Imagine the aliens of Prettyfaraway had developed deployed the PrettyHuge Space Telescope.
This pretty impressive array of gravitational-lensing space faring telescopes was capable of resolving Earth surface with a detail of 1 pixel every n^2 square meters. That means an area of n x n meters on the surface of Earth would be resolved by 1 pixel in the final image of the telescope.
The color of that pixel was the mean color of the original area.
A grass field would be a hue of green.
A lake a hue of blue.
A cloud would be white.
A shore line 50% blue and 50% green would be a cyan pixel.
A hypothetical area with 50% red and 50% green would be a yellow pixel.

The telescope resolved only visible light (the reason is pretty silly and I will omit it here). You can assume visible light for the Prettyfarawayans is pretty much the same as it is for us.

I want the aliens in the story to form scientific hypotheses about human civilization without managing to reach indisputable proof.

What would the smallest suitable value of n in meters be if the light they were receiving during the scans was that reflected by Earth in the 14th century?

Consider the aliens know Earth is capable of sustaining evolved life and their observations went on for several years although not continuously.
The telescope focuses only on one area of Earth at a time. The size of the area is 2000x2000 pixels (with the corners not usable due to vignetting and distortion).
Over the years about 70% of the surface of Earth was scanned. The remaining 30% (mainly Antarctica and parts of the southern hemisphere) being not visible during the scans.
Aliens already had other more general data about Earth by different instruments.
After the deployment of the PrettyHuge Space Telescope they were not capable to deploy anything more accurate for their studies about Earth. You know, the cheese wars happened.

Aliens are comparable to us in intelligence (and silliness) and slightly more advanced technologically.

The aliens can scan the same area multiple times.
Furthermore to have full coverage of a larger area they have to take overlapping images.
The telescope though was in function for a little more than our ten years before breaking down.

Additional: in the question the telescope is defined also as 'gravitational-lensing'.
If you are more interested in this approach I suggest this link and additional this video
Yes, the aliens in the question are slightly more advanced than us technologically. They deployed the telescope but did not build it (or did they?...)

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    $\begingroup$ Do the aliens obtain one and only one scan of any given area? Do they take one scan of, say, the area where Rome is, and then never scan that area again? I think it would be much easier for them to detect civilization if they take regular scans of the same area, even if at lower resolution. $\endgroup$ Commented Jul 4 at 15:46
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    $\begingroup$ Don't you mean largest value of n? $\endgroup$
    – Monty Wild
    Commented Jul 5 at 1:21
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    $\begingroup$ @MontyWild No, the smallest, as stated in the question. Basically I want to reach a pretty good resolution that allows them to suspect and make hypotheses but not such a good one that makes them see clearly human made structures. Imagine: if n = 100km then they would hardly spot major orographic details. If n=1m they would be able to see even details in building. Am asking for the lowest value of n that still leaves uncertainty given human made changes to the surface in the Middle Ages. $\endgroup$ Commented Jul 5 at 6:32
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    $\begingroup$ @DuncanDrake The smallest n would be fractions of metres, then. You can get a really great view of something if you can resolve an image to 5-10cm. You're actually asking for the largest n that allows determination that the action of sentient beings is involved. $\endgroup$
    – Monty Wild
    Commented Jul 5 at 12:31
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    $\begingroup$ "I want the aliens in the story to form scientific hypotheses about human civilization without managing to reach indisputable proof." So smallest n for NON factual determination of a civilization. $\endgroup$ Commented Jul 5 at 12:38

9 Answers 9


This is an almost very interesting question, and I have upvoted it. (The really interesting question would have been to ask how large does the light-capturing mirror of a telescope located say 100 light-years away need to be in order to resolve the surface of Earth with say 10 meters per pixel.)

Anyway, the question has been asked the way it has been asked. So let's answer the question that has been asked. Let's pick two selected pieces of Earth's surface, and look at them:

Two selected parts of Earth's surface at different resolutions

At the top, a view of the westernmost part of Long Island in America at different resolutions of meters per pixel; at the bottom, a view of the Nile delta and the Suez Canal at 500 meters per pixel. The entire set of images is taken from Google Maps, set in satellite view with labels off: Brooklyn view, Nile delta view.

  • In the views of Brookly, the two massive piers of the Port Jersey stand out at 350 meters per pixel, and at 200 meters per pixel the artificial nature of the terrain becomes quite obvious with multiple linear features. At 15 meters per pixel the particularly American obsession with rectangular grids is plainly visible.

  • In the view of the Nile delta we see that a resolution of 500 meters per pixel is more than enough to realize that the landscape has been extensively modified by an advanced civilization, with lots of linear features clearly visible. Especially the Suez Canal stands out; it helps that it is a straight, 300 meters wide waterway in what was originally a desert.

In conclusion, 500 meters per pixel is definitely enough to realize that at least some parts of Earth's surface have been modified by an advanced civilization; at 250 meters per pixel the ingenious aliens would see very many areas which show unmistakable signs of civilization. And at 50 meters per pixel cities become obvious, be they modern, medieval, or ancient.

Unfortunately we do not have a time machine, so that we cannot directly view images of Earth in the Middle Ages; but we do know that some structures existed which might have shown up at similar resolutions:

  • The Grand Canal of China existed in various forms throughout the Middle Ages; at least some parts of it are sufficienly linear and constrasty on the surrounding terrain to give a hint that something unnatural was happening.

  • Constantinople was bounded by the Theodosian Walls which might have provided sufficient contrast; and the City had multiple wide long straight streets, such as the famous Mese.

  • In the earlier part of the Middle Ages, when the city of Alexandria in Egypt was still a thriving metropolis, the 1,200 meters long Heptastadion mole linking the island of Pharos with the city proper might have attracted attention, as would have the rectangular plan of the streets.

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    $\begingroup$ Just to answer the "really interesting question" in your first paragraph: The Rayleigh criterion says that you cannot resolve objects that are much less than an angle $\theta \approx \lambda / D$ apart in your field of view, where $\lambda$ is the wavelength of the light used $D$ is the size of your telescope. For an object of size $\ell$ at distance $r$, we have $\theta \approx \ell / r$. Combining these, and ballparking $\lambda \approx 500$ nm, $r \approx 10$ ly, and $\ell = 1$ km, you get $D\approx 50,000$ km. ... $\endgroup$ Commented Jul 5 at 15:02
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    $\begingroup$ ... In other words, to resolve the Earth at a 1000-m resolution from relatively close by in the Milky Way, the telescope would have to have a diameter about four times larger than the diameter of the Earth. The required size increases proportionally to the distance of the civilization from Earth, and inversely proportionally to the level of detail desired on the surface. I'm skeptical that an alien civilization that's "slightly more advanced technologically" than us would be capable of this. $\endgroup$ Commented Jul 5 at 15:05
  • $\begingroup$ @MichaelSeifert: Oh yes, I know that. (Amateur photographer.) That's why I said that the problem would have been so much more interesting. Next you may want to calculate the minimum exposure time to ensure (with some reasonable certainty) that at least 100 photons hit every pixel. How much did the Earth rotate in this time? This would provide a lower bound for the motion blur... $\endgroup$
    – AlexP
    Commented Jul 5 at 16:34
  • $\begingroup$ @MichaelSeifert Does this consider the solar gravitational lens methos? "In 2020, NASA physicist Slava Turyshev presented his idea of direct multi-pixel imaging and spectroscopy of an exoplanet with a solar gravitational lens mission. The lens could reconstruct the exoplanet image with ~25 km-scale surface resolution in 6 months of integration time, enough to see surface features and signs of habitability.". Regarding building and deploying such a telescope by the aliens...don't mind about it ^.^ $\endgroup$ Commented Jul 5 at 20:44
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    $\begingroup$ @DuncanDrake I haven't looked at Turyshev's paper, but from your quote, it would require an exposure time ("integration time") of 6 months. This would mean that the image of the planet would be blurred due to the rotation of the Earth, as AlexP alluded to in their comment above. I'd have to read the paper to see what assumptions were made in their design, though, and whether a more outlandish design might be able to get the exposure time down to a fraction of an hour (which is what you'd need to eliminate this problem.) $\endgroup$ Commented Jul 5 at 21:37

What every answer here so far seems to neglect is farmland. Farmland is the largest product of human civilisation, and humans have a love of straight lines.

Have a look at this Google Maps satellite image (view it at full size):

Google Satellite photo of France

The resolution isn't great, but when viewed at full resolution, what can be seen? Farmland. Farmland with straight-sided fields. There are towns here too, but that doesn't matter, because the first thing you see is all the farmland with those unnatural straight lines.

Nature doesn't produce straight lines. Things naturally 'go with the flow'. It's only humans with their need to measure and work who make straight lines to make things easier for themselves.

The resolution here is approximately such that each pixel is 47 metres along each side... much less than the 10 or so metres per pixel that other answers have suggested to resolve cities.

We also need to consider that in the 14th century, cities would be small, and farmland would be the biggest thing we produce. I chose France because the farm plots there are smaller than in other places... in Australia or the US, modern farms huge, but we're considering 14th century farms, not modern farms.

I can still see the patterns if I reduce the resolution to 50% (i.e. twice the distance per pixel)

So, I'd say the n would be around 50m to 100m to the pixel to pick up European farmland.

  • $\begingroup$ farmland would be especially visable in areas, where there is still quite a bit of forest cover. And the change might even be noticeable in 10 years, when further land is cleared (or the inverse, the 14th century is the time of the black death, after all). $\endgroup$
    – Chieron
    Commented Jul 5 at 9:44

It is incredibly unlikely. Maybe almost completely impossible.

Biggest obstacle is atmospheric distortion, and it hinders even our own ability to observe other celestial objects. The images are always inherently somewhat blurry because of this. Eg. stars seem to blink because of it, so the effect can be observed even with naked eye.

That is one of the reasons why Hubble Space telescope provided an exceptional view to the Universe. It does not suffer from atmospheric distortion at all.

Another obstacle, one that they may have been able to overcome due to the sheer size of their telescope, is that such images tend to need long exposure times. The Earth rotates, so nothing stays still, so the image might suffer from speed blur. The bigger the telescope, the shorter exposure time they need, and an enormous telescope might be able to take snapshots that eliminate speed blur.

However, atmospheric distortion is still incredibly hard to overcome. Snapshots suffer from it, too, and the bigger the telescope, the bigger the distortion between individual light paths. But, who knows, maybe they have been able to figure out how to eliminate its effects in a reliable way.

In conclusion: Prettyfarawayers can potentially see that something is happening here, but it is quite unlikely that they can see enough details to decipher what is going on.

  • $\begingroup$ Just to add: if your story needs it, go for it. Prettyfarawayers have the technology and understanding that they need, it is our limited understanding that limits us, not them. $\endgroup$ Commented Jul 4 at 18:46
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    $\begingroup$ Uh... it's a space telescope. The only distortion would be Earth to space, wouldn't it? $\endgroup$
    – Monty Wild
    Commented Jul 5 at 0:54
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    $\begingroup$ @MontyWild Their telescope is in space, but they are observing things here that are distorted by our atmosphere; distortion works the same way for light coming in and light going out. Small details will be inherently blurred. $\endgroup$ Commented Jul 5 at 1:07
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    $\begingroup$ @JaniMiettinen Distortion works the same way whichever direction the light is going, but the fact that the distortion is next to the source not next to the the telescope makes a huge difference. For a distant telescope (with sufficient resolution) atmospheric seeing would still allow sub-metre resolution. See also this paper $\endgroup$
    – Jack B
    Commented Jul 5 at 9:48
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    $\begingroup$ @JaniMiettinen Assuming there is nothing but vacuum between 320km above the Earth's surface and the far away telescope, there is no reason to think the light would be disturbed. A far away telescope should in principle be able to take the same quality pictures as our own satellites, assuming the size of the telescope is not limited. $\endgroup$
    – fishinear
    Commented Jul 5 at 13:27

The pyramids of the Sun and Moon complex at Teotihuacan Mexico might be the biggest structure around at the time (225m across for the pyramid of the Sun) although it might be hard to spot as the city had been abandoned for many centuries by then. Nearby Tenochtitlan was highly populated and might have shown up better with the central plaza being hundreds of metres across https://tenochtitlan.thomaskole.nl/

The pyramids at Giza were of a similar size and perhaps more importantly were also highly geometric.

To see this scale of object n probably needs to be at least 20 to get a 10x10 pixel image or at the very least 40.

Paris was a large city even then with 429 acres in the central area in 1328. But there was little in the way of height, it would not have been very geometrical (back then) and wouldn’t have been very vivid in shades of brown, grey, black and green it could easily have been mistaken for something else unless viewed with a lot of pixels. Hard to say what sort on n might be appropriate.

Perhaps the best bet would be spotting field/park/agricultural patterns. There must have been some large estates, palaces or agricultural areas where there was a sharp divide between woodland and ploughed fields with occasionally a kilometre or more of distinct straight line boundary. Perhaps n=100 might spot that.

Tips for the aliens (that they should have thought of): Concentrate most carefully on coastal areas and big rivers (tick Paris and Giza). Get multiple images of targets of interest to check for variation during the year, vegetation and snow may change the colour (or not or not as much as expected eg Paris). Also get multiple images at different times of the day to capture shadow or lack of to estimate height (eg pyramids). Look for similar areas, perhaps the brown, grey, black and green smudge that is Paris might look a little like the brown, grey, black and green smudge that is London.

In summary At n=1000 it will be very hard indeed. At n=10 it should be possible but a vast amount of work will still be required.

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    $\begingroup$ Underling to boss: it’s a city with sky scrappers! media.nationalgeographic.org/assets/photos/000/285/28557.jpg $\endgroup$
    – Slarty
    Commented Jul 4 at 19:11
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    $\begingroup$ What about the Pyramids of Mars? They looked artificial, until we saw them at higher resolution. $\endgroup$
    – Monty Wild
    Commented Jul 5 at 1:25
  • $\begingroup$ @MontyWild The thing is, you'd see 100s or 1000s of stuff that looked like a technological civilization, not 1. $\endgroup$
    – Yakk
    Commented Jul 5 at 14:51
  • $\begingroup$ @Monty Wild yes true as I said "Get multiple images of targets of interest to check for variation during the year, vegetation and snow may change the colour (or not or not as much as expected eg Paris). Also get multiple images at different times of the day to capture shadow or lack of to estimate height (eg pyramids)." Also looking at the Martian pyramid area shows a lot of other mesas of a vaguely similar nature that gives the game away. $\endgroup$
    – Slarty
    Commented Jul 5 at 16:40
  • $\begingroup$ To give some idea for sizes, the typical farm field in the Ganges-Brahmaputra Delta is 25 meters by 50 meters, and is farmed using traditional methods -- but that's the richest farmland in the world, and field sizes are atypical. England uses modern farming techniques, but the fields mostly haven't been merged despite that, and a typical size is on the order of 200 meters by 300 meters. $\endgroup$
    – Mark
    Commented Jul 6 at 21:08

If what you're looking for is a way to rationalize ambiguity, there's plenty to be had.

  • Average cloud cover on Earth is 67%. So when you look at the planet is very important.

  • The only way you could look at the planet without significant solar interference is if the planetfarawayrians' telescope is looking down on Sol's ecliptic plane (north or south solar pole). In that case, you could only see half of Earth illuminated at one time and (ignoring the axial tilt) you'd only see half the world ever during the course of a year. If the view is parallel the ecliptic plane then you could see the whole of Earth... for a fraction of the year. So we've narrowed the window of opportunity even more.

  • Shadows are not your friend, which means the same spot on the planet (e.g. grasslands) isn't the same color of green throughout a day or a year. It varies considerably due to shadow. And rain. And snow. And wind. And drought. Over the course of time a spot of land will host an entire range of hues and brightnesses. If all you have to work with is the color of a pixel, you'll soon discover that you can't trust it easily to know grassland from farmland from swamp from even desert.

  • Society changed a lot during the middle ages! But most cities didn't. No electric lights, so very low illumination can be detected at night (if any, really). London, for instance, changed more-or-less from 3 km2 to maybe 10 km2. From an interplanetary perspective with a (shall we say) low resolution telescope, that's nothing. Considering a hemisphere is about 250,000,000 km2, we're talking about no real change at all. And that was a change over one-thousand years.

So, lots of cloud cover (mostly white pixels); narrow windows of opportunity to see illuminated surface; color variations due to shadows, weather, season, and a lot of other issues; and a very low and slow impact of humanity on the planetary surface compared to the whole. Consequence: with a maximum resolution of 3-10 km2 per-pixel your scientists will be arguing forever over whether or not civilization exists on the planet.


Look at Lansat 8 : https://landsat.gsfc.nasa.gov/satellites/landsat-8/ and some of the urban images it can produce: https://landsat.visibleearth.nasa.gov/view.php?id=89363

That image is in the visible range @ 30m resolution. Assuming the aliens are somewhat similar to us and can comprehend artificial urban developments, and they spend enough time surveying the planet, they'll likely be able to detect civilization. They can detect large cities (Rome, Constantinople, Bagdad, etc) and recognize them as artificial constructs. Ancient Greek cities were built on a grid, so that will stand out as artificial.

Obviously cloud cover and atmospheric distortion will be an issue but they should be able to work around those fairly easily if they were able to build that large of a telescope.


N in hundreds or more

I think n can even be over a thousand, but I'll err on the side of caution.

So, first, I think the easiest way to visually detect a sign of civilization would be cities. They will produce a different color pixel than the terrain they're built on would normally have. However at very low resolution I don't think the color of the pixel alone would prove that this is a city. A city built from stone could produce the same pixel color as a rocky area.

What would point to this being a civilization is the changing of the pixel color over time as the cities are being built, expand or are sacked by a hostile army or abandoned for some other reason. The timing and pattern of change would be very different than any natural process that could change the terrain.

Given that, medieval cities could cover a very large area. Constantinople covered over 6 square km, there were probably cities in China that covered an even larger area. So a somewhat smaller resolution would I think definitevely indicate that the terrain changed due to activity of sapient species.

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    $\begingroup$ 14th century cities were pretty small, and at that resolution, how could you tell that it's a city and not something natural? $\endgroup$
    – Monty Wild
    Commented Jul 5 at 1:24
  • $\begingroup$ @MontyWild Geology? Spectral properties of the materials? Strange polarization caused by human obsession with strait walls? $\endgroup$
    – Yakk
    Commented Jul 5 at 14:53
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    $\begingroup$ @MontyWild, you don't look for cities, you look for fields. Crop rotation under the three-field system produces a very obvious year-over-year color change. $\endgroup$
    – Mark
    Commented Jul 6 at 21:11
  • $\begingroup$ @MontyWild I didn't explain it well in the post I guess. You may not be able to tell there's a city there just looking at the color of the pixel (but see Yakk's comment). But if you took that pixel a couple of years ago, and the color suggests there's forest there, and you take the same pixel from the same area a couple of years later and color suggests a lot of stone suddenly (and/or wood without leaves), because a new city has been founded there, or an existing city expanded, you know something took place there that's not natural. $\endgroup$ Commented Jul 8 at 12:47
  • $\begingroup$ @Mark that's a good point as well. $\endgroup$ Commented Jul 8 at 12:48

(This should just be a comment, but not enough rep)

Whatever you go with, keep in mind that I think the part "Aliens are comparable to us in intelligence (and silliness) ..." may be your biggest loophole. I'm sure there are plenty of people on earth that, given the 15m/pixel image from @AlexP's answer, would argue that it's a mega-crystal from the dehydration of a potassium sea or something. And just as many that would argue that, instead, it's a left-over mega circuit indicating a world taken over by some non-biological techno-organism.

As it is, we can get extremely high resolution images of the Bimini Road and some people can't decide whether it's man-made or not, and we have pictures of the earth from space and people still argue that it's flat. So it may be more important who's viewing the images and making the decisions than how good the images are.

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    $\begingroup$ Rather than 'people' I was thinking more about the scientific community of the aliens. $\endgroup$ Commented Jul 6 at 7:16

Obviously Yes!

You didn't tell me what n is equal to, so I'm going to posit that the pretty gargantuan budgets coupled with pretty huge advances in telescopic technology have at last reduced n to a usefully small size of n=0.0001m. If I did my maths right, that means the PrettyHuge Space Telescope can easily resolve the pretty gross pustules on plague victim Joan of England's face. For that matter, your telescope can just about catch the ecstatic expressions on the flies buzzing about her necrotic corpse after she expired.

Given the pretty awesome success of diagnosing plague from Prettyfaraway, the scientologers of the place ought to very easily be able to read any text on church, pillar, pyramid or bed chamber they aim at. When the angles are pretty good, they should be able to check on Chaucer's progress and Milton's pilgrims; catalogue Henry's cologne and which Charles lost his head.

In short, when I'm given the pretty grave responsibility of setting the relevant parameters, the answer shall always be a pretty resounding yes!

...unless it happens to be no...


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