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[I am sorry if this isn't the best place for this - it was either here or maybe on the Worldbuilding SE.]

I recently re-read one of my favourite childhood sci-fi books (Chocky by John Wyndham), and in it a young boy is asked by an alien being, where in the Universe our planet is.

It occurred to me that this is almost impossible to describe.

Nowadays, with Wikipedia and the Internet, we can get some of the way by stating that we're in a galaxy that is approximately 10 billion years old, light takes approximately 100000 years to cross it, and which is part of a local group, itself part of a cluster, and that part of a super-cluster.

Unfortunately the alien might then ask a follow-up clarification question such as what is a year?

So we go to basics - in base 60 (as opposed to binary or base 10), our basic unit of time is called a second, and there are 60 seconds in a minute, 60 minutes in an hour and 24 hours in a day - which is the time our planet takes to rotate once completely. Our planet orbits a local star (that we call the sun) and each complete orbit takes approximately one year, and light takes around 8 minutes to get from our local star to our planet.

Unfortunately our alien might then ask, but how long is a second? - so we then get into atomic clocks, caesium 133 and phases of radiation, followed by the next inevitable question: what is caesium. So we have to get down to the Periodic Table of the Elements and decribe an atom, atomic weight, and how to define caesium in a way that a far off advance civilization could relate to - not to mention perhaps a tangent about Prime Numbers.

So if our alien was lucky enough to be in contact with someone like Professor Brian Cox, or a physyicist with astronomical leanings, how would such a description and conversation go?

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It all depends on shared knowledge. What you are getting at is known in philosophy as indeterminacy of translation. But note that the alien is already talking to the human: there has to be a language present, and languages do contain a lot of assumptions about the world (tenses imply that there is time, and the question itself implies space, for example).

Now, consider a sequence of larger and larger scale maps of the neighbourhood, running from one showing the solar system to one showing the cosmic web. That seems to settle the "where" question using pattern matching fairly well...

...except that there is the obvious question of what the maps show. In this particular example it is stellar baryonic matter, about 0.002 of the total mass/energy budget. If the alien is made of dark matter this will not make much sense except that it would on the larger scales recognise the topology of the web of halo structures it was familiar with. If it knew about baryonic matter it would infer that this was a map of baryonic stuff. Similarly a gaseous alien might think we have left out the 90% of baryonic matter that is intergalactic plasma. But the point is, the right kind of map or explanation would latch onto something in the knowledge of the alien and allow them to start inferring more meaning.

Since this is not just sending a single message but a conversation there is a lot of room for testing and exploration:

"So you are telling me where you are using a map showing 'pulsars'. Are they [untranslatable1] or [untranslatable2]?"

"What is the difference between [untranslatable1] and [untranslatable2]?"

"[untranslatable1] is spatially localised but extends across time, [untranslatable2] is temporally localised but spread out in space."

"Then [untranslatable1] sounds more reasonable. We know them as compact stars that rotate fast and send radio waves."

"Are 'stars' also spatially localised and extend across time?"

...

It won't be easy, and it is quite possible that our map doesn't correspond to a known region (if the aliens are communicating in some weird non-local way; had they communicated in a local way they would have known the answer to the questions already). But pattern matching and interactive bootstrapping from the shared language and knowledge-base would be a way of getting around the indeterminacy of translation.

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