Monday, February 24, 2020

Thoughts about intervisibility, Part 2

In my last post I tried to suggest that intervisibility was a human idea and not one strictly mathematical.  Sure, if the math shows a big obstacle between sites A and B then they are not intervisible.  There are gradations however.  Suppose a town is just barely behind an obstacle (like a ridge).  Mathematically speaking your town and that town are not intervisible.  But you can see the smoke from their fires during the day and a glow in the sky at night.  If, imagining the worst, an enemy destroys that town you will surely see the smoke from the fires and know that something is wrong.

I've tried to make allowances for such situations in the intervisibility software on the Mycenaean Atlas.  Of course I add 1.8 m to the elevation of the source site (site A) in order to mimic the height of an observer.  And now I've also added 3 meters to the elevation of the target site (site B) in order to get rid of some edge cases where site B sits juuuussst below the horizon but really should be counted as intervisible.

The point is that this intervisibility page is a tool for exploring intervisibility.  The mathematics cannot definitively make a decision about a fundamentally human idea.  If you see a result that you don't agree with then you should pursue it further and make up your own mind.

It's easier to do that now because my friend Xavier Fischer, of, has provided an additional tool.  Now you can generate an intervisibility graph that addresses the sites pairwise.  Here's an example:

This shows the intervisibility sightline from, on the left, Kastro (C714) in the neighborhood of Gla to Magoula   Kavkala (C984) about 2.25 km. distant.  Because no obstacles intrude on the red line then the sites are intervisible.  The bottom scale is distance in km.  The left side scale is elevation in meters.  Notice that I add 1.8 m. to the starting elevation (on the left) and a few meters to the right.  That helps to tip the two sites into intervisibility.

So how do you exercise this fine new tool?

On the new intervisibility page you simply click on the 'true' or 'false' values in column 3 of the intervisibility list.  When you do that the graph will display. 

Here is an example of the I. graph between Kastro (C714) and one of the cemeteries at Hagia Marina (C728) directly to its east.  These two sites are intervisible; the resulting graph is:

You should keep in mind that this graph's x-axis (distance) is compressed in comparison to the y-axis (elevation).  In this particular graph one major division in the vertical (5 m) has the same size as 250 m. in the horizontal - a ratio of 1:50.  So all these graphs are what statisticians call 'Oh boy!' graphs.  Always be sure that you understand the relative scales on these graphs before trying to interpret them.

News of the Mycenaean Atlas Project

On February 12 I delivered version 131a of the database.  It contains many additions and minor changes.  At that time a new version of the software was delivered in order to support intervisibility.


And, by the way, friends don't let friends use Facebook.

Saturday, February 8, 2020

Thoughts about Intervisibility

‘ … and now I watch for the light, the signal-fire
breaking out of Troy, … [1]

Before the systematization of linear perspective in the 1400’s painters still needed a way to show that certain things in their paintings were further away. How did they do this?

They used a set of techniques that are collectively known as ‘aerial (or atmospheric) perspective’. These techniques consist of using certain observations about distance with which we are all familiar but which we rarely consider. Its principles are:

a. Things further away are smaller than the very same things up close
b. Things further away are bluer than the same things up close.
c. Things further away are of lower contrast (grayer) than the same things up close.
d. Things further away are hidden or occluded by things which are nearer to us.
e. Detail is poorer in further things than it is in closer things.

There’s a nice example of this in a painting from 1520 by Joachim Patinir:

J. Patinir, Landscape with the Flight into Egypt, ca. 1516.

Here we can clearly see aerial perspective at several removes. There is a slight graying of the fields in the center. This fades into the grayer and bluer mountains at the upper right. 
These in turn transition to the entirely gray and nearly detail-free mountains on the horizon.

Time of day might be a factor in intervisibility. A town to the west that’s visible in the morning might be lost in the sun’s glare in late afternoon and evening. The reverse for towns to your east.

There’s also the curvature of the earth to consider. Consider that towns A and B are sitting on a perfectly smooth earth. At some distance town B will be below the horizon relative to an observer at A. What distance? Well, an object 10 m. in height (32.81 ft.) will be below the horizon at about 16 km (9.9 mi.). [2] This might be a factor in coastal town intervisibility. Otherwise the main factor in intervisibility is height above the horizon of the object to be observed. That’s why signal fires are placed on towers or heights.[3]

Sometimes intervisibility is achieved by indirect means. Crowe details how Polynesian navigators relied on the color of the underside of clouds to pinpoint islands still well beyond the horizon[4]

Kure Atoll, Northwestern Hawaiian Islands.
Image courtesy of NOAA/LT Elizabeth Crapo

These are just some of the circumstances that might prevail such that lines of sight between A and B may be entirely unobstructed and yet B not really visible from A (or vice-versa).

Intervisibility consists of more than just unobstructed lines of sight.  

But the Mycenaean Atlas cannot take any of these factors into account. Here the analysis is strictly mathematical – it seeks only to determine whether there is an unobstructed sight-line between location A and location B. This is achieved in the following way.

1. construct a linear function (y = f(x) = Ax + B) that joins the two sites. Here the coefficient A is the tangent line that connects the two sites (Δ elevation (A,B) / Δ distance (A,B)). The coefficient B is merely the elevation of site A.

2. Now the function can be evaluated for any position on a line between A and B.  This is to determine whether any features between sites A and B are higher than the function value at that point.

If no elevations between the sites have an elevation greater than the function evaluation at that point then the two sites are intervisible. If there is some real elevation higher than the function would predict then the two sites are not intervisible. This algorithm is a modification of an intervisibility algorithm described by Blelloch[5]. 

I have had the great good fortune to work with Xavier Fischer of who, at my request, created a single call that returns the intervisibility status for any two lat/lon pairs. In my original design I needed an internet call for each point evaluated between A and B (at least 16). Such an algorithm runs on Oinp (order of time of average internet fetch * the number of pairs(A’,B’) * the number of partitions between A and B). With the new internet call of Mr. Fischer’s the new algorithm runs on Oip (order of average internet time * number of pairs(A’,B’).

When using this new algorithm I add 1.8 m to the start point to mimic an average observer’s height. This helps, I think, to make some sights intervisible which would not be so if the elevation of the observer was taken as ground level.  This would not be very realistic.

In the Mycenaean Atlas I have created an intervisibility page. It is reached from the Place Key Report by clicking on the new ‘Intervis’ button.

Clicking on that button brings you to this new  page.

The main feature on this page is a map which shows the starting point (A) in blue.  Sites that are intervisible with A are shown with green push-pins.  Sites that are NOT intervisible with A are shown with red push-pins.  Each of the pins on the map has tool-tips which provide the name and place key of the sight.  If you click on a pushpin you will get an info box that contains more information along with a link.  Clicking on the link takes you to the Place Key Report page for that specific site.

The other main feature on this new page is the intervisibility list on the left.  This list shows all the sites that are within 6.5 m. from the center site (A).  Each line has a link.  If you click on that link you will be taken to the intervisibility page with your clicked-on site as the new center (A) site.  That way you can remain in the intervisibility domain while you check sight lines from various origins.  The list's intervisibility column simply gives the values 'true' or 'false' for each of the set of sites.  Each column in this list is sortable.

Here's one more view of our new page.  It shows the intervisibility from a  peak sanctuary C6228,  Petsofas Peak Sanctuary in Siteia.   Its elevation is 251 m.

We can check the accuracy of this very easily in Google Earth.  I drew a straight line from the peak sanctuary at C6228 to C5107 which is one of the sites that is supposed to be intervisible with C6228.  I then did a 'Show Elevation Profile' on that straight line and this is the result:

You can clearly see from the Elevation  Profile that there are no obstacles intervening between the two sites.

I hope that you will enjoy using this new tool and that you'll find it useful.

Some Bibliographical Remarks

A general survey of the history of intervisibility in archaeological practice may, perhaps, be had here:

Wheatley, David   'Making Space for an archaeology of place' (especially part 4. Visibility Studies), [2004]  Internet Archaeology, (15) Online here.

Two  nice case studies of the use of intervisibility as part of landscape analysis are:

1. Sylviane Déderix, 'Patterns of Visibility, Intervisibility and Invisibility at Bronze Age Apesokari (Crete)' Open Archaeology (5), 187-203.  Online here.

I particularly recommend this article.  She proposes a number of hypotheses about the position of this tholos and supports or refutes them using intervisibility and viewshed ideas.  This is a good example of how it should be done.

2. Criado Boado, Felipe, and Victoria Villoch Vázquez. 'Monumentalizing Landscape: From Present Perception to Past Meaning of Galician Megalithism (Northwest Iberian Peninsula).' European Journal of Archaeology (3:2) (2000): 188–216.  Online here.


[1] Aeschylus. Agamemnon, ll. 4-11.

[2] For a calculator see this.  

[3] For an amusing discussion of signal fire parameters in The Lords of the Rings see this.

[4] Often attested. Crowe [2018] 91. Worth quoting in full:

In the case of a particularly shallow lagoon, the navigator even may be guided to it by the turquoise tint of the water reflected up onto the underside of a cloud. Striking examples of this include the unusually shallow lagoons of Aitutake (S. Cook Is) and ‘Ana ‘a (Tuamotus), where the presence of these low-lying atolls can be discerned in fine weather from up to 70 km away. This kind of phenomenon can show up in other cases, too, where the destination island can even be distinguished by the colour of the cloud hanging over it – a green tinge in the case (of) a forested island; an unusually bright cloud over white sand or surf, or a pink tinge warning of a reef.” And see notes 37-43 for this chapter.

At 70 km from the observer the curvature of the earth will completely occlude an object up to 334 m (1095.8 feet) in height.

[5] See De Floriani and Magillo [1999] 549. Also Blelloch [1990] 40.


Aeschylus: The Oresteia, Translated by Robert Fagles. Penguin, 1975

Blelloch [1990]: Blelloch, Guy E. Vector Models for Data-Parallel Computing. MIT Press, Cambridge, Massachusetts. 1990.

Crowe [2018]: Crowe, Andrew. Pathway of the Birds; The voyaging achievements of Maori and their Polynesian ancestors. University of Hawaii Press, Honolulu, Hawaii. 2018. ISBN: 978-0824878658

De Floriani and Magillo [1999]: De Floriani, Leila and Paola Magillo, ‘Intervisibility on Terrains’, 543-556. 1999. It is online here.