Suppose we wish to send a message to the stars (via radio signal or mechanical probe) and attempt to describe various measurements understandable to extra-terrestrial intelligences.
We cannot use such distances known to us like Astronomical Units or Light Years or Parsecs, because such measurements are based on time units particular to Earth.
The three distances I figure would be recognizable to alien mathematicians/physicists/chemists would be:
Quantum scale…the Planck Length, 1.616 10^-35 meters,
Atomic scale…Hydrogen Atom Diameter, 21210^-12 meters,
“Real World” Scale…Hydrogen Emission Line, 21.106 centimeters.
What “mega-distance” would be universally recognized on the macro-scale?
The second is now officially defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. The meter is now officially defined as the length of the path traveled by light in a vacuum in 1/299,792,458 of a second. The kilogram is now officially defined by fixing the numerical value of the Planck constant (h) to be exactly 6.62607015 x 10^-34 when expressed in the unit J s (which is equal to kg m^2 s^-1)
And those modern measurements are hyper-accurate re-adjustments to earth-natural measurements using physics to fine tune what was first formulated by humans.
A Second was 1/60th of1/60th of a 24 hour day…and a meter was one ten-millionth of the distance from the North Pole to the Equator.
The Golden Records aboard the Voyager probes were made in a way our scientists assumed another intelligent race could decipher. Maybe they are right. Maybe they are wrong. But the records were built with the notion of an alien race having to figure out what is on them.
Or even before Voyager, the Pioneer plaques. Both Voyager and Pioneer use the same spin-flip hydrogen atom as a basic unit and then those units as distances to several pulsars from our sun. (Don’t ask me how, I’m not a physicist!). Plus it had the nude humans in relation to the size of the Pioneer spacecraft itself. Thanks, Carl Sagan!
Or more precisely, one ten-millionth of the shortest distance from the North Pole to the equator passing through Paris along the Paris Meridian.
But while this is interesting, it does not address the OP. I agree that the measurements depicted on the Pioneer and Voyager plaques are a good start, specifically the hydrogen emission line of 21.106 cm. It’s not a large unit like a light-year or a parsec, but it’s relatively easy to use scientific notation to represent any distance you like.
The only mega-distances I can think of are the distances between stars or between our galaxy and the nearest neighboring galaxies, but I don’t think we know those distances all that precisely, plus the distances in question are not static.
With that said, the Pioneer and Voyager plaques did include a representation of various pulsars that could be used to triangulate the location of our solar system.
If you reread my post I think you’ll find that I suggested base-2 already .
But it’s not a big deal anyway. It’s easy enough to convey which base we use. Maybe only a little harder to convey the use of a positional number system.
One slight flaw in the radio wavelength approach is the existence of redshift. However, it’s very small on the scale of nearby stars, and radio signals aren’t likely to progress very far in our own galaxy, let alone others. And assuming we can transmit our position (via our stellar neighborhood), the aliens can figure out the red (or blue) shift and correct for that.
You only need one unit of distance. Once you’ve established the hydrogen atom diameter or the 21 cm hydrogen line or whatever, mega distances can be expressed as a multiple of that distance.
True, but depending on the conversation you’re trying to have, it might be very useful to give those scaled-up dimensions their own unit name, just because baking a cake with the ingredients measured in multiples of the weight of a proton might get cumbersome.
It also might help to reinforce the logic of the communication itself, if you were to define, then redefine units, for example specifying the diameter of a hydrogen atom, then also stating that X-multiple of that unit, called Y unit, is the distance travelled by light in a vacuum for a period that is equal to the half-life of some isotope or other - the recipients of the message can cross-check these things against each other to be really sure that they understand what we’re saying.
Which is what the Pioneer plaque did. The map of where we are used lines marked with cross hatches, with a cross mark for a one, and space for a zero. These gave the distances along the lines in units of the hydrogen wavelength from a set of pulsars that might reasonably be well known markers.
I remember when the plaque was unveiled, the British satire magazine Punch (sadly now since gone) had a parody piece of an alien trying to decode the plaque. It was concerned about the spider like creature depicted, but given the presence of the naked blonde, concluded that the whole thing was a joke.
I vaguely remember a story that Sagan gave the design to some colleagues to see if they could work out what the message was. Some could, or at least could work out what the navigational bits were.
Any species so advanced that it has mastered interstellar space travel undoubtedly has technology that we haven’t even dreamed about and a totally different form of communication. It takes our form of communication 4 years to reach just the nearest star. To send a message to a star that is 100 light years away which, in astronomical terms, is the neighbor 2 doors down, would take 100 years. Judging by our present rate of technological development, whatever we sent them would be extremely dated.
That is all to preface my comment that I agree with you. We have to send them something that will not be outdated in 100 years, in other words scientific constants like the diameter of a hydrogen atom, etc.
We can only hope that an advanced civilization will even be monitoring a form of communication as primitive as ours. Heck, we don’t monitor smoke signals because they are long obsolete.
And also Base-10.
My contribution was taking your Base-2 idea and making it exponential because of the wide range of distances in the universe from Planck length to the observable boundary of the universe
What is the point of that? They surely know those constants as well as we do. This redundant messages serve to establish a common ground, set a communication form (language, code, medium…) and start communicating the interesting things. And those can only be the bits they don’t know. We should think hard about what those are, and I bet there will be endless bitter debates about whether we should even mention the word “god” or “war”, but the message will not be the diameter of the hydrogen atom. The message wil be rather:
“Look at us! We are the human race, this is who we are. And who, pray tell, are you?”
.