One of my long-term projects has been developing a mathematical model for scheduling in Jarrett Walker-type transit systems. Today, I made a breakthrough--
I had previously realized that a model of such a system would yield two intersecting planes in my defined 3-space, and that desired overall frequencies could be model by stacking instances of these planes atop each other. But I'd been at a loss as to how to model the routes within the planes (other than the fact that they were vectors).
What I realized today, however, is that the planes are actually a set of null space vectors; this means that a prescribed eigenvalue in the null space will seed an eigenvector that corresponds to that value. What that means is that the entire system can be modeled with nothing more than the equations of the two intersecting planes, and the set of eigenvalues that yield the eigenvectors corresponding to the known bus routes.
Fortunately, we remain in vector space so far, but it appears the apparatus I'm constructing will wind up generalizing into a differential equation, to accommodate "gridlike" systems which attempt to install a mass transit grid even over non-grid street networks.
Crossing the Lines: Site, Urban, Environmental, and Transportation Planning
Showing posts with label Jarrett Walker. Show all posts
Showing posts with label Jarrett Walker. Show all posts
Wednesday, March 19, 2014
Sunday, January 5, 2014
Decline and Fall
I am continuing to think about Tverberg, the strengths and weaknesses of her work. Today, I want to focus on what I think is her greatest weakness--her doomerist belief, not well backed by the evidence, that a collapse of civilization means a collapse back to a hunter-gatherer lifestyle, or worse, hominid extinction.
Why is this a problem? First off, it ignores the archaeological evidence regarding the collapse of civilizations. The vast majority of all human civilizations have collapsed, and only a tiny minority of these collapses have ever resulted in pre-agricultural regression. A tinier--to the point of statistical insignificance--minority resulted in local extinction. In fact, in the known record of hundreds and hundreds of civilizations, only two resulted in self-caused* extinction--Easter Island and Viking Greenland. Indeed, of all known literate civilizations, just two--Harappa and Minos/Mycene--clearly succumbed to pre-literate regression**, and there is no known example whatsoever of either a literate civilization with an alphabet, abugida, abjad, or syllabary regressing to a pre-literate state***, or a literate civilization regressing to a pre-agricultural state.
To me, these statistics suggest that there is a negative feedback cycle in place that arrests further decline after a civilization's fall. Recall that a feedback cycle is two of four things: either positive--that is, amplifying--or negative--that is, canceling--and either virtuous--working properly--or vicious--out-of-control. Hence this hypothesis does not imply "negative" connotations, but rather simply states that the positive (amplifying) feedback cycle associated with the decline and fall of civilizations is arrested, braked by a negative (canceling) cycle at a certain point.
It is likely that this latter cycle is linked to easily-transmitted information--consider that all alphabets, abugidas, abjads, and syllabaries are orders of magnitude easier to master than ideographic systems, regardless of phonetic (mis)match; or that e.g. basic agricultural information is easy to understand and disseminate--and it also implies that the bare handful of instances of total regression, either to extinction (as in Easter Island and Greenland) or to pre-literacy (as in Harappa and the Minoan Aegean) were caused not only by the decline and fall cycle, but also by the failure of its stabilizing countercycle to kick in.
The easiest to understand in this regard is Easter Island. Its inhabitants stripped the land bare of its already-meager resources, and its total isolation prevented meaningful contact with neighboring civilizations of any kind. That is, they removed the necessary conditions for their own survival. The failure of the stabilizing cycle to kick in was almost undoubtedly caused by the lack of catalyst for it to get going in the first place. Similar holds true for Greenland, although here the Vikings chose not to tap the last two resources they had had left by the onset of the Little Ice Age: the island's fjords' wealth of fish, and their contact with the "skraeling" Inuit.
So a resource meagerness comes into play here--and it implies that an exceptional resource constraint is a necessary condition for the failure of the stabilizing cycle as well. Normal agrarian resources--a nutritionally complete suite of food crops and the arable land to plant them in, a reasonable fuel source for heating (where necessary) and cookery, raw material for simple tools, and neighbors to trade and war with--are almost ubiquitous on the continental landmasses, which explains why (a) there is but one example of pre-agrarian regression archaeological record (Australian Aborigines), and (b) paradoxically, why gatherer societies have persisted in the most resource-rich regions on Earth^: agrarian societies are solutions to the problem of not being able to gather enough caloric content in one's territory for a burgeoning population; so long as they are able to, agrarian impulses are weak. So long as the fundamental resources for maintaining an agrarian society have remained in place, no society has ever collapsed beyond that baseline.
So what exactly is the arresting mechanism? I do not know, but I do know some catalyst events and some historical stages that imply catalyst events:
Perhaps these are intertwined cycles. That is, the stabilizing cycle that arrests decline and fall and the civilization-building cycle are one and the same thing, just looked at from different points of view; so too the decline and fall cycle begins life as the negative feedback cycle that arrests the civilization-building one. Feedbacks linked in such a manner are not a new phenomenon: ecologies and economies are chock-full of them. And in the end, as itself a complex adaptive system, isn't it meet that civilization should as well?
Let us end with the two key takeaways. First, cultural knowledge of agriculture, once gained, is not easily lost--at least, as long as the conditions for supporting an agrarian lifestyle--and there are not many--are met. And second, that^^ the knowledge of a mass writing system has not once been lost, on a cultural level, in any decline and fall. I suspect that, in the event of collapse, we would never fall beyond the level of post-Roman Europe; even more likely is that we never fall below the level of the early Renaissance (mass literacy being a new benchmark in the history of civilizations). Even in general collapse, stabilizing and growth forces are still at work.
___________________
* Obviously, local extinctions caused by unpredictable natural events (e.g. volcanic eruptions) are not counted. This is because what we are looking at is the decline, not just the fall. Extinctions caused by catastrophic natural events represent an interruption in the course of civilization.
** 1. While Minoan Crete and Mycenean Greece are clearly separate civilizations, they were also deeply interrelated, and had, for the purposes of this discussion, essentially the same writing system (Linear A and Linear B). We could also call the Minoan/Mycenae complex the "Minoan Aegean".
2. One would then suggest that the loss of knowledge of the Maya and Egyptian hieroglyphs is evidence of pre-literate regression. This is not the case. Egyptian hieroglyphs were supplanted, first by demotic scripts and then by Coptic; knowledge of their decipherment was lost until translation materials (the Rosetta Stone) and linguistic reconstruction techniques became available in the early 19th century. Mayan hieroglyphs were one iteration of a broader ideographic writing tradition throughout Mesoamerica--the Aztecs were in the process of developing one for Nahuatl when Cortés landed--and the Spaniards had, and destroyed, an extensive Maya library.
*** Indeed, the Amharic abugida is still in use, despite the fact that Ethiopia is clearly in a dark age relative to its late-medieval period status. Nor did the Roman alphabet ever fall out of use after the fall of its formative culture, despite the fact that very nearly every other trapping of civilization was lost in Western Europe in the period 500-1000 CE.
^ Australian Aborigines stand out as the biggest exception. But Aborigine societies had the benefit of neither contact with neighboring agrarian societies, nor suitable arable land, nor local potential domesticables that could provide for a nutritionally complete diet^*.
^* Incidentally, the presence of the dingo does indicate that the proto-Aborigines did undergo pre-agrarian regression (dogs were among the first thing domesticated, and dingoes are very feral dogs); but as has been outlined above, much of Australia--due, probably, to the continent's extreme geological age--lacks many of the basic resources agrarian societies need. Is it really all that fair to expect an agrarian society to persist when, in the fortuitous circumstance that one actually has land fit for growing things in, one doesn't have anything to grow in it?
^^ This is less of a sure thing, considering the fact that all civilizations that have used either (a) an alphabet, (b) an abjad, (c) an abugida, or (d) a syllabary are only a very minor subset of all civilizations; they are, however, a much larger subset of known civilizations.
Why is this a problem? First off, it ignores the archaeological evidence regarding the collapse of civilizations. The vast majority of all human civilizations have collapsed, and only a tiny minority of these collapses have ever resulted in pre-agricultural regression. A tinier--to the point of statistical insignificance--minority resulted in local extinction. In fact, in the known record of hundreds and hundreds of civilizations, only two resulted in self-caused* extinction--Easter Island and Viking Greenland. Indeed, of all known literate civilizations, just two--Harappa and Minos/Mycene--clearly succumbed to pre-literate regression**, and there is no known example whatsoever of either a literate civilization with an alphabet, abugida, abjad, or syllabary regressing to a pre-literate state***, or a literate civilization regressing to a pre-agricultural state.
To me, these statistics suggest that there is a negative feedback cycle in place that arrests further decline after a civilization's fall. Recall that a feedback cycle is two of four things: either positive--that is, amplifying--or negative--that is, canceling--and either virtuous--working properly--or vicious--out-of-control. Hence this hypothesis does not imply "negative" connotations, but rather simply states that the positive (amplifying) feedback cycle associated with the decline and fall of civilizations is arrested, braked by a negative (canceling) cycle at a certain point.
It is likely that this latter cycle is linked to easily-transmitted information--consider that all alphabets, abugidas, abjads, and syllabaries are orders of magnitude easier to master than ideographic systems, regardless of phonetic (mis)match; or that e.g. basic agricultural information is easy to understand and disseminate--and it also implies that the bare handful of instances of total regression, either to extinction (as in Easter Island and Greenland) or to pre-literacy (as in Harappa and the Minoan Aegean) were caused not only by the decline and fall cycle, but also by the failure of its stabilizing countercycle to kick in.
The easiest to understand in this regard is Easter Island. Its inhabitants stripped the land bare of its already-meager resources, and its total isolation prevented meaningful contact with neighboring civilizations of any kind. That is, they removed the necessary conditions for their own survival. The failure of the stabilizing cycle to kick in was almost undoubtedly caused by the lack of catalyst for it to get going in the first place. Similar holds true for Greenland, although here the Vikings chose not to tap the last two resources they had had left by the onset of the Little Ice Age: the island's fjords' wealth of fish, and their contact with the "skraeling" Inuit.
So a resource meagerness comes into play here--and it implies that an exceptional resource constraint is a necessary condition for the failure of the stabilizing cycle as well. Normal agrarian resources--a nutritionally complete suite of food crops and the arable land to plant them in, a reasonable fuel source for heating (where necessary) and cookery, raw material for simple tools, and neighbors to trade and war with--are almost ubiquitous on the continental landmasses, which explains why (a) there is but one example of pre-agrarian regression archaeological record (Australian Aborigines), and (b) paradoxically, why gatherer societies have persisted in the most resource-rich regions on Earth^: agrarian societies are solutions to the problem of not being able to gather enough caloric content in one's territory for a burgeoning population; so long as they are able to, agrarian impulses are weak. So long as the fundamental resources for maintaining an agrarian society have remained in place, no society has ever collapsed beyond that baseline.
So what exactly is the arresting mechanism? I do not know, but I do know some catalyst events and some historical stages that imply catalyst events:
- For medieval Europe, two arresting mechanisms seem to have kicked in. First, the stabilization of social order under the feudal hierarchy. Second, the retranslation of the Hellenic library from Arabic into Latin (yes, all knowledge of Greek was lost, despite the proximity of a major Greek-speaking state), which halted its intellectual free-fall.
- For the Greek dark age, the principal catalyst seems to have been the refashioning of the Phoenician abjad into the world's first true alphabet; it is probable that their city-states also emerged around the same time. This dark age also appears to be part of a broader cultural discontinuity associated with the end of the Bronze Age and the beginning of the Iron Age throughout the Levant.
- The creation and codification of Vedic liturgy, as well as the expansion of the culture associated with it, appears to have marked the end of the post-Harappan dark age.
- The rise of the Hohokam, Navajo, and Pueblo cultures appears to mark an end to the post-Anasazi dark age.
- The Andean Late Intermediate period effectively represents a dark age from the fall of the Tiwanaku and Wari cultures (states?) and the rise of the Inca state, Tawantinsuyu.
Perhaps these are intertwined cycles. That is, the stabilizing cycle that arrests decline and fall and the civilization-building cycle are one and the same thing, just looked at from different points of view; so too the decline and fall cycle begins life as the negative feedback cycle that arrests the civilization-building one. Feedbacks linked in such a manner are not a new phenomenon: ecologies and economies are chock-full of them. And in the end, as itself a complex adaptive system, isn't it meet that civilization should as well?
Let us end with the two key takeaways. First, cultural knowledge of agriculture, once gained, is not easily lost--at least, as long as the conditions for supporting an agrarian lifestyle--and there are not many--are met. And second, that^^ the knowledge of a mass writing system has not once been lost, on a cultural level, in any decline and fall. I suspect that, in the event of collapse, we would never fall beyond the level of post-Roman Europe; even more likely is that we never fall below the level of the early Renaissance (mass literacy being a new benchmark in the history of civilizations). Even in general collapse, stabilizing and growth forces are still at work.
___________________
* Obviously, local extinctions caused by unpredictable natural events (e.g. volcanic eruptions) are not counted. This is because what we are looking at is the decline, not just the fall. Extinctions caused by catastrophic natural events represent an interruption in the course of civilization.
** 1. While Minoan Crete and Mycenean Greece are clearly separate civilizations, they were also deeply interrelated, and had, for the purposes of this discussion, essentially the same writing system (Linear A and Linear B). We could also call the Minoan/Mycenae complex the "Minoan Aegean".
2. One would then suggest that the loss of knowledge of the Maya and Egyptian hieroglyphs is evidence of pre-literate regression. This is not the case. Egyptian hieroglyphs were supplanted, first by demotic scripts and then by Coptic; knowledge of their decipherment was lost until translation materials (the Rosetta Stone) and linguistic reconstruction techniques became available in the early 19th century. Mayan hieroglyphs were one iteration of a broader ideographic writing tradition throughout Mesoamerica--the Aztecs were in the process of developing one for Nahuatl when Cortés landed--and the Spaniards had, and destroyed, an extensive Maya library.
*** Indeed, the Amharic abugida is still in use, despite the fact that Ethiopia is clearly in a dark age relative to its late-medieval period status. Nor did the Roman alphabet ever fall out of use after the fall of its formative culture, despite the fact that very nearly every other trapping of civilization was lost in Western Europe in the period 500-1000 CE.
^ Australian Aborigines stand out as the biggest exception. But Aborigine societies had the benefit of neither contact with neighboring agrarian societies, nor suitable arable land, nor local potential domesticables that could provide for a nutritionally complete diet^*.
^* Incidentally, the presence of the dingo does indicate that the proto-Aborigines did undergo pre-agrarian regression (dogs were among the first thing domesticated, and dingoes are very feral dogs); but as has been outlined above, much of Australia--due, probably, to the continent's extreme geological age--lacks many of the basic resources agrarian societies need. Is it really all that fair to expect an agrarian society to persist when, in the fortuitous circumstance that one actually has land fit for growing things in, one doesn't have anything to grow in it?
^^ This is less of a sure thing, considering the fact that all civilizations that have used either (a) an alphabet, (b) an abjad, (c) an abugida, or (d) a syllabary are only a very minor subset of all civilizations; they are, however, a much larger subset of known civilizations.
Tuesday, January 3, 2012
South Philly Crosstown Bus Is a Mistake
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| Courtesy The Transit Pass |
The Crosstown sounds ... Continue reading at Hidden City Philadelphia.
Wednesday, July 27, 2011
Rt. 17
The proposal I'm putting forward is a simple one--consolidate the 17 and 33 into a single new route, eliminating the current Market East jog both take in favor of connections offered to the Market Street buses at Market and JFK. This route would run service at a 15-minute headway and would be, like the 2, 7, 23, 47, 57, and C buses (and Broad Street Line and Philadelphia2050's proposed Loop Network) part of a frequent service core in the, er, urban core.
Consolidating this service would still allow for connections to other core frequent services at Cecil B. Moore (3), Girard (15), Spring Garden (43), Market/JFK (10, 11, 13, 34, 36, and the MFL), Chestnut/Walnut (21, 42), and Lombard/South (40)--as well as possible frequent service route modifications along Race/Arch (31, 48) and Spruce/Pine (12, 30), and expanded light rail service along Girard (37 proposal) and Washington (49, 64) (see here). The bus sections of this proposal can be implemented with relatively minimal cost: putting out a new schedule and map, and putting up new bus station signs; the buses (and drivers) taken off the now-defunct 33 would go to augment some of the more poorly bused routes in this network (mostly east-west).
Sometime in the near future I'm thinking of showing a map of this (unwieldy-named) Core Frequent Bus Network and connections, in the contexts of both current, and suggested Philadelphia2050, operations.
Consolidating this service would still allow for connections to other core frequent services at Cecil B. Moore (3), Girard (15), Spring Garden (43), Market/JFK (10, 11, 13, 34, 36, and the MFL), Chestnut/Walnut (21, 42), and Lombard/South (40)--as well as possible frequent service route modifications along Race/Arch (31, 48) and Spruce/Pine (12, 30), and expanded light rail service along Girard (37 proposal) and Washington (49, 64) (see here). The bus sections of this proposal can be implemented with relatively minimal cost: putting out a new schedule and map, and putting up new bus station signs; the buses (and drivers) taken off the now-defunct 33 would go to augment some of the more poorly bused routes in this network (mostly east-west).
Sometime in the near future I'm thinking of showing a map of this (unwieldy-named) Core Frequent Bus Network and connections, in the contexts of both current, and suggested Philadelphia2050, operations.
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