Is this relevant? It is "well known" that log2(world population) is about equal to 33, so theoretically if you numbered every human alive consecutively you would only need 33 bits to store the number. But this is a long shot from estimating the amount of data required to pick someone out of a crowd. For example, perhaps you are just given a bunch of low-resolution pictures of people's foreheads: do you only need "33 bits"? What does that mean?
Likewise, identifying a random location on earth from a photo is certainly doable, but I would say it has less to do with the logarithm of the surface area of the earth and much more to do with expertise in geography, geology, etc.
I find it interesting. I make no claims for relevance.
Knowing the 33 bits trivium, I was curious what the equivalent was for individual spatial locations. The maths are easy and GNU units near.
You're right that trying to ascertain the number of bits contributed by any one item of data is difficult. I broke that down in part in a reply to the Reddit comment (after posting here): knowing the feature was in Utah (280k km^2) and having the flight track probably narrowed the region to about a 10km square (100 km^2) region ... which still contained 10,000 10m^2 areas. The geographic clues were enough to find the specific one. It's easier to work backwards and determine how much information was deduced by given data, based on search space eliminated.
Keep in mind that "expertise in geography, geology, etc." is specifically the capability of extracting geospatial information from available data. This could have included, say, sun height and angle based on date and time (exif image data frequently encodes this, if not geolocation itself), cues from aircraft noise in live video (mentioned in another geolocation example within the thread), correlated with flight data.
That claim seems to be accurate --- Al Qaeda forces were found in the Tora Bora cave complex in the region.
The practical upshot is that if you know where something is and don't want others to know the location, virtually any information leakage can be critical.
For your crowd example, much depends on the number of suspects you already have. The question is usually one of mapping between two sets --- which of the blurry foreheads matches which another set of interest. Determining intersections is key to ost investigations.
And more generally, almost any process of discovery can be modled as searching through a space. The more irrelevant targets are excluded, the smaller the remaining space remains. Insight is exclusion. The search itself might not be binary in the classic sense, but it is one of ever narrowing scope.
It's relatively well known that 33 distinct bits is enough to uniquely identify any individual person now alive on Earth.[1]
Geospatially, assuming 10m resolution, 44 bits is enough to identify any unique location on Earth's land surface (46 bits buys you the oceans).
Searching for a ~1m^2 monolith visually within a 10m^2 square is reasonable.
GNU units:
49 bits buys 1m accuracy, 63 1cm, 69 1mm. Land or sea.For comparison, cellphone positioning accuracy is typically 8--600m:
- 3G iPhone w/ A-GPS ~ 8 meters
- 3G iPhone w/ wifi ~ 74 meters
- 3G iPhone w/ Cellular positioning ~ 600 meters
https://communityhealthmaps.nlm.nih.gov/2014/07/07/how-accur...
https://www.gps.gov/systems/gps/performance/accuracy/
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Notes:
1. https://web.archive.org/web/20160304012305/33bits.org/about/