To join the discussion, herewith my comments on the two questions:
Simply put, there is no unit for integration. Instead it is a relatively
ranking order while putting all streets/axial lines as an interconnected
whole. Given the fact that it is a relative order, it is not good idea
to put one street's integration in one city in comparison with another
street's integration in another city. Such a comparison is meaningless.
In other words, the ranking order makes a good sense only for streets
within a same city.
To my understanding, space syntax is initially for understanding (rather
than for making) complexity of street structure, i.e., to see whether or
not there are far more less-connected streets than well-connected ones
(ht-index>3), and to what extent there are far more less-connected than
well-connected (the higher the ht-index, the better hierarchical the
structure is); see a case study in this paper:
https://www.researchgate.net/publication/236627484_Ht-Index_for_Quantifying_the_Fractal_or_Scaling_Structure_of_Geographic_Features.
Such an understanding adds insights into planning and design. For
example, if there are already many well-connected streets, we should
avoid creating more well-connected streets, but rather making more
less-connected streets. HOWEVER, to make the kind of space syntax
analysis (I called it topological analysis more broadly) really useful
in practical planning and design, I would strongly suggest turn to
Alexander's theory of centers, which aims not only to understand
complexity but also to create complexity (= living structure). It is a
long story. To cut it short, differentiation and adaptation are two
basic principles, governed by two fundamental laws: scaling law and
Tobler's law. I have explored these two principles and two laws in this
paper:
https://www.researchgate.net/publication/305638074_A_Topological_Representation_for_Taking_Cities_as_a_Coherent_Whole
Thanks and cheers.
Bin
On 8/14/2016 10:25 PM, Penn, Alan wrote:
> Dear anonymous,
>
> a good pair of questions, but ones that requires a bit of detail and some history as the way things have been done has evolved over time.
>
> The ‘units’: The earliest measures of integration were applied to graphs of rooms connected by doorways in houses. These were mainly small graphs with just tens of nodes. So the first method of allowing comparison was the measure of relative asymmetry (RA). This is a dimensionless measure which places the mean depth of the graph from the point of view of each node on a 0-1 scale between the shallowest and deepest it could possible be given that number of nodes. When H&H moved on to analysis of urban space they found that variations in size of graph were not adequately handled by RA, and an additional step was added in an attempt to control for the fact that as systems get larger they tend not to get as deep as they could with that number of nodes. This D-value correction also involved a dimensionless quantity - the RA of the Diamond shaped system with that number of nodes. This produces Real Relative Asymmetry (RRA) which is also dimensionless. Today in regular use the term ‘integration (Hillier & Hanson)' refers to the reciprocal of RRA; there are variants that use different approaches to relativisation e.g. P-value (a pyramid shaped graph) and Teklenburg’s.
>
> the algorithms are as follows (thanks to Tasos for these):
>
> d_value = 2.0 * (t_nodecount * ( math.log( (t_nodecount+2.0)/3.0, 2) - 1.0) + 1.0) / ((t_nodecount - 1.0) * (t_nodecount - 2.0))
> p_value = 2.0 * (t_nodecount - math.log(t_nodecount, 2) - 1.0) / ((t_nodecount - 1.0) * (t_nodecount - 2.0))
> teklinteg = math.log(0.5 * (t_nodecount - 2.0)) / math.log(t_totaldepth - t_nodecount + 1.0)
> t_meandepth = t_totaldepth/(t_nodecount - 1)
> t_ra = 2.0 * ( t_meandepth - 1.0)/( t_nodecount-2 )
> t_raa = t_ra / d_value
> t_intHH = 1.0 / t_raa;
> t_intP = 1.0 / ( t_ra / p_value )
> t_intTKL = teklinteg
>
> Now, to come onto your first question - in the angular segmental representation, we have yet to develop any corrections for size of system as applied to the measures of depth. This is perhaps because we now use radius measures in maps that are much lager than the radius concerned. Here the measure of angular integration is actually a measure of ‘mean angular depth’ of all other segments (within the given radius) from the segment in question. This is therefore a measure of angle and so has a dimension. The code quantises 360 degrees into 1024 bins, but in the measures we essentially work on 2 x radians - so straight ahead = depth 0, right angle turn = depth 1 and a hairpin bend approaches depth = 2. The number you see is total angle change (always using the smallest angle travelling forwards at each intersection - so a left right angle turn and right right angle turn each only count as a ‘1’), divided by the number of segments at that radius.
>
> [** NB, I say that we have not relativised angular depth for size of system, however we have relativised the measure of betweenness. Remember the a major reason for doing a segmental representation is that this makes sense for the measures of betweenness (the ‘choice’ measures in space syntax terminology) since different sets of segments of an axial line will figure on trips between different origin destination pairs. Clearly for a map with N segments there are (N-1)^2 origin destination pairs that give rise to a measure of betweenness. Since one is computing least angle change routes through the map you need to work with trips from A-B and from B-A. Anyway suffice to say there are a lot of trips potentially passing through each segment, and the number is very dependent upon the number of segments, so relativising for number of segments is important. Bill has shown that you can use the total angular depth at a given radius to relativise the total betweenness measure at that radius giving NAChoice.]
>
> In terms of your second question, I would respond along the following lines. ‘Absolutely, if you are unable to intervene in the morphology of interest, the finding that morphology matters might seem to be of limited value. However, it can still be useful when we consider how a given city spatial structure might most appropriately be used. Although it is true that the physical morphology of street systems tends to change only slowly, the land use occupancy of the buildings fronting onto those streets (and the development density) change more rapidly. These changes are the result of markets with many different actors involved (including planning regulators), and understanding the way that morphology gives rise to footfall can be helpful in guiding decisions about how to best optimise these markets. I would go on to question the assertion that street systems do not change over time. In fact they do. In any rapidly evolving economy buildings are demolished and rebuilt as patterns of land value change, and on each occasion redevelopment creates opportunities for either block aggregation or subdivision. Arnis Siksna mapped these processes for example. Amongst the earliest applications of space syntax methods were to understand and propose changes to some of London’s most socially problematic public housing estates, and to counter on behalf of tenants groups, the housing management’s proposals for large-scale demolition. We were able to show exactly how the problematic aspects were produced by the spatial morphology, and to propose relatively minor changes, often only to landscaping features, that would simplify and reintegrate these estates into the surrounding public realm. One of the key features of space syntax is that the axial map is sensitive to relatively minor deformations of the boundary, and so can be changed quite markedly by removal of rather small obstacles to vision and movement. At a slightly larger scale the demolition of a single property can create a new alignment and radically change patterns of integration. These kind of changes happen all the time in urban processes. One of the main values of the space syntax approach is that it can give theoretically well argued and empirically supported basis for policy makers and decision takers to use to decide whether these kinds of moves are worth making. The current state of practice relies on human experience and intuition to inform these kind of decisions. What we do is open those intuitions (which can be tremendously powerful) to a level of testing against evidence from prior experience and other similar cases. What we find this does is help give a voice to those with good local knowledge (the tenants of the housing estates for example) in the face of other kinds of models sitting in the hands of the professions. For example in Trafalgar Square we were able to demonstrate in advance that the demolition of the Grade 1 listed heritage retaining wall on the north side, its replacement by open stairs and the removal of vehicular traffic on that side of the square would transform they use of they body of the square. The planning inspector accepted the analysis as ‘evidence of fact’ - very important since this was equivalent to the results of the vehicular traffic modellers who most often achieve a prioritisation of design for vehicles rather than pedestrian users of urban space. Usually architectural and urban design decisions are supported by ‘evidence of opinion’.
>
> All the best,
>
> Alan
>
>
>> On 14 Aug 2016, at 06:27, SUBSCRIBE SPACESYNTAX Anonymous <[log in to unmask]> wrote:
>>
>> Hi everyone,
>>
>> I have two questions about the unit (sorry if they sound too basic).
>> First, I've been asked by several reviewers (who are mainly outside of the space syntax community) that 'what is the unit for integration?'. For example, when we say this segment has 112 score on integration (using angular method not turns), can we put a unit there (like when we say 3 meters away).
>> Second, space syntax deals with the street layout. But, street layouts are difficult elements to modify in existing neighborhoods. As such, what would be the key message from space syntax for practitioners and policy makers? Again, I've been criticised that space syntax may not be useful, as it deals with an element which cannot be modified easily. Can we address this criticism using the concept of 'natural movement'? (space syntax identifies the most integrated segments, and these segments may be important hot spot for interventions?) Any thoughts are appreciated.
>>
>> Thanks,
--
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Bin Jiang
Division of GIScience
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