Marc-Antoine Mahieu

Mickaël Popelard

'A People of Tractable Conversation': A Reappraisal of Davis'

'A PEOPLE OF TRACTABLE CONVERSATION': A REAPPRAISAL OF DAVIS'S CONTRIBUTION TO ARCTIC SCHOLARSHIP (1585-1587) MARC-ANTOINE MAHIEU AND MICKAËL POPELARD

Compared to other Elizabethan mariners who also engaged in exploratory voyages and maritime expeditions, such as Martin Frobisher, Sir Francis Drake or Sir Walter Ralegh, John Davis has received surprisingly little attention in recent years. In her recent book about early modern voyages and English travel narratives, Mary Fuller devotes ample space to Frobisher's voyages but makes only two passing remarks about John Davis, whose name features only once in her introductory chapter about 'the English Worthies' ; in a similar fashion, Robert McGhee acknowledges that Davis outmatched Frobisher in terms of both his sailing and cartographic skills and yet his brief comments on Davis's three expeditions are confined to the end of his chapter on 'Martin Frobisher's Gold Mines'. [START_REF] See | Remembering the Early Modern Voyage[END_REF] If, as Fuller explains, 'the celebration of a "heroic Age of Discovery" depends on a number of deliberate and specific omissions -in other words on remembering some things and forgetting others', then it seems fair to say that John Davis's early contribution to the discovery of the Northwest Passage has often been 'forgotten' by the historians of the field. Fuller goes on to remind her readers that: Forgetting may be ideological, and operate along the lines of particular interests; it can result from a deliberate suppression of certain memories or histories. It is also a function of narrative. To tell a story, one creates a frame, a beginning and end and a central line that moves from one to the other. Likewise, as a history is composed, some things will be brought to the center and some moved to the side, or off the margins of the page altogether. 2 In John Davis's case, 'the suppression of memories' does not appear to be ideological and it probably does not 'operate along the lines of particular interests' either. But it can be argued that as the story of the Northwest Passage was written and re-written by historians, John Davis's important contribution to the quest for the Northwest Passage was increasingly moved to the margins of the page, if not pushed off the page altogether. It will be the aim of this paper to suggest that Davis should be brought back to the center of the narrative, if only to restore some historical balance with Frobisher. [START_REF]A simple search for 'John Davis' as a subject in the British Library integrated catalogue yields only two relevant results whereas a similar search for 'Martin Frobisher' yields about twenty records[END_REF] It is true that Davis failed to reach his intended goal and never discovered the Passage to Cathay -which he still believed to be 'most probable' after his third and last voyage in 1587. But so did Frobisher, whose three voyages may be described as geographic and economic fiascos. In that regard, Davis proved more successful than Frobisher since he unwittingly discovered the key to the Northwest Passage by reaching Sanderson's Hope -present-day Upernavik -at latitude 72°46'. We would like to suggest that the real legacy and import of Davis's three northern voyages lie in his scientific approach, which characterized both his navigational techniques and his description of the Inuit. For Davis was not just the author of The Seaman's Secret or the inventor of the 'backstaff', an instrument that made it easier for mariners to 'shoot the sun'. He also described the natives he encountered with such open-mindedness and objectivity that his account of the Greenlanders has been seen with some justification as the 'first ethnological notes of any consequence' made about the Inuit. [START_REF] Dodge | Northwest by Sea[END_REF] John Davis was born into a yeoman family in 1543 and grew up in Sandridge near Dartmouth, on the right bank of the river Dart. After qualifying as a master mariner in the late 1570's, he embarked on a successful career as a privateersman and a shipmaster. He finally retired at the rather early age of thirty-six, only to be recruited by Adrian Gilbert so as to take part in a fresh attempt at finding the Northwest Passage, less than ten years after Martin Frobisher's first foray into the Arctic. There is conclusive evidence that Davis met the philosopher and mathematician John Dee at his house in Mortlake in January 1583 to prepare a new voyage into the Arctic, in the presence of Adrian Gilbert and Secretary Walsingham. Dee believed that three of the five existing passages from Europe to Cathay were yet to be discovered: in addition to the Northeast Passage -the search for which had hitherto been the preserve of the Muscovy Company -there still remained the Northwest Passage and the route over the Pole, which he believed were to make it possible for English 'princes to possess the wealth of all the East parts', as Sir Humphrey Gilbert put it in his Discourse of a discoverie for a new passage to Cataia (1576). [START_REF] Quinn | North America from Earliest Discovery to First Settlement. The Norse Voyages to 1612[END_REF] Adrian Gilbert and his associates were granted a patent by the queen to sail 'Northwestward, Northeastward or Northward' and they enlisted the financial support of a rich merchant, William Sanderson, who had developed a strong interest in maritime expeditions and scientific instruments, including celestial and terrestrial globes. According to Samuel Eliot Morison, who relies on the testimony of John Janes -the chronicler of the first and third voyages -it was Sanderson who persuaded the associates to appoint 'one Mr. John Davis, a man well grounded in the principles of the arte of navigation, for Captain and chief Pilot of the exploit'. [START_REF] Morison | The European Discovery of America: The Northern Voyages A. D. 500-1600[END_REF] Having been granted the royal patent in February 1585, Davis was able to embark on his first northern voyage in June. [START_REF]For a detailed summary of Davis's voyages[END_REF] Davis's attempts at discovering the Passage have survived in the form of the narratives written by Janes, who happened to be Sanderson's nephew. His two accounts were published by Richard Hakluyt in his Principall Navigations, Voyages and Discoveries of the English Nation (1589). The report on the second voyage was written by Davis himself and was also printed in Hakluyt's collection of travel narratives. We shall examine this second account at greater length because it contains Davis's list of Inuit words which, we believe, is pivotal to the reassessment of Davis's role and importance in the history of Arctic exploration. Like Thomas Harriot's Brief and True Report of the Newfoundland of Virginia (1588) or some of Montaigne's most famous essais -such as 'Des cannibales' or 'Des coches' -Davis's notes constitute a fine example of pre-ethnography. Of course, not all the comments made by Davis and Janes were devoid of a sense of cultural superiority. Yet, on reading their reports, one cannot fail to be struck by the explorers' relatively unprejudiced tone as they describe the natives' mutual solicitude or even their fundamental honesty. It is true that Davis sometimes seems to contradict himself: commenting on the Inuit's apparent passion for iron -which caused them to steal the ship's anchor -Davis felt bound to denounce their 'vile nature'. But both Davis and Janes display a genuine interest in the Arctic people they interacted with. Failing to find a new maritime route to China, Davis appears to have turned part of his attention to the Inuit instead. The Inuit often take pride of place and it looks as if the description of their mores had been substituted for the traditional list of profitable 'commodities' that can be found in so many travel narratives. This is all the more remarkable as the quest for a Northwest or Northeast maritime route to China partly originated in the English merchants' desire to remedy their financial woes after the cloth trade with Antwerp and the Low Countries had become less profitable. [START_REF] See | A Note and a Caveat for the Merchant": Mercantile Advisors in Elizabethan England[END_REF] What is more, Davis did not content himself with listing their drinking and eating habits, or 'the many little images' and diverse cultural artefacts they produced. Our main contention is that Davis also approached their language with linguistic acuity.

Encountering 'very tractable people': Arctic pre-ethnography Davis set sail in June 1585 with a total crew of forty-two. He was the captain of a ship called the Sunshine while the other ship, the Moonshine, was under the command of one William Bruton. John Janes was Davis's supercargo and a member of the Sunshine's crew. Davis and his men sighted Greenland for the first time on 20 July. He seems to have been far from favourably impressed if one is to judge by the name he chose to give it:

The 20. as we sayled along the coast the fogge brake up, and we discovered the land, which was the most deformed rockie and montainous land that ever we saw ... the shoare beset with yce a league off into the sea, making such yrksome noyse as that it seemed to be the true patterne of desolation, and after the same our Captain named it, The Land of Desolation. [START_REF] Janes | The first voyage of M. John Davis, undertaken in June 1585 for the discoverie of the Northwest[END_REF] Davis and his men then turned Cape Farewell (Uummannarsuaq) without trying to explore the coast and entered what is now the fjord of Nuuk (Nuup Kangerlua, previously Godthaab Fjord), which Davis named 'Gilbert Sound', at latitude 64°11'. It was there that they first encountered a group of Inuit. If the very first contact proved a little baffling and rather disconcerting, Janes tells us that surprise and diffidence rapidly gave way to 'many signs of friendship':

The Captain, the Master and I, being got up to the top of an high rock, the people of the countrey having espied us, made a lamentable noise, as we thought, with great outcries and skreechings: we hearing them, thought it had been the howling of wolves ... Whereupon M. Bruton and the Master of his shippe, with others of their company, made great haste towards us, and brought our Musicians with them from our shippe, purposing either by force to rescue us, if need should so require, or with courtesie to allure the people. When they came unto us, we caused our Musicians to play, ourselves dancing, and making many signs of friendship. 10 It is perhaps significant that the first interaction between the two parties should have taken such a musical form as this scene may be said to set the tone for Davis's subsequent encounters with the different groups of Inuit he met. On the whole, it seems that concord prevailed over disharmony, though it is important not to oversimplify the necessarily complex and ambivalent feelings that both sides mutually experienced towards the other party. It should also be noted that, from the start, the Inuit's 'speech' and their 'pronunciation' aroused Janes's linguistic curiosity: 'their pronunciation was very hollow thorow the throat, and their speech such as we could not understand'. 11 If Frobisher's first contact with the natives gave rise to a display of gymnastic virtuosity on the part of the Inuit, 12 in Davis's case the first encounter between the explorers and the natives concluded with music, dancing and a scene of rejoicing: 'one of them came on shoare, to whom we threw our cappes, stockings and gloves, and such other things as then we had about us, playing with our musicke, and making signes of joy, and dauncing'. 13 In the rest of his narrative, Janes often insists on the feelings of 'trust' and 'familiarity' that gradually developed between the two groups. On the second day, the English gained the trust of the Inuit by mimicking their attitudes and 'swearing by the sun after their fashion': 'so I shook hands with one of them, and he kissed my hand, and we were very familiar with them. We were in so great credit with them upon this single aquaintance, that we could have anything they had.' 14 Much like Thomas Harriot who also admired the ingenuity of the native Algonkians, [START_REF] Janes | northeast passage not to meddle with religion when dealing with 'uncivilised people': 'the subject of religion was to be avoided[END_REF] Janes marvelled at the skill of the Inuit. In particular, he showed deep interest in their fine -and warmsealskin buskins, gloves and hoses, for which he willingly exchanged his much less comfortable clothes, 'all being commonly sowed and well dressed: so that we were fully perswaded they have divers artificers among them.' 16 In fact, except for their religion 17 -or lack thereof -Janes did not find anything wrong with them, as can be seen from the following description of the first group he came into contact with: 'they tooke great care one of another ... They are very tractable people, void of craft or double dealing, and easie to be brought to any civility or good order: but we judge them to be idolaters and to worship the Sunne.' 18 Leaving the fjord of Nuuk on 1 August 1585, Davis and his men proceeded on their quest for the Passage, crossing the strait from Greenland to Baffin Island (i.e. Davis Strait) and anchoring their ships in Exeter Sound under a mount they called Mount Ralegh. They found the latitude to be 66°40 and the sea to be 'altogether void from the pester of ice'. The land was also devoid of any Inuit, though it was home to many white bears which the English hunted and killed before departing. This was the northernmost point that Davis reached in the course of his first voyage and on 8 August they set sail southward and doubled the cape of Cumberland Peninsulawhich they named Cape God's Mercy, 'as being the place of our first entrance for the discovery.' 19 They then entered a deep sound -Cumberland Sound (Kangiqtualuk)and seeing that the water was 'of the very colour, nature and quality of the maine ocean', they thought that they had finally discovered the entrance to the Passage. However, they did not have the time to confirm, or rather disprove, their (erroneous) theory as they contented themselves with sailing up and down the sound for four days. On 14 August, they went ashore but could not establish contact with the Inuit. This was the same group of Inuit that Frobisher had met less than ten years before and Samuel E. Morison's suggestion that they 'remembered Frobisher's kidnapping' and 'kept out of sight' seems more than likely. 20 Davis and his men heard dogs howling and they found a few cultural artefacts which Janes described in some detail, 21 but they were not to see the Inuit again for the rest of their voyage. On 24 August, they finally resolved to sail home and they reached Dartmouth on 30 September 1585. Davis's second voyage began on 7 May 1586 with a fleet of four ships, two of which (the Sunnshine and the North Starre) were to go their own way and explore the straight-over-the-pole route. They did so, but met with little success -as one can easily surmise. The other two ships, the Mermayd and the Moonshine, were to resume their quest for the Northwest Passage with John Davis leading the way on the Mermayd. Doubling Cape Farewell, Davis returned to the area of modern Nuuk, where he met the same Inuit with whom the English had played music the year before. Though the account of the second voyage was written by Davis himself, it may be noted that he used the exact same words as Janes had done in his own narrative, describing the Inuit as 'a people of tractable conversation'. [START_REF] Davis | The second voyage attempted by M. John Davis with others, for the discoverie of the Northwest passage[END_REF] Like Janes, Davis also insisted on the fact that the English had formed a true friendship with the Inuit and he depicted the hearty welcome they were given as soon as they landed: But after they had espied in the boat some of our company that were the year before here with us, they presently rowed to the boat, and took hold on the oar, and hung about the boat with such comfortable joy, as would require a long discourse to be uttered: they came with the boates to our ships making signs that they knew all those that the year before had been with them. After I perceived their joy and small fear of us, myself with the Merchants & others of the company went ashore, bearing with me twenty knives: I had no sooner landed, but they leapt out of their canoes and came running to me and the rest, and embraced us with many signs of hearty welcome: at this present there were eighteen of them, and to each of them I gave a knife: they offered skins to me for reward, but I made signs that they were not sold, but given them of courtesy. [START_REF] Davis | The second voyage[END_REF] That Davis was genuinely interested in the Inuit's way of life is evidenced by the rest of his narrative, for he then set about exploring the land and 'searching for the habitation of this people'. [START_REF] Davis | Davis gives a succinct description of the Inuit's tents, 'made with seal skins set up upon timber wherein they found great store of dried Caplin, being a little fish no bigger than a pilchard; they found bags of trane oil, many little images cut in wood, seal skins in tan-tubs, with many other such trifles[END_REF] Instructing some of his men to inspect the country, he made it clear that they should neither shoot at nor injure the people in any way. If Davis's narrative is anything to go by, the first days of his stay in Gilbert Sound seem to have been almost entirely taken up by various exploratory missions. On 3 July, Davis explored another sound 'where the people by signs willed me to go, hoping to find their habitation: at length they made signs that I should go into a warm place to sleep, at which place I went on shore'. 25 More often than not, the explorers turned into friends, sharing the Inuit's games and participating in their leisure activities, as when the English engaged in a wrestling contest with the natives. Because the Inuit kept following the English about, Davis 'was desirous to have our men leap with them, which was done, but our men did overleape them: from leaping they went to wrestling, found them strong and nimble.' 26 Having achieved such a degree of familiarity with the Inuit, it should come as no surprise that Davis was able to describe the natives with more objectivity than Frobisher, whose men, it will be remembered, famously stripped an old woman of her clothes to 'see if she were cloven-footed'. [START_REF] Settle | The second voyage of Martin Frobisher to the West and Northwest Regions in the yeere 1577[END_REF] The following description bears witness to Davis's comparatively neutral, almost pre-ethnographic tone. It should be noted that Davis never presented the Inuit as deformed or devilish creatures, as Settle had done with the elderly Inuk. True, Davis also acknowledged that the natives were sometimes given to practising witchcraft. But his tone is considerably more balanced and cautious than Settle's, and his physical description of the Inuit sounds emotionally disengaged and as factual as was possible for a late sixteenth-century observer:

The people are of good stature, well in body proportioned, with small slender hands and feet, with broad visages, and small eyes, wide mouthes, the most part unbearded, great lips, and close toothed. Their custom is as often as they go from us, still at their returne to make a new truce, in this sort, holding his hand up to the Sun with a loud voice he crieth Ylyaoute, and striketh his brest with like signs, being promised safety, he giveth credit. These people are much given to bleed, and therefore stop their noses with deeres hair, or the haire of an elan. They are idolaters and have images great stores, which they weare about them, and in their boats, which we suppose they worship. They are witches, and have many kinds of inchantments, which they often used, but to small purpose, thanks be to God. 28 This is not to say that Davis never behaved in a partial way or that he proved always immune to ethnocentric feelings. Being invited to witness what the English believed to be a sacrificial ceremony, Davis ordered one of his men to put out the fire and 'spurne it into the sea, which was done to shew them that we did contemne their sorcery.' 29 This was hardly the response characteristic of a detached ethnographer dealing with a shamanistic ritual. In this, he was no different from most of his contemporaries who could not 'recognize the validity of Indian society' (or Inuit society, for that matter) 'in its own terms -something beyond sixteenth century thinking'. [START_REF] Quinn | Englishmen and Others[END_REF] What really caused Davis to lose his temper was the Inuit's repeated attempts to steal iron -something a ship captain in a hostile environment could not turn a blind eye to. Essentializing their 'nature', Davis judged that the Inuit: ... were marveilous theevish, especially for iron, which they have in great account. They began through our lenity to show their vile nature: they began to cut our cables: they cut away the Moonlight's boat from her stern, they cut our cloth where it lay to air ... they stole our oares, a caliver, a boar speare, a sword, with diverse other things. [START_REF] Davis | The second voyage[END_REF] Yet, at the same time, Davis prevented his crew from retaliating and harming the natives, and he soon regained his calm, especially after the Inuit had brought the English seal skins as a token of restored amity. But, Davis continued: Seeing iron they could in no wise forbeare stealing: which when I perceived it did but minister unto me an occasion of laughter to see their simplicity, and I willed that in no case they should be any more hardly used, but that our own company should be the more vigilant to keep their things, supposing it to be very hard in so short time to make them know their evils. 32 It was at this point that Davis inserted his famous list of Inuit words into his narrative, to be commented upon later on in this chapter. This passage is also interesting because it suggests that Davis was convinced that the Inuit could ultimately be made to 'know their evils' -provided the English were given more time to educate them. According to Quinn, this belief in the natives' perfectibility was one of the key differences separating those who thought that the 'civilised' and 'the savage' were 'two distinct and mutually incompatible categories of human beings, the former incapable of being raised to the level of the latter', from those who held the opposite view that the Indians -or the Inuit -were 'by nature capable of reaching a level of civilisation comparable with that of the English'. [START_REF]European Approaches to America[END_REF] Like Harriot, but unlike Frobisher, [START_REF] Davis | Fuller points out that 'most of Frobisher's encounters with the Inuit were or became violent in varying degrees', which was certainly not the case with Davis (Remembering[END_REF] Davis probably belonged to the latter category. In fact, his narrative clearly reveals that he was considerably more open-minded and sensitive to cultural differences than the rest of his men who complained that 'his lenity' and 'friendly using' caused the Inuit to misbehave, giving them 'stomacke to mischief'. This is one of the rare instances when the reader may actually hear two very distinct voices in the narrative as Davis gives a verbatim account of the conversation he had with his men, using direct speech:

Our Mariners complained heavily against the people, and said that my lenitie and friendly using of them gave them stomacke to mischief: for they have stolen an anchor from us, they have cut our cable very dangerously, they have cut our boats from our sterne, and now since your departure, with slings they spare us not with stones of halfe a pound weight: and will you still indure these injuries? It is a shame to beare them. I desired them to be content, and said, I doubted not but al should be wel. 35 However, all did not go well, for the Inuit started slinging stones at the Moonlight, with the result that Davis eventually lost his temper for good. For all Davis's lenity, his patience and understanding had certain limits: 'whereat being moved, I changed my curtesie, and grew to hatred.' 36 He pursued the Inuit in his boat but never caught up with them as they manoeuvered their kayaks much too swiftly. On the following day, however, the natives offered to conclude a new truce with the English and Davis kept one of the emissaries as a hostage for the anchor the Inuit had stolen. Yet, when the wind started to blow in a favourable direction, Davis decided that they should set sail immediately and the English took the Inuk with them. Like Frobisher, Davis therefore abducted a native inhabitant, but unlike his predecessor he had not planned the kidnapping, at least if we are to believe him: 'then we pointed to him and his fellowes for our anchor, which being had, we made signs that he should be set at libertie.' 37 Whereas Frobisher's captive bit his tongue in two so as not to communicate with his enemies, Davis's hostage, we are told, became 'a pleasant companion among [them]' -yet another sign that Davis probably managed to interact with the Inuk in a more competent way than Frobisher did. Relating an episode from Frobisher's second voyage, Settle judged the Inuit 'to be altogether voyde of humanitie and ignorant of what mercy meaneth'. [START_REF] Settle | A True Report of the last voyage into the West and Northwest regions (1577), quoted in Mancall[END_REF] Davis and Janes, on the contrary, never doubted that the Inuit were human beings and that they should be treated as such. Reaching the area of present-day Sisimiut, at latitude 66°33' on the west coast of Greenland, the fleet split, with the Moonshine continuing its search for the Passage while the Mermaid began her homeward voyage. In this area, Davis met another group of Inuit. He observed them carefully enough to notice some linguistic differences: 'they differ not from the other, neither in their canoes nor apparel, yet is their pronunciation more plain than the others, and nothing hollow in the throat'. 39 Davis then sailed southward and the end of his second voyage was comparatively uneventful, except for a short -and dangerous -encounter with natives off the coast of Labrador, in latitude 56°. [START_REF]Secretly lurking in the wood' the natives attacked a group of five English sailors, two of whom they killed (Davis[END_REF] The Moonshine finally arrived in the West Country at the beginning of October, after a voyage of five months. In many respects, Davis's third voyage was a repetition of his previous two expeditions, and it is not necessary for us to discuss it in extensive detail. Suffice it to say that Davis's purpose was to explore the northern part of Davis Strait -which later came to be known as Baffin Bay -in the hope that he could find the entrance to the Passage there. Davis visited some of the sites he had already explored on his previous voyages, including Gilbert Sound, Exeter Sound, Cumberland Sound and the Cape of God's Mercy. But he also visited places he had never been to, such as the modern Upernavik, at latitude 72°46 on the west coast of Greenland. This was Davis's furthest north and he named the place Hope Sanderson, coming very close to discovering the actual entrance to the Northwest Passage, Lancaster Sound, between Devon Island and Baffin Island. Davis and his men did meet some Inuit in the course of their third voyage, but the novelty of the first encounters had worn off by now, and Janes's narrative contains little new information in the way of the Inuit's language or way of life.

Reappraising Davis's linguistic contribution to inuitology

Before discussing the list of words which Davis inserted into his narrative, it is important to turn the perspective around in order to get a clearer idea about who were the Inuit that Davis met in the course of his three voyages. The ancestors of the modern Inuit started leaving Alaska between AD 1.000 and AD 1.200, entering and, for some of them, settling down in the western Central Arctic before reaching the eastern Arctic and Greenland. Those migrants spoke the language ancestral to the present-day Inuit dialects, which is reconstructed by linguists under the name of Proto-Inuit. [START_REF] Fortescue | the term 'Eskimo' primarily refers to the linguistic family comprised of the Inuit dialect continuum and the Yupik languages. In some parts of the Arctic, one also calls 'Eskimos' the people whose ancestral language belongs to the Eskimo linguistic family, namely the Inuit and the Yupiit. 42 The list features in Hall's account of Frobisher's first voyage: C. Hall, 'The first voyage of Mr Martin Frobisher to the Northwest for the search of a passage to China; anno 1576[END_REF] Thanks to the new culture they had developed (known as the Thule or Neo-Eskimo culture), they moved quickly and efficiently across the continent, which accounts for the surprising homogeneity of their dialect continuum. In some areas on their way eastwards, Thule Inuit met and assimilated the descendants of the Paleo-Eskimo populations. Preceding the Thule Inuit by about two thousand years, the Paleo-Eskimos had also left Alaska and settled across the American Arctic. Around AD 1.000, at the same time the Thule Inuit were entering Greenland through the northwest, Scandinavian Vikings from Norway and Iceland (starting with Erik the Red) undertook to colonize southwest Greenland which had been deserted by its Paleo-Eskimo population. As the first wave of Thule people moved into the island and progressed downward along the east coast, the Europeans did not meet the Inuit until the twelfth century, when Norse colonists exploring north Greenland encountered a second wave of Thule migrants who had started progressing along the west coast. We know from different sources that relations between the two groups rapidly turned sour. Owing to unfavourable climate changes, the Vikings finally left Greenland towards the end of the fifteenth century, thus making it possible for the Inuit to settle around the entire west coast. Following his encounter with a group of Inuit on southeast Baffin Island in 1576, Christopher Hall, one of Frobisher's assistants, had put together a first list of seventeen Inuit words. 42 Two years later Martin Frobisher had landed on the west coast of Greenland but had only found uninhabited ruins and recent traces of Inuit presence. Though Frobisher's wordlist has tended to attract more attention for the simple reason that it predated Davis's by ten years, the forty words which Davis wrote down after coming into contact with a group of Inuit on the west coast of Greenland represented an improvement on Frobisher's compilation, if only because his list was twice as long as Hall's. It has been argued that 'European visitors to the Inuit Arctic waited for over a hundred years before again producing wordlists equivalent to Hall's and Davis's compilations'. [START_REF] Dorais | The Language of the Inuit[END_REF] The forty Inuit words compiled by Davis are reproduced here in their original orthography and translation, as found in Davis's account of his second voyage which was printed in Hakluyt's Principall Navigations. The first two columns of the following table contain the words and their translations as printed in Hakluyt. Column three summarizes Hinrich Johannes Rink's pioneering attempt at deciphering the list -a task that had been assigned to him by Albert Hastings Markham, the late nineteenth-century British explorer, who printed Rink's conclusions in his edition of the Voyages and Works of John Davis the Navigator. [START_REF] Markham Explains That 'dr | the Director of Royal Greenland Trade at Copenhagen, and formerly Royal of South Greenland, has very kindly examined these Eskimo terms, and compared them with those now in use amongst the Greenlanders, with the following result[END_REF] The words therefore appear in their nineteenth-century forms and spellings. Column four consists of the words deciphered by Louis-Jacques Dorais, a leading specialist in the language of the Inuit. [START_REF] Dorais | The Language of the Inuit[END_REF] They are given in their supposedly original forms. Finally, in the last three columns we present our own hypotheses, giving first what we believe to be the original form of the word, then its morphological analysis and finally its translation. [START_REF] We | for kindly considering our hypotheses. We are also grateful to Naja Trondhjem, a native speaker of West Greenlandic and a teacher and scholar at the Institute of Eskimology[END_REF] When only the stem can be identified, it is placed after the symbol √. [START_REF]ANTIP, antipassive; DU, dual; FUT, future; IMPER, imperative mood; INDIC, indicative mood; INSTR, instrumental case; INTERJ, interjective form; LOC, locative case; PL, plural; POSS[END_REF] Davis ( 1586 The words compiled by Davis pose serious problems and they certainly constitute difficult material but they are less impenetrable than might be thought at first sight.

There is some sort of coherence in Davis's notation and this allowed us to decipher words which had not been explained so far. For example, it is clear that Davis did not hear the initial /qu/ syllable: 'lethicksaneg' stands for quliksanik while 'blete' stands for qubliit. Similarly, he missed the initial /u/ in several cases: ugguuna becomes 'gounah' and umiamik probably led to 'ponameg'. We have reason to believe that Davis consistenly wrote gn for /rn/, not only in 'ugnera' (irnira), but also in two more words whose ending is not recognizable, 'sugnacoon' (stem: sirnaak-) and 'pignagogah' (stem: pirniq). There is one exception to this pattern: 'ugnake' stands for uqaq. But here as in a number of similar instances (e.g. 'uderah', qingara), the problem comes from the voiceless uvular stop /q/, which is a difficult phoneme for any native speaker of English. It must also be acknowledged that the way Davis rendered vowels and some endings is somewhat erratic and often erroneous. But Davis seems to perceive the length opposition in 'maccoah' (makkua) and 'macuah' (makua), which are two distinct forms of the same lexeme manna. All in all, more than three fourths of the words compiled by Davis may be accounted for. Besides, the table clearly shows that Davis more or less correctly understood about fifty percent of the words, so that we tend to agree with Markham that many of these words have a great similarity, both in sound and sense, to those of the present day. The collection of them reflects great credit on the accuracy and perspicacy of Davis; for the difficulty of obtaining and writing down the words and phrases of an unknown tongue is very very great, more especially after such a short intercourse with the natives as Davis had, both parties being totally ignorant of each others's language. [START_REF] Markham | Many of their words are thus unrecognizable. Moreover, the explorer did not always understand what his informants were trying to tell him[END_REF] The meaning of the forms compiled by Davis is quite revealing about both his and the Inuit's degree of communicative involvement. Whereas Frobisher and Hall's list consists exclusively of concrete object nouns -thirteen out of the list's seventeen words denoting body parts - [START_REF] Hall | callagay "a pair of breeches", attegay "a coate", polleuetagay "a knife", accaskay "a shippe", coblone "a thumbe", teckkere "the foremost finger", ketteckle "the middle finger", mekellacane "the fourth finger", yacketrone "the litle finger[END_REF] the words collected by Davis include an important proportion of verbs and interjections, which tends to prove that he was indeed possessed of a certain sense of language, for such words are considerably more difficult to identify and translate than common descriptive words.

Bearing in mind that an Inuit word may include one full clause, and sometimes even more than one clause, a central question is whether Davis's wordlist did or did not include references to verbal and non-verbal interactions. Some words speak for themselves, most notably 'yliaoute' (or ilauvutit, which translates as 'you are a friend') and canyglow (or 'kunigluk!', meaning 'let us kiss each other!'). Judging from such phrases, we may reasonably conclude that Davis did achieve some degree of familiarity with the Inuit he met on the coast of Greenland. Further evidence of Davis's interaction with the Inuit may be found in words like 'nugo' (naagga, 'no'), 'cocah' (qaa qaa, 'hurry up'), 'quoysah' (? qaissavat, 'you will hand it over'). Davis's list also abounds in imperative forms: 'kesinyoh' (kiisiniaruk!, 'please let him have a bite!'), 'aginyoh' (aginiaruk!, 'please go and fetch it!'), 'unuicke' (tuniguk!, 'give it!'), 'mysacoah' (misuguk!, 'dip it!'). It should be noted that the affix -niaq-, which may be translated as 'please' here, somewhat softens the order, making it sound more gentle and polite.

The spatial deictic words point to the deictic anchoring of the list, as is made manifest in such interjections as 'sambah' (samma!, meaning 'it is down there!'), 'aba' (avva!, 'it is over there!'), as well as in pronouns like 'macuah' (or makua, which Davis wrongly takes to mean 'a beard' but which actually means 'these things here'), 'maccoah' (or makkua, misconstrued by Davis as meaning 'a dart', but actually meaning 'of these things here'), or 'maconmeg' (makkuninnga, 'with these things here'). Locative nouns such as 'icune' (ikani, 'here'), 'awennye' (avani, 'over there'), and 'gounah' (ugguuna, 'through this way here') are also of special interest. Although about half the words in the list consist of object words, they do not always appear in the absolutive singular, which is their most basic form. On the contrary, even some of the nouns referring to concrete objects are given in the instrumental, a case form with various possible functions, which indicates that they were embedded in a dialogue: 'lethicksaneg' (quliksanik, 'with caribou skin coats'), 'asanock' (assangnik, 'with hands'), 'sawygmeg' (savingmik, 'with a knife'), 'sasobneg' (sapanganik, misinterpreted by Davis as meaning 'a bracelet', but actually meaning 'with beads'), 'ataneg' (aataanik, 'with harp seals'), 'ponameg' (? umiamik, 'by boat'). Interestingly enough, the list also includes kinship terms, which indicates that the Inuit tried to introduce themselves by explaining and elucidating their family reationships: for example, in Davis's list, the word 'ugnera' stands for irnira, which means 'my son' while 'panygmah' (in fact paningma) means 'my daughter's'.

Apart from what it tells us in terms of his interaction with the Inuit, Davis's compilation is not entirely devoid of scientific merits. His list is the second document that was written in an Inuit dialect, but it is the first document in Greenlandic. As such, it contains capital information about the language spoken by the Inuit in the late sixteenth century. From a phonological perspective, the significance of Davis's wordlist is threefold. 1) It is known (from comparisons with other Eskimo languages) that the Proto-Eskimo form for 'to go' was *aɣə-. 50 In all present-day Inuit dialects, the intervocalic */ɣ/ has disappeared from this stem, giving way to ai-in Alaska and Canada, aa-in Greenland. As Davis's list includes the word 'aginyoh', we may reasonably conclude that the /ɣ/ still existed in the sixteenth century (aginiaruk). 2) In modern West Greenlandic, the only possible consonant clusters are the following: two identical consonants; a uvular followed by a labial or a dental; the cluster /ts/. Now, it is obvious that many more consonant clusters were allowed five centuries ago, as is apparent from the following examples: /bl/ in 'blete' (qubliit), /kt/ in 'tuckloack' (tuktuuk) and 'tucktodo' (taktuk), /ks/ in 'lechiksah' (quliksaq), /ɣl/ in 'canyglow' (kunigluk), /ŋm/ in 'panygmah' (paningma) and 'savygmeg' (savingmik). All these clusters have undergone regressive assimilation since Davis's time. 3) Whereas Frobisher and Hall's list suggests that a distinction was still made between the vowels /i/ and /ə/ on Baffin Island, the words collected by Davis show no evidence for such a distinction -a difference which was inherited from the Proto-Eskimo fourvowel system. It is highly probable that /ə/ had merged with /i/ and other vowels in Greenland, or at least that /ə/ had become recessive. In fact, Davis erratically uses the letters y, u and i to transcribe reflexes of both */i/ and */ə/. [START_REF]As can be seen by comparing the words mysacoah, uderah, and pignagogah (Proto-Eskimo stems: *məcuɣ-, *qəŋaʀ, *pəʀnəʀ) with the words yliaoute, sugnacoon, icune (Proto-Eskimo stems: *ila-, *ciqni[END_REF] In addition to its phonological significance, the list is also remarkable for a number of morphological reasons. 1) Davis's list clearly proves that the dual number still existed in the sixteenth century, as can be seen from the words 'tuckloack' (tuktuuk, 'two caribous') and 'canyglow' (kunigluk, 'let (both of) us kiss each other'), while it has now disappeared from standard West Greenlandic. 2) Several inflexional affixes still in use in West Greenlandic can be recognized, in particular the instrumental case (-mik: 'ponameg', 'maconmeg', 'savygmeg'; -nik in the plural: 'sasobneg', 'ataneg', 'lethicksaneg', 'asanock'), the possessive affix in the first-person singular (-ga in the absolutive case, as in 'ugnera', 'uderah'; -ma in the relative case as in 'panygmah') and a double-person imperative ending, -guk (notably in 'aginyoh' and 'mysacoah').

3) The last word in the list, 'quoysah' (? qaissavat, 'you will hand it over'), is noteworthy. It possibly suggests that the future tense affix -ssa-, which is specific to Greenlandic -albeit derived from the Proto-Inuit suffix *tya- [START_REF] Fortescue | Comparative Eskimo Dictionary[END_REF] -already existed in the sixteenth century and is not a recent innovation. Finally, the list also commands attention because of its lexical features. To give but one example, the word Davis noted for 'fog', 'tucktodo' (taktuk, Proto-Eskimo *taɣətuɣ [START_REF] Fortescue | Comparative Eskimo Dictionary[END_REF] ) has disappeared from Greenland, where the word pujoq is used today. However, it is still in use in the western part of the dialect continuum and it is therefore interesting to know that a reflex of *taɣətuɣ used to existed in Greenland.

All in all, it can be inferred that the variety of Greenlandic that was spoken in the sixteenth century bears more similarities to the dialects currently spoken in the western part of the continuum (i.e. in Canada and Alaska) than it does to modern Greenlandic. There is no compelling evidence as far as the seventeenth century is concerned, but documents dating from the eighteenth century show that, by then, the language had remained phonologically and morphologically quite conservative. [START_REF] Dorais | Pioneers of Eskimo Grammar (Copenhagen: The Linguistic Circle of Copenhagen[END_REF] All these elements strongly suggest that Davis's contribution to the history of the quest for the Northwest Passage should be reappraised. Real though they may be, the linguistic merits of Davis's list failed to impress critics like Louis-Jacques Dorais who stressed the 'poor linguistic skills' of its author. Comparing Davis's wordlist to Hall's compilation, he argued that the latter could 'be understood in a proportion of 100%' and went on to speak disparagingly of Davis's linguistic capabilities:

The explorer did not always understand what his informants were trying to tell him. For example, the word for 'needle' is translated panygmah, which evidently stands for paningma, 'my daughter's'. Davis's informant probably tried to explain whose needle it was, while the explorer thought it to be the name of the object itself. 55 There is no point in denying that Davis did make some interpretative mistakes. But we would like to suggest that the mistakes he made may partly be attributed to the risks he took in interacting with the Inuit. In other words, his errors were the price to pay for his conversational boldness and they probably deserve to be judged less harshly than has sometimes been the case. To put it at its simplest, Davis's situation examplified Quine's concept of 'radical translation'. The English mariner behaved in much the same way as the linguist imagined by Quine in his 'gavagai' problem: confronted with a form of life that was totally unfamiliar to him, he formed analytical hypotheses in an attempt to catapult himself into the natives' language. [START_REF] See | Word and Object[END_REF] If, as James Axtell argues, [START_REF] Axtell | After Colombus, Essays in the Ethnohistory of Colonial North America[END_REF] judgments are intrinsic to the writing of history, then John Davis's three northern voyages probably deserve at least some degree of praise for the way he managed to interact with the Inuit. Davis never considered the people he encountered as being beyond the pale of humanity, nor did he believe them to be 'naturally gyven to fierceness and rapyne', as Michael Lok -Frobisher's financial backer -would have it. [START_REF] Lok | East India by the Northwestward[END_REF] This may go some way to explaining why his three expeditions to the Arctic did not give rise to any lethal skirmishes. Of course, one must be careful not to paint too simplistic a picture of Davis's northern ventures and we do not want to suggest that he invented modern ethnography -though, in this regard, he certainly fared much better than most of his contemporaries. Our aim is not to pit Davis's scientific successes against Frobisher's economic and moral fiascos. In the field of maritime exploration as in so many other fields, successes and failures are often relative. But it seems to us that both Davis's careful dealing with the natives he came into contact with and the wordlist he compiled provide strong grounds for a revaluation of his role in the history of the quest for the Northwest Passage, quite independently of the fact that he did pave the way for the discovery of the passage.


Sébastien Forestier
email: sebastien.forestier@inria.fr

Pierre-Yves Oudeyer
email: pierre-yves.oudeyer@inria.fr

Overlapping Waves in Tool Use Development: a Curiosity-Driven Computational Model

The development of tool use in children is a key question for the understanding of the development of human cognition. Several authors have studied it to investigate how children explore, evaluate and select alternative strategies for solving problems. In particular, Siegler has used this domain to develop the overlapping waves theory that characterizes how infants continue to explore alternative strategies to solve a particular problem, even when one is currently better than others. In computational models of strategy selection for the problem of integer addition, Shrager and Siegler proposed a mechanism that maintains the concurrent exploration of alternative strategies with use frequencies that are proportional to their performance for solving a particular problem. This mechanism was also used by Chen and Siegler to interpret an experiment with 1.5-and 2.5-year-olds that had to retrieve an out-of-reach toy, and where they could use one of several available strategies that included leaning forward to grasp a toy with the hand or using a tool to retrieve the toy. In this paper, we use this domain of tool use discovery to consider other mechanisms of strategy selection and evaluation. In particular, we present models of curiositydriven exploration, where strategies are explored according to the learning progress/information gain they provide (as opposed to their current efficiency to actually solve the problem). In these models, we define a curiosity-driven agent learning a hierarchy of different sensorimotor models in a simple 2D setup with a robotic arm, a stick and a toy. In a first phase, the agent learns from scratch how to use its robotic arm to control the tool and to catch the toy, and in a second phase with the same learning mechanisms, the agent has to solve three problems where the toy can only be reached with the tool. We show that agents choosing strategies based on a learning progress measure also display overlapping waves of behavior compatible with the one observed in infants, and we suggest that curiosity-driven exploration could be at play in Chen and Siegler's experiment, and more generally in tool use discovery. 0

I. INTRODUCTION

The development of tool use in children is one of the essential questions for the understanding of the global development of human cognition. Indeed, children progressively learn to interact with multiple objects in varied ways which shows an understanding of objects' shapes, relations, the action of forces, and other physical properties used for mental transformations and planning: crucial tools to human cognition.

Different theories have been developed to explain child development, beginning with a description of successive stages in development by Piaget [START_REF] Piaget | The origins of intelligence in children[END_REF]. Piaget described the developmental stages as necessary behaviors that infants should display in a given order. Related views proposed that in the context of reasoning, a single child reasons with only one method at any given age. However, different views were developed more recently which describe more variability in the possible developmental paths that children are driving. Siegler's overlapping waves theory [START_REF] Siegler | Emerging minds: The process of change in children's thinking[END_REF] is describing and modeling the way infants represent and select a set of currently available methods to solve a problem. In the overlapping waves theory, infants maintain their set of methods (also called strategies) with associated frequencies depending on the past history of the use of those methods. The frequencies evolve over time while new strategies are discovered which explain the observed changes in behavior. For instance, when learning the mathematical addition, infants use different methods from one trial to another, and may continue to use non-optimal methods for a long period of time even if they already know more efficient methods. Siegler has speculated that such continued exploration of alternative and sub-optimal methods to solve a family of problem may be useful to acquire skills that will later facilitate the resolution of new problems. This cognitive variability could be an essential mechanism to acquire greater knowledge, which might be more important for learning in childhood than just having high quality performances on specific tasks.

Siegler et al developed several computational models of strategy selection and evolution to account for how children learn how to add integer numbers: ASCM (Adaptive Strategy Choice Model [START_REF] Siegler | Emerging minds: The process of change in children's thinking[END_REF]), and SCADS (Strategy Choices and Strategy Discoveries [START_REF] Shrager | Scads: A model of children's strategy choices and strategy discoveries[END_REF]). Those models are argued to closely parallel the development of addition strategies with the use of several strategies, with errors in the execution of those strategies. In SCADS, furthermore, a mechanism allows the discovery of new strategies and the authors show that the same strategies are discovered and in the same sequences as with children. In the two models, the strategies are selected with frequencies that are directly proportional to (called a "matching law" on) their success rate in the corresponding previous problems. This model also included a novelty bias to explore new strategies more than their success rate would allow: the value for exploring new strategies was initialized optimistically (then decreasing in time if success rate did not rise). The focus of this model has been the mode of strategy selection (matching law), with a measure of the value of strategies based on their performance to solve a given task.

However, these models have not considered other forms of value systems, such as curiosity-driven information seeking, which could play a key role in child development [START_REF] Oudeyer | How evolution may work through curiosity-driven developmental process[END_REF].

In the context of tool use development, Chen and Siegler [5] conducted an experiment with 1.5-and 2.5-year-olds that had to retrieve an out-of-reach toy with one of the six available tools. Children were exposed to a sequence of three similar problems with different tool shapes and visual features, but for each problem only one tool was effective to retrieve the toy. They designed three conditions. In the control condition, the mother just asked the child to get the toy. In the hint condition, the experimenter moreover suggested to use the target tool. Finally, in the modeling condition, the experimenter actively showed to the infant how to retrieve the toy with the target tool. First, they show that in the control condition only few children succeeded to retrieve the toy with the tool even after three problems (less than 10% of the 1.5-year-olds and less than 20% of the 2.5-year-olds). However, in the hint condition and modeling conditions, a large proportion of 1.5-year-olds and most of the 2.5-year-olds succeeded to use the tool strategy by the end of the experiment. With respect to the strategic variability, the authors measured that 74% of toddlers used at least three strategies. The different strategies observed were to lean forward and try to retrieve the toy with the hand (forward strategy), to grab one of the tool and try to catch the toy with the tool (tool strategy), to ask to the mother if she could retrieve the toy for them (but she was told not to) or to walk around the table to look at the toy from different angles (indirect strategy), and finally some of the children did not engage in any of those strategies (no strategy).

Firstly, the authors reported the dynamics of strategy choice as an average over children. They showed that the tool strategy frequency was on average increasing with the successive trials and the forward strategy was decreasing in the hint and modeling conditions, whereas in the control condition the tool strategy remained stable. This pattern was interpreted by the authors as a clear overlapping waves pattern besides the fact that it was a pattern of the average over children. The overlapping waves theory suggests that this pattern of strategy change should be visible on a per child basis, meaning that each child should always use a set of strategies and smoothly change their frequency use. However, the observed average pattern does not imply that each child (or most of them) display an overlapping waves pattern. It could be that in Chen and Siegler's experiment, each child begins with the forward strategy, and at some point in the experiment (different for each child), switch to the tool strategy and never uses again the forward one. In that case, an average of the strategy use would also show a smooth increase in the tool strategy and decrease in the forward strategy use. Nevertheless, the authors also reported a measure that could disentangle the different hypothesis [5, p42]. They measured the average proportion of trials where children used other strategies than the tool strategy after the first trial where they used the tool strategy. The toddlers in the control condition did use the other approaches than the tool strategy on more than half the trials after the first time they used the tool strategy (84% of the trials for 1.5year-olds, 48% for 2.5-year-olds). In contrast, in the hint and modeling conditions, the young infants used other approaches in around 20% of the trials, and older infants in only 4%. This result showed that strategic variability did continue after children began to use the tool strategy in the control condition but not in the hint and modeling conditions. Consequently, we do not agree with the conclusions of the authors saying that a clear overlapping waves pattern was visible regarding the change in forward versus tool strategy use. According to this analysis, overlapping behaviors were observed in this experiment only in the control condition where the mother just asked the infant to retrieve the toy, and the experimenter did not add further incentive.

In this paper, we consider the problem of the modeling of overlapping waves of behaviors in the context of tool learning and use. We will target to model alternative mechanisms that could be at play in Chen and Siegler's experiment. In addition this model will also be used to model learning and strategy selection mechanisms happening before the experiment (hence modeling learning of tool use taking place "at home" during the months preceding the lab sessions). These unified learning mechanisms will be used for both free play exploration/learning of tool use (from scratch) and for exposure to evaluation in lab sessions with an incentive to solve a task. Indeed, a source of difficulty to interpret the results of behavioral experiments in babies is that it is difficult to control for what happened before the lab sessions. In particular, we can't know exactly how much prior experience the toddlers had playing with objects and tools at home, what kind of tools were available, and how the caregivers were interacting with the child or answering its requests to get toys. Furthermore, understanding how the object saliency and the cues of the caretaker are interpreted by the children is an open question. The interpretation of these experiments has implicitly assumed that the experimental setup was designed so that the children would "want" to catch the toy (this also applies to similar experiments such as [START_REF] Fagard | What does it take for an infant to learn how to use a tool by observation?[END_REF]). However, as we will suggest through the model below, alternative hypotheses can be considered (and be non-exclusive). In particular, we will suggest that a salient object may trigger curiosity-driven exploration, where the child explores to gain information about which strategy allows to get it (rather than trying to maximize its probability to actually catch it).

We build upon a previous model of curiosity-driven development of tool use in a simulated 2D environment with objects and tools [START_REF] Forestier | Curiosity-driven development of tool use precursors: a computational model[END_REF]. Intrinsic motivations, or "curiosity", have been shown to play a fundamental role in driving spontaneous exploration in infant free play [START_REF] Kidd | The psychology and neuroscience of curiosity[END_REF]. Intrinsic motivations have been defined as mechanisms that push infants to explore activities for their own sake, driven by the search of novelty, surprise, dissonances or optimal challenge [START_REF] Gottlieb | Informationseeking, curiosity, and attention: computational and neural mechanisms[END_REF]. This model is learning different sensorimotor models structured in a hierarchy that represents the environmental structure. The use of an intrinsic motivation for the exploration of sensorimotor mappings yielding a high learning progress allowed the emer-gence of a smooth progression between overlapping phases of behavior similar to the one found in infants [START_REF] Guerin | A survey of the ontogeny of tool use: from sensorimotor experience to planning[END_REF]. In the model, the intrinsic motivation self-organized a first phase where the agents were mainly exploring movements of the arm without touching objects, then the exploration of the interaction with a single object, and finally a smooth shift towards behaviors experimenting the interaction of multiple objects.

In the present paper, we use a similar model and study different mechanisms for adaptively selecting alternative strategies to reach a toy, which were not studied in our previous work focused on evaluating the impact of hierarchical representations of sensorimotor spaces [START_REF] Forestier | Curiosity-driven development of tool use precursors: a computational model[END_REF]. We hypothesize that not only do the type of decision mechanism to select an action (matching law, or greedy: choose the best one) can influence the resulting behavior and match observations in infants as explained in Siegler's models, but also the measure on which the decision is based, whether it is a competence measure, as in ASCM and SCADS, or an information-gain based measure such as learning progress.

To test this hypothesis, we designed an experimental setup with two phases. In the first one, the agents are autonomously exploring their environment through three sensory spaces (representing the hand, stick and toy), and can learn how to move their hand, how to grab an available stick, and how to reach a toy with either the hand or the stick. In a second phase, the agents use the same strategy selection procedure as in the first phase, but are now only exploring towards retrieving the toy, which mimics the incentive given by the mother to retrieve the toy in Siegler's lab experiment [START_REF] Chen | Across the great divide: Bridging the gap between understanding of toddlers' and older children's thinking[END_REF]. In Siegler's experiment, several tools where available but only one allowed to grab the toy, and the tool strategy was defined as trying to use any of the tool to reach for the toy. We simplify this setup and we place only one tool in the environment so that the tool strategy only contains one type of actions and is easier to interpret. We measure the success rates to grab the toy and we study the evolution of the use of tool and hand strategies in this second phase depending on the mechanism of strategy selection, for individual agents.

Together with this paper, we provide open-source Python code 1 with Jupyter notebooks explaining how to reproduce the experiments and analysis.

II. METHODS

A. Environment

We simulate a 2D robotic arm that can grasp a block or grasp a stick and use it to move the block. In each trial, the agent executes a motor trajectory and gets the associated sensory feedback. At the end of each trial, the arm and the stick are reset to their initial state, and the block is reset to a random location every 20 iterations. The next sections precisely describe the items of the environment and their interactions. See Fig. 1 for an example state of the environment. 1 Source code and Jupyter notebooks available as a Github repository at https://github.com/sebastien-forestier/ICDL2016 A state of the environment. The initial position of the arm is vertical so in this position the first and third joints are rotated to the right and the second joint to the left. The magnetic stick is at its initial position and is reset at each iteration. The block can be caught either by the magnetic side of the stick or directly by the hand as it is reachable here. The block is only reset every 20 iterations to a random position reachable by the hand.

1) Robotic Arm: The 2D robotic arm has 3 joints. Each joint can rotate from -π to π (rad) around its resting position, which is seen by the agent as a standard interval [-1, 1]. The length of the 3 segments of the arm are 0.5, 0.3 and 0.2 so the length of the arm is 1 unit. The resting position of the arm is vertical with all joints at 0 rad and its base is fixed at position (0, 0). A trajectory of the arm will be represented as a sequence of vectors in [-1, 1] 3 .

2) Motor Control: We use Dynamical Movement Primitives [START_REF] Ijspeert | Dynamical movement primitives: learning attractor models for motor behaviors[END_REF] to control the arm's movement as this framework permits the production of a diversity of arm's trajectories with few parameters. Each of the 3 arm's degrees-of-freedom (DOF) is controlled by a DMP starting at the rest position of the joint. Each DMP is parameterized by one weight on each of 2 basis functions and one weight specifying the end position of the movement. The weights are bounded in the interval [-1, 1] and allow each joint to fairly cover the interval [-1, 1] during the movement. Each DMP outputs a series of 50 positions that represents a sampling of the trajectory of one joint during the movement. The arm's movement is thus parameterized with 9 weights, represented by the motor space M = [-1, 1] 9 .

3) Objects: A stick and a toy (block) are available in the environment. The stick can be grasped by the handle side and can be used as a tool to catch the block. The stick has length 0.3 and is initially located at position (-0.75, 0.25) as in Fig. 1. If the hand reaches the block (within 0.2), we consider that the block is grasped until the end of this movement. Similarly, if the hand reaches the handle side of the stick (within 0.1), the stick is considered grasped and follows the hand's position with the direction of the arm's last segment until the end of this movement. If the magnetic side of the stick reaches the block (within 0.1), then the block follows the stick's magnet.

4) Sensory Feedback: At the beginning of each trial, the agent gets the context of the environment: the position of the block (Context, 2D). At the end of the movement, it gets sensory feedback from the following items in the environment.

First, the trajectory of the hand is represented as its x and y positions at 3 time points: steps 17, 33, 50 during the movement of 50 steps (S Hand , 6D). Similarly, the trajectory of the magnet of the stick is a 3-point sequence of x and y positions (S Stick , 6D). It also gets the initial and final position of the block, and the minimal distance during the movement between the hand and the block, if the stick was not grasped, or between the magnet and the block, if the stick was grasped (S Block , 5D). The total sensory space S has 17 dimensions.

B. Learning Agent

The problem settings for the learning agent is to explore its sensorimotor space and collect data so as to generate a diversity of effects in the three available sensory spaces, and to learn inverse models to be able to reproduce those effects. In this section we describe the hierarchical learning architecture.

1) Global Architecture of Sensorimotor Models: The agent learns 4 sensorimotor models at the same time (see Fig. 2). Model 1 learns a mapping from the motor space M to S Hand , model 2 from S Hand to S Stick , model 3 from S Hand to S Block and model 4 from S Stick to S Block . The block is the only item that can have a different initial position at the beginning of each iteration. We thus call contextual models the two models that have to take into account this context (models 3 and 4), and non-contextual models the two others (models 1 and 2). Those two types of models provide the inverse inference of a probable motor command m (in their motor space) to reach a given sensory goal s (in their sensory space), but their implementation is slightly different (see next sections).

In order to get interesting data to build its sensorimotor model, the agent performs Goal Babbling. It first chooses one of the three sensory spaces, and then self-generates a goal in the sensory space and tries to reach it. To generate those goals, different strategies have been studied [START_REF] Baranes | Active learning of inverse models with intrinsically motivated goal exploration in robots[END_REF]. Here we use a random generation of goals for the exploration of spaces S Hand and S Stick (Random Goal Babbling), which was proven to be highly efficient in complex sensorimotor spaces [START_REF] Rolf | Goal babbling permits direct learning of inverse kinematics[END_REF]. For S Block , we just define the goal as moving the block to the origin position (0, 0).

If the goal is in S Block , the agent also has to decide which method to use in order to try to retrieve the block: either the forward method, with model 3, or the tool method with model 4. In the other cases, if the goal is chosen in S Hand or S Stick , then model 2 or respectively 3 is used. Once the babbling model is chosen, it performs inverse inference and uses lower-level models to decide which motor command m will be experimented in the environment.

Finally, when motor parameters m have been tested in the environment and feedback s received, the mappings of models 1 and 2 are updated, and if the agent grasped the tool, then model 4 is updated, otherwise model 3 is updated. Also, a measure of success to reach the goal and of learning progress are computed and will be used to help choosing the space to explore. We use the Explauto autonomous exploration library [START_REF] Moulin-Frier | Explauto: an open-source Python library to study autonomous exploration in developmental robotics[END_REF] to define those sensorimotor models and the learning progress measure. 2) Non-Contextual Models: Each non-contextual model has a motor space (e.g. motor space of model 2 is S Hand ) and a sensory space (respectively S Stick ). They learn a mapping and provide the inverse inference of a probable motor command m (in its motor space) to reach a given sensory goal s (in its sensory space). They store new information of the form (m, s) with m ∈ M being the experimented motor parameters and s ∈ S i the associated sensory feedback in their sensory space. They compute the inverse inference with the nearest neighbor algorithm: they look at the nearest neighbor in the database of a given s in the sensory space, and return its associated motor parameters. Model 1 also adds exploration noise (gaussian with σ = 0.01) to explore new motor parameters.

3) Contextual Models: The inverse inference is computed differently for contextual models (models 3 and 4). Whatever the position of the block (context), the agent tries to grasp it (with the hand for model 3 and with the tool for model 4) and to put it at the origin location (0, 0). To do so, if the context is new (not within 0.05 of any previously seen context), then the agent chooses the motor command that in the past led to the grasping of the block in the closest context. If the context is not new, then the model chooses the sensory point in the database with the smallest cost among the points that had a similar context (context within 0.05 of the current one), and a gaussian noise (σ = 0.01) is added to the motor position. The cost of a sensory point s block with context c is

cost(c, s block ) = D S b (traj, c) + D S b (origin, p f inal ) (1)
where D S block (traj, c) was the minimal distance between the hand (for model 3) or tool (model 4) and the toy during the trajectory. Also, origin is the position (0, 0) and p f inal is the final position of the toy. Finally, D Si is a normalized distance in a sensory space S i ,

D Si (s, s ) = ||s -s || max s1,s2 ||s 1 -s 2 || (2)
4) Active Space Babbling: At each iteration, the architecture first has to choose the sensory space S i to explore. This choice is probabilistic and proportional to the interest of each space (but with = 5% of random choice). We call this procedure Active Space Babbling.

When space S Hand is chosen to be explored, a random goal s g (hand trajectory) is sampled and then sensorimotor model 1 is used to infer a motor command m to realize this hand trajectory. When space S Stick is chosen, a random goal s g (stick trajectory) is sampled and model 2 is used to infer a hand trajectory to make this stick trajectory (and model 1 used to realize the hand trajectory). When space S Block is explored, then model 3 or 4 (hand or tool strategy) has to be chosen (see next section) to reach for the toy and the goal s g is to catch the toy and put it at position (0, 0).

We now define the learning progress and interest of a sensorimotor model mod that tries to reach the goal s g (e.g. model 1 if S Hand was chosen, or model 4 if S Block and the stick were chosen). Once the motor command m is executed, the agent observes the current sensory feedback s in the chosen sensory space S i . This outcome s might be very different from s g as this goal can be unreachable, or because lower-level models are not mature enough for that goal. We define the progress P (s g ) associated to the goal s g ∈ S i :

P (s g ) = D Si (s g , s ) -D Si (s g , s) (3)
where s g and s are the current goal and reached sensory points, and s g and s are the previous goal of the model mod that is the closest to s g , and its associated reached sensory point. The progress of model mod is initialized at 0 and updated to follow the progress of its goals (with rate n = 1000):

P mod (t) = n -1 n P mod (t -1) + 1 n P (s g ) ( 4
)
where t is the current iteration. The interest of model mod is its absolute progress, meaning that a negative progress is also interesting:

I mod (t) = |P mod (t)| (5)
Now we define the interest of space S Hand and S Stick as the interest of models 1 and 2 respectively. The interest of space S Block is the sum of the interest of models 3 and 4.

5) Choice of Method to Reach the Block: When the agent has chosen to explore S Block , and given a block position (context), it has to choose one of its two available methods to reach the block: the hand method (model 3) or the tool method (model 4). We define 4 conditions with different choices, based on two measures; competence and interest. The competence measure estimates for each method if the agent will be able to grasp the block. It is computed as follows: if the block was never grasped with the method, then it is -1, otherwise it is the distance of the closest context where the block was grasped. The interest measure estimates the learning progress of each method to reach the current block position. If the context is strictly new, then the interest is the inverse distance of the closest context where the block was grasped (or 1 if there was no such context). If the context is not new, which means that the block was not grasped in the previous attempts, then the interest is computed as a derivative of the costs of the previous attempts for this context. If there were n previous attempts a i , then the interest is

mean n 2 +1..n [cost(a i )] -mean 1.. n 2 [cost(a i )] (6)
where the cost of an attempt is the one of Section II-B3. Finally, for each of those two measures, we define two types of choice for both measures. The -greedy choice is a random choice with probability = 5%, and the choice of the highest with probability (1 -). In the matching law choice, the probability of choosing each method is proportional to the measure, but also with = 5% probability of a random choice. This results in 4 possible conditions:

• GC: greedy on competence • MC: matching law on competence • GI: greedy on interest • MI: matching law on interest

C. Experiments

The experimental procedure is composed of two phases. In phase 1, the agents are autonomously learning for 1000, 2000, 5000 or 10000 iterations where we reset the toy to a random position (but reachable directly with the hand) each 20 iterations. In phase 2, the agents are successively exposed to 3 new problems (or contexts) while they keep updating their sensorimotor models, for 200 iterations allowed per new problem. In those 3 problems, the toy is set at a location reachable with the tool but not reachable with the hand (problem A: (-0.1, 1.2), B:(0, 1.25), C:(0.1, 1.2)). Those locations are distinct enough so that given the solution to one of them, solving another one requires some exploration, but close enough so that the previous one helps. Finally, we simulate 100 independent trials for each condition.

III. RESULTS

Fig. 4 shows an example of the evolution of the interests to explore the sensory spaces during phase 1 for an agent of condition MI. After some iterations, the interest of S Block becomes greater than the interest of S Hand and S Stick and thus is more often chosen to be explored. Fig. 3 shows in each condition and for each of the 3 problems of phase 2, the proportion of the 100 agents that succeeded to reach the toy, depending on experience (the number of iterations performed in phase 1, i.e. the number of sensorimotor experiments/movements already achieved by each agent). We see that in all conditions and for all problems, the success rate increases with experience. For instance, for problem A in condition MI, the success rate goes from 25% when agents have experimented 1000 iterations to 50% when they have experimented 10000. Also, for all conditions and experiences, the success rate increases from problem A to B and from problem B to C. For example, the success rate is 21% for problem A of condition MC at experience 1000 and it goes to 27% for problem B and 33% for problem C. Finally, the success rates of all problems in condition GC are smaller by 5 to 20% than the success rates of the three other conditions, and the success rates of condition MI are slightly higher than those of condition MC. Fig. 5 shows 2D maps of the preference between the hand and tool strategies to reach the block depending on its 2D position (on a 100 × 100 grid), for one agent of experience 10000 iterations of each condition that succeeded to catch the block on the three problems. Also, the maps are computed at different times of phase 2 for each condition: at the beginning of phase 2 before problem A, after problem A, after problem Fig. 3. Proportion of 100 agents that succeeded to reach the toy in each of the 3 problems of phase 2, depending on condition and experience (the number of iterations experimented). Success rate increases with experience and with the problems encountered, and are better in conditions MC, GI and MI than GC. B and after problem C. The preference is computed as the probability of choosing the hand strategy, and is reported on a two color scale. A completely blue region means that if the block is located in that region, then the corresponding agent would certainly (with probability 1) choose the hand strategy. This is almost the case in conditions GC and GI where the choice is -greedy with = 5%. Similarly, in green regions of those conditions, the choice is almost always for the tool strategy. However, a whiter region (in conditions MC and MI) means that the choice is more balanced, and in completely white regions the choice is equiprobable. It should be noted that the arm is located at position (0, 0), has length 1, and can catch the block within 0.2 so it could theoretically reach the block within a circle of radius 1.2. However, in the 3 problems of phase 2, the block is unreachable directly with the hand. In those problems, the block is located at positions (-0.1, 1.2), (0, 1.25) and (0.1, 1.2) (black dots).

In all conditions (from top to bottom) we can see modifications of the preference around those points across exposure to problems (from left to right), from a hand (blue) to a tool (green) preference. For instance, in condition GC (first row), before phase 2 (first column), this agent already preferred the tool. This is indeed possible because even if during phase 1 we reset the position of the block every 20 iterations to a random position reachable by the hand, this agent could have the time to move the block out-of-reach for the hand and then learn that it could catch it with the tool at that position. This is also part of the reason why success rate increases with experience in all conditions for problem A. Then, after the success to retrieve the toy in problem A (second column), the preference around problem A has changed in a small region around A, but towards the completely different choice: almost always choosing the tool strategy instead of always choosing the hand strategy. The results for the agent in condition GI are similar. However, the results for the agents of conditions MC and MI are different. In condition MC, the agent has no preference in problem A before phase 2, which means that for the first trial to retrieve the toy in problem A, it will choose the strategy randomly, and then the preference might change as the competence value depends on how far from the toy the strategy allowed to reach for. After problem A (second column), the preference changed in a large region around problem A, but this time the change is more gradual, with a high probability to choose the tool strategy only very close to A. The results for the agent in condition MI is similar, but here the preference before phase 2 was for the hand strategy (slightly: 60%, but for other agents it could have been for the tool strategy).

IV. DISCUSSION

We designed an experimental setup where an agent controling a 2D robotic arm could learn two strategies to grab a toy depending on its position: grabbing the toy directly with the hand or first grab a tool to reach for the toy. We defined two dimensions of strategy choice: the type of decision, with a matching law or a greedy choice, and the measure on which to make this choice: the performance of the strategies to retrieve the toy in its current position, or the progress made with each strategy to get the toy. The decision based on the performance measure means that the learner is interested to get the toy, and the decision based on the learning progress means that the toy raises the curiosity of the learner about its affordances or relation with the hand and the stick. The agents have unified learning mechanisms for both free play exploration/learning of tool use from scratch (phase 1) and for exposure to evaluation in lab sessions with an incentive to solve the task (phase 2).

First, the success rates in our setup are compatible with the ones of 1.5-and 2.5-year-olds in the experiment of [START_REF] Chen | Across the great divide: Bridging the gap between understanding of toddlers' and older children's thinking[END_REF], where the success rates increase with experience and also across the successive problems. In this experiment, the toddlers in the control condition did use the other approaches than the tool strategy on more than half the trials after the first time they used the tool strategy in the lab experiment (84% of the trials for 1.5-year-olds, 48% for 2.5-year-olds). However, in the hint and modeling conditions, where the experimenter moreover suggested to use one of the available tools, or actively showed to the infant how to retrieve the toy with the tool, younger infants used other approaches in around 20% of the trials, and older ones in only 4%. In our setup, at each iteration in phase 1 the agents have the choice to explore one of the three available sensory spaces. In phase 2, to model the incentive to get the toy given by the mother in the lab sessions of [START_REF] Chen | Across the great divide: Bridging the gap between understanding of toddlers' and older children's thinking[END_REF], the agents could only explore the space of the toy, S Block , but could choose either the hand or tool strategy. However, we did not model the hints given by the experimenter in the hint and modeling conditions. Our setup is thus more similar to the control condition of [START_REF] Chen | Across the great divide: Bridging the gap between understanding of toddlers' and older children's thinking[END_REF] and we observe that only our two conditions using a matching law, MC and MI display a concurrent use of the tool and hand strategies, with smooth evolution to new sensorimotor experience. The behavior of agents in conditions MC and MI are compatible with the overlapping pattern observed with children in the control condition of [START_REF] Chen | Across the great divide: Bridging the gap between understanding of toddlers' and older children's thinking[END_REF] where the mother just asked the child to get the toy. The fact that the average use of the tool strategy in the control condition did not increase across problems might be because children did not have enough time to discover by themselves that the tool can help to get the toy, without the hint given by the experimenter.

Siegler [START_REF] Siegler | Emerging minds: The process of change in children's thinking[END_REF] suggests that the cognitive variability observed in infants could be essential to learning in childhood, and model it as matching law on the competence of the strategies. Our results suggests that an alternative mechanism that was not proposed in Siegler's model could be at play in [START_REF] Chen | Across the great divide: Bridging the gap between understanding of toddlers' and older children's thinking[END_REF]: strategy selection mechanisms could be based on a measure of learning progress instead of performance.

More generally, a matching law on performance could waste too much experimental trials on high-performing but not improving strategies, even with a novelty bias (that would expire irrespective of progress). On the contrary, a matching law on the monitored learning progress of each strategy could focus the training on low-performing but improving strategies and avoid wasting trials training high-performing but not improving strategies. Indeed, our results also suggests that condition MI could be more beneficial for learning in our setup than condition MC as success rates are slightly better in condition MI. Also, a currently bad strategy could turn out later to be interesting for other related tasks and thus benefit from training. On the other hand, an emphasis on learning progress might too often lead to the choice of an improving strategy that will turn to be sub-optimal. A particular situation with respect to this exploration/exploitation tradeoff is when social feedback is available. In the hint and modeling conditions of [START_REF] Chen | Across the great divide: Bridging the gap between understanding of toddlers' and older children's thinking[END_REF], the experimenter respectively suggests to use the target tool or actively shows how to retrieve the toy with the tool. The strategic variability is much lower in those conditions, e.g. the 2.5-year-olds used other strategies than the tool one in only 4% of the trials after the first time they use it. We interpret this decrease in variability as the result of the incentive given by the experimenter, supposed to focus attention towards the target tool and to trigger the tool strategy. In our model, the hint condition could be integrated as social bias to select the tool strategy. Also, the demonstration provided by the experimenter in the modeling condition could be added to the sensorimotor models as examples to reach the toy given the trajectory of the tool and the hand, the agent only having to finding motor parameters to realize the hand trajectory (with sensorimotor model 1).

Finally, several strategy selection mechanisms (e.g. based on competence or interest) could be available across all situations, and children could switch between them or combine them depending on the estimated interest of exploration, the desire to actually get the toy, or social cues as the mother or experimenter incentive in Chen & Siegler's experiment.

  Fig.1. A state of the environment. The initial position of the arm is vertical so in this position the first and third joints are rotated to the right and the second joint to the left. The magnetic stick is at its initial position and is reset at each iteration. The block can be caught either by the magnetic side of the stick or directly by the hand as it is reachable here. The block is only reset every 20 iterations to a random position reachable by the hand.

Fig. 2 .

 2 Fig. 2. Architecture of models. The green circle is the motor space and the blue ones are sensory spaces. The gray squares are the 4 models.

Fig. 4 .

 4 Fig. 4. Evolution of the interest of spaces for one agent of condition MI during 10000 iterations of phase 1.

2) (black dots). Each 2D map represent the preference between the hand and tool strategies to reach the block depending on its 2D position. In those 2D maps, the arm is located at position (0, 0), has length 1, and can catch the block within 0.2 so it could theoretically reach the block within a circle of radius 1.2 without the tool. The colors reads as follows: a completely blue region (respectively green) means that if the block is located in that region, then the corresponding agent would certainly (with probability 1) choose the hand strategy (respectively tool strategy), and a whiter color means a more balanced probabilistic choice, a pure white being the equiprobable choice. In all conditions (from top to bottom) we can see changes in the preference around those points (from left to right), from a hand (blue) to a tool (green) preference.