Enoch made up a page of text, a column of numbers double-spaced down the left side, starting with zero, counting to 32. Next to each number on the same line he put that many asterisks, separated by spaces. The larger numbers spilled over to the next line, but he tabbed over to keep the asterisks together, and he kept a blank line before the next number, so the grouping was clear.

Then on a second page he did the same thing, but the numbers were in binary.

OK, he thought before uploading them, where do we go from here? What good is knowing numbers? How do we get from numbers to abstract ideas like feelings?

Then he started thinking random thoughts about how printing out and going through the cell phone was clumsy and imprecise. Enoch wondered if he could improve on it. This is the digital age, after all, and these guys are pretty sharp.

They had a sophisticated radio technology, but that wasn't much good going the other way -- oh wait, Enoch thought, I wonder if they can tap into my local wireless net?

He got his laptop out of his car and fired it up. It immediately connected to the local wireless net. He sent the email images over to the laptop, then sent them back. Did they notice? He snapped a photo of the binary numbers page and emailed it to himself. But then he went into the laptop email client to receive it, and forwarded it to himself. Back and forth through the local net. Did they notice?

Enoch waited. Nothing.

Of course not, he thought. The local net is encrypted. Why he bothered here with nobody around within miles was anybody's guess, probably just habit and general principles. He turned the encryption off and tried again.

Sure enough, another email came from the aliens, this time with the laptop headers. They got it, and could respond.

He looked to see what they sent, and was astounded to see almost an exact duplicate of his own decimal numbers page, but the numbers continued to 53. Enoch had never sent that page. They obviously could read and write decimal numbers using the familiar Arabic numerals. This was progress.

Images are still pretty inefficient. Maybe they could handle text email? Enoch emailed the text of his original binary numbers page with the image attached. Surely they would notice the extra text?

Then he did a page of the full alphabet and numerals, plus a few punctuation symbols, and emailed both the text and an image of it. He followed it with another email -- best to keep it simple, one page per transmission -- with his decimal numbers page, but the numbers spelled out in text, "one" then "two" then "three" and so on, up to "thirty-two". He followed that with another page with just a couple lines, still both text and image:

1+1=2     one + one = two
1+2=3     one + two = three

That should be enough for them to get the idea.

They got it. His last page came through again with seven more lines, the equations extended up to ten, including the spelled-out versions. Oh wait, they had not changed the text, only the image. Enoch typed in the text version of what they had just sent, and resent it with their image unchanged.

And waited.

After what seemed like a longer time -- just a few minutes, actually -- another email came through with their original decimal page, both text and image. They got it.

Enoch added a couple more lines to the equation text, and sent it without the image. They immediately sent it back extended to 32, again with no image. They had graduated from images to text, and they understood words as equivalent to numerals.

Now to build a dictionary, starting with numbers and math. This part was fairly easy. All the numbers from zero to ten, then in tens to 100, then by hundreds to 300, then in thousands. That's probably enough, he told himself. The numbers in one column, double-spaced, and on each line in a second column -- he tabbed over -- the spelled-out versions. They should easily see that hundreds and thousands don't have odd names like the numbers under 100. For good measure, he added a few intermediate numbers, both as numerals and spelled out: sixty-four, one hundred twenty-eight, one thousand twenty-four, thirty-two thousand seven hundred sixty-eight. He wondered if they would notice that those are even powers of two.

They did. Their reply was -- again in two columns, decimal and spelled out -- all the powers of two from one to 1048576, except that they spelled it "one thousand forty-eight thousand five hundred seventy-six".

Enoch sent back the last line, with the second word replaced by "million", and on a second and third lines, 1000000 with "one million" and 1000000000 and "one billion". He thought about going to a trillion, but decided it was not necessary. He wanted to get to non-numeric concepts.

How to do that?

Enoch thought about his dad's church. Every once in a while they would bring in missionaries working in foreign countries. They wanted money, so they would explain what they were doing, hopefully to convince the congregation that they should be funded from the monthly church budget. Or something like that. Enoch figured they were mostly a scam.

One of the missionaries was working in some South Pacific island (New Guinea? Enoch couldn't remember, and didn't really care), where they were the first outsiders to learn the language. They gave a little demonstration, right there in front of the congregation. Now Enoch wished he had paid more attention.

The missionary pointed to his wife's hand. She pretended to be a native and said some unintelligible word, presumably in their native language. He pointed to his own hand and repeated the word. She repeated the word again, and he wrote it down on the chalk board with the English word "hand". Then he pointed to his ear, tugged on the lobe, and they went through the charade again, for another word.

That works for people of the same species, who use the same vocal system to communicate, but could Enoch apply the same technique to these guys? We don't have vocalizations -- yet -- but we have numbers and images and text. His first attempt had failed, but it was too big a leap. Enoch would go at it much more gradually now.

He started another page of his dictionary project, this time with mathematical symbols and their names. Then an example page:

1+2=3    one plus two equals three
2*3=6    two times three equals six
3*6=18    three times six equals eighteen
6-2=4    six minus two equals four
6/3=2    six divided by three equals two

He wondered how many examples of each he needed to provide. He sent this off and waited. They were on the same wavelength, and sent back a single line:

18-8/2=5    eighteen minus eight divided by two equals five

Enoch corrected the operator precedence problem with parentheses and commas, and then added second and third lines:

(18-8)/2=5    eighteen minus eight, divided by two, equals five
18-(8/2)=18-8/2=14    eighteen minus (eight divided by two) equals fourteen

Would they understand operator precedence? In any case, this was definitely progress. They obviously did, with a couple new lines:

18+8*2=34      eighteen plus (eight times two) equals thirty-four
(18+8)*2=52    eighteen plus eight, times two, equals fifty-two

Enoch needed to think of what other ideas he could add to his dictionary. Maybe that image of himself and the plane would work now. He attached it to a simple message consisting of "Enoch" and "space ship" on separate lines. There's a problem, he thought to himself before sending it, they don't know about capital letters yet. So he added a column of capital letters to the alphabet page and resent it with its new image, then followed it immediately with another email, himself and the plane and the words in text. He wondered if the capitals would confuse them.

They did not respond immediately. Maybe they were waiting for more information.

Enoch grabbed a digital camera and went outside. He snapped pictures of the house, the water tower and the countryside, then went back inside and uploaded them into his computer. He also pulled up the images of their plane from his cell phone and copied out parts of the plane -- the wings, the windows, the exhaust nozzle from the tail, landing gear -- into separate images, and labelled them in long columns, a sort of pictorial dictionary. He added parts of his own body from the saved images, and sent it.

Then he looked at their images. Still very little he could identify, except a few windows and doorways in the background, and some alien faces. He added his own facial features to a new page of the dictionary, then replicated the features -- eyes and mouth, and of course the face itself; there didn't seem to be any hair or ears or nose -- from the face they sent him and gave them the same labels.

This time they responded with a full-body picture of one of themselves -- Enoch assumed that's what it was -- labelled "space person", then individual body parts (arm, leg, foot, and so on) labelled appropriately.

The color model was another thing they seemed to understand, so Enoch looked around in all the images for some primary colors, red, green, and blue. He wanted to extract several pieces of images in each color and collect them together into one cluster with the color name, but he did not have enough, and their colors were not pure enough. It would probably be confusing to them. Radio waves were much too abstract; there's no way he could attach a name to that yet.

Maybe it was time to attempt face-to-face contact. He cut out the image of himself taking a picture, and pasted it on top of the image of their plane, like as if he were standing next to the plane, and labelled it "meet". He sent it, then waited to see if they had an immediate response. He wasn't sure what to expect, but the reply came back with the same picture, but an image of one of the guys in the shiny suit and motorcycle helmet -- Enoch guessed it was some kind of protective space suit -- pasted in next to himself.

Enoch wondered if his wireless local network would reach over the hillock and decided probably not, but it was worth a try. Just in case it was out of range, he also grabbed a tablet of paper and a marking pen, and then went outside. As he came around the corner of the house into the rising sunlight, it occurred to him that these guys were piggy-backing on his wireless net from their space ship, so it probably would work after all. Maybe they had more power than his laptop did. He would soon find out.
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