The human stood and the other being composed itself on something not quite like a chair. The alien furniture had been the only furnishing in the otherwise bare craft that had borne it to Earth, along with tanks of whatever sustenance the thing required and a hardcoded transmitter.
The human stretched out her hand with a marker and wrote, on the matte stainless surface of the table between them,
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The other reached out immediately and wrote
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and as the human watched and counted she exhaled softly in relief. They had managed to immediately establish a fundamental method of exchange of information and skip directly to complex, abstract mathematical thought. Now to figure out the parts in between.
When the other finished it leaned back to its place and waited.
The other had appeared, seemingly out of nowhere, at the edge of the solar system in a craft that was not much more than a crude cylinder with sets of chemical thrusters, moving slowly and broadcasting a simple, repeating message in the same format as the first television broadcasts from Earth. The message was a simple set of images, showing the creature, the craft, and its trajectory through the solar system, culminating in a touchdown in the center of Australia.
Humanity had watched it slowly make its way inward, towards Earth, on the exact path it promised. Bombardment by every instrument and sensor at Earth's disposal indicated that it was, as far as anyone had a way of knowing, exactly what it represented itself to be.
The human pointed to the empty space before the first tallymark. The other had recognized the Fibonacci sequence immediately, but there was no way to represent zero with tallymarks.
The other did nothing.
The human wrote
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1 2 3 4
| + | = ||
1 + 1 = 2
1 + 3 =
And the moment the marker stopped, the other answered with a smooth string of imitation numbers and signs.
1 + 3 = 4 = |||| = 2 + 2
The human wanted to smile, but even thinking about that level of communication was a long way away.
Instead, she listed out the numbers 1-9 without bothering with tally marks, and then
9 + 1 = 10
10 + 1 = 11
10 + 5 = 15
10 + 10 = 20
The other reached out with its two larger limbs to the center of the table, and set down its marker. Each of its hands, for lack of a better term, had a pincer-like main structure, which was covered in large plates of what looked like horn or bone. Humans would learn later that these were lined with organically produced ceramic blades, and deadly in close combat. This main structure was held closed, as it had been since the human had first observed the other, but delicate, jointed protrusions emerged from clusters on one side of the tip of each pincer jaw, two on the upper jaws and three on the lower.
It tapped each of its digits down on the table, one at a time, from its rightmost to its leftmost.
Ten, the human counted. She was certain it was telling her they used base 10 too - and what's more, why.
This time, the human did smile.
Neither the broadcast, nor the craft itself yielded any information whatsoever about the other or where it came from, or even what its level of intelligence or understanding might be. In fact, some openly opined that the craft seemed to have been deliberately built to the most primitive possible standards, as if to deny any insights or advancements to the receiving civilization. There had been nothing, from materials to apparent construction techniques, that hadn't been possible on Earth for a century or so.
In the back of her mind, the human couldn't help but notice that even now, the other was letting her lead. It was clearly blisteringly intelligent and well prepared - why show up empty handed and stumble along at whatever pace the humans decided to set? Altruism? The best way they could figure to avoid misunderstandings? An evil alien plot?
At least, she thought, they were willing to work down to our level.
And they were - until we objected to the machines.