[The idea is to start with a concrete situation, like a mother preparing a meal for an extended family, and discovering numbers in their different form: natural, whole, negative, rational (including radicals), real, imaginary, complex, etc...

Mother is of course an archetype and can include many generations of mothers. There are 12 family members and, to make things simpler, they all eat the same amount of food.  Some kind of grain.]

1) Mother knows how much grain she needs to cook for all of them. She just keeps taking handfuls of grain and putting them in the cooking pan until she is satisfied that it will be enough. She has no way of knowing or naming exact quantities. Her experience as a cook is sufficient for the task. She can also enumerate each family member by name, including herself, while grabbing grain, since she also knows how much each member approximately eats. To be sure she does not forget anyone, or count somebody twice, she starts with Father, then herself, and then with each child according to his order of birth. As a mother, she has no trouble remembering that order.

2) some members are gone for a few days on a hunting expedition. She knows of course who is gone and who stayed. So, she has no difficulty cooking the right amount for the latter group. She needs, just like in (1), only to name them one by one while grabbing grain. Sometimes she forgets and grab enough for all, instead of only for those not gone. She learns that instead of pouring the grain back and starting anew, she can just take away as many rations as there are hunters to get the right amount.
She has learned, even though she would know how to express it, that:
rations for everybody = rations of hunters + rations of non-hunters.  
But also:
rations of non-hunters= rations for everybody - rations of hunters.

3) The family has a few wedded children, and their partners count as family members. Mother very often thinks of the couples as such. All she has to do, once she gets to the name of one married child, is to double the ration. She does not know the number 2, but she has no trouble with grabbing two times consecutively a ration without changing names.
After a while, she realizes that she and Father, are also a couple, and, being a modest and respectful woman, she then starts using only Father's name for their 2 rations.

4) Waiting on a hill for the hunters to come back, Mother, sitting on the ground, starts playing with the small stones she finds near her. That reminds her of her childhood and fills her with melancholy. To distract herself she starts naming the pebbles like she did with the grain, and putting them apart. She looks at the heap and wonder if she did not make any mistake. She had used the double ration method, and this time, just to be sure, she reverts to her old method of one name, one ration or pebble. That does not stop her from keeping the doubles apart from the rest, even though she makes sure to name every family member in turn, whether married or not, whether born in the family or not.

5) Father, who had been observing her for a while from behind a tree, hears her saying the names of each family member. He understands immediately what she is doing, having very often witnessed the same scene while sitting near the fire, as she was preparing the meal. Amused, he approaches her silently and inquires whether they are supposed to eat pebbles this evening. Later on he tells her that, when on a hunt, he is the one cooking for everybody (there is always more than one family involved in a hunting expedition), and that he uses the same method to determine how much grain is needed. Also, he tells her how he divides the heart of an animal in equal parts first, before giving each his due. He first cuts the heart in half, and then one half again in half, and so in, making sure that there are no more parts than there are hunters. Here again he makes use of the same method of naming each hunter. Sometimes there is one part left that does not belong to anybody, he the puts it aside before dividing the other half in as many parts as the first one. Because not all parts are of equal size, he uses the second half to even up each part, adding one small part to one large part. Since there are now two parts left, he takes one for himself and gives the other one for the second in command. "I have never had troubles with my groups he said proudly." Mother knew that already. Many hunting expedition came back too soon, and with hardly any catch, because of conflicts about the sharing process. Father was very often asked to lead expeditions, because people trusted his fairness. She also learns that other wives also use her method, but whether they had discovered it themselves, or were just copying her, nobody knows.

6) Mother is thinking about all those women, naming all their family members to get the right amount of grain in the pot. She imagine herself enumerating the names of her neighbors' family members, wondering if she would get more or less than she needs for her own family. Unable to sleep, she decides to try it out while the fire is still going strong. She starts putting handfuls of grain in the dry cooking pan, while whispering the names of their neighbors the same way she did for her own. once she was finished, she looked at the result and was not really surprised to see that the grain did not stand as high as for her own family. Still, she could not be sure that she had not made any mistake, but the fire was growing cold, and she could not see clearly anymore, so she decided to talk to her neighbor tomorrow.

7) Her neighbor, right over the hill, was of course family. Their mothers were sisters, and they had always known each other. She was therefore not surprised at all by Mother's query. They were both old enough that they could start playing with pebbles without having toddlers distracting them by stealing from or adding pebbles to their heaps.
Laughing, they each for herself started gathering enough pebbles for each of their family members. Some of the younger children soon joined the fun. And before long, everybody was gathering pebbles for the different families they knew. It did not take very long for the girls to realize that they could safely swap boys this way. That in turn encouraged the boys to start doing the same with the pebbles representing the girls in the different families, each trying to outbid the other by shouting the qualities of her boys or his "girls". Mother had long forgotten what she had come for, but she was having too much fun to really care.

Nobody gave a thought to the fact that names were used to get the right amount of pebbles, but also that each pebble had become the symbol of a real person, instead of a handful of grain. People's names, just like pebbles, had undergone this transformation earlier in Mother's mind. She had used them to count handfuls of grain, and then to count people, without standing still by the enormity of her discovery.

8) Lying in bed she recounted to Father the events of the afternoon, and soon they were giggling under the blankets like small children. Once they calmed down Mother wondered how names could be used to know how much grain to cook, or how big a family was. She thought about her own mother who, in her last years, had trouble remembering the names of her own children. Luckily, she did not have to cook anymore, being more than half-blind also.
"Maybe if I keep the pebbles, I won't need to remember their names", mumbled Mother dreamily before falling asleep.

9) Mother was cooking the evening meal, going through her usual rituals, while Father lay on his side, watching her, a satisfied smile on his lips. This was his favorite moment, the tiredness of a hard days' work seeming to be washed away by the warmth of the hearth and the soft voices of his children. He waited until Mother took out the grain to start counting the rations before he came up with his gift. "Why don't you use these?", he said teasingly. Mother looked at the colored pebbles in his hands and knew immediately that there was one for each of her family members. She grabbed them in a fake brisk manner and grumbled:"afraid I might forget all your names?". But inwardly she was close to tears of joy for such a an affectionate gesture from the part of her man. The pebbles were certainly of no use to her while counting the grain rations. Just saying the names was much easier that moving pebbles from one heap to another after each handful. But who cared about that. She certainly did not, and neither did her husband who hid a smile when she slid the pebbles between her breasts and went on with her cooking. 

10) Father was again away hunting, and mother was playing with her colored pebbles sitting in her favorite watching place, up on the hill. Every one in the family had now his or her own set after she adamantly refused to let anyone play with hers. So Father had no choice but to make one for all the children, whatever their age. They had all heard of the playful afternoon and the idea of having their own mark was strangely exhilarating. Father had not taken any special care in the coloring of the different pebbles, so that each one had a different set of colors. That made the pebbles even more valuable, giving the freedom to each one to name his or her own pebbles according to a private scheme.
Before long, the whole valley was in the grip of a benevolent epidemy. Everybody, young and old, wanted his own set. Hunters did not leave for their hunt before making sure that had their pebbles, somehow feeling that there were taking their family with them, instead of leaving them behind. Mothers put one pebble away for each hunter, giving the stones a prominent place near the hearth. Before long, the women started building small altars where they kept the pebbles of their beloved, which made it somehow easier to pray to the gods for their safe return.

11) Mother was worried about the hunters. Father was getting older and she knew that he had trouble keeping up with the younger ones. Soon he will have to give up hunting and learn a trade to make a living. He was certainly handy enough, but also so proud. Not a very good trait in a trader who had to bow to please his customers and not frighten them away. She was turning the colored pebbles absently in her palms when she realized what she was doing. Could those pebbles bring security to her family, the way they had brought her joy? 

12) She thought about what Father had told her about dividing the heart between the hunters and put all the pebbles in front of her. "I divide the heart in half", had Father said. She did just that with all the pebbles, trying to make both halves as equal as possible, thinking that the hart of an animal was certainly not easily divided in equal parts. "But what if each pebble was a heart?" said a small voice in her head. After all, if each pebble could be a hunter, it certainly could be an animal! She put the colored pebbles away and started gathering stones around her. She was most certainly not using her family marks to represent animals destined to be hunted!

13) She had now enough unmarked pebbles to represent hunters and hunted without distinction. She knew exactly who had gone with Father and named each one of them silently in her mind lest she inadvertently bound a soul to a stone. Still, she did not hesitate to use Father's stone, the one she had decided represented Father, instead of using one of the anonymous stones. This was his stone, and he already had put a piece of his soul in it when he colored it. "For me." She thought with pride. She looked warily around her to see if anyone was watching or listening. What if she brought bad luck upon the hunting party? Promising herself to be careful she started again on the task of dividing the heart upon the hunters led by Father. "I make sure there are as many parts as there are hunters". How did he do that? She divided all the new stones in two heaps, one in which she placed Father to know it represented the hunters. She then named again each hunter silently and putting a stone near Father for each name. The rest of the stones she put with the others representing the parts of the hearts. She started laughing and berating herself for her blindness. She was lucky she never had to divide a heart between hunters. They would mutiny against her!

14) "as many parts as there are hunters". Of course! one part for a hunter, then another part for another hunter, then another part for again another hunter, until each hunter had had a part. 

15) With a sigh of relief, she put Father's stone away between her breasts where it seemed to fit very snuggly. She did not need it anymore, any more than that she now needed the hunters' names. "one part for each hunter", she thought. "one handful of grain for everyone of us. And one pebble for every hunter". There was a mystery lurking behind these words, but she had no idea how to start interpreting them, even though they were her own.

16) Then she remembered herself using pebbles to count rations of grain, and it struck her that it did not matter whether one used names or pebbles, as long as one knew what the pebbles stood for.

17) Still, pebbles without names were pretty useless for cooking, like she already knew. And what if she dropped a pebble without realizing it, or more than one? Would she know? she took her colored pebbles again, also the one between her breasts, and let them fall softly on the ground. "I would know, she thought. I certainly would notice if someone's color was missing". She looked at the unmarked stones and let a sigh escape her thoughtful lips. How could she ever know if there were any stones missing when they all looked alike?

18) "There is no hope for old people, thought Mother, remembering how her own mother seemed to forget everything. Even if we give them pebbles, they will still need the names".

19) She jerked half up in the middle of the night, her eyes wide open in the dark of their sleeping place. "Why not give the pebbles names? Their own names?"

20) "But what kind of names? Said Father bewildered the following morning. They already have a name, they are stones!"

21) Mother was baking sweet cookies for all the little ones in the big family. Today her youngest daughter was being mated and would soon leave with her man. Everybody in the valley had come to pay their respects to Father and Mother and bring gifts and good wishes to the new couple. When the cookies were finally ready she turned to the wide, brilliant eyes, and extended little hands. And a thought, unsummoned, forced itself to the fore of her mind: " for every little hand, a little cookie, and for every little finger a big kiss!" That is what her mother used to say to her grandchildren before her mind went away long before her body.

22) It took Mother a long time, and many whisperings in bed with Father, before she could convince herself that she could give names of body parts to stones without harming anyone. After all she was not a witch, and did certainly not intend to curse anybody! Still, a little caution never hurt anybody.

23) Mother had arrived to a compromise with herself. She would use animal parts names instead of human ones. That way, nobody could accuse her of bewitching people. Not that animals names could not be used against her, but they were certainly less dangerous. But first she had to make sure that there was no connection whatsoever between those animal names and her people.

24) Mother had taken the habit of leaving all her colored stones on the little altar one of her step daughters had so lovingly built and decorated, before retiring to her hill. She did not do much cooking anymore, and sometimes she felt a dread settling around her heart at the idea that she could soon forget all the names of her children. That made her quest even more urgent, and there was hardly a day she did not dedicate to her self appointed task.

25) Trees and big rocks were the only permanent objects in her surroundings that did not depend on humans for their existence. Mother learned very quickly that they were much more easily accounted for than sheep, goats, or clouds. At least they were still there the following morning. She had thought of the stars, but the idea of climbing at night to her hill, or even standing in the dark next to their dwelling filled her with dread. And stars were much too close to the gods for her comfort.

26) She had now quite a bundle of names, but the problem was remembering the order that she had used them in the day before. She had taken a goat as her model and gathered as many pebbles as all the body parts of a goat she could think of. She had no difficulty remembering that the head came first, but what did come next? The left eye or the right one? And how about the horns, or the legs? And the idea of using the names of the genital parts was not really appealing. People would never stop laughing at her! But where should she stop? When would she ever have enough names?

27) She was deep in her thoughts when she heard Father climb slowly the hill. Once he had stopped hunting, time seemed eager to catch him in its claws, because it almost looked like he got older every day. The idea of losing him was more than she could bear. With a little luck, she would go before he did, or at least stop remembering like her mother did soon after her father died. She saw with stupefaction that he was carrying her old cooking pot filled with grain. 

28) Het started gathering wood for a fire, but she called to him in a laughing voice and tapped softly on the ground beside her. His toothless grin filled her with joy and she looked up to him with brilliant eyes. He helped her pour the grain on a hide he had carried on a shoulder, then said in his still youthful voice: "I miss hearing you saying all our names, woman. Goat parts are not really that fascinating, unless your are a young lonesome shepherd." She giggled and gave him a playful tap on the shoulder.
And so they played with the rice and the colored pebbles.

29) Father noticed that when she said the name of one of the married children, and only a couple of young boys were still single, she took two handfuls of rice while she said the name, and only after that did she put the partner's stone with the rest.
" You do not need those stones at all, he said after a while". She looked at him and said with a shy smile: "I know, but I do not dare take them away. lest ill luck befalls them"

30) "So, what have you learned?"
"Well, mother said teasingly, your part, and my part, are as much as his part, she pointed at one of her son's stone, and his mate's part.
- Ah, he said, playing along. So his male part is the same as my male part, and her female part is the same as your female part?
- Old fool", she said tenderly. She could never have said such a thing when they were young. It looked like they were small children again, saying what was on their mind without care of offending each other. But even small children fought because of words ill spoken. Luckily, they had passed that hurdle many years ago.
- This reminds me of sharing the heart of a deer with my companions.
- Yes, I wanted to ask you about that? When did you keep a part that was not destined to anyone, and when did you not?
- Well, I only knew after the first half. Still, it was obvious before I was finished cutting, that I would have one part left.
- Yes? How so?
- Let us say that there was someone else with us right now, and I had to divide a heart between us. Cutting once, would not be enough. You would get one part, and I would get the other one. But what about our guest?"
Mother started feverishly to realign the stones. Soon she had two heaps, one with all those mated and their partners, including herself and Father, the other, those of the young boys. Of these she made couples she put closer to the other heap, without actually mixing them, until she was left with only one single stone all by itself. She quickly put it with the rest not to afflict him with solitude for the rest of his life, and Father nodded his assent.
-" We need new stones, he said. And new colors."

31) The next day Father had a whole bag of stones, and when he emptied it carefully on the ground, Mother saw that there were only 2 colors, none of which had been used on her family stones. There were also many more stones that they had ever used before. Now she knew why she had not seen him all day yesterday.

32) She started eagerly dividing the stones according to color. "Which shall be the mated ones, asked Father ironically.
- You're the man, she replied readily, you marry them!
- Let the Blues be mated!" He answered immediately with a solemn voice. Mother giggled.

33) After a few days it became apparent that they would never be able to recall all the possibilities they had discovered with only 2 colors. It also became evident, that they would need many more colors the coming time.
"We need Son Number One", said Father with a sigh.
Mother could only agree. Their oldest son had left them when he was barely a man to become a priest, to their great sorrow. Father and herself certainly believed in the gods, and the necessity to treat them with respect and caution. But to search their presence was something they thought was better left to others. The shock was that much greater because the boy was their first born, and they were afraid that others might follow his dangerous path.
Priests were also the only one who could understand the signs they had received from the gods, and which allowed them to communicate with the higher ones.
Those signs, it was said, made it possible to remember what the gods had said to them, and even words men had said to each other so long ago that no one still lived that had heard them.

34) Son listened incredulously to his parents while they stumbled over each other like two children eager to tell the tale first. "You have discovered this on your own?
- Your mother did, replied Father proudly.
- Only because you were there to help." She said affectionately.
Son, a grown man now, was still a little bit shocked to be witness to such an intimate dialogue. It would have been unthinkable in his time to hear Mother speak so casually to Father. At least, he thought, remembering his own relationship with his wife, not when there were children or other people around.

35) He told them that in the temple there were wise men who busied themselves with these very questions, and that, as far as he could tell, they had not come any further than they themselves had!
"Still, he said, we should ask them for advice, because they are truly wise men.
- No! Said Father vehemently. This is Mother's, and Mother's alone. The priest would take it away and pretend it was theirs in the first place!"
Mother was secretly pleased with Father's refusal, and Son knew better than to insist in front such a strong opposition. So the next few hours were spent rehearsing what all the stones had taught them, while Son elaborately penned down what he heard, as well as he could. Mother was quite curious about those strange signs Son was drawing on the rabbit skins he had brought with him. But no less than Father who continuously asked what that sign was for, and that, until Mother hushed him with a soft grip on his arm. Son was answering very reluctantly and it was obvious that he considered the signs the property of the temple, and not something that could be freely shared, even with his own parents.

36) With son's help they had soon exhausted the possibilities the two colors offered, and not one day passed without bringing with itself the need for even more. They had started naming the different groups very naturally with their color, and saying without thinking:" the blues do that and that, and when the reds are more than there are greens then..." Son had told them that the priests used body parts instead of colors, but then, they were priests and no one would dare accuse them of anything. 

37) One day, when the men were enthusiastically juggling with colored stones, Mother asked suddenly: "What are we doing?" They looked at her with a confused look. " I mean, she continued hesitantly, when I started telling the names of everyone while I was cooking, I exactly knew what I was doing. How much rice I needed for whoever was present. But now? I have no idea what those colors mean anymore?
- Have you forgotten, Mother? The Blues are the mated ones, the reds are the singles, the greens are the mated with a first-born.
- Yes, Yes, I remember all that. She said impatiently. But imagine those were all people, how would I know how much rice to cook if they were all present. How much when the reds were gone hunting, or the greens have gone to their husband's family?
- Mother, the wise men at the temple do not cook, said Son with a smile. So I really would not know."
Father chuckled, but held wisely his mouth when she regarded him indignantly.

38) After a while Father said: " we know at least this"
He took some blue stones, some reds and some greens.
Each time he set down a blue stone, he put two reds in front of it. then he started replacing the blues one by one, and adding each time a red one in front of them.
Mother then took it over without thinking and started with the red, than the blue, and lastly the green. Those were the colors they had found a meaning for.
She then put a red in front of the red, two reds in front of the blue, and three reds in front of the green.

39) "Now I remember! Exclaimed Son. This is the big finger, he pointed at the red, wiggling his thumb. This is this finger, he pointed with his index at the blue, and this is the long finger. Now all we have to do is..."

40) Mother had the impression they had gone full circle and back. Colors were really not as easy to remember as fingers. So the priests used all fingers, and they even had special names for each finger. But then, they had to if they used written signs. Normal people had only to wiggle the right finger to show which one they meant. 

41) She looked at her son placing the stones, and started whispering to herself the names of the family members. But Father heard her and his face lit up with a smile. He started pointing at the stones in succession, repeating the same litany: Father, Mother, Son, Daughter....

42) Mother ran, as fast as her old legs permitted, down to the house and fetched her old cooking pot without bothering with the rice. There was enough sand and dirt on the hill to fill it with! Nobody used it for cooking anyway. It was so obvious, how could they have forgotten it! Those pretty colors had blinded them to this simple truth: You had to know who was born first, and who came after him, down to the youngest. And each time you said a name, it was more rice than the name before. Her name meant more rice than Father! She realized shamefully. Maybe she should start with the last born, and end up with Father! Yes, that is what she will do, before she put him to shame in front of his first-born, the priest!

43) The biggest surprise since a very long time came one day when the neighbor asked her: did you teach the children your naming game?
- My naming game? Said Mother bewildered.
- Come with me." Said her cousin.
Mother followed her to the small garden behind the house where the woman grew her herbs. Neighbor put a finger on her lips to signal Mother to be quiet.
A group of children. of different age, where playing with bones, a pile of dried fruit in front of each one of them, some piles definitely bigger than others.
Mother was wondering what it was all about, when one of the children, apparently the loser, started putting dried raisins on the extended palm of the winner. She heard the child very distinctly say the different body parts each time he let go of a raisin.
"They have been using colors since a long time, but they have all changed to body parts since a few days. I suppose that was Son's idea?"
One of the children who had no dried fruits in front of him, said in a whiny voice:" why can i not play? If I lose, i will get the raisins tomorrow from my mother. I promise!"

43) "We need new colors", said Mother the next time they met on the hill again. She had been observing the children for a few days now and was amazed at how easily they had adopted the rules the adults had discovered with so much difficulty. In fact, not only had the children listened while they were busy with their serious occupations, the little ones had found applications the adults would never have thought of.

44) She told them about the "debts" children could have, and how they had had to pay back more then they had received, just to be able to play the same day.
One child, who was always losing, seemed to have accumulated a huge debt, and still, the other children let him play. But only after they had all, each time, agreed on what he owed. They had no difficulty remembering each what they were supposed to get back, and the loser apparently did not either. He could vehemently protest when some one tried to cheat him, and he would recount each game he had lost without hesitation. Mother then realized that his uncanny skill was appreciated by everybody, he was also called Genius, and that was certainly one of the reasons why they still let him play, even if he really was a lousy player. The other reason seemed that the children had as much fun with the naming game, as with the game itself! She chuckled by the memory of a child clutching his crotch instead of one of his fingers to make his point clearer. But she was certainly not going to tell that to the men, at least not while Son was listening!

45) But how do you represent debts? That was the problem that kept them busy for a few days. Playing the game was not difficult once somebody had lent you the raisins. But once the game was finished, then what? The only obvious thing was that the raisins the child had to pay were no more than a promise. As long as his mother did not give him enough raisins to pay his debts, the other children had nothing. But suppose he won a few times, against all odds. What then?
They definitely needed more colors, or more names!

46) The children had found out a new rule. To be sure that there would be enough raisins to continue playing the game, some mothers had started complaining, they had decided that nobody would be allowed to eat his or her raisins. And to make sure of that, all raisins were to be kept by their genial loser who did not like the dried fruit anyway. Everyday they came together, the first thing they did was to divide the big heap among the players, each no more than what he owned. Because ten fingers were for most not enough they each had made a a bunch of sticks all with a unique, personal color, and for each ten fingers of raisins, they were allowed a notch on the stick. Sticks and raisins were of course kept together when the children separated.
The idea of notches was known since memorial times, but this, Mother recognized, was a brand new application.

47) The matter of debts was also solved by the children. Their solution was as simple as it was ingenious. They created debt sticks! And before long, they were trading debts like they did with raisins or other valuables.

48) The raisins were no more. The children had found other games and decided that it was best to give everyone his or her share. Most children kept their sticks though, and years later, they still could be heard joking about what others owed them. Though, only the (self proclaimed) winners seemed to have a good memory. But they never forgot the naming game, and used it in many other occasions.