Patrice Cohen
email: patrice.cohen@univ-rouen.fr

CANCER, THE MAKING OF PROOF AND THE EVALUATION OF CAM IN THE U

may come

Cancer, the making of proof and the evaluation of CAM in the USA

safety and placebo effect of such CAM are mainly structured around cancer and chronic illnesses. Since 2014, a new turning point is emerging: "integrative oncology", part of the "integrative medicine" movement, as shown by different articles in systemic journals and the new name of the NCCAM, the National Center for Complementary and Integrative Health (NCCIH).

This new wave of the institutionalization of CAM is co-constructed by a plurality of agents mobilizing a variety of discursive and practical elements such as the complementarity and the integration of such CAM, terms and practices that I consider as many social, historical, political and economical characteristics of the legitimizations I try to analyze.

These two federal institutions dedicated to medical research on CAM question the different, sometimes competing and conflicting, modalities of evaluating the efficacy of CAM, research ethics, public health policies and health practices regarding cancer and CAM and the various challenges at stake in the legitimizations of an integrative model towards cancer CAM. It addresses the issues faced by agents within processes of evidence building for such CAM, practices which are often hardly fitting in experimental frameworks.

The focus on cancer answers not only to the historical context and shifts in CAM research but also to the missions of the institutions at stake. It reveals the manners how the medical evaluation of CAM and its legitimizations are part of the co-construction of the medical work, namely the management of patients' care, the prevention and treatment of the disease, and the advice offered to the patients by healthcare teams, the constitution of "integrative" wards and in particular the task allocation between biomedical and CAM practices. It investigates how medical research on cancer and CAM impacts the meanings and directions of this medical work as well as the experience of the disease. This "negotiated order" is the product of interactions between a variety of both institutional and individual agents. It questions the significance of this making on "cancer stages", on the agents and spaces upon which they depend, and the influence of such legitimizations on "therapeutic itineraries or trajectories". This research also examines the management of the heterogeneity of health practices, its shaping and reshaping, by sets of multiple agents and institutions belonging to different networks of interrelations. The question of the plurality of medical practices, conceptualized under the term of "medical/therapeutic pluralism", is at the core of different historical, legal, philosophical, economical and sociological studies, both in Europe and in the U.S., more particularly interactions between medicine and CAM. Nonetheless, only very few sociological and anthropological investigations focus on the scientific evaluation of CAM in this regard. This question of the plurality of medical practices usually involves about five broad categories of agents: the State and its apparatuses, the medical profession and its institutions, other medical practices, and patients and their respective institutions. This on-going research also departs from these broader questions and participates in studies aiming at understanding more closely the mechanisms at stake within the complex construction of plural medical practices. This presentation will be articulated around five main points:

1. Research aims and methodological perspectives 2. CAM and medical research: An institutional setting 3. Different regimes of proof in the evaluation of CAM 4. The plurality of CAM categories and models of integration 5. Mapping the variety of networks, agents and interactions

Since the 1990s, this original institutionalization is implemented through the creation of two federal entities in charge of medical research on CAM: the NCCAM and the OCCAM at the NCI both part of the National Institutes of Health (NIH


Extensions of the I&AB method for the reliability assessment of the spent fuel pool of EPR

INTRODUCTION

The standard PSA method (based on fault tree linking) is not well suited for the reliability assessment of the spent fuel pool of a nuclear power plant, for several reasons. Firstly, the dynamics of the phenomena to be modeled are relatively slow because of the large amount of water available in the pool itself and in the safety systems. It is thus not sufficient to look at what can happen in only 24 hours after an initiator. Secondly, the fact that components are repairable, and the existence of multiple standby redundancies cannot be ignored.

EDF has developed several tools for creating and quantifying dynamic models, better suited for this kind of system study. In particular, BDMPs (Boolean logic Driven Markov Processes) are a powerful modeling tool for the dependability analysis of dynamic systems [START_REF] Bouissou | A new formalism that combines advantages of fault-trees and Markov models: Boolean logic driven Markov processes[END_REF]. For more than ten years, they have been used for assessing the reliability, availability, and safety of complex reconfigurable systems. BDMPs have a graphical representation close to fault trees, yet they specify (potentially very large) CTMCs (continuous time Markov chains). A BDMP model with the same detail level as fault trees of a standard PSA would not be quantifiable by analytical methods, even with classical approximations. On the other hand, it would require too large computation times with Monte Carlo simulation, because the probability of reaching a too low level in the spent fuel pool is very small. For these reasons, we have developed a new approximate method for the quantification of very large BDMPs, and more generally any model able to generate minimal products containing one initiating event and the failures of the barriers activated after it in order to avoid the undesirable event. This is why the main foreseen application domain is nuclear PSA, all the more so as existing PSA models will be very easy to adapt to I&AB, merely by adding repair rates to component data. In a PSA context, I&AB can be used to take repairs into account instead of postulating that 24 hours after an initiating event, either the undesirable event is unavoidable, or the system is in a safe state. The I&AB (Initiator and all barriers) main principles were published in a paper at ESREL 2016 [START_REF] Bouissou | Boolean approximation for calculating the reliability of a very large repairable system with dependencies among components[END_REF]). In the present paper, we give all analytical formulae of I&AB and of its extension in the case of grace times and deterministic failures. We also give some numerical application examples, comparing the I&AB approximation to "exact" calculations performed on a dynamic model via Monte Carlo simulation.

THE INITIAL I&AB METHOD (2016)

Hypothesis on the system and definitions

Suppose we want to calculate the reliability of a repairable system with standby redundancies; it may be a good approximation to take into account only one level of dependences between the components. In Extensions of the I&AB method for the reliability assessment of the spent fuel pool of EPR M. Bouissou EDF Lab Saclay, 7 Bd Gaspard Monge, Palaiseau 91120 ABSTRACT: The I&AB (Initiator and All Barriers) method was first introduced at ESREL 2016, as an efficient means to calculate, thanks to closed form formulae, the reliability of a very large repairable system with dependencies among components. The mathematical support of I&AB is continuous time Markov chains, and therefore it cannot be used for modeling the spent fuel pool of a nuclear power plant, because for this system, there are two kinds of deterministic delays that must be taken into account: grace times (for example, after the total loss of cooling of the pool, it takes exactly 14 hours for the water to start boiling), and deterministic failures due to the limited capacity of water tanks. In the present paper, we extend the I&AB method to account for deterministic delays. We explain how we could apply this method in the case of the fuel pool of the EPR (European Pressurized Reactor) starting from a model in the form of a BDMP (Boolean logic Driven Markov Process), and how results and computation times compare to a Monte Carlo simulation of the same BDMP.

other words, one is capable to distinguish failures of "normal" components (they are called "initiating events") and failures of components in standby (that function only in case of failures of normal components). But one cannot discriminate between a component of "primary standby" (that assures the functioning of the system after a failure of the corresponding normal component) and a component of "secondary standby" (that operates only after a failure of the primary standby component).

The I&AB method relies on the two following approximations:

A0: When an initiating event occurs, all standby components are supposed to start functioning (or maybe refuse to start) immediately after the initiating event; then, they may fail and be repaired independently from each other until the initiating event is repaired.

A1: Once an initiating event is repaired, the system cannot anymore fail, whatever happens.

We suppose that the real system is described by a CTMC where the initial, "perfect" state is the state into which the system always returns, until it is absorbed by a failure state. Then its unreliability can be estimated from the following formula [START_REF] Bouissou | Fiabilité des grands systèmes séquentiels: résultats théoriques et applications dans le cadre du logiciel GSI[END_REF]:

≤ 1 -exp -Λ (1)
where Λ is the frequency of initiating events (sum of rates of all transitions exiting the initial state) and p is the probability that the initiating events lead to an accident before the system goes back to the perfect state.

In I&AB, in order to estimate p we use the "minimal content of (failure) sequences" (MCS) of the Markov chain, as it was defined in [START_REF] Bouissou | Détermination efficace de scenarii minimaux de défaillance pour des systèmes séquentiels[END_REF]. The formal definition of a MCS is given ibid, but it can be defined informally as the result of a Boolean reduction of the following fault tree: a single OR gate with one son per failure sequence, each son being presented as an AND gate over the events appearing in the sequence. Initiating events must be distinguished from other events, so that for example, the MCS of a system made of 2 components Y and Z in active redundancy is {Y_init, Z} {Z_init, Y} and not simply {Y, Z}.

For real, complex systems, the MCS can be obtained in (at least) two ways: by building a PSA type model made of event trees and fault trees, and calculating its minimal cut sets, or by building a BDMP and applying the steps described in [START_REF] Bouissou | Boolean approximation for calculating the reliability of a very large repairable system with dependencies among components[END_REF] to transform it into a standard fault tree whose minimal cut sets are the MCS of the Markov chain specified by the BDMP. In the remainder of the paper, we will therefore suppose that we have the MCS of the studied system at hand, and we will call its elements "minimal products".

I&AB general formulae

Let us suppose that there are n initiating events that can lead out the system from its perfect state. Then, according to (1), the system unreliability at time t can be found from

≤ 1 -exp -∑ λ (2)
where λie is the failure rate of initiating event ie and pie includes probabilities for all k minimal products corresponding to it. In calculations we distinguish two time intervals. The first interval is the mission time figuring in (2). The second time interval is infinite and starts once an initiating event takes place. The probability that all components in a minimal product c fail within time interval [0, ∞[ is simply the unreliability of a parallel system made of these components ∞ ; then we can use the following upper bound for pie, that will be a good approximation when all failure probabilities are small:

≤ ∑ ∞ (3)
Using the Murchland approximation, we obtain:

≤ ∑ E ∞ ( 4
)
where ∞ is the number of failures of the minimal product c on an infinite horizon. What keeps pie small is the fact that in the initial state considered for c, the initiating event is realized with probability 1, but once repaired, it never fails again, contrary to other elements of the product. (this is the approximation A1).

In order to calculate E we need to give first a few definitions. We will utilize the following reliability characteristics: -Unavailability Q(t) -the probability that a component is in a failure state at time t; -Unconditional failure intensity W(t): W(t)Δt is the mean number of failures of a component between t and t + ∆t. For markovian basic events, depending on their type, these quantities are given by the following expressions:

-Initiating event (the repair is definitive)

= exp -μ # = 0 -Failure in operation (it can fail several times) = λ λ + μ [1 -exp -λ + μ % # = λ 1 - -Failure on demand (the repair is definitive) = γexp -μ # = 0
Because of the lack of space, we will not recall here the demonstration given in [START_REF] Bouissou | Boolean approximation for calculating the reliability of a very large repairable system with dependencies among components[END_REF] that leads to the following formula, written for a minimal product c containing l failures on demand and m failures in function.

E = ∏ γ , ( × * exp -μ , + , + -+ . / (5)
with 5) assumes that a minimal product contains at least one basic event with a failure in operation. However, sometimes minimal products are only composed of basic events corresponding to failures on demand (plus one initiating event, as usually). In such a case, we suppose that these events happen at t = 0 and the unreliability for minimal product c is given by: 6)

, + = exp -+ ∑ μ ,0 ( 0 ∑ # , + ∏ ,0 + 1 0 02 1 . Equation (
∞ = Pr top = true at = 0 = ∏ γ , ( . (

I&AB formulae in the markovian case

The general equation ( 5) yields a closed form formula in the purely markovian case, where all components have constant failure and repair rates.

In order to simplify notations, we will omit the index c in the remainder of this section: we will implicitly give formulas for a single minimal product.

Taking an infinite time horizon and replacing # + by its expression given in section 2.2 for a failure in operation, equation (5) becomes:

9 ∞ = ∏ γ ( × * exp -μ + , + -+ : / (7)
with

, + = exp -+ ∑ μ 0 ( 0 ∑ λ ; 1 - 1 ; + ∏ 0 + = 1 0 02 exp -+ ∑ μ 0 ( 0 ∑ λ ; <∏ 0 + -∏ 0 + 1 0 1 0 02 = 1 .
Here we need to introduce new notations in order to simplify upcoming formulas. Let:

> = μ ;? + ∑ μ @ A @=1 B = λ ; + μ ;
Hence, replacing the functions Qj by their definitions and using these new notations, we obtain:

9 ∞ = ∏ γ ; A ;=1 ∑ λ × C ;=1 D∏ E F G F 1 0 02 * ? HIJ ∏ 1 -? HG F J 1 0 02 -+ : / - ∏ E F G F 1 0 * ? HIJ ∏ 1 -? HG F J 1 0 -+ : / K. (8)
Each integrand includes a product of functions, which can be represented in the following way:

∏ 1 -? HG F J 1 0 = = 1 -∑ ? HG M J 1 + ∑ ? HG M J ∑ ? HG F J 1 0N 1 - ∑ ? HG M J ∑ ? HG F J 1 0N ∑ ? HG O J 1 N0 1 + ⋯ + -1 1 exp -∑ B + 1 . (9)
Hence, after the integration from 0 to infinity, we obtain an alternating series, every term of which, in its turn, is a sum of fractions. For instance, the second integral results in:

* ? HIJ ∏ 1 -? HG F J 1 0 -+ : / = I -∑ IQG M 1 + ∑ ∑ IQG M QG F 1 0N 1 -∑ ∑ ∑ IQG M QG F QG O 1 N0 1 0N 1 + ⋯ … + -1 1 μ + ∑ B 1 H . ( 10
)
The first integral is calculated in a similar way, the only difference is that one should exclude current element ; from the product.

These analytical formulae ( 8) and (10) seem very cumbersome; however, they permit to considerably reduce the processing time (in comparison with a numerical integration) while ensuring an excellent accuracy.

I&AB EXTENSIONS

Taking grace times into account

In this section, the focus is on systems such that, after the loss of all components subject to random failures in a minimal product, the undesirable event is delayed by some physical process that guarantees a deterministic grace time. The spent fuel pool is a good example: after the complete loss of the cooling system, the water will heat until it boils, but this process is deterministic and it would give an excessively conservative evaluation to replace the grace time by a random delay, exponentially distributed in order to stay in the markovian framework.

We first suppose that we need to quantify minimal products containing failures of components (with the same hypotheses as in § 2.3) and a single deterministic grace time. Let Xc be the failure time of the set Ac of markovian elements of the minimal product c, Yc the time needed to repair at least one of the markovian components, starting from the state where they are all failed, and Tc the grace time. For sake of simplicity, we suppose that after a given occurrence of the initiator, the basic event corresponding to the grace time behaves like a Heaviside function: it becomes true at Xc +Tc and stays true forever (it is "not repairable"). The probability pie to go from the state where the system is just after the initiator ie to the failure state can be estimated as:

≈ ∑ 9 ∞ • Pr U > W . (11)
The total repair rate when all markovian components are failed is the sum of their repair rates. Hence

Pr U > W = exp -W ∑ μ ∈Y Z . (12)
As for 9 ∞ , it can be computed using the formulae of §2.3.

To conclude this section, let us mention that the grace delay may depend on the minimal product, and that a minimal product can contain two or more grace delays: in this case, only the last one must be taken into account (cf. §4.1.2 for more details about this choice).

Taking deterministic failures into account

If, after a non-recovered loss of cooling, the water starts to boil in the fuel pool, there is a possibility to add water coming from tanks. However, the capacity of tanks is limited and after a given time the water flow is interrupted: this is what we call a deterministic failure. After a given initiator, such failures can be considered as non-repairable: it is impossible to replenish the tanks in a short amount of time (the same applies to batteries). However, in a dynamic model, they can be associated to a repair (with a small repair rate, see discussion on that topic in §4.1.2) in order to allow the model to return to its initial state. In order to be consistent with general assumptions of I&AB, we will suppose that the "timers" associated to deterministic failures start just after the initiating event; this is obviously conservative, as in fact they start after some failures. This assumption has an immediate consequence: if there are two or more deterministic failures in a minimal product, the one associated to the greatest delay suffices to prevent the minimal product from becoming true until it happens. So, without loss of generality, we will consider in this section that we want to quantify a minimal product containing l failures on demand, m failures in function, and one deterministic failure.

We define the unavailability Q and unconditional failure intensity W, needed in equation ( 5), for this type of basic event. Q is a Heaviside function and W a Dirac distribution:

= = H / = \ 0, < / 1, ≥ / # = _ -/ .
With these notations, equation ( 5) can be written as follows (with an infinite time horizon, and omitting the minimal product index c):

9 ∞ = ∏ γ ; A ;=1 × * exp -μ + -∑ μ + ( × : / ∑ # + ∏ 0 + 1Q 0 02 1Q -+ (13)
Taking, as in § 2.3,

> = μ ;? + ∑ μ @ A @=1 and B = λ ; + μ ; 9 ∞ = ∏ γ ; A ;=1 × * exp -μ+ ∑ # + `∏ 0 + 1 0 02 × 1 : / H / a -+ + * exp -μ+ _ + - : / / ∏ 0 + 1 0 -+ Finally, 9 ∞ = ∏ γ ; A ;=1 × * exp -μ+ ∑ # + ∏ 0 + 1 0 02 1 -+ : . b + exp -μ / ∏ 0 / 1 0 (14)
The second term (the integral) of equation ( 13) can be written, using the same notations as in §2.3:

∑ λ D∏ E F G F 1 0 02 * ? HIJ ∏ 1 -? HG F J 1 0 02 -+ : . b - 1 ∏ E F G F 1 0 * ? HIJ ∏ 1 -? HG F J 1 0 -+ : . b K. ( 15
)
After integration from t0 to infinity, we obtain for the second integral the following alternate sum:

* ? HIJ ∏ 1 -? HG F J 1 0 -+ : . b = cde HI. b I - ∑ cde H IQG M . b IQG M 1 + ∑ ∑ cde H IQG M QG F . b IQG M QG F 1 0N 1 - ∑ ∑ ∑ cde H IQG M QG F QG O . b IQG M QG F QG O 1 N0 1 0N 1 + ⋯ … + -1 1 μ + ∑ B 1 H exp -μ + ∑ B 1 / .
Of course, taking t0 = 0, we obtain again the formula (10) given in §2.3.

All these formulae are so complicated that it is necessary to carefully validate their implementation in a program. The next section has two purposes: give what we believe is the result of I&AB (we cannot guarantee that our Python implementation is totally bug free) and see how I&AB approximations compare to more precise calculations made by Monte Carlo simulation (the only possible method because of deterministic times) on a truly dynamic model.

ACCURACY TESTS OF I&AB EXTENSIONS

The small examples of this section were designed just to make comparisons between I&AB and "exact" calculations performed with Monte Carlo simulation. In practice the models were input graphically as BDMPs in KB3 (see Figure 1 for an example), then processed both by I&AB and by the Monte Carlo simulator YAMS. An overview of EDF tools including KB3 and YAMS is given in [START_REF] Bouissou | Automated dependability analysis of complex systems with the KB3 workbench: the experience of EDF R&D[END_REF].

In all calculations, failures are associated to a failure rate of 10 -3 /h and repair rate of 2 10 -2 /h. The grace times and delays of deterministic failures are indicated in § 4.1 and 4.2. Table 1 gives a synthesis of all comparisons. The numbers in the first column correspond to the numbers of sections below that explain the test cases. All calculations with I&AB require a negligible time, whereas some of the Monte Carlo simulations require a few minutes for sufficient precision.

Table 1. I&AB accuracy on various simple test cases. Columns 2 and 3 are the estimations of the unreliability at 10000 hours computed by I&AB and Monte Carlo simulation (the last column is the width half of the 90% confidence interval of the YAMS result). Below are the descriptions of the test cases and comments on the results.

Grace times

Single grace time

The minimal product to quantify is {Initiator, A, B, grace_time}. In the dynamic model, there are only two sequences: Initiator, A, B, grace_time and Initiator, B, A, grace_time (A and B are in active redundancy). The grace time is successively taken equal to 25h (line 4.1.1.a of Table 1), 50h (line b), 100h (line c).

In this case, I&AB works quite well, and it is not surprising, given the fact that the dynamic model corresponds exactly to the simplifying assumptions made in § 2.1.

Two grace times

The minimal product to quantify is {Initiator, A, grace_time_1, B, grace_time_2}. In the dynamic model, there is only one sequence: Initiator, A, grace_time_1, B, grace_time_2. The grace time is fractioned, and the component B can fail only after the failure of A and the end of grace_time_1. The two grace times (in hours) are successively taken equal to (5, 20) (line 4.1.2a of Table 1), (20, 5) (line b), (15, 35) (line c), (35, 15) (line d), (30, 70) (line e), (70, 30) (line f). Note that in the dynamic model, the basic event grace_time_1 is considered as repairable (with repair rate equal to 1/250h), so that after an initiating event, the system can return to its initial state provided it does not reach the undesirable event; the value chosen for the repair rate is not sensitive as long as the mean time to repair components is much smaller than the mean time to repair the grace time: in such a case, after a given occurrence of the initiator, the grace time can be considered as "not repairable" just like in I&AB. In the simulation model, the order of the two grace times makes a difference if they are not equal. In I&AB, it is also the case because only the last grace delay is taken into account. We have also tested the idea of taking the sum of the two grace delays like a single one in I&AB: it yields results much closer to those of the dynamic model, but this approximation can produce optimistic results in some cases (for case f the result is 5.85 10 -5 ). Intuitively, this is due to the fact that in the dynamic model only the last grace delay is competing with all repairs of the markovian elements of the cut set. Cf. also § 5.

Deterministic failures 4.2.1 Barriers in active redundancy

Let us consider a little hydraulic system modeled by the BDMP below: When the initiator Leak occurs, the two barriers (each one composed of a pump and a tank) are activated. The undesirable event occurs if, before the repair of the leak, the two pumping systems are lost, either because of a random failure of the pump, or because the tank is empty. The failure and repair rates for random events are as described at the beginning of §4, except that the repair rate of the Leak is 0.1/h in order to get small enough probabilities.

The results given in Table 1 correspond to the following values for the times after which Tank1 and Tank2 are empty: (40, 30) (line 4.2.1a), (80, 60) (line b), (150, 100) (line c). Note that the order of the two numbers is not important here, because of the symmetry of the two barriers. I&AB performs quite well on this example, where the minimal product containing the two deterministic failures is dominant. In the dynamic model as well as in I&AB, the amount of water in the biggest tank is the most influent parameter.

Barrier 2 activated on failure of barrier 1

In this case, in the dynamic model, the functioning times of the two tanks add up, unless a failure of pump1 forces to start barrier2 before depletion of tank1. It is therefore not surprising that I&AB is more conservative in this case than when the two barriers are in active redundancy. The BDMP corresponding to this case is not shown, because it is the BDMP of Figure 1 with just one additional trigger (red dotted line), going from gate Barrier1_lost to gate Bar-rier2_lost. There is no need to re-run the calculations with I&AB, since for this method, this case gives the same results as the previous one (active redundancy of barriers). But here, the capacities of the two tanks are not exchangeable in the dynamic model, this is why we ran YAMS with the following couples of values for deterministic delays: (40, 30) (line 4.2.2a), (30, 40) (line b), (80, 60) (line c), (60, 80) (line d), (150, 100) (line e), (100, 150) (line f). The unreliability increases a bit when the greatest delay is the last one. Going from line a to f, the results of I&AB range from extremely conservative (by a factor 10) to acceptably conservative (by a factor 2). On the other hand, using the sum of the delays instead of the greatest cannot be recommended because it could lead to optimistic results.

DIFFERENCES BETWEEN GRACE TIMES

AND DETERMINISTIC DELAYS In a dynamic model like a BDMP, both grace times and deterministic delays are represented as leaves associated to a deterministic time to failure. So the difference between those two concepts is not obvious. In essence, the difference between a grace delay and a deterministic failure is that: -Once the grace delay has started, whatever happens on the system can only postpone (case of a repair) the undesirable event, or leave it unchanged (case of a failure); -In the case of a deterministic failure, whatever happens on the system can only make the undesirable event happen sooner (case of a failure), or leave it unchanged (case of a repair).

The I&AB theory makes a very clear distinction between the two concepts, because it considers that the grace time starts when all other components of the cut set have failed, whereas the timer of a deterministic failure starts just after the initiator. An intermediate grace time such as in the example of § 4.1.2 corresponds to none of these cases, this is why in I&AB it should be simply ignored. It is the user's responsibility to mark leaves as grace delays, deterministic failures or "to be ignored" in the BDMP before transforming it into input data for I&AB.

On a large model, it is probable that the few minimal products with a too conservative quantification will be "hidden in the crowd" and that the global result will not be much affected.

APPLICATION TO THE SPENT FUEL POOL

To perform all our tests so far, we have used the implementation of I&AB that we described in [START_REF] Bouissou | Boolean approximation for calculating the reliability of a very large repairable system with dependencies among components[END_REF]. It is not the most efficient because it separates the search for minimal products from their quantification, therefore preventing the use of a probability threshold to discard at an early stage in the calculations most minimal products, as it is done by the MOCUS algorithm [START_REF] Fussell | A new methodology for obtaining cut sets for fault trees[END_REF]. In spite of this limitation, we have been able to demonstrate impressive performances of I&AB in the spent fuel pool application.

We have built a model relative to the spent fuel pool of the European Pressurized Reactor and its support systems. Although less detailed than a classical PSA model, the BDMP we have built takes into account all dependances due to standby redundancies, common cause failures, sharing of electrical sup-plies… The model takes into account both the grace time of 14 hours before boiling of the water and deterministic failures of tanks used to replace evaporated water.

This BDMP (326 leaves, 77191 minimal products of order up to 6) could be processed by I&AB in a few minutes on a laptop. This model happened to be also quantifiable by YAMS: the Monte Carlo simulation gave a failure probability smaller than the result of I&AB by a factor around 2, but the calculation took 25 minutes to reach a 10% precision with 95% of confidence on the same machine.

Besides, with Monte Carlo simulation, it is very hard to get qualitative results: for that particular model, there is only one dominant sequence and all other sequences are much less probable: it would require many hours of simulation to get results comparable to the, say, 10 most probable minimal products that are easily identified by the I&AB method.

I&AB is an analytical method for the reliability calculation of large repairable systems with dependences between components. Two kinds of models can serve as input for this method: BDMPs or standard nuclear PSA models complying with the fault tree linking method. Both of them can be transformed into a set of minimal products that are the basis of the calculation. I&AB as it was described in [START_REF] Bouissou | Boolean approximation for calculating the reliability of a very large repairable system with dependencies among components[END_REF] cannot readily be used for the fuel pool case, because for this system, there are two kinds of deterministic delays that must be taken into account: grace times, and deterministic failures due to the limited capacity of water tanks.

In the present paper, we have given two theoretical contributions: the analytical formulae of the I&AB method (so far, they were only available in the French patent file FR3044787) and their extension in the case of deterministic delays. In addition, we have shown on several examples that the extended method can yield reasonably conservative results, in times incomparably shorter than Monte Carlo simulation.

Thanks to a partnership between EDF and Lloyd's Register, I&AB will soon be available for the large community of users of the RiskSpectrum PSA tool. This could revolutionize PSA praxis in upcoming years. 9 ACKNOWLEDGEMENT This paper is based on work done in collaboration with Olga Hernu, the co-author of the I&AB method and patent file [START_REF] Bouissou | Boolean approximation for calculating the reliability of a very large repairable system with dependencies among components[END_REF].

Figure 1 .

 1 Figure 1. BDMP modeling a system with bounded capacities


Geoffroy Carpier

Patrice Cohen

published or not. The documents may come

ABSTRACT

In 2015, the National Institutes of Health (NIH) centre dedicated to medical research on CAM, formerly the National Center for Complementary and Alternative Medicine (NCCAM), changed its name to the National Center for Complementary and Integrative Health (NCCIH). Instituting CAM as adjuncts rather than alternatives to conventional care, the political decisions behind this semantic shift reveal processes of re-legitimisation after crises as well as the critiques and controversies federal institutions had to face in the field of medical research on CAM from the 1990s until today.

These re-legitimisations at the federal level now revolve around the emerging project of 'integrative health' in the U.S. in answer to non-federal and multiform configurations taken by the promotion and practice of 'integrative medicine' (consortia, academic hospitals and research units, private clinics, professional groups, etc.). 'Integrative medicine' has already been through processes of legitimisation since the 1990s (such as evidencebased and standardised practices). In 2008, 'integrative medicine' became an official physician specialty. In fact, both federal and non-federal legitimisations towards integration are now being articulated together.

Based on a networked ethnography of those institutions and their related network of interactions, this presentation will show how those double processes of legitimisation are still set in place through interactive institutional arrangements. Nonetheless, this double legitimisation towards 'integrative health' does not always meet the general consensus and is confronted by oppositions and resistances from both federal and non-federal agents and institutions, notably when cancer is concerned. These institutional arrangements bring into question not only conflicting places assigned to CAM within the American health system but also the construction of various CAM categories and the particular place assigned to them within research protocols and their translationality, thus fostering new challenges to medical research.


Barter and the Origin of Money and Some Insights from the Ancient Palatial Economies of Mesopotamia and Egypt

Keywords: Money, Unit of Account, Medium of exchange, Barter, Palatial economies, Transaction costs, Mesopotamia, Sumerian city-states, Ancient Egypt, Phoenician city-states

The "Metallist" origin of money, used as a medium of exchange, is based on the presumed low efficiency of barter. However, barter is usually ill-defined and archaeological evidence about it is inconclusive. Moreover, the transaction costs associated with barter seem to have been exaggerated by metallists. Indeed, the introduction of a unit of account reduces the complexity of the relative prices system usually associated with barter. Similarly, in-kind transactions have timing constraints which are often labeled as "the double coincidence of wants"; with a system of debt and credit, delayed exchange, that is lending, is possible. Such adaptability of barter is confirmed by the study of Mesopotamian and ancient Egyptian palatial economies. They provide evidence that non-monetary transactions have persisted during millennia, challenging the metallist vision about the origin of money.

Introduction

Money is a fascinating object which, apart from economists, has attracted the attention of other social scientists, especially philosophers, historians and archaeologists. For the latter, the introduction of money in past societies represents one of their major socio-economic changes -as does the introduction of agriculture or metalworking. This should, therefore, lead them to analyze it by means of the usual set of queries, when and where, why and how? However, this is not the case, i.e. this set, or package, of usual queries is not well-tailored for the study of the origin of money.

It is widely agreed by scholars that, for southwestern Asia, coinage was introduced for the first time in Lydia1 around the seventh century B.C.E.. Such evidence seems to provide a convincing answer to the when and where queries. However, it does not explain why it was introduced. Before coinage, other forms of money existed. Indeed, coining was designed to facilitate the free transferability of metallic money by providing a guarantee of the fineness and weight of metal uses as money. Pre-coinage currencies were not restricted to pieces of metal, i.e. various commodities, such as salt, cattle, barley (...) could also be considered as primitive monies [START_REF] Einzig | Primitive Money[END_REF][START_REF] Geva | From commodity to currency in ancient history: On commerce, tyranny and the modern law of money[END_REF][START_REF] Grierson | The Origins of Money[END_REF][START_REF] Powell | Money in Mesopotamia[END_REF][START_REF] Quiggin | A Survey of Primitive Money[END_REF].

The problem with all these primitive monies (including metal ingots) is that there were used for two different purposes, as a means of exchange, and as commodities; therefore, it is very difficultalmost impossiblefor archaeologists to identify primitive money from artefacts provided by archaeological excavations. For instance, a retrieved silver ingot could have been kept either for casting jewelry or to be used as a medium of future transactions. Thus, before the introduction of coinage is considered, the when and where queries about the origin of money remain unanswered. This is because unlike agriculture or metalworking, which are both from a mixed-product of nature and culture, money is a purely cultural invention, an "idea". Therefore, since the functions of money evolved and because much of this evolution was not as a result of conscious thought, it is vain to try to find out when and where this idea emerged.

Given this previous restriction on the determination of the origin of money, scholars have focused their attention on the two remaining queries: why money has been introduced in past societies, and how such an introduction unfolded? Starting in the Classical period in ancient Greece, attempts to answer these questions have led to controversies among famous philosophers which are still alive today. On the one hand, Plato (1992) suggested that currency should be regarded as an arbitrary "symbol" 2 to help exchanges. He was against using precious metals (such as gold and silver) because, in his opinion, the value of currency should be independent from the material from which money is made. On the other hand, for [START_REF]Politics[END_REF] currency was a third merchandise with intrinsic value rather than an abstract monetary sign. For him, the inconvenience of barter led people in ancient societies to choose metals as a means of exchange, because of their physical features. This Aristotelian or "metallist" vision of currency has been dominant over the Platonic vision until nowadays. Indeed, and as shown in economic textbooks, the origin of money is usually presented according to the metallist vision by "orthodox" or mainstream economists, i.e. economists who firmly believe in the virtues of the market-economy (Clower, 1969;[START_REF] Jevons | Money and the Mechanism of Exchange[END_REF][START_REF] Menger | The origin of money[END_REF][START_REF] North | Transaction costs, institutions, and economic history[END_REF][START_REF] Samuelson | Economics: An Introductory Analysis[END_REF][START_REF] Smith | An Inquiry into the Nature and Causes of the Wealth of Nations[END_REF]. For these economists, money, as a medium of exchange -and implicitly also as a unit of account -has been introduced in the economy owing to the lower efficiency of the barter system. Barter -pure and simple -or cashless exchange, is defined as the direct exchange of commodities (or services) between agents, without any intermediate object in the transaction (Chapman, 1980, p. 35). The presumed inefficiency of barter stems from two main transaction costs associated with it. On the one hand, unlike monetary transactions in which money is automatically a unit of account, barter does not imply the introduction of a standard of value. Then as the number of tradeable goods present in the economy increases, the number of relative prices is growing exponentially. On the other hand, since there is no medium of exchange, the transactions necessitate the double coincidence of wants. Even in an economy with a large number of goods and agents, such double coincidence of wants can hardly happen without incurring important searching costs.

2 Some contemporary authors agree with Plato's vision even though they used different expressions such as "Money as a metaphor" [START_REF] Cribb | Money as a metaphor 1: Money is justice[END_REF] and "Money is a creature of law" [START_REF] Knapp | The State Theory of Money[END_REF].

From the mid-eighteen century onward, orthodox economists have supported the metallist vision of the origin of money, because it matches with the economic system they were describing and promoting, namely capitalism. Indeed, money fosters market transactions and the division of labor as well as it promotes economic prosperity. Even though capitalism has been the dominant mode of production only for the last few centuries, scholars are divided about how economies operated in past societies [START_REF] Davies | Ancient economies: Models and muddles[END_REF]. On the one hand, there are the "modernizers" and the "formalists" who share the view of orthodox economists that ancient economies were similar in kind to modern ones and only different in degree, i.e. they were driven by the rational behavior of self-interested optimizing individuals. On the other hand, there are the "primitivists" and the "substantivists" [START_REF] Polanyi | The Great Transformation: The Political and Economic Origins of Our Time[END_REF] who consider that ancient economies were socially embedded or mainly driven by institutions and social obligations, i.e. that the role of individuals as well as markets were secondary. This controversial issue about ancient economies raises doubt about the relevance of the metallist vision for explaining the origin of money in past societies. This doubt becomes even more important when evidence about the existence of barter and pre-coinage currencies in past societies are considered. Indeed, this evidence is either lacking or ambiguous, i.e. can be interpreted according to different and even from opposite points of view. If the analysis of the evidence about barter and money is inconclusive, it is also because barter and the use of coins are not discrete caseseven if the reverse is often thought to be so. Indeed, they are both located at the extremes of a continuous spectrum which includes several intermediate cases such as different media of exchange and primitive monies.

As pointed out by Schumpeter (1972, p. 63), "whatever may be its shortcomings, this theory [Aristotle's], though never unchallenged, prevailed substantially to the end of the nineteenth century and even beyond. It is the basis of the bulk of all analytic work in the field of money".

Recently this theory has been challenged on the grounds that it is historically inaccurate. Indeed, recent anthropological studies question the idea that early societies went from a barter economy to money and instead contend that money arose to keep track of pre-existing credit relationships [START_REF] Douglas | The Philosophy of Debt[END_REF][START_REF] Graeber | Debt: The First 5,000 Years[END_REF][START_REF] Martin | Money: The Unauthorised Biography[END_REF]. It is therefore our purpose to provide some insights about its relevance for explaining the origin of money in ancient palatial economies. To do this, we assess the extent to which market exchanges are hindered by the presumed transactions costs associated with barter. Then we examine how ancient Near Eastern societies -Mesopotamian and ancient Egyptianmanaged to rely on barter for exchange, despite their growing economies. The available evidence provides some support to Plato's explanation of the origin of currency, and therefore confirms our doubt about the relevance of the metallist vision.

The Origin of Money: Metallism vs.Chartalism

As stated previously the origin of money has led to a controversy at least from the Classical period in Greece. This controversy was also present among economists, and is still present today.

According to the epoch considered, the Aristotelian vision of currency is often labeled "Metallism". Metallists believe that money developed spontaneously as a medium of exchange in order to eliminate the obvious limitations of barter. In other words, the origins and the early evolution of money are viewed as an unintended consequence of spontaneous individual actions in the context of barter. Thus, money emerged via a natural process of transaction cost minimization. Metallism was an economic principle stating that the value of money derived from the purchasing power of the commodity upon which it is based. It has deeply influenced monetary policies during the most recent centuries, at least until the end of the Bretton Woods system in the late 1970s, even though the latter issue is still controversial.

Nowadays, economists have kept the label "Metallism" even though they are perfectly aware that the value of money has nothing to do with metals. As pointed out by [START_REF] Ingham | The Nature of Money[END_REF], even though it is no longer argued that money needs to consist of a material with an intrinsic exchange-value, it is still conceptualized as a commodity since it is understood, as any other commodity, by means of an orthodox methodology in micro-economics.

On the other hand, there is the Platonic vision of currency, also called the credit theory of money [START_REF] De Bruin | Philosophy of Money and Finance Accessed June 23[END_REF]. This contends that money is a social construction rather than a physical commodity. The abstract entity in question is a credit relationship; that is, a promise from someone to repay a favor (product or service) to the holder of the token. In order to function, two further features are crucial. First, the promise must be sufficiently credible, that is, the issuer is "creditworthy". Second, the credit must be transferable, that is, others will also accept it as payment for trade. This Platonic vision of currency led to "Chartalism", a term3 coined by [START_REF] Knapp | The State Theory of Money[END_REF]. Indeed it is commonly thought that the most creditworthy issuer of money is the State. Thus, Chartalism, also called "Modern Monetary Theory" in its most recent form, is a theory which argues that money originated with states' attempts to direct economic activity rather than as a spontaneous solution to the problems with barter. It states that fiat currency has value in exchange because of sovereign power to levy taxes on economic activity payable in the currency they issue. Such claim is even grounded on some historical cases, such as for archaic Greece and ancient Mesopotamia [START_REF] Semenova | The origins of money: Evaluating chartalist and metallist theories in the context of ancient Greece and Mesopotamia[END_REF]. Even though it has fewer proponents than Metallism, some famous economists have supported it to some extent (for example, Galbraith, 2010; [START_REF] Keynes | What is money?[END_REF][START_REF] Keynes | Keynes and ancient currencies[END_REF][START_REF] Minsky | Stabilizing an Unstable Economy[END_REF][START_REF] Mitchell-Innes | What is money?[END_REF].

To some extent, the origin of the controversy between metallists and chartalists relies on different points of view about barter. The metallist view posits that individuals engaged in trucking and bartering developed money to minimize their transaction costs [START_REF] North | Transaction costs, institutions, and economic history[END_REF]) [START_REF] North | Transaction costs, institutions, and economic history[END_REF]. Hence, the adoption of money as a medium of exchange is simply considered as a technical development. One may note that the process described in Clower's example is grounded on the rationality of agents, i.e. it seems to be the outcome of an intended process decided and organized by rational agents. We contend a different view, i.e. the introduction of money is rather the outcome of social selection of the fittest media of exchange for the purpose it serves in exchange. It is a process external to individuals per se and involves social selection from sets of new possibilities as they arise. Given the presence of embedding, the overall development is independent of individual rationalism.

Ancient Economies: Formalists vs. Substantivists

In fact, the origin of the controversy between metallists and chartalists is deeper than a mere opposition of different views about barter or even money. Indeed, it is related to the tremendous controversy between formalists/modernizers and substantivists/primitivists who, when compared to modern ones, explain how ancient economies were operating [START_REF] Davies | Ancient economies: Models and muddles[END_REF].

Here again, the origin of this controversy can be understood by starting from the view metallists/orthodox economists have about barter. For them, the complexity of the relative price system and the double coincidence of wants are two main drawbacks demonstrating that economic transactions are hindered in a barter economy. Since Adam Smith seminal work (1776), it is well known that economic prosperity results from the division of labor, and that the latter necessitates that market transactionsespecially between workers who have specialized tasksshould be facilitated. Money, as a medium of exchange is therefore an important pre-requisite (as well as property rights) for the development of market transactions. Without money, market exchanges are hindered as well as the division of labor, and therefore economic growth remains lower than what has been observed during the last centuries as a consequence of the spread of capitalism. Given this previous statement, it seems that from the mid-eighteen century, the way orthodox economists have explained the origin of moneyassuming that barter inefficiency had led individuals to introduce moneyhad been chosen simply because it was consistent with their vision of the economy and the society.

Indeed, by assuming that money had been introduced thanks to individuals initiatives, and that this had ultimately led to the development of the market-economy (and capitalism), they highlighted the virtues of an egalitarian society based on individuals, i.e. a society in which State agency is lacking or merely useless.

The preceding viewassuming that the introduction of money triggered the development of markets and finally of the whole economyis shared by orthodox economists as well as by some other social scientists (especially anthropologists and historians) labeled as the "modernizers". Unlike their opponents, the "primitivists", they consider that ancient economies only differ in degree, not in kind, compared to modern economies. This dichotomy echoes another one between the "formalists" and the "substantivists". The former who mainly agree with the "modernizers", assume that economic behavior based on rational self-interested individuals and market exchanges were already the cornerstones of ancient economies. This orthodox/modernizers/formalists view is then at odds with the view contended by the primitivists/substantivists as well as by some economists labeled as "heterodox" [START_REF] Keynes | What is money?[END_REF][START_REF] Keynes | Keynes and ancient currencies[END_REF][START_REF] Marx | Capital, Foreign Languages Publishing House[END_REF][START_REF] Mitchell-Innes | What is money?[END_REF][START_REF] Schumpeter | History of Economic Analysis[END_REF]. According to the latter view, ancient economies were socially and politically embedded. In other words, individuals did not exist as relevant social entities since all their actions were constrained by various social obligations. This has led [START_REF] Polanyi | The Great Transformation: The Political and Economic Origins of Our Time[END_REF] to distinguish three modes of exchange, namely reciprocity, redistribution and market-exchange. While he agreed that these three modes of exchange co-existed at any epoch, he stressed that it was only during the last few centuries -and the spread of capitalism -that market-exchange had become the dominant one.

Polanyi's term, "the great transformation," refers to the divide between modern, marketdominated societies and non-western, non-capitalist pre-industrial societies.

As explained above the academic literature is far from having any consensus among scholars concerning what were ancient economies. Thus, if we assume that ancient economies were closer to what [START_REF] Polanyi | The Great Transformation: The Political and Economic Origins of Our Time[END_REF]1957) described, i.e. were socially embedded with very few market exchanges, then the question is whether the view of metallists/orthodox economists about the origin of money is consistent or not with such economies?

Archaeological and Ethnographical Evidence About Bartered or Monetary Transactions Are Inconclusive

Even though all scholars agree that barter is universal [START_REF] Chapman | Barter as a universal mode of exchange[END_REF], i.e. can be, in theory, organized at any place and at any moment, empirical evidence about it is quite limited. [START_REF] Humphrey | Barter and economic disintigration[END_REF] even claims that there is no evidence, historical or contemporary, of a society in which barter is the main mode of exchange. Most, if not all, the evidence we have about barter comes from ethnographic studies of remote (and often shrinking) communities who -for various reasons -are living at the margins of our capitalist and monetary modern world. Then, it is quite sure that our knowledge of barter is biased, i.e. must be quite different from the system on which all human living on earth have organized their exchanges during millennia. In other words, our empirical knowledge of barter is biased and can hardly be used to infer how economic transactions were operated in ancient societies.

As it is well known by biologists, many plants, insects or animals have a symbiotic relationships, i.e. they obtain mutual advantages from the direct exchange of resources or services. Since Homo sapiens is a 'social animal', it is not surprising to claim that barterthe direct exchange of resources or services between humanis as old as the recorded history of man [START_REF] Davies | A History of Money[END_REF]. While it is certain that barter has existed during prehistory, it remains very difficult to identify it from the archaeological records. Several reasons explain why this is so. It is likely that many commodities used, even frequently, for bartering, have let no or very few archaeological record since they were perishable (e.g. furs, salt, cattle) or have been transformed in subsequent periods (e.g. due to metal recycling). Even for non-perishable goods (such as shells, stones), researchers face several methodological problems [START_REF] Tykot | Trade and exchange[END_REF]. Indeed, even though a durable good is found in large quantities at a given place where it can be considered as "exotic", it nevertheless remains difficult to identify all the different steps associated with its chaîne opératoire. These steps include the provenance of the object, its production, transportation, use and disposal. For some objectssee e.g. the obsidian [START_REF] Tykot | Trade and exchange[END_REF])such traceability can be realized by using specific technologies (e.g. isotopic analysis); however, a fundamental mystery remains about the motivation underlying the flow of these goods [START_REF] Oka | The Archaeology of Trading Systems, Part 1: Towards a New Trade Synthesis[END_REF]. Was the presence of this type of good associated with a one-way flow or with a two-way flow? Was this flow motivated by reciprocity, redistribution or was is market-exchange? Moreover, different artefacts of the same item can be found at the same place but each of them could be there for different reasons.

According to primitivists, societies from the remote past were characterized by fundamentally distinct modes of socio-economic integration which are not found in modern days. More specifically, it seems likely that both domestic and foreign trade were marginal, at least before the Bronze Age, even though we do not know precisely to what extent it was marginal.

In addition to these problems of evidence about barter, it is widely agreed by scholars that hunting and gathering societies were based on sharing [START_REF] Benz | The principle of sharing: An introduction[END_REF], or the "rule of hospitality" [START_REF] Henry | The social origins of money: The case of Egypt[END_REF]. Indeed in most foraging societies, exchanges based on self-interest and this includes barterwere inexistent and sometimes even forbidden. Except for personal belongings, such as clothes, there was no private property in such economies. It is likely that the same social rule was present in the small farming communities of the Early Neolithic, since they were also socially organized on kin, as pre-Neolithic foraging groups [START_REF] Quiggin | A Survey of Primitive Money[END_REF]. When compared to a more advanced money, primitive monies are "all money that is not coin or, like modern paper money, a derivative of coin" (Grierson, 1977, p. 14). More precisely, and as stated by Einzig (1966, p. 317), a primitive money is "A unit or object conforming to a reasonable degree to some standard of uniformity, which is employed for reckoning or for making a large proportion of the payments customary in the community concerned, and which is accepted in payment largely with the intention of employing it for making payments." However, the available ethnographic examples of primitive monies can hardly be used to determine what has precisely happened in ancient economies. Indeed, even though a particular object is found in large quantities in the archaeological excavations at a given location, several interpretations are possible: it could have been used as either only a commodity, or as a commodity and a means of exchange, or only as money. Even if we assume that a commodity was used exclusively as primitive money, we do not really know why and how it became part of the economy. In other words, were primitive monies introduced because barter was inefficient, as claimed by orthodox economists, or was it for another reason? Or was it a result of a process of social selection?

5.

Barter: Its Motivations, Timing, and Finality.

In addition to the reasons detailed in the previous section, archaeological evidences about the existence of barter or money are inconclusive also because both concepts do not have a unique and widely agreed definition. While it is beyond the scope of the present paper to provide an analysis of the definition of money, a brief analysis of the definition of barter helps to illustrate such difficulties.

According to the Cambridge dictionary of English, the verb "to barter" is defined as "to exchange goods for other things rather than for money". 5 Even though it is clear from this definition that under barter, goods (or services) are exchanged for other goods (or services), there are three additional dimensions which remain vague in this definition.

The first is about the motivations of the agents leading to the exchange of goods. For some authors, such as [START_REF] Chapman | Barter as a universal mode of exchange[END_REF], barter should be restricted to pure economic transactions, i.e. only to market exchange. However, it is also possible to consider that exchanges motivated by social obligations or even coercion (e.g. by reciprocity or redistribution, according to Polanyi's terminology) are also barter if they are cashless.

The second dimension is about the timing of the exchange. What is implicit in the above definition of barter, is that the terms of exchange of goods are settled at the same time. This does not exclude the possibility that the goods are delivered at different times. In such a case, we should talk about delayed barter. According to Graeber (2011), "gift economies" were common, at least at the beginnings of the first agrarian societies, when humans used elaborate credit systems. In other words, if we do not allow the existence of delayed barter -and therefore of the associated debt/credit systemthen barter is a pure abstraction.

The third dimension concerns the finality of the exchange, i.e. what the goods are used for once they have been exchanged. What is implicit with the above definition of barter, is that the exchanged goods are used as goods (consumed or invested), immediately or later.

However, this may give rise to an intricate outcome. Let us consider the following example:

one may assume that a good is exchanged today and that initially its buyer wanted to consume it later. Let us now assume that for some reasons, its owner decides in the future to use this good for (the payment of) another exchange. Then this good, which is not consumed, is used in the future as a medium of exchange. In other words, the way this good is used in the future 5 https://dictionary.cambridge.org/fr/dictionnaire/anglais/barter accessed on June 13, 2019.

implies that the initial transaction should not be considered as pure barter because the latter excludes the existence of any intermediate object.

The latter situation is also useful in demonstrating that the boundaries between bartered and monetary transactions are blurred. Indeed, once a good is exchanged not for itself, i.e. not to be consumed, it becomes a medium of exchange. Once a good is exchanged mainly not to be consumed as a good but to be used as a medium of exchange, it becomes a primitive money.

The Complexity of the Relative Price System and the Unit of Account

The first presumed drawback associated with barter is the complexity of the relative price system. From a theoretical point of view, such complexity can be illustrated as follows.

Let us assume a given economy in which

N n *  
goods (and/or services) exist and can be exchanged. In a monetary economy, money is used as a medium of exchange and is also, implicitly, a standard of value. So, once one of these n goods is considered as money, the value of the (n-1) remaining goods can be expressed with respect to it. In other words, the number of relative prices in this economy is equal to (n-1).

In a pure barter economy, the value of any good must be expressed with respect to all the (n-1) remaining goods. Thus, the total number of relative prices is equal to (n-1).(n/2), given that, obviously, the relative price of a good with respect to itself is equal to 1.

While the total number of relative prices is proportional to the number of goods when money is introduced, it increases exponentially in the barter-economy. Then, in such a theoretical framework, the relative price system associated with barter is very difficult to handle.

However, one may wonder whether such limit associated in theory with barter also exists in practice? Two cases deserve special attention.

The first one is deduced from what happens in a monetary economy, as we have described previously. In such economy, the complexity of the price system has been reduced by introducing money, given the fact that one of the three functions of money is to be a unit of account. However, the converse is not necessarily true, i.e. a good can be used as a unit of account without being considered as a money, i.e. without fulfilling the two other functions of money (medium of exchange and store of value). Indeed, a unit of account is simply the unit by which the prices of all other items are quoted. Therefore, a pure and simple bartering system may be associated with a simple price system (similar to the one associated with money) as long as a unit of account has been introduced. As a remark, even though the value of the exchanged goods is expressed with respect to a standard of value, it does not mean that the latter is also exchanged during the transaction. In other words, barter can also be realized when an object of an agreeable value is used as a measuring device of the exchanged goods.

This object can be anything acceptable to the parties of the transaction; then the buyer and the seller reckon the present value of their goods against a third commodity of common use.

The second case, which is less demanding when compared to the first one, is to introduce some "set rates" or "customary rates" [START_REF] Chapman | Barter as a universal mode of exchange[END_REF]. This means that some relatives prices for instance those concerning the goods which are most frequently exchangedare set or decided arbitrarily. This case is worthwhile since it highlights the fact that the presumed complexity of the relative price system depends on the scale at which the economy is analyzed, namely either at the micro or at the macro level. Let us consider both levels.

At the micro or individual level, we may assume, especially since we consider ancient economies, that the total number of goods present in the economy was quite limited. We may also assume that, given his preferences and income (both depending on the social class he belongs to), a representative agent of such ancient economy could afford only a limited number of different goods. In other words, it is likely that an agent was used to exchange a limited number of goods, and moreover that these exchanges were repeated several times per year, month or even days, depending on the goods considered. Therefore, this agent was very aware of the relative prices of the goods he was intended to buy or to sell; then, the computation of all the relative prices was completely useless from his point of view since only a limited set of prices was relevant for him.

On the contrary, at the macro level, computing all the relative prices could be important and even necessary. However, one may wonder what does it mean to talk about the "macro level" in ancient economies? For sure it can make sense only from the development of city-states and empires, such as the ones which have emerged in Mesopotamia and ancient Egypt. For the others social organization, such as the band, the tribe or the chiefdom, according to Service's (1966) classification of the stages of social evolution, it is of no value to know all the relative prices of the goods present in the economy since most exchanges were based on either sharing/reciprocity or redistribution. Nevertheless, such knowledge was crucial in the early states which have appeared later, at the turn of the Neolithic and the metal age periods (namely during the Chalcolithic period). Indeed, Sumerian city-states as well as Pharaonic

Egypt were based on palatial economies, as were later Minoan and Mycenaean economies [START_REF] Svizzero | Economic management of Minoan and Mycenaean states and their development[END_REF]. In these palatial economies it was crucial for the administration to know all the relative prices in order to compute, to record and to enforce the payment of various social obligations (e.g. taxes, levies, corvée labor, slavery...) and to measure their wealth. Hence, it is very likely that it was in these early states that a unit of account had been introduced in order to solve the problem encountered by the barter system. Indeed, while agriculture was present in the Near East from around 10,000 B.C.E., the emergence of these early states coincides with the extensive development of irrigated agriculture, during the third millennium BC. The latter has led to the hydraulic civilization [START_REF] Wittfogel | Oriental Despotism: A Comparative Study of Total Power, Random House[END_REF], characterized by an increase of the agricultural production, an expansion of the population, the development of non-agricultural activities associated with the "urban revolution" [START_REF] Childe | The urban revolution[END_REF]. In other words, the implementation of extensive irrigated agriculture triggered an increase of the number of goods as well as of the number of persons in the economy. This would have led to a growing complexity if a unit of account had not been introduced.

The Double Coincidence of Wants and the Credit System

The second presumed drawback of barter is, for an exchange to occur, there is the necessity to have the double coincidence of wants, a term used by Jevons (1875). In fact, in-kind transactions require three conditions to occur: a) both parties must agree about the relative price or the terms of exchange, b) each party is motivated for buying the good supplied by the other party, c) the goods involved in the exchange are available immediately.

Let us consider what happens when any of these three conditions is not fulfilled.

If, unlike condition a), an agreement is not reached, even after both parties have bargained for a while, one may expect that the competitive pressures provided by the other members of the economy could finally lead both parties to agree. However, such an outcome is not certain.

What is more important is that whatever the economy, with or without money, the previous conclusion remains the same.

When condition b) is not verified, it means for instance that one party is not attracted by the good sold by the other party, whatever its price. In other words, there is no coincidence of wants. Agent A wants to buy the good sold by agent B, but B is not attracted by the good sold by A. Despite this lack of coincidence of wants, there are two situations in which agent A could nevertheless buy the good sold by B. The first, as suggested by the metallists, is to introduce a medium of exchange -which is socially accepted, for example money. In this case, A obtains the good sold by B, and B gets some money with which he/she will be able to buy the good he wants from another agent. The second situation occurs when the intermediate is not a commodity but a third person (a middleman), agent C. Then, what may happen is the following sequence of exchanges: C first exchanges with B, and then he exchanges with A. At the end of the process, A and B are satisfied (and C as well), but this process requires the coincidence of wants between B and C as well as between C and A. The question is then which situation is the more likely to occur, the first one based on money, or the second one, which includes a third person? Both situations may lead to an exchange, but it is impossible to say a priori which is the easiest one to implement. Indeed, the first situation requires money, but money has first to be socially accepted, and this is not straightforward to achieve. In the second situation, the exchanges require two coincidence of wants, and here also this adds some costs.

When condition c) is not verified, it means that there is no immediate coincidence of wants.

The problem here is about the timing, i.e. the goods can only be delivered at different dates.

For instance cherries and grapes ripen respectively in May and September, so they cannot be physically exchanged at the same date. However, both parties may agree to exchange since the delayed coincidence of wants is reached. What is needed is an agreement explaining that cherries are delivered in May for grapes which will be delivered in September. Such agreement implicitly means that a debt and credit system is introduced between both agents.

This system implies that the lender gets sufficient information about the borrower in order to be sure to be repaid on the due date. It also necessitates the definition of some compensation for the lender if, for any reason, the borrower cannot repay in due time.

The previous demonstration leads us to the following conclusion.

If there is no coincidence of wantsimmediate as well as delayedthen the exchange requires the introduction of an "intermediate". The latter can be either money or a third person. However it is a priori impossible to determine which of these two casesthe monetary transaction or the in-kind transactionis the easiest to implement in society. In other words, barter is not necessarily more difficult to achieve than monetary transactions.

If the coincidence of wants is not immediate but is delayed, then the exchange may nevertheless occur if an appropriate system of debt and credit is introduced.

Therefore, it seems that the importance of the transaction costs implied by the double coincidence of wants associated with barter has been largely exaggerated in the academic literature. Indeed, most economic activities are based on temporal processes. Production is not a one-shot event but a process which takes time, i.e. one has first to incur the costs associated with the investments in order to be able to reap the benefits provided by the production later.

Irrigated Agriculture and Complex Societies of Mesopotamia and Ancient Egypt

The general history of Mesopotamian (especially from the Early Dynastic period (2990-2300)

to Ur third dynasty (2047-1940)) economic and social development accords nicely with that of ancient Egypt (the Old kingdom, 2700-2200).

The first reason in support of this comes from the fact that both civilizations, which have emerged during the IV to the III millennia B.C.E., were located in the Near East and therefore experienced quite the same bio-geographic conditions. The latter encompass the climate, the quality of the soil, the access to fresh water, animal species suitable for domestication and plant species suitable for cultivation. As is well known, agriculture first occurred in the Near East about 10,000 BCE. The transition from foraging to farming societies was probably very slow and gradual -despite the label of "Neolithic revolution" -because farming was a trial and error process during its early ages. Mixed economies, combining food procurement and food production would have been the rule for a while [START_REF] Smith | Low-level food production[END_REF]. In this context, and despite the emergence of agriculture, the social structure remained almost unchanged during most of the Neolithic period, i.e. quite similar to the one which prevailed during the pre-Neolithic period. Band of foragers were egalitarian, i.e. their social structure was not hierarchical. With the development of agriculture, such social relationships gradually vanished; sharing and the rule of hospitality mostly disappeared and social obligations between social groups or classes became the rule. This pattern of social evolution is well documented in the academic literature and has been labeled the transition from simple to complex societies [START_REF] Tainter | The Collapse of Complex Societies[END_REF]. In ancient Egypt for instance, this transition happened in the period 4400-3000 BCE (Henry, 2004, p. 80).

The second common factor of Mesopotamian and Egyptian civilizations was that the level of agricultural production was tremendously enhanced by the building of large irrigation systems [START_REF] Wittfogel | Oriental Despotism: A Comparative Study of Total Power, Random House[END_REF], thanks to the existence of large rivers (Nile, Euphrates, Tigris). According to Malthus's law, a greater amount of agricultural production results in a higher level of population. However, such a catalytic relationship between agriculture and demography increased the dependency of the human population on food production. Since the bulk of the population became dependent on irrigated agriculture for its survival, it has also become dependent on a small group of people -let us call these "the elite" -who were able to conceive, to build and to maintain the irrigation systems (consisting mainly of canals, dykes and water tanks). Of course, this elite rapidly took advantage of the situation to impose several social obligations on the commoners (e.g. taxes, levies, corvée labor, slavery...) [START_REF] Tisdell | The ability in antiquity of some agrarian societies to avoid the Malthusian Trap and develop[END_REF]. This led to the emergence of palatial economies, i.e. to economies which were dominated by temples and palaces.

Even though they have most features in common, the palatial economies of Mesopotamia and ancient Egypt also had differences. In Egypt, the Pharaoh had total control of the society; his power was economic, political and religious [START_REF] Henry | The social origins of money: The case of Egypt[END_REF]. He, and his administration, were therefore able to collect social obligations from any Egyptian village. Such control was quite easy to monitor since most (if not all) villages were dependent on the Nile"s flows. As illustrated by the Sumerian city-states, the Mesopotamian economy was dual [START_REF] Hudson | The archaeology of money: Debt versus barter theories of money's origins[END_REF]).

On the one hand there was the rural-family economy present in hamlets and small villages.

These centers were mostly independent entities. On the other hand, there was the palatial economy comprised of temples and palaces owning land, seed corn, flocks, tools and various other commodities that were all rented to a significant part of the population. The Mesopotamian temple was the dominant social institution [START_REF] Seaford | Money and the Early Greek Mind: Homer, Philosophy, Tragedy[END_REF]. It organized the collection and redistribution of the agricultural surplus. The production was also administrated from the center the bureaucrats at the temples.

Barter, Credit and Unit of Account in Mesopotamian and Ancient Egyptian Palatial Economies.

Even though the Sumerian and the Egyptian palatial economies had different structures, they had a common thread. Unlike current governments which are debtors with respect to their population, they were creditors. Indeed they provided the population with advances, such as grain to farmers, or commodities to traders. These advances created social obligations or debts, i.e. commoners owed something to the temple. These debts were paid at some precise periods, such as, for farmers, during the harvest time, and for traders, once they came back from their trip. In fact, most economic activities, such as crop cultivation, animal husbandry, and trade are temporal processes, i.e. they take time to be achieved. They necessitate important initial investments and a delay before production can be achieved. Therefore, with such features, the immediate coincidence of wants s not verified and barter seems to be impossible. Indeed, if for instance a farmer wants to sow grain in his fields, but has nothing to barter against the seed corn he wants, he cannot start any agricultural activity. Even though the immediate coincidence of wants is not verified, the delayed coincidence of wants can hold. Then, by introducing a system of debt and credit, exchanges of goods were possible in palatial economies even though no medium of exchange was introduced because they were relying on a system of delayed exchange. It is important to note that a condition for these delayed exchanges to occur is that an agreement between the parties is reached in advance to exchange commodities.

The introduction of writing

It is commonly agreed that the concept of writing was conceived and developed in ancient ). The lease gave the tenant farmer of one particular plot of land the use of it to grow barley and to graze his goats on condition that he made the following three separate payments to the temple treasury [START_REF] Cribb | The origins of money -evidence from the ancient Near East and Egypt[END_REF]):

-a number of basketfuls of barley, representing a proportion of the grain harvested from the land, to be paid as rent, -a weighted amount of silver to pay for his right to graze goats on the land, -a specified number of goats paid to cover the costs the temple has incurred in irrigating the land.

The details of the previous agreement provide two insights. On the one hand, because this agreement was between the temple and a mere farmer, it demonstrates that a system of debt and credit was ubiquitous in ancient economies, i.e. was not restricted to high-value transactions or international trade. On the other hand, since the payments had to be made in barley, silver and goats, i.e. in various commodities, it shows that the system of debt and credit was associated with bartered transactions rather than with monetary payments.

The standardization of weights and measures

The main problem for the administration and the elite with this system of social obligations based on debt and credit was to define its precise accounting. Indeed, it was important to define these obligations, to record them and to enforce their payment in due time. It is widely agreed by scholars that it was for solving such accounting problems that writing was developed. Besides writing, the administration has also had to define various standards of measure related to weight, length, capacity and also to value. Concerning the latter, the administration of palatial economies introduced a unit of account. It is important to note that such unit of account was a "good" only used for this purpose, i.e. was not used as a medium of exchange. By doing so these administrations have resolved the problem of the complexity of the relative price system associated with barter.

In Pharaonic Egypt, this unit of account was called the Deben and was in fact a measure of weight equal to 91 grams [START_REF] Henry | The social origins of money: The case of Egypt[END_REF]). Initially, it was a weight measure of barley, then of metal (copper) and finally of silver. These changes of the goods used to define the Deben show that it was not these goods per se that were important, but the fact that it was a unit of account of all the goods of the economy. In fact, the Deben had no actual existence, as, for example does a dollar today. In Sumerian city-states, the unit of account was called the Shekel. It was also a unit of weight which initially was defined as the weight of 180 grains of barley (which corresponds to a handful of barley grains) [START_REF] Hudson | The archaeology of money: Debt versus barter theories of money's origins[END_REF]. Once again, Urukagina, king of Lagash (2400 B.C.E.), fixed the official weight standards by which all commodities were to be measured in all payments [START_REF] Cribb | The origins of money -evidence from the ancient Near East and Egypt[END_REF]):

-the talent (about 30 kg) which was divided into 60 mina, -the mina (about half kg) which was divided into 60 shekels, -the shekel (about 8.3 grams) was divided into 180 grains, -the grain (about 0.045 grams) represented the average weight of a grain of barley.

It is worth noting that the previous system of units of account was a system based on the measure of weight (and volume) and was not based on any specific commodity which could be interpreted as money. Indeed, by considering various commodities such as, for instance barley and silver, it was possible with this system of units of account to define the value of any object present in the economy. One may easily imagine that for luxury goods, their values were defined with respect to silver (or other scarce goods) while for everyday goods, such as staples, their values were most likely defined with respect to barley.

In both Mesopotamia and Egypt, their administrations introduced these units of account in order to define arbitrarily the relative prices of all the commodities. Indeed, in these palatial economies market exchange was marginal since most prices were regulated. For instance, the silver Shekel was equal in value to the monthly consumption unit of barley (which was called a bushel). In Mesopotamia also, from 2400 to 2000 B.C.E., there is much evidence of payments of many kinds based on laws issued from legal codes drawn up on clay tablets [START_REF] Cribb | The origins of money -evidence from the ancient Near East and Egypt[END_REF]. For instance, king Ur-Nammu (2047-2030 B.C.E.), founder of the third dynasty of Ur in southern Mesopotamia, is chiefly remembered today for his legal code, the oldest known surviving example in the world. This code, from which 20 laws have been retrieved on clay tablets, set the amounts due in certain payments, as compensation. His law 25 is the following:

If a man appeared as a witness in a lawsuit and was shown to be perjured he must pay 15 shekels of silver.

Similarly, the law 1 of the Eshnunnan legal code -written at the end of the third millennium by a king of the northern city of Eshnunna -lists the official prices (exchange rate) of 1 shekel of silver for several other commodities. For instance, it has to be exchanged for:

1 kor (an ancient unit of capacity) of barley, 6 mina of wool, 2 kor of salt, 3 mina of copper.

In its law 2, this Eshnunnan code defines similar relative prices in terms of barley. Law 7 defines the payment of wages, either in silver or in barley.

All these legal codes provide evidence that prices were administrated in ancient economies and that even though these prices were often defined with respect to some commodities, especially silver and barley, it does not imply that these were used during the exchanges [START_REF] Powell | Money in Mesopotamia[END_REF]. These legal codes also confirm that the debt and credit system was ubiquitous and therefore that most -if not all -transactions were in fact delayed exchange. Indeed, these codes also describes loan with interest. Law 21 of the Eshnunnan code states that:

If a man gives silver as a loan at face value, he shall receive the silver and its interest, one sixth of shekel and six grains per shekel.

Similarly, law 20 describes the payment of barley for the return of a loan and its interest.

The existence of loans with interest demonstrates that the credit system was ubiquitous in ancient economies. Money played no part since these loans and their repayments were defined in terms of commodities. For example, repayments were in terms of items such as silver and barley.

Conclusion

According to the metallists, the origin of money in the economy comes from the lower efficiency of barter. It is because transaction costs associated with barter hindered exchanges that agents adopted a medium of exchange. This view expressed in the late 19th century which is supported by orthodox or neo-classical economists, became dominant among economists as well as in other social sciences. However, this view is subject to two main criticisms. First, the metallist perspective projects the notion of a preeminence of markets and trade into ancient economies. On the one hand, unlike substantivists, we do not believe that individuals are disembedded, even though we agree that they were modern market economies and embedded ancient economies. We contend that individuals are still embedded in the current socio-economic system, possibly more so than in the distant past [START_REF] Tisdell | Economics and Environmental Change: The Challenges We Face[END_REF], but the current socio-economic system radically differs from the ancient one. Institutions, habits of thought, transactional modes, and forms of socio-economic integration which characterized past societies are not found in modern societies. With these modern institutions transplanted into ancient societies, the origins of money follow logically rather than based upon historically situated and institutional grounded inquiry. On the other hand, it is a fallacy to project today"s notions of trade and commerce in analyzing ancient societies without a good deal of qualification. These activities were both quite marginal compared to the importance they have nowadays.

Second, the metallists specify money's origins and nature in terms of purely logical reconstructions. The adoption of money -as a medium of exchange -is conceived by metallists as the outcome of a rational process, i.e. as a result of foresight or forethought by individuals. Rather than such rational choice theories of the adoption of money, we opt for a more evolutionary and adaptive approach based on the process of social selection. The use of money and its spread are not explained as the consequences of intended decisions taken by rational agents but simply because it had evolutionary advantages which were revealed quite late, as shown by the late adoption of coinage in the Near East. Nevertheless, we posit that some elites hindered the introduction of monetary exchange because it was to their advantage e.g. it enabled them to retain more political power and more easily extract a larger portion of the economic surplus.

Theseancient economies of Mesopotamia and ancient Egypt were palatial. There was very little market exchange. Barter, associated with a system of debt and credit, and including an arbitrary unit of account, was ubiquitous. Such economies, without any monetary transactions existed for millennia. Indeed, money as a medium of exchange was introduced in these economies long after the 3rdmillennium. For instance, while coinage was well known from its it was crisscrossed by trade routes connecting it with Asia, the Mediterranean, and the Indian subcontinent (Powell, 1996, pp. 225-226). What seems likely, it that the success of their system of payment -based on delayed barter and a system of units of account -postponed the adoption of primitive monies and ultimately the introduction of coinage. It is also likely that in these ancient societies, the elite (temple and palace) hampered or hindered the introduction of coinage because with its centralized system of debt and credit, their control over the whole economy was total and so the surplus extraction was easier. Other more recent historical examples strengthen this view. For instance [START_REF] Szabo | Shelling Out: The Origins of Money Accessed June 24[END_REF] quoted the following :

"From the very start, England's 17th century colonies in America had a problema shortage of coins The British idea was to grow large amounts of tobacco, cut timber for the ships of their global navy and merchant marine, and so forth, sending in return the supplies they felt were needed to keep the Americans working. In effect, early colonists were supposed to both work for the company and shop at the company store. The investors and the Crown much preferred this to paying in coin what the farmers might ask, letting the farmers themselves buy the suppliesand, heaven forbid, keep some of the profit as well."

It is because money, whatever its form, is the most liquid asset, and therefore its uses are very difficult to monitor, that elites have favored in-kind transactions, as is illustrated by the 17th century mercantilist policy which England imposed on its American colonies.

  Sumer between 3400 and 3300 B.C.E.. Similarly, writing systems also arose in ancient Egypt around 3100 B.C.E.. Mesopotamian cuneiforms as well as Egyptian hieroglyphs were both introduced in order to keep account related to crops and farm animals. By the mid third millennium B.C.E., the inhabitants of Mesopotamia and ancient Egypt were recording in writing details of payments. These writings -inscribed in cuneiform on clay tablets in Mesopotamia -list the charges made to inhabitants for the lease of temple land for agricultural use. The details of such lease agreement are provided for instance by clay tablets associated to the reign of Urukagina, king of Lagash (2400 B.C.E.

  Lydian seventh century B.C.E. adoption, it was only introduced in Egypt during the Ptolemaic period (i.e. during the last three centuries B.C.E.). Similarly, it is only at the end of the Achaemenid period (about 330 B.C.E.) that the presence of coins is attested to archaeologically in Mesopotamia. Such apparent disinterest in coinage cannot be because Mesopotamia was an economic backwater, since by the third millennium B.C.E., at the latest,

  were. Hence, it is difficult (even impossible) to define accurately to what extent barter was present in foraging groups as well as in early farming hamlets and villages. In fact, accurate knowledge about barter in practice can only be obtained from the historical period, i.e. from the period in which writing exists. As explained below, the first evidence of writings (or pre-

writings) are found in Mesopotamia (especially in Sumerian city-states) and ancient Egypt around the end of the fourth millennium B.C.E.. If, as stated previously, it remains difficultif not to say impossibleto find archaeological evidence of barter in prehistoric societies, the same can be said of money. With such claim we do not challenge the fact that money, used as a means of exchange, has been introduced in economies at some early stage of their evolution. On the contrary, we have numerous examples provided by ethnographic studies, realized on all continents, that various objects (e.g. shell, stone, metal ingots, salt, cattle...) have been used as primitive monies

There is evidence that coinage did not originate in Lydia but was imported from elsewhere; however, because Lydian coinage was the first to spread and to gain universal expansion, Lydia can be regarded as the first effective source of coinage(Geva, 1987, p. 130).

The name derives from the Latin charta, in the sense of a token or ticket.

For the sake of simplicity we present this evolution in discrete stages. However, archaeological and historical evidence support the view that evolution has rather occurred along the lines suggested.

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