take 900 sq m because a substantial amount of grains grown goes in shell, for eg the shell of wheat removed in milling.
(iii) The grains includes barley and millet because they are nitrogen fixing crops.
(iv) Oil is vegetable oil. Since vegetable yield is 1000 kg and oil extraction rate is 25% so 250 kg is its yield.
(v) The above calculations are based on a 400 days diet per year, the extra number of days allow more-than-normal eating in feasts and parties, roughly 10% of the entire year.
(vi) For simplicity straight forward figures about crops directly eaten by humans is given first, the more complex subject of crops grown by humans but eaten by animals and then those animals and their milk consumed by humans is discussed below.
It should be known that per kg mass animals and infact insects and birds too require same number of calories as humans for same level of activities. So a cow which is lactating needs 60 calories per kg per day and which is not lactating needs 40, so average is 50. It should also be noted that for each kg gain in both animals and humans same 7,500 calories are needed. Since about 60% mass of an animals is meat (including bones), therefore 12,500 calories are needed per kg meat at minimum.
Another important point to consider is calories in hay, but first what is hay? Hay is a general term that includes all grass, straw, leaves etc eaten by animals but not all grass, straw and leaves are hay. Fresh grass which have visible moisture on its surface is only 15% dry matter and 85% moisture, fresh grass and leaves with no visible moisture contains 20% to 30% dry matter and rest is moisture, brown grass and leaves contains may be 50% dry matter. The point is, when fresh moisture level is high and when time pass and the green matter becomes brown its moisture level decreases. It should be kept in mind that the energy needed by the animals is only in the dry matter, there is no energy in moisture.
Hay is grass, straw or leaves that has atleast 80% dry matter but dry matter may rise upto 90%. For our calculations we ignore the higher proportion and assume that only 80% of hay by mass is dry matter to be safe. Each gram of dry matter contains 2.5 calories. So the hay as a whole contains 2 calories per gram.
It should be noted that all over this website the term "calorie" actually refers to "kilo calorie" which is equal to 4200 joules and has enough heat energy to raise temperature of 1 kg of water 1 degree celsius.
When grain is grown along with it an equal amount of straw is grown. This is the covering substance in which the grain is contained. Note that it is different than the shell of the grains which is still present in the cultivated crop. For example if you buy wheat (not flour) from market the covering shell is still present but the straw was removed at the time of cultivation. The straw is already hay, that is, it already contains 80% by mass dry matter and each gram of it has 2 calories.
For all grass and grass like crops grown with prominent exception of alfalfa, the same 1600 kg hay is grown per acre per year at 1k land. Note that we only are concerned with the mass of hay grown, not the mass of fresh grass etc. The trick is to store it until it lose all the moisture it can, then what is left is hay. It means that usually not more than 10 to 20 percent of moisture is left in grass and grass-like crops and not all the moisture is lost in storage.
In case of leaves, the hay yield is 600 kg per acre per year provided the land is properly covered with trees. By properly I mean the usual number of trees per acre as used to be the norm in traditional (pre-1950) agriculture. In an orchard and also in a forest, that is, in all tree lands, another 200 kg grass hay is also grown per acre per year. Note that the figure 200 came from the natural figure of 400 kg hay yield in natural pastures halved. It is halved because due to the presence of trees only half as much grass can be grown as would be in a tree less pasture. Natural pasture is a tree-less land where grass and grass-like crops are naturally grown without any farming by humans. Note that when humans do farming in a traditional way the yield is already 4 times than what is grown naturally.
Last thing to consider is that after complex calculations and data reviews I came to the conclusion that 2.56 kg hay is the minimum amount of hay needed to produce 1 kg cow milk assuming there is no meat production, but since meat production cannot be avoided as some of the food eaten by cow converts into a calf and the cow itself needed food to grow up when it was a calf and not producing any milk therefore a relation of 3.2 is the minimum practical ratio, meaning 3.2 kg hay results in 1 kg milk and along with it 1/16 kg meat. Note that in case of cows our emphasis is on milk production, not meat production. Also note that since the "meat" produced in this case would not be pure meat but would be containing bones too which are not edible by humans and since in our calculation above we only consider pure meat therefore we actually have to produce more meat-with-bone to have the desired amount of pure meat. In simple words we have to increase the ratio to 3.6. Note that if we make it 4 then milk production would be same but meat production would be 1/8 of milk production.
We want to produce 200 kg milk, half of which that is 100 kg would be drunk directly and rest half would be converted into ghee and butter. To produce 200 kg milk we need 200 x 3.6 = 720 kg hay. In above calculation we account for 110 kg grain production which means 110 kg straw-hay is produced. The straw is supposed to be stored for maximum 6 months so that food is available for our cows in autumn and winter when fresh grass-hay is not available. During storage at maximum 20% of the straw may lose its nutrients therefore we take 80% of that, 0.8 x 110 = 88 kg straw. So, we have 88 kg straw available for our cows.
We keep some land in form of pasture but that is not natural pasture. It is called pasture only because certain grass like crops would be grown on it for our cows. We keep a 1600 sq m patch of land for this purpose. Since per acre yield of grass hay is 1600 kg, therefore 1600 sq m or 0.4 acres produce 640 kg grass-hay.
We add the straw-hay and grass-hay, 88 kg + 640 kg = 728 kg. It is enough to produce 200 kg cow milk and along with it beef and beef-fats. The ratio between milk and hay is 3.6, so 200 kg x 3.6 = 720 kg. Note that about 89% of the cow food is grass or grass-like crops so unlike western industrial farming we don't feed grains to the cows which their stomach are not made for.
We also have an orchard whose size is 600 sq m. Since the per acre yield of orchard hay is 800 kg, from 600 sq m we can get 120 kg hay. Note that this is fed only to goats to have mutton and mutton-fats. Along with that there is ofcourse some opportunity to get goat-milk but we ignore that to have some flexibility. It is known that each kg of edible beef (with bones) requires atleast 12 and usually 16 kg hay to be produced and each kg of edible mutton requires 10 kg hay usually. So 120 kg hay results in 12 kg mutton. I take that as 12.5 kg mutton to get the daily figure of 31.25 grams.
While we are on this it is suitable to calculate the other crops needed per capita which are not included in food items. They are tea/coffee and cotton. Tea/coffee is considered a non-food item because it contains no calories at all. The world per person average of cotton consumption in year 2000 was 3.125 kg per year. Ofcourse non-cotton clothes items are also consumed by people included silk etc but for the purpose of this calculation we ignore all those and assume that only cotton is consumed, because we are ignoring all other clothes items we double the per capita cotton consumption estimate to 6.25 kg. In other words, it can be said that cotton is consumed as usual and an equal amount of other clothes items are also consumed. Per capita tea/coffee consumption figure is taken as 12.5 kg per year which is closed to reality.
Item Kgs/Day Yield Land
Cotton 6.25 250 100
Tea 12.50 500 100
So in addition of the 2000 sq m land needed per person shown in chart above, a 1600 sq m pasture and 100 sq m tea farm and 100 sq m cotton farm is also needed, this brings the figure to 3900 sq m. To be one acre a 100 sq m is still lacking which I leave to readers to fill in an item of their choice. It could for example be grain farm to support chicken which should result in 12.5 kg chicken meat or a pond of fresh water fish which should result in 12.5 kg fish meat or dry fruits farm which should result in 12.5 kg dry fruits.
In short, to support one person, we need on average, 1 acre of arable land, that is of category 1k meaning it either has 10 inches rain or 1 acre-ft canal water or a combination of them providing 800 cubic meter water to crops.
I stress that this is the natural arable land need per person. We can see from history that in case of subcontinent (land comprising today's india, pakistan, bangladesh, afghanistan, burma and nepal) in mughal era (1526-1739), that is, when the entire land was ruled by mughals, a population of 100 million was supported by 400 million arable acres. This give us the figure of 4 arable acres per person, how was it? Well, since by large due to absence of refrigeration a large amount of food cannot be stored so 2 arable acres were kept per person in a village, that was the norm. 2 acres so that if crop fails and half crop is grown then too the village population could be supported, usually in case of crop failure over a wide area of land the yield falls to half, not to quarter or zero. It is not to deny that locally that is in a village almost no crop is grown but due to presence of trade the risk is shared over a district so as a whole half crop is failed and half is saved. It can be seen in another way too that for example grain crops failed but the fruits and vegetables and animal products were still there. So, 2 arable acres per person in a village. In case of usual crop, twice-than-village-need crop is grown which is exported to cities. The other 2 arable acres were left for wild life, in form of forests, natural pastures, un-touched lakes etc.
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