Yves I Ngounou Bakam

Denys Pommeret

Non-parametric Clustering of Multivariate Populations with Arbitrary Sizes BY

Keywords: Copula coefficients, data-driven, Legendre polynomials, nonparametric clustering, smooth test

) is used to construct automatically such clusters. The procedure is data driven and depends on the asymptotic level of the test. We illustrate our clustering algorithm via numerical studies and through two real datasets: a panel of financial datasets and insurance dataset of losses and allocated loss adjustment expense.

INTRODUCTION AND MOTIVATIONS

The knowledge of the companies that dominate the capitalization of international stock markets and their classification can allow portfolio managers a much more active strategy and a better diversification of risks. In particular, the knowledge of their dependence structure makes it possible to group together various portfolios with similar risks.

In this paper, we propose a data-driven strategy to regroup portfolios or risks having the same dependence structure. Their similarities are measured through their copulas and our procedure is based on simultaneous multiple comparisons. The implementation of our clustering procedure therefore requires a multiple comparison method that has been introduced in Ngounou- [START_REF] Ngounou-Bakam | Nonparametric estimation of copulas and copula densities by orthogonal projections[END_REF]. This K-sample test is a data-driven procedure with a chi-square limit distribution making the method very fast and very easy to implement. The algorithm is based on this test procedure and is also data-driven, depending only on the asymptotic level of the test. The basic idea of this algorithm is to use the test statistics to measure the proximity between populations. If the statistics are close, it is proposed to form a cluster with their associated populations and the test procedure accepts or rejects the validity of the cluster.

Our method applies to K(≥ 2) iid sample observed on K populations, eventually paired. This is the case in the considered problem of portfolios. Our approach differs from recent based copulas clustering algorithms as for instance: the clustering methods which rely on hierarchical Kendall copula with Archimedean clusters (see [START_REF] Su | Modelling hierarchical clustered censored data with the hierarchical kendall copula[END_REF], [START_REF] Joe | Multivariate models for dependent clusters of variables with conditional independence given aggregation variables[END_REF], among others); a clustering algorithm based on the likelihood of the copula, called CoClust, which has been introduced in Di Lascio and [START_REF] Lascio | A copula-based algorithm for discovering patterns of dependent observations[END_REF] and further developed and implemented in Di Lascio and [START_REF] Lascio | CoClust: copula based cluster analysis[END_REF]; Di Lascio (2018); Di Lascio and [START_REF] Marta | Clustering dependent observations with copula functions[END_REF]; the clustering algorithms where an iid sample from a finite mixture model is usually considered (see for instance [START_REF] Kosmidis | Model-based clustering using copulas with applications[END_REF]; [START_REF] Zhang | Mixtures of gaussian copula factor analyzers for clustering high dimensional data[END_REF] and reference therein); the approach which relies on time-varying copula-based estimators via minimization of the value-at-risk (see [START_REF] De | Dynamic tail dependence clustering of financial time series[END_REF]) and the copula-based fuzzy clustering algorithm for spatial time series, called COFUST (see [START_REF] Disegna | Copula-based fuzzy clustering of spatial time series[END_REF]). All these previous works concern parametric copulas and classify each individual and not populations.

A numerical study first shows the good behaviour of the proposed clustering algorithm. We then apply the procedure on financial assets [ a detailler un peu le ou les jeux de donnees ici].

The paper is organized as follows: in Section 2 we set up notation and we recall the main result of the the test statistic presented in Ngounou-Bakam and Pommeret (2022), making the paper self-contained. Section 3 presents the clustering algorithm. Section 4 is devoted to the numerical study and Section 5 contains two real-life illustrations.

NOTATION AND TEST PROCEDURE

Let briefly recall here the test procedure proposed in [START_REF] Ngounou-Bakam | K-sample test for equality of copulas[END_REF]. Let X = (X 1 , • • • , X p ) be a p-dimensional continuous random variable with joint probability distribution function (pdf) F X that can be expressed in terms of copula as

F X (x 1 , • • • , x p ) = C(F 1 (x 1 ), • • • , F p (x p )), (1)
where F j denotes the marginal pdf of X j , and C denotes the copula associated to X. Writing

U j = F j (X j ), for j = 1, • • • , p,
we have for all u j ∈ (0, 1)

C(u 1 , • • • , u p ) = F U (u 1 , • • • , u p ), with U = (U 1 , • • • , U p )
, and deriving this expression p times with respect to u 1 , • • • , u p , we get an expression of the density copula

c(u 1 , • • • , u p ) = f U (u 1 , • • • , u p ), (2)
where f U denotes the joint density of the vector U. Write L = {L n ; n ∈ N} the set of orthogonal Legendre polynomials (see Appendix ?? for more detail). Write j = (j 1 , • • • , j p ) ∈ N p and define

ρ j 1 ,••• ,jp = E(L j 1 (U 1 ) • • • L jp (U p )), (3)
the j-th copula coefficient associated to U. Note that ρ 0 = 1 where 0 = (0, • • • , 0), and ρ j = 0 if only one element of j is non null. The sequence (ρ j ) j∈N p * permits to summarize the copula and we propose a clustering procedure based on the distances between these coefficients.

In this way assume that we observe K iid samples, possibly paired, with associated copulas denoted by

C 1 , • • • , C K .
Our aim is to regroup populations having the same copula coefficients, that is, satisfying the following equality

H 0 : ρ (i 1 ) j = • • • = ρ (i k ) j , ∀j ∈ N p * , (4)
where i 1 , • • • , i k are the label of the tested populations and ρ (i k ) stands for the copula coefficients associated to

C i k . Clearly if C 1 = • • • = C K then H 0 is immediately satisfied.
In order to implement our clustering algorithm we propose to use the statistic based on the estimation of these quantities proposed in Ngounou-Bakam and Pommeret (2022). We denote by

X (1) = (X (1) 1 , • • • , X (1) p ), • • • , X (K) = (X (K) 1 , • • • , X (K) p ),
the K continuous random variables associated to the K populations, with joint cumulative distribution function (cdf) ) , and with associated copulas

F (1) , • • • , F (K
C 1 , • • • , C K , respectively. Assume that we observe K iid samples from X (1) , • • • , X (K) , possibly paired, denoted by (X (1) i,1 , • • • , X (1)
i,p ) i=1,••• ,n 1 , • • • , (X (K) i,1 , • • • , X (K) i,p ) i=1,••• ,n K .
We assume that

for all 1 ≤ k < ℓ ≤ K, n k /(n k + n ℓ ) → a kℓ , with 0 < a kℓ < ∞. (5)
We will denote by

F (k) j
the marginal cdf of the jth component of X (k) and we write

U (k) i,j = F (k) j (X (k) i,j ).
For testing (4) we first estimate the copula coefficients by

ρ (k) j 1 •••jp = 1 n k n k i=1 L j 1 ( U (k) i,1 ) • • • L jp ( U (k) i,p )), (6)
where

U (k) i,j = F (k) j (X (k) i,j ),
and where F denotes the empirical distribution functions associated to F . Considering the null hypothesis H 0 as expressed in (4), the test procedure is based on the sequences of differences

r (ℓ,m) j := ρ (ℓ) j -ρ (m) j , for 1 ≤ ℓ ≤ m ≤ K, and j ∈ N p * ,
with the convention that r (ℓ,m) j

= 0 when only one element of j is different of zero. In order to select automatically the number of copula coefficients, for any vector j = (j 1 , • • • , j p ) we denote by

∥j∥ 1 = |j 1 | + • • • + |j p |,
its L 1 norm and for any integer d > 1 we write S(d) = {j ∈ N p ; ∥j∥ 1 = d and there exists k ̸ = k ′ such that j k > 0 and j k ′ > 0}.

The set S(d) contains all non null positive integers j = (j 1 , • • • , j p ) with norm d and such that j k < d for all k = 1, • • • , p.

We also introduce the following set of indexes:

V(K) = {(ℓ, m) ∈ N 2 ; 1 ≤ ℓ < m ≤ K}.
Clearly V(K) contains v(K) = K(K -1)/2 elements which represent all the pairs of populations that we want to compare.

We construct an embedded series of statistics as follows

V 1 = V (1,2) D(n) , V 2 = V (1,2) D(n) + V (1,3) D(n) , • • • , V v(K) = V (1,2) D(n) + • • • + V (K-1,K) D(n) ,
or equivalently,

V k = (ℓ,m)∈V(K);rank V (ℓ,m)≤k V (ℓ,m) D(n) ,
where

V (ℓ,m) k = n j∈H(k) (r (ℓ,m) j ) 2 (7)
where the set H(k) contains the k first integers of N p with respect to the order of S(d) and where

D(n) := min argmax 1≤k≤d(n) (V (1,2) k -kq n ) , (8)
where q n and d(n) tend to +∞ as n → +∞, kq n being a penalty term which penalizes the embedded statistics proportionally to the number of copula coefficients used. Moreover, we have the following relation: for all k ≥ 1 and j

= 1, • • • , c(k + 1) V (1,2) c(1)+c(2)+•••+c(k)+j = T (1,2) k+1,j , were c(k) denotes the cardinal of S = (⌈) with the convention c(1) = 0. We have V 1 < • • • < V v(K)
. The first statistic V 1 compares the first two populations 1 and 2. The second statistic V 2 compares the populations 1 and 2, and, in addition, the populations 1 and 3. And so on. To choose automatically the appropriate number k we introduce the following penalization procedure, mimicking the Schwarz criteria procedure [START_REF] Schwarz | Estimating the dimension of a model[END_REF]:

s(n) = min argmax 1≤k≤v(K) V k -kp n . (9)
We make the following assumption:

(A) d(n) (p+4) = o(q n ), (A') d(n) (p+4) = o(p n ),
and we recall here main result of Ngounou-Bakam and Pommeret (2022).

Theorem 2.1. Assume that (A) and (A') hold. Then under H 0 , s(n) converges in probability towards 1 as n → +∞. Moreover,

V s(n) / σ 2 (1, 2)) converges in law towards a χ 2 1 distribution, where σ 2 (1, 2) is given in Appendix.
It is important to note that if p n = o(n) then the test is consistent against alternative where at least one copula coefficient differs between two copulas.

CLUSTERING PROCEDURE

Clustering principle

In the sequel we propose to adapt the previous test procedure to obtain a data-driven method to cluster K populations into N subgroups characterized by a common dependence structure. The number N of clusters is unknown and will be automatically chosen by the previous procedure and validated by our testing method.

More precisely, assume that we observe K iid samples from K populations, possibly paired. The clustering algorithm starts by choosing the two populations that are the most similar in terms of dependence structure, through their copulas.

In this way, it chooses the smaller two-sample statistic. If the equality of both associated copulas is accepted these two populations form the first cluster. Then the algorithm proposes the closer population of this cluster, that is the smaller statistic having a common population index. While the test accepts the simultaneous equality of the copulas, the cluster growths. If the last test is rejected then the cluster is closed and the last rejected population forms a new cluster. One can iterate this several times until every sample is associated with a cluster.

Clustering algorithm

We can summarize the clustering algorithm as follows:

Algorithm: K-sample copulas clustering

1 Initialization: c = 1. Set S = {C 1 , • • • , C K } and S 0 = ∅ ; 2 Select {ℓ ⋆ , m ⋆ } = argmin{V (ℓ,m)) D(n) ; ℓ ̸ = m ∈ S \ c k=1 S k-1 } ; 3 Test H0 between all ρ (ℓ ⋆ ) j and ρ (m ⋆ ) j ; 4 if H0 is not rejected then 5 S 1 = {C ℓ ⋆ , C m ⋆ }; 6 else 7 STOP. There is no cluster. 8 end 9 while S \ c k=1 S k ̸ = ∅ do 10 Select {j ⋆ } = argmin{T (i,j) D(n) ; i ∈ S c , j ∈ S \ c k=1 S k };
11 Test H0 the simultaneous equality of all the ρ (i) j , i ∈ S c and ρ

(j ⋆ ) j ; 12 if H0 not rejected then 13 S c = S c {C j ⋆ }; 14 else 15 S c+1 = {C j ⋆ }; 16 c = c + 1 ; 17 end 18 end
This clustering procedure can solve several complex problems in a very short time and is useful in practice, particularly in risk management and more generally in the world of actuarial science and finance markets by making it possible to detect mutualizable risks and not mutualizable; but also to build a well-diversified portfolio.

Tuning the algorithm

As evoked in Remark ?? we can choose the penalty q n = p n = α log(n). We fix α = 1 in the proofs of this paper for simplicity. But in practice we can empirically improve this tuning factor by using the following data-driven procedure:

• Assume we observe K populations.

• We merge all populations to get only one (larger) population.

• Split randomly this population into K ′ > 2 sub-populations.

• Clearly these K ′ sub-populations have the same copula and then the null hypothesis H0 is satisfied.

• We then approximate numerically the value of the factor α > 0 such that the selection rule retains the first component, that is s(n) = 1. From Theorem ?? this is the asymptotic expected value under the null.

• We can repeat N times such a procedure to get N K ′ -sample under the null.

Finally we fix α = min{α > 0; such that s(n) = 1 for the previous N selection rules}.

In our simulation we fixed arbitrarily K ′ = 3, which seems to give a very correct empirical level. Note that this transformation only slightly modified the empirical results.

Concerning the value of d(n), the condition (A) is an asymptotic condition and from our experience choosing d(n) = 3 or 4 is enough to have a very fast procedure which detects alternatives such that copulas differ by a coefficient with a norm less or equal to d(n).

NUMERICAL STUDY OF THE ALGORITHM

Simulation design

In order to evaluate the performance of the algorithm, we consider the following classical copulas families: the Gaussian copulas, the Student copulas, the Gumbel copulas, the Frank copulas, the Clayton copulas and the Joe copulas which we denote for hereafter Gaus, Stud, Gumb, Fran, Clay and Joe respectively. For the explicit functional forms and properties of these copulas we refer the reader to Nelsen (2007) and ?. For each copula C, the sample is generated with a given kendall's τ parameter, and we denote this model briefly by C(τ ). When τ is close to zero the variables are close to the independence. Conversely, if τ is close to 1 the dependence becomes linear.

Clustering simulation

We consider the following designs:

• A100: n = 100, p = 3, K = 6 populations with 3 groups C 1 = Gumb(0.8)

and C 2 = C 3 = Gaus(0.2) and C 4 = C 5 = C 6 = Clay(0.9)

• A500 = A100 with n = 500

• B100: n = 100, p = 5, K = 4 different populations with 4 groups C 1 = Gumb(0.8), C 2 = Gaus(0.2), C 3 = Clay(0.9), C 4 = Gumb(1)

• B500 = B100 with n = 500

• C100: n = 100, p = 4, K = 5 populations with one group 5) = Clay(0.9)

C (1) = C (2) = C (3) = C (4) = C (
• C500 = C100 with n = 500

• D100: n = 100, p = 2, K = 10 populations with two unbalanced groups

C 1 = C 2 = • • • = C 9 =
Clay(0.9) and C 10 = Gumb(0.9)

• D500 = D100 with n = 500

We applied the clustering algorithm described in Section 3. The results are summarized below:

• Results for A100:

-In 82.5 % of cases the algorithm found 3 groups. In such cases, 74 % of the time it was the 3 correct groups.

-In 11.4 % of cases the algorithm found 4 groups -In 5 % of cases the algorithm found 2 groups -In 0.1 % of cases the algorithm found 5 groups.

-Note that the first group (with the Gumbel copula) was well identified 99 % of the time.

• Results for A500: The three groups were well identified in 92 % of cases. In other cases the algorithm essentially obtained 4 groups (merging populations of the second and the third group).

• Results for B100: In 78 % of cases the null hypothesis was rejected and we obtained 4 different groups. In other cases the algorithm merged two groups (Clayton with Normal or Clayton with Gumbel) and then proposed 3 clusters.

• Results for C100: In 70 % of cases the algorithm found one group. In other cases it gave two groups.

• Results for D100: More than 80% of cases the algorithm found the 2 correct groups. In other cases the algorithm found 3 group obtained by a rejection of one of the 9 similar populations.

REAL DATASETS

Financial data

The knowledge of the companies that dominate the capitalization of international stock markets and their classification can allow portfolio managers a much more active strategy and a better diversification of risks. We build 33 portfolios.

From the 500 component stocks of the S&P 500 stock market index, which are issued by 500 large capitalization companies traded on American stock exchanges, we choose in each sector following the Global Industry Classification (there exists 11 stock market sectors)

• the stocks index of the 3 most high weighted companies. We denote Sih, i = 1, • • • , 11 hereafter,

• the stocks index of the 3 companies with the middle weight. We denote

Sim, i = 1, • • • , 11 hereafter,
• the stocks index of the 3 companies with the lowest weight. We denote Siℓ, i = 1, • • • , 11 hereafter.

Table 6 presents the weight, symbol, company and sector of each selected stock index.

The data employed are weekly closing adjusted prices from January, 26 th , 2006 to December, 30 th , 2021 for a total of 825 observations. Data are available from Yahoo Finance and we consider the rate returns series by using the standard continuously compounded return formula. We note that each price of stock is expressed in the reference country currency.

The application of non-parametric tests of randomness [START_REF] Wang | Nonparametric tests for randomness[END_REF]; Cho and White (2011); Gibbons and Chakraborti (2014)) to these weekly rates of return for each of the 33 stocks in Table 6 reveals that there is no evidence that these series are not iid.

We begin by considering the populations (denoted pop in Table 6) of each group (high (h), middle (m) and lower (ℓ)).

Applying the clustering procedure with nominal level α = 5%, we obtain 6,4 and 8 clusters of group ℓ, group m and group h, respectively. The Figures 1,2 and 3 displays the dendrogram of groups (Grp.) ℓ, m and h respectively. In the three dendrogram we observe that the sector Material is isolated. Moreover at 1% level (see Figures ?? ?? and ??), the number of clusters and the elements of each cluster remain unchanged. But it is clear that moving this level is an interesting way to reduce or increase the number of clusters. By looking at the three groups, we now ask whether if there are populations in different groups of similar dependence structure. To this end, we apply the clustering algorithm to all 33 populations with 5% nominal level. We get 12 clusters of populations and the associated dendrogram is presented in Figure 4. We observe that clusters C4,C5 and C9 contain only the populations of group ℓ and clusters C8, C11 and C12 only the populations of group h.

We thus obtain a way to group stocks with the same dependence structure into homogeneous portfolios, while forcing these portfolios not to have the same behavior. This allows for risk diversification, for example.

Insurance data

Insurance is an area in which the knowledge of the dependence structure between several portfolios can be useful in pricing particularly for risk pooling or price segmentation. As an illustration purposes, we consider the well-known example of pricing insurance contracts involving pairs of dependent variables which consist to compute the premium of a reinsurance treaty on a policy with unlimited liability, some retention level of the losses and a prorata sharing of ALAEs. ALAEs in this context are types of insurance company expenses that are specifically attributable to the settlement of individual claims such as lawyers' fees and claims investigation expenses. The database at issue is the SOA Group Medical Insurance Large Claims Database over the period 1991-92 and is available online at the web page of Society of Actuaries. The database includes more than 171,000 claims of 25, 000 or more, representing over $10 billion in total charges with information collected from 26 insurers. Each row of the database presents a summary of claims for an individual claimant in fields. Fields include diagnosis, type of coverage (HMO, PPO, Indemnity, etc.), claimant status (E-employee or D-dependent), claimant gender (M-male or F-Female) claimant age and charges split into hospital and non-hospital. We refer to [START_REF] Grazier | Group medical insurance large claims database collection and analysis[END_REF] for a detailed and thorough description of the data.

Here, we deal with the 1991 data of females, insured by a Preferred Provider Organization (PPO) plan. We split the variables losses (hospital charges) and ALAEs (other charges) by ten-year age groups shown in Applying our algorithm procedure at 5% level, we obtained four clusters and the dendogram is presented in Figure 5. It appears that the dependence structure of claim charges change over age where it shows that the status of the policy holder is irrelevant and that premiums charged to both types of individuals should be the same if the size of the observations are substantially identical.

Figure 1 :Figure 2 :

 12 Figure 1: Clustering of group ℓ at 5% level. c 1 , • • • , c 6 denote the clusters and s 1 , • • • , s 11 are defined in Table6.

Figure 5 :

 5 Figure 5: Dendogram of SOA91-Female at 5% level. C 1 • • • C 4 denote the cluster.

Table 2 :

 2

	1	2	3	4	5	6	1	2	3	4	5	6
	1 100 0	0	0	0	0	1 100 0	0	0	0	0
	2	100 100 0	0	0	2	100 73 29 30 29
	3		100 0	0	0	3		100 22 25 21
	4			100 100 100	4		100 78 82
	5				100 100	5				100 79
	6					100	6					100
	Table 1: Population associations (in %) under model A100 (n=100). Left: theoret-
	ical; Right: observed. The true associations are {1}; {2, 3}; {4, 5, 6}.
	1	2	3	4	5	6	1	2	3	4	5	6
	1 100 0	0	0	0	0	1 100 0	0	0	0	0
	2	100 100 0	0	0	2	100 93	0	0	0
	3		100 0	0	0	3		100 0	0	0
	4			100 100 100	4		100 99 99
	5				100 100	5				100 100
	6					100	6					100
			1	2	3	4	1	2	3	4
		1 100 0	0	0	1 100 0	0	0
		2		100 0	0	2	100 12 11
		3			100 0	3		100 10
		4				100	4		100
	Table 3: Population associations (in %) under model B100. Left: theoretical; Right:
	observed. The true associations are {1}; {2}; {3}; {4}.

Population associations (in %) under model A500 (n=500). Left: theoretical; Right: observed. The true associations are {1}; {2, 3}; {4, 5, 6}.

  • • • s 11 are defined in Table 6. Clustering of group h at 5% level. c 1 • • • c 8 denote the cluster and s 1 • • • s 11 are defined in Table 6

	Information Technology Communication Services Health Care Energy Utilities Real Estate Figure 3: Sectors Pop Symbols S1h AAPL MSFT NVDA S1m PAYX CDNS MCHP S1l FFIV JNPR DXC S3h GOOGL GOOG VZ S3m WBD EA MTCH S3l DISH LUMN IPG S5h UNH JNJ PFE S5m BAX A IDXX S5l UHS XRAY DVA S7h XOM CVX COP S7m OXY VLO WMB S7l CTRA MRO APA S9h NEE DUK SO S9m ES DTE EIX S9l AES NI PNW S11h AMT PLD CCI S11m EQR ARE VTR S11l REG FRT VNO	Grp. h Companies Apple Inc. Microsoft Corporation NVIDIA Corporation Paychex Inc. Cadence Design Systems Inc. Microchip Technology Incorporated F5 Inc. Juniper Networks Inc. DXC Technology Co. Alphabet Inc. Class A Alphabet Inc. Class C Verizon Communications Inc. Warner Bros. Discovery Inc. Series A Electronic Arts Inc. Match Group Inc. DISH Network Corp. Class A Lumen Technologies Inc. Interpublic Group of Companies Inc. UnitedHealth Group Incorporated Johnson & Johnson Pfizer Inc. Baxter International Inc. Agilent Technologies Inc. IDEXX Laboratories Inc. Universal Health Services Inc. Class B DENTSPLY SIRONA Inc. DaVita Inc. Exxon Mobil Corporation Chevron Corporation ConocoPhillips Occidental Petroleum Corporation Valero Energy Corporation Williams Companies Inc. Coterra Energy Inc. Marathon Oil Corporation APA Corp. NextEra Energy Inc. Duke Energy Corporation Southern Company Eversource Energy DTE Energy Company Edison International AES Corporation NiSource Inc Pinnacle West Capital Corporation	C1 C2 C3 C4 C5 C6 C7 C8 Weights Sectors Pop Symbols S4 S7 S9 S8 S6 S11 S5 S1 S2 S10 S3 659.67 Consumer Discretionary S2h AMZN 582.47 HD 133.75 MCD 11.26 S2m GPC 12.26 BBY 11.47 POOL 2.85 S2l PENN 2.88 RL 2.50 PVH 192.14 Financials S4h JPM 178.22 BAC 61.40 WFC 11.78 S4m MTB 11.14 AMP 6.42 TROW 1.57 S4l ZION 3.27 BEN 3.60 IVZ 135.88 Consumer Staples S6h PG 135.63 KO 86.10 PEP 10.79 S6m SYY 11.20 STZ 9.61 KR 2.59 S6l HRL 2.46 TAP 1.71 CPB 117.49 Industrials S8h UNP 97.79 RTX 42.47 HON 17.82 S8m RSG 15.28 ODFL 12.90 LUV 8.18 S8l AOS 6.94 ROL 4.91 ALK 43.23 Materials S10h LIN 24.95 SHW 22.94 NEM 9.09 S10m PPG 7.38 ALB 7.54 BALL 4.24 S10l AVY 3.51 EMN 2.53 SEE American Tower Corporation Prologis Inc. Crown Castle International Corp Equity Residential Alexandria Real Estate Equities Inc. Molson Coors Beverage Company Class B Companies Amazon.com Inc. Home Depot Inc. McDonald's Corporation Genuine Parts Company Best Buy Co. Inc. Pool Corporation Penn National Gaming Inc. Ralph Lauren Corporation Class A PVH Corp. JPMorgan Chase & Co. Bank of America Corp Wells Fargo & Company M&T Bank Corporation Ameriprise Financial Inc. T. Rowe Price Group Zions Bancorporation N.A. Franklin Resources Inc. Invesco Ltd. Procter & Gamble Company Coca-Cola Company PepsiCo Inc. Sysco Corporation Constellation Brands Inc. Class A Kroger Co. Hormel Foods Corporation Campbell Soup Company Union Pacific Corporation Raytheon Technologies Corporation Honeywell International Inc. Republic Services Inc. Old Dominion Freight Line Inc. Southwest Airlines Co. A. O. Smith Corporation Rollins Inc. Alaska Air Group Inc. Linde plc Sherwin-Williams Company Newmont Corporation PPG Industries Inc. Albemarle Corporation Ball Corporation Avery Dennison Corporation Eastman Chemical Company Sealed Air Corporation Ventas Inc. Regency Centers Corporation Federal Realty Investment Trust Vornado Realty Trust	Weights 286.65 91.66 53.55 5.65 5.17 4.62 1.52 1.36 1.44 110.32 74.88 50.74 9.19 8.82 8.47 2.46 2.15 1.89 101.38 71.55 67.62 12.25 11.49 10.08 3.90 2.96 2.79 40.32 41.10 38.30 8.15 7.02 7.68 2.31 2.31 1.71 48.08 18.91 15.57 8.75 8.98 6.83 4.08 4.02 2.71 33.82 26.80 23.70 7.55 6.98 6.51 2.99 2.30 1.59

Table 6 :

 6 33 components of S&P500

Table 7

 7

	.

Table 7 :

 7 Age groups of females in SOA91

 6.


William Carlos Williams

Allen Ginsberg

Alexandre Ferrere

Neal Cassady

Mechanics And Poetics

like we will see in "Howl"

according to Allen Ginsberg, Williams did not see the "strength and gaiety there is beyond"20 the poem.

The relation between Ginsberg and Williams began when Ginsberg, as an admirer, wrote to Williams "in the late forties". 21 Indeed, in Ginsberg's reading list of the late forties, we can find several mentions of Williams' books like for example Collected Poetry 1921-1931 or The Wedge in July 1946, 22 Paterson Book 2 in August 1946 23 or Paterson Book 1 in September 1946. 24 Allen Ginsberg would also read Williams in August 1954 ("Complete Collected Poems", "The Build Up (Novel)", "The Desert Music" 25 ), in April-May 1955 ("Selected Essays" 26 ) and between August and December 1956 ("Kora in Hell" 27 ). Of course, those reading lists, distant from several years, show the lingering admiration Allen Ginsberg maintained regarding Williams. What is more is that Allen Ginsberg wrote a "review of William Carlos Williams' Paterson (Book 1) for the Passaic Valley Examiner […] expecting to catch the eye of Williams" 28 in September 1946. This reveals the direct, almost immediate impact and fascination Allen Ginsberg had on Williams, which is maybe why Ginsberg wrote in his journals: "Dedicate New Book if any ever to Williams". [START_REF] Ginsberg | Journals Mid-fifties[END_REF] Moreover, Allen Ginsberg appeared to believe in being the only one with Williams to "stand so solidly on terra firma". 30 He also wrote to his father that "Williams stands out as the only beautiful soul among the great poets who has tearfully clung to his humanity […]". [START_REF] Ginsberg | Family Business: Selected Letters between a Father and Son[END_REF] This link between them is mentioned in a 1956 letter to Mark Van Doren, in which Allen Ginsberg declared that he "wrote a long poem still Williams style", referring to "Siesta In Xbalba" [START_REF] Tytell | Naked Angels: Kerouac, Ginsberg[END_REF] written in 1954. Indeed, the structure of the poem is close to some of Williams' poems. This is revealed by the use of triadic verses [START_REF]A group of three verses[END_REF] and of short lines in order to mimic the natural breath:

Jump in time to the immediate future, another poem: 34 In fact, in another letter to John Hollander of 1958, Allen Ginsberg explained that this poem was "fragments of mostly prose" of his journals then re-arranged on the page. 35 According to Ginsberg's biographer Barry Miles, it was Williams who "suggested the poetic possibilities of his journal prose"36 which led to the composition of Ginsberg's "The Bricklayer's Lunch Hour" 37 in 1947. Allen Ginsberg talked about this idea in an interview: "I went over my prose writings, and I took out little four-or five-line fragments [...]". 38 He also recommended this method to Herbert Huncke in a 1965 letter. [START_REF] Ginsberg | The Letters[END_REF] This notion of arrangement is very important when it comes to analyzing the poetry of Allen Ginsberg regarding Williams' influence. In fact, even Louis Ginsberg recommended his son reading Williams on this idea of arrangement: "All art is arrangement (see W.C. Williams)". [START_REF] Ginsberg | [END_REF] For example, the poem "For The Soul of The Planet is Wakening" published "before September 21, 1970" [START_REF] Ginsberg | [END_REF] is a re-arrangement of the end of a text written on "Dec. 14-15, 1969". 42 This is also the case for the poem "Her Engagement", which is according to Bill Morgan a "prose journal description […] created in 1952" which "reappeared as a poem in 1955". [START_REF] Ginsberg | Wait Till I'm Dead: Uncollected Poems[END_REF] Concerning the poem "Siesta in Xbalba", it is indeed made of lines extracted from Ginsberg journals and, according to him, it shows "no improvements on Williams". [START_REF] Ginsberg | The Letters[END_REF] For example, the passage below is taken from his 1953 journals:

But Deathhead in front of me on portal's here and thinks its way thru centuriesreveal to me, eyesee, the thought of the same night I sit in sat once and many times before by artisan other than I [...] and only the crude skull figurements left with its wornaway plumes and indecipherable headdresses of intellect and thought [...] [START_REF] Ginsberg | Imagism is an Anglo-american poetic movement of the 20 th century[END_REF] This very extract had been rearranged in the poem and became a time and space transcending poetic meditation: but deathshead's here on portal still and thinks its way through centuries the thought of the same night in which I sit in skully meditation sat in many times before by artisan other than me […] and only the crude skull figurement's gaunt insensible glare is left with broken plumes of sensation headdresses of indecipherable intellect, [...] 46 The semantic shift from journals to a poem is interesting to analyze. Indeed, there are several changes that show a deliberate choice with a poetic tool giving more importance to sensations than to precise meanings. For example, as written above, Allen Ginsberg wrote in his journals "indecipherable headdresses of intellect and thought". This later becomes "headdresses of indecipherable intellect" in the poem. The "headresses" are not "indecipherable" anymore, whereas the "intellect" becomes conversely "indecipherable". In a way, the new word targeted by "indecipherable" adds mystery to mystery, and gives birth to new sensations. By underlining the mysterious ways "intellect and thought" work, a mystic sensation and an invisible sense of impenetrable eternity arise. This is firstly because the intellect and thoughts are inner perspectives which involve interpretations, and then because even when interpreted, they are lost in time. In his journals, the sensation is purely material and so it gives a documentary background for his reflexions. To some extent, it is a principle Allen Ginsberg would use a lot, like for example the famous association "hydrogen jukebox" we found in "Howl". The aim is to reveal new sensations as well as new meanings, as if to uncover the reality behind the words or to unmask the affective charge stuck on words. In this poem, the background is purely factual and material and his poetic vision offers a timeless bridge leading toward a contemplation the reader can share with the poet. This is, in a way, what John Tytell concluded about the influence of Williams on Ginsberg. Indeed, this example can be an illustration of "Williams' theory that objects actually surrounding the poet could be assembled into the stuff of poetry as effectively as myth or history". 47 The influence of Williams is once again paradoxical when it comes to his use of triads. Indeed, Allen Ginsberg stated that the use of triads came without his influence:

Later in revising I've noticed a tendencyrevising year pile of notesto adjust notes to small groups of lines as in 3-line stanza, begun however before reading Williams late forms -48 But at the same time, in a list about "mindful arrangement of open verse forms", Allen Ginsberg wrote that the "breath stop" of open verses and the idea of "new breath, new line" 49 are inherited from Robert Creeley, Charles Olson and Williams. Allen Ginsberg also happened to advocate the "division of mental ideas", inherited from Gregory Corso and Williams. 50 Therefore, we can say that Allen Ginsberg was in a way instinctively attracted by Williams' poetry because he found in it a better way to express his inner poetry. 46 Ginsberg,Allen. Collected...,op. cit.,p. 109. 47 Tytell,John. op. cit.,p. 98. 48 Ginsberg, Allen. Journals Mid-fifties..., op. cit., p. 125. 49 Ginsberg, Allen. Composed on the Tongue. Ed. Donald Allen. Bolinas, CA: Grey Fox, 1980, p. 153. 50 Id.

imagism 51 and triadic verses, or to extend it. In a way, he chose both. In the notes concerning a long stanza, 52 he admitted that "the triadic form of William Carlos Williams definitely broke down". He had to change and he decided to quit the Williams' "little breath groups" to "longer breaths", close to the process of thinking. 53 At this moment, Allen Ginsberg went toward long lines, extending the tradition of Christopher Smart and Walt Whitman as a claimed inspiration, and he wrote the final long lines of "Howl". Allen Ginsberg developed the idea of how longer lines corresponded more to his own poetry and how it irritated Williams in the notes of the recording of "Howl", in 1959:

Ideally each line of Howl is a single breath unit. My breath is longthat's the measure, one physical-mental inspiration of thought contained in the elastic of a breath. It probably bugs Williams now […] [START_REF] Ginsberg | [END_REF] This difference of opinion between them concerning the long lines is also revealed in a letter to Richard Eberhart: W.C. Williams has been observing speech rhythms for years trying to find a "regular measure"he's mistaken I think. [START_REF] Ginsberg | The Letters[END_REF] But while Allen Ginsberg came to this statement in the writing of "Howl", he acknowledged his experimentation with Williams' poetry. Allen Ginsberg recalled in an interview "using William's basic perception" before "extending the line out". [START_REF] Ginsberg | [END_REF] To summarize Allen Ginsberg's poetic orientation, we can quote a line of his journals: he was trying to write "Poetry like Williams but with magical vocabulary". [START_REF] Ginsberg | Journals Mid-fifties[END_REF] Furthermore, what appears to be at the center of Ginsberg's interests in Williams is not really the measures and rhythms in themselves, but the fact that a poet can find his own measures and rhythms. This is implicitly written in a 1960 short essay entitled What Way I

Write:

Short lines in William Carlos Williams are balanced mainly by a relative weight of phrasingspeech-size, special emphasis, weight as mental imagery, silence indicated, etc. [START_REF] Ginsberg | [END_REF] The most important word in this extract is "relative". It means that it is a deliberate choice and though Williams influenced Ginsberg, the latter used his own "relative weight of phrasing", corresponding to his own aim. Therefore, William Carlos Williams opened a road for a subjective form of poetry, useful for Ginsberg just like Walt Whitman's open verses and William Blake's visionary poetry. In fact, Allen Ginsberg followed "the prosodic precepts of William Carlos Williams based on breath-mesure". 59 This subjectivity of form is later explained by Allen Ginsberg:

[…] I generally compose in long lines, depending on how falls my attempt to become conscious of my thought, look aside and notate it. 60 Another important point between Allen Ginsberg and Williams is that both have influenced each other. Indeed, impressed by the work of William Carlos Williams as we saw, Allen Ginsberg started an epistolary relation with Williams, before finally meeting him. And this epistolary correspondence had an influence on Williams too. In fact, Williams informed Allen Ginsberg in a letter that he put one of his letters in his long and famous poem Paterson. 61 This event is also recalled in Ginsberg's 1952 journals in "Notes after an evening with William Carlos Williams". 62 In this letter, Allen Ginsberg described himself as an "unknown young poet" writing to an "unknown old poet" and attached some of his poems. He also wrote about finding his own poetic voice: I envision for myself some kind of new speech […] I am not following in your traces to be poetic: though I know you will be pleased to realize that at least one actual citizen of your community has inherited your experience […]. But harking back to a few sentences previous, I may need a new measure myself [...] 63

The fact that Williams included this letter reveals he felt like Allen Ginsberg was being an important figure of the city of Paterson, as a young aspiring local poet and as a part of "the local material" 64 as Williams would say. Later, Williams would also, unsuccessfully, attempt to help Ginsberg to earn a Guggenheim grant. 65 Therefore, including Ginsberg's letter into the poem Paterson shows that he considered him as part of the landscape, completed thus the poem as a whole description of Paterson, with people who influenced and who were influenced by the city, making the personal public and the public personal. Allen Ginsberg also campaigned for Williams' work. This is the case for his play Many Loves as Barry Miles wrote:

Allen had also been trying to help the Living Theater raise money to put on William Carlos Williams' play Many Loves, and gave a benefit reading. 66 As the title indicates, this play explores some of the different aspects of love. Allen Ginsberg composed a poem entitled "Many Loves" too, which described his homosexual relation with Neal Cassady. This poem is echoing the play because Allen Ginsberg also wrote about the many facets of love, never separating physical from spiritual love: "he taught me the love of his cock and the secrets of his mind" 67 , "we felt each other other's flesh and owned each other / bodies and souls" 68 59 Ibid., p. 257. 60 Ibid., p. 256. 61 Ginsberg,Allen,and Bill Morgan. op. cit.,p. 354. 62 Ginsberg, Allen. Journals: Early..., op. cit., p. 3. 63 Williams, William Carlos. Paterson. New York: New Directions, 1951, p. 174. Print. 64 Williams,William Carlos. Interviews...,op. cit.,p. 71. 65 Ginsberg,Allen,and Bill Morgan. The Letters...,op. cit.,p. 298. 66 Miles,Barry. op. cit.,p. 257. 67 Ginsberg,Allen. Collected...,op. cit.,p. 164. 68 Ibid., p. 165.

or "ass of lone delight, ass of mankind, so / beautiful and hollow, dowry of Mind and Angels". 69 It seems that Allen Ginsberg used crude words throughout this poem as a contrast tool for the mindfulness this erotic relation provided him, as if to make the situation both down-to-earth and spiritual, like two sides of the same coin. But what is more is that there are similarities between the play and the poem. For example, the expression "she was a somewhat plump but alluring little animal" 70 from the play echoes to the opening verse of the poem "Neal Cassady was my animal". 71 In fact, Allen Ginsberg wrote a complementary poem in his journals which begins before the published one. 72 Both are put together under the same title, "Many Loves". In this additional poem, Allen Ginsberg claimed to "speak out boldly" and confessed: Dom why reject me years thereafter? I was ever your lover, that was my great pleasure, remember me then, and bless me again 73 This is the same the case of disillusionment we can read in the play:

[…] I say whatever he does you may be sure when you flatter yourself that he's deceiving you or slighting you, running here and there, it's nothing of the sort. You'd be fortunate if he had that much feeling in him for you. 74 In fact, it depicts the relationship between Allen Ginsberg and Neal Cassady quite well. The latter was known for being sexually active with both men and women. As Barry Miles recalled, after sleeping with Allen Ginsberg (as described in "Many Loves") Neal Cassady "reorganized his schedule" in order to split his time between his work, learning how to write with Jack Kerouac, his relation with LuAnne (Cassady's sixteen-year-old wife at that time), his nights with Allen Ginsberg and later his relation with another future wife, Carolyn Cassady. 75 Allen Ginsberg accepted this strange relation by love but it really grieved him. It soon was worse when Neal Cassady started to claim that he was not attracted by men and that he was "forcing" himself "unconsciously". 76 This situation clearly depressed Allen Ginsberg who deeply fell in love with him. As Barry Miles noted: 69 Id. 70 Williams, William Carlos, and John Connop. Thirlwall. Many Loves and Other Plays. New York: New Directions, 1961, p. 83. Print. 71 Ginsberg,Allen. Collected...,op. cit.,p. 164. 72 Ginsberg,op. cit.,p. 300. 73 Ginsberg,op. cit.,p. 302. 74 Williams,William Carlos,and John Connop. Thirlwall. op. cit.,p. 102. 75 Miles,Barry. op. cit.,p. 82. 76 Ibid., p. 85.

"Allen had become obsessed with him and his rejection hurt deeply". 77 This situation corresponds to the words of Williams' play and of Ginsberg's in the poem:

But I made my first mistake, and made him then and there my master, and bowed my head, and holding his buttock

[…]
-And I lie here naked in the dark, dreaming 78 About dreaming, and not as anecdotal as it may sound, Allen Ginsberg dreamed a lot about Williams. This shows obviously how influential and important Williams came to be in Ginsberg's life. For example, he dreamed of a family reunion with Williams, 79 of a "class in the New School with sick W.C. Williams course in Abstruse Mobility [...]". 80 He also wrote about much more revealing dreams underlining how close he felt to Williams, like when he dreamed he found his drafts and unseen poems "returned from Williams […]", 81 of a radio broadcasting "a class with a program interlocuted by WC Williams […] 82 or when he dreamed about Williams teaching him in China 83 , advising him "take your / chances / on / your accuracy". 84 Allen Ginsberg, following Williams' precepts, wrote about those dreams and put some in his poetry. In fact, the advice Williams gave him in a dream described above is to be found in a 1984 a poem entitled "Written in My Dream by W.C. Williams", written with Williams' style and ideas. 85 Actually, they became so close that Ginsberg sent postcards to him 86 and at one point Williams even confided to Ginsberg his fear of death. 87 This idea of death hovering over Williams is also present in Ginsberg's poetry, as in a 1959 poem entitled "Mescaline": What can Williams be thinking in Paterson, death so much on him so soon so soon Williams,what is death? 88 In fact, when William Carlos Williams died in 1963, Allen Ginsberg was in India, on the campus of the University of Benares. A professor of German handed him the newspaper about Williams' death.

According to Barry Miles, he wrote to Gregory Corso "I saw the Big Dipper in the sky, that's all". 89 77 Ibid., p. 86. 78 Ginsberg,Allen. Collected...,op. cit.,p. 166. 79 Ginsberg,Allen. Journals: Early...,op. cit.,p. 7. 80 Ibid.,p. 56. 81 Ginsberg,op. cit.,p. 360. 82 Ibid., p. 134. 83 Ginsberg,Allen,and Bill Morgan. The Letters...,op. cit.,p. 432. 84 Id. 85 Ginsberg,Allen. Collected...,op. cit., Ginsberg,Allen,and Bill Morgan. The Letters...,op. cit.,p. 161. 87 Ginsberg,op. cit.,p. 146. 88 Ginsberg,Allen. Collected...,op. cit.,p. 237. 89 Miles, Barry. op. cit., p. 314.

Just like Williams' advised him at the beginning of his career, he arranged his prose in a poem entitled "Death News": "Williams is in the Big Dipper. He isn't dead [...]". 90 He also mentioned the "Passaic" and "a Goddess in the river",91 referring of course to the figure of the muse in Williams' "The Wanderer" (we will focus on it later), as if everything came to a full circle. But the most important notion of this poem is that Williams is not dead (though the first longer version of the poem is more sensitive92 ). In fact, even if he later wrote that Williams' poetry followed Tennessee Williams "to a white dusty grave",93 Allen Ginsberg explained in "Death News" that "there's a life moving out of his pages". 94 Furthermore, in a poem entitled "CXXV" written in 1984, Allen Ginsberg wrote about Williams "surviving death". 95 This vision of an eternal poetry echoes in a way to Allen Ginsberg's own approaching death. Indeed, he wrote in "Things I'll Not Do (Nostalgias)", which can be considered as his last poem, "No more sweet summers with lovers, teaching […] Williams". 96 But before teaching Williams, he had to read him, if not imitate him, in order to find his own poetic style.

The influence of Williams on Ginsberg's poetry is many times admitted by Ginsberg himself.

It was not unusual for Allen Ginsberg to describe William Carlos Williams as his "own best teacher". 97 And because Williams and Allen Ginsberg have met, he also described him as a "living poetry guru". 98 Moreover, biographer Barry Miles wrote that "under the influence of William Carlos Williams", Allen Ginsberg made "radical changes in his writing style".99 This is particularly visible in Ginsberg's major poem "Howl". According to the poet himself in his annotated drafts of the poem,100 several passages had been written with William Carlos Williams' poetry in mind. For example, the following passage contains a reference to Williams' poetry: who sang out of their windows in despair, fell out of the subway window, jumped in the filthy Passaic, [...] 101 According to Ginsberg in his notes, 102 the mention of the "filthy Passaic" refers the Williams' poem "The Wanderer". Though the expression "the filthy Passaic" in the passage above is to be found two times in Williams' poem (the first one being "The Passaic, that filthy river" 103 ), Allen Ginsberg rather mentioned a precise verse:

And the filthy Passaic consented! 104 This particular verse is meaningful when it is re-contextualized in Allen Ginsberg's "Howl". First, it is necessary to understand the background of Williams' poem from which "the filthy Passaic" is taken. In fact, the poem is about "a youthful poet" who "plunges his hands" in the Passaic River asking to be blessed by "his Muse". 105 This takes the form of an exchange: "Enter, youth, into this bulk! Enter, river, into this young man!" 106 Then, once the context of Williams' poem is in mind, it is interesting to wonder why Allen Ginsberg wrote this passage of "Howl" with this specific reference. In fact, the ones who "jumped in the Filthy Passaic" are "the best minds of [his] generation" and it also includes Allen Ginsberg himself.

Moreover, the Williams' poem is the story of a young poet, which is the case of Allen Ginsberg in 1955 (he was then twenty-nine years old). Therefore, we can estimate that Allen Ginsberg is talking about himself in this passage, involving himself in the quest of a poet struck by a mystical inspiration. This thus made the verse "and the filthy Passaic consented" of Williams' poem prophetic regarding Ginsberg's career. Furthermore, concerning a genetic origin of the very structure of "Howl", Allen Ginsberg admitted that his "original intention was to build on the triadic ladder form established by W.C. Williams" 107 and this intention can be seen in the first draft of the poem:

I saw the best minds of my generation generation destroyed by madness starving, mystical, naked, 108 This passage of course looks like the use of triads Williams made in his poems, for example in "Shadows": Shadow cast by the street light under the stars, the head is tilted back, 109 103 Williams, William Carlos. The Collected Poems of William Carlos Williams: Volume I 1909-1939. New York: New Directions, 1986, p. 115. Print. 104 Id. 105 Ginsberg, Allen. Howl: Original..., op. cit., p. 128. 106 Williams, William Carlos. The Collected Poems of William Carlos Williams: Volume I..., op. cit., p. 116. 107 Ginsberg,Allen. Howl: Original...,op. cit.,p. 11. 108 Ibid., p. 13. 109 Williams, William Carlos. The Collected Poems of William Carlos Williams: Volume II 1939-1962. New In a long letter he wrote to Richard Eberhart, Allen Ginsberg described meticulously all the mechanism of "Howl". In this letter, he wrote several times about how Williams influenced his poetry and the writing of "Howl":

The Long Line I use came after 7yrs. Work with fixed iambic rhyme, and 4 yrs. Work with Williams' short line free formwhich as you must know has its own mad rulesindefinable tho they be at present - 114 And Allen Ginsberg added about his use of juxtaposed words:

This is a curious but really quite logical development of Pound-Fenelossa-Chinese Written Character-imagist W. C. Williams' practice. 115 These two extracts underline how influential Williams was on Allen Ginsberg's way of writing poetry. These lines imply that Allen Ginsberg had a solid knowledge of Williams' skills. As an imagist, Williams stated in Paterson "no idea but in things" 116 which becomes "no idea besides facts" 117 later in the poem. According to Allen Ginsberg in an essay on Williams, this means having "actual contact with the object, rather than verbal". 118 Furthermore, still according to Ginsberg, this also implies that the poet has to write about the particulars:

If you want to describe a tree, don't try to describe every atom, and don't try to describe every leaf […]. You have to pick out that aspect of the tree […]. Whatever details, whatever "particularity" of the tree that strikes your eye first, or stands out in the tree. 119 He also quoted Williams in his journals about focusing on a particular detail to describe an object:

"The true value is that peculiarity which gives an object a character by itself". 120 In fact, Ginsberg and Williams would work on this idea when they made a poem "about a piece of old concrete, a sliver of tin, a pin from a loom, and some ancient dogshit". 121 His interpretation of imagism led to substantial changes and choices in Ginsberg's "Howl". For example, in the first draft of the poem (influenced by the triadic verses of Williams), we can read:

who passed through universities with radiant cool eyes hallucinating anarchy & Blake-light tragedy among the post-war cynical scholars,122

In the notes, we learn that the word "anarchy" is changed to "Arkansas" in the final poem. The reason is that it is a "more concrete thing-name for an abstract word". 123 This is exactly the sense Allen Ginsberg gave to Williams' "no idea but in things". He would indeed say in a short essay on Williams about his principles that what should prevail is "not a change of ideas" but "a change of directive stance". 124 Another example of his vision of Williams' concepts is to be found in his 1955 journals:

Williams has refined the reproduction of images to a science -that is stripped bare for utility.

[…] Do away with symbols and present the facts of the experience. 125 To a certain extent, this is implicitly written in a mention removed from the final poem in the draft of the last part of "Howl", entitled "Footnotes to Howl": "Holy Particulars". 126 It also refers to advice Williams gave to Ginsberg: to focus on "the minute particulars". 127 And these "minute particulars" are taken from William Blake's "Jerusalem" ("every Minute Particular is Holy"128 ).

Moreover, each verse of "Howl" refers to a particular event or is a specific reference transformed into a global evocation and thought-provoking juxtapositions. This cannot be understood without the influence of Williams. Indeed, in the letter to Richard Eberhart, Allen Ginsberg described his technique of "imagery" as based on the "1920's W.C.W imagistically observed detail collapsed together by interior associative logic". 129 Allen Ginsberg also admitted in a class on Williams 130 (as well as in a documentary on Williams 131 ) that the poem "To Elsie" was a great inspiration for "Howl". In a 1975 Naropa class, Allen Ginsberg exchanged with one of his students after reading an extract of "To Elsie":

Student: Had you read that when you started Howl?

Ginsberg: Yes, I had read that -I had that very much in mind when I wrote Howl. 132 The comparison between the opening lines of both poems offers a concrete parallelism. In "To

Elsie", William Carlos Williams wrote:

The pure products of America go crazymountain folk from Kentucky […] 133 And Allen Ginsberg wrote at the beginning of "Howl": If we add to this intention of form the content of the poem, the lexical field of madness and of a whole generation being oppressed by an era, the similarities are uncanny. To some extent, it is interesting to notice that there are also resemblances between the second part of "Howl" and some of Williams' poems like "April". In "Howl", there is a base word (Moloch) which acts both as a rhythmic tool and as a symbol: In "April", there also is a base word: "Moral" (there is the expression "I believe" repeated too, later in the poem137 ): But though Williams' sentence (he heard from a "Polish laborer"150 ) cannot be put in the usual poetic categories of rhythms, it is still a particular rhythm corresponding to the American speech, making thus a true American poetry both in style and content. Williams' poetry appeared to Allen

I
Ginsberg to be "absolutely natural" 151 and to come "from the ground that he stood on", 152 that is to say a demystified poetry operating on a new level of measures; Williams was "hearing with raw ears" 153 and by doing so, discovering "all sorts of new unknown rhythms", 154 that can be described as "pure products of America". 155 In an interview, Allen Ginsberg said that Williams "remarked that American speech tends toward dactylic" 156 and according to his journals, Williams came to the conclusion that the anapest was "characteristic of American idiom". 157 This "American idiom" is for Williams separated from English 158 and "has much to offer […] that the English language has never heard of". 159 Just like John Lardas underlined in The Bop Apocalypse, Williams and Ginsberg "rejected the idea of America as curator of an inherited European tradition". 160 This is maybe why Williams was satisfied with the re-arrangement of Ginsberg's prose into poetry, like for example with "The Bricklayer's Lunch Hours", 161 for the realist thematic, the pure language and the antipoetical observations. In fact, Allen Ginsberg wrote in a letter that if he "ever worried about a technique in advance [he] wouldn't be able to write a line". 162 This revealed how much Williams'

poetry corresponded to what he was looking for, that is to say "the discovery of new appropriate forms" 163 and of "real rhythms of American poetry" from "raw spoken talk". 164 In a letter in which Allen Ginsberg applied for a MacArthur Foundation grant, he wrote about his career and influences.

In this letter, he enumerated some of his achievements:

15) Advancement of lineage and techniques of modern experimental verse forms in tradition and under direct guidance of W.C. Williams. 165 At that point, it is necessary to study why Allen Ginsberg felt closer to William Carlos Williams than to Ezra Pound, for both of them were working on new forms. Williams even told Ginsberg that

Pound "had a mystical ear", 166 the pure sounds being what influenced a part of Ginsberg's work. In his journals, Williams and Pound are studied side by side by Ginsberg about the use of the ellipsis.

To illustrate Williams, Ginsberg chose "The Red Wheelbarrow", focusing on the "gap" between "upon" and "a red wheelbarrow" and underlining the "no significant relationship" between them. 167 For Pound, he chose "In a Station of The Metro", studying once more the "gap", this time between "faces" and "petals" and writing that it is "almost a simile". 168 Later, he eventually came to the conclusion that he felt closer with Williams:

However the Cantos are too literary and [much of] the experience is aesthetic experience of aesthetic experience. He is concerned with generalizations, ethical, esthetic, etc. I am concerned with personal generalizations, or rather concretions of personal experience.

Williams has refined the reproduction of images to a sciencethat is stripped bare for utility. 169 What is underlined in this passage is what Ginsberg liked in Williams: an experience, not an overpoetization of an experience. In an interview, Allen Ginsberg also highlighted another difference between Pound and Williams: while Pound was focusing on what can be called an emotional rhythm ("each rhythm had to rise out of a real emotion" 170 ), Williams was listening to the "little rhythms" contained in "actual speech". 171 Nevertheless, he would later declare that Williams and Pound's "sense of meter and music" were "at the heart of [his] white space idea", 172 and that both of them, also helped to get beyond the traditional poetry. 173 In fact, though Ginsberg met and taught classes on Ezra Pound, it seems that Williams had a greater influence on him. This is maybe because of the bridge Allen Ginsberg built between Williams and his Buddhist beliefs.

The influence of Williams on Ginsberg can indeed be defined according to Ginsberg's 163 Id. 164 Ginsberg,Allen,and Bill Morgan. Deliberate...,op. cit.,p. 278. 165 Ginsberg,Allen,and Bill Morgan. The Letters...,op. cit.,p. 408. 166 Ibid., p. 340. 167 Ginsberg,op. cit.,p. 140. 168 Id. 169 Ginsberg,op. cit.,Allen,and David Carter. op. cit.,p. 107. 171 Ibid.,p. 148. 173 Ibid., p. 255.

personal projections on Williams' poetry. For example, he dreamed about Williams "entering Non-Being" after his death,174 asked him if he was "prepared to be reborn" in a poem,175 considered himself an "apprentice […] to spiritual teachers" including Williams176 and even compared him with Buddhist figures of compassion ("Tara, Quan Yin, Kannon"177 ). In other words, Allen Ginsberg seemed to have projected his own personal history into the poet's works: He saw in it what he wanted and needed to realize in order to achieve his own aim in his poetic work. This is why Ginsberg said that he wrote "mindful" poetry "based [it] on elements of William Carlos

Williams". 178 But it goes beyond the simple fact that Williams embodied a poetic whole expressing Ginsberg's mind. Indeed, as a Buddhist enthusiastic, Allen Ginsberg found in the poetry of Williams an echo to the poetic wisdom and eastern assertions he encountered in his life. For example, when talking about Williams' engaged poem "To Elsie", Allen Ginsberg would describe it twice as a vision of "the karmic situation of America".179 He would also call Williams' appreciation of pure sounds as "Williams' particular physical yoga […] to yoke the mind".180 Allen Ginsberg took as an example the verse "Atta boy! Atta boy!" from "To Greet a Letter-Carrier". 181 The poet precised later that Williams had expressed a "new modern emotion", that is to say a raw exchange that was not conveyed by poetry before Williams. In this poem, the truth of language is preserved, there are no filters holding back the reality of a situation, no separation between what is perceived and what is written. The poet disappeared behind the language and life takes its place back. The process is shaped like a circle, non-deformed like it can be when a particular event is transcribed. But it is not a simple act, for the poet offers a new poetic mediation between the individual and the external world, like rediscovering a poetic world, already there but hidden from accustomed eyes. The genius of Williams according to Ginsberg is then the unveiling of the poetry in everyday life. In Buddhism, one of the aims of meditating is to find the pure reality of the world, annihilating this way the differences between the one who meditates and the object of meditation. In fact, this relation between seeing and perceiving in Buddhism is very close to Williams' poetry: meditating means to erase the subjectivity contained in the act of perceiving; Williams' poetry aimed the preservation of the poetical purity of language, saving an "American prosody". 182 In a way, it is a manner to counter the decline of consciousness. Like Allen Ginsberg said quoting Williams: "A new world is only a new mind",183 that is to say to offer a new way of collecting an exterior's information, it is necessary to develop in oneself the tools enabling this new reception of stimulus, free from subjectivity. Williams' work on finding an American prosody with its own rhythm is based, as we have seen, upon direct observations. This sense of pure perception is the one Ginsberg gave to Williams' famous poem, "The Red Wheelbarrow":184

When Williams said "so much depends", he means all human consciousness depends on direct observation of what's in front of you. 185 In another class about Williams' poetry, Allen Ginsberg also underlined the Buddhist vision of this poem:

I always figured that 'so much depends" means his whole mind depends on the image. Or "so much", a clear apprehension of the entire universe: just being there completely mindful. 186 It is once again Allen Ginsberg projecting his own Buddhist interpretation on Williams' poem, giving it a new meaning, a direct and poetical application of a direct observation as described in Buddhism. Allen Ginsberg would also consider this poem as a true work of "spontaneous awareness", 187 which he added corresponds to the Buddhist notion of "the Unborn". 188 This is what Ginsberg would later explain: the practice of both a visionary poetry and of an "ordinary mind". 189 It is interesting to know that Allen Ginsberg added an expression of his own in "Mind Writing Slogans": "Ordinary Mind includes eternal perceptions". 190 Therefore, this line contextualizes the aim of a poetry made with an "ordinary mind": a poetry which is made of reality, not of realism. He declared:

[…] one's perception of everyday life becomes clear because there's no obstacle of trying to impose a thought on it, or there's no trying to impose a poem on it. Or obstacle trying to impose another world on it. 191 Allen Ginsberg then depicted a poetry that was not trying to be a poetry, like Williams'. For example, still in his "Mind Writing Slogans", we encounter Williams' expression "close to the nose", 192 which means that what is most important for a mindful poetry is to learn how to look at what is before one's eyes. Ginsberg would also take the famous poem "This is Just to Say", asking "What's so poetic about that?" and answering that, because of Williams' objectivity and "clarity", the poem is "a picture of their entire domestic life". 193 It means that thanks to Williams' practice of true perception, without asking himself whether this was a poem or not, whether it was good or bad, a new natural poetry was able to bloom. The spontaneous picture, giving the reader a complete and poetic mindfulness to be experienced, is therefore a practical poetry corresponding to Ginsberg's Buddhism.

This Buddhist interpretation of Williams' poetry seems to be linked with specific contextual years and with the converging ideas of these years. Indeed, Allen Ginsberg recalled the year of 1948, when Gary Snyder and Philip Whalen (both beat poets) were already into Buddhism. What is interesting is that this is the year they met Williams, along with Ginsberg. 194 This maybe explain why Allen Ginsberg saw in Williams a Buddhist poetry: because everything was echoing, mixing a new poetry with statements on observation. Furthermore, Ginsberg often used the lexical field of Buddhism when speaking about Williams. For example, he declared in an interview "having to take refuge in Williams' "No idea/but in things". 195 The expression "to take refuge" is to be found in the Dharma, that is to say the teaching of Buddhism. Indeed, one of the main concepts in Buddhism is to take refuge in the three jewels which means the Dharma (the teaching), the Sangha (the spiritual community) and the Buddha (enlightenment). 196 The choice of vocabulary is intended because once again, in the same interview about his Buddhism, Allen Ginsberg established a link between what he called "spontaneous mind" (that is to say "first thought, best thought"197 ), and Williams' poetry:

That was always a basic principle, to write a poem by not writing a poem. It's Williams' practice. […] because the spontaneous mind was more straightforward, full of strong detail. 198 Later, he would emphasize the fact that William Carlos Williams was able to write the extraordinary ordinary of a "quotidian reality". 199 Ginsberg illustrated this idea with Williams' "Danse Russe ", 200 and established parallels between "wakefulness"201 and Williams' poem "Thursday". This poem is indeed about being present in a state of absolute consciousness and about wakening to the real world: In this poem, which Allen Ginsberg also linked with "the tradition of vipassana203 practice"204 and to "what people are like at heart", 205 Williams experienced some Buddhist concepts. For example, he remained "carelessly" that is to say without any attachment. This is a central Buddhist idea: in order to find equanimity, one has to cut attachment to feelings and objects. Williams also wrote about numerous physical sensations, "feeling" his feet on the ground, his clothes, his weight, his hat and so on. This is once again linked to Buddhism and more precisely with what is called mindfulness:

being able to live in the instant, to feel time passing and to be aware of the physical impact of one's body. Finally, Williams mentioned being aware of the "air passing in and out" in his nose. This situation is clearly a reminder of the practice of meditation. Indeed, one of the first meditation methods is to breathe while being focused on the flowing of the air. Traditionally, this method offers to the practitioner a meditative state. Allen Ginsberg wrote in a short essay on Williams, and especially in a passage about this poem, that breathing is "where Buddhism starts". 206 Thus, the poem is clearly depicting a meditation process without explicitly being aware of it. Allen Ginsberg would also compare Williams' "Smell!" with the practice of meditation:

That's a key poem in the canon of William Carlos Williamsthat is, picking up on his nose, and noticing his nose, which is not very very far from yogic beginning with the nose of meditation, vipassana practice. 207 But this meditation process was a writing process for Williams, as he himself explained his writing method:

Forget all rules, forget all restrictions as to taste, as to what ought to be said, write for the pleasure of it […] every form of resistance to a complete release should be abandoned. 208 Allen Ginsberg also mentioned explicitly the poem "Thursday" in one of his poems he wrote in Ginsberg wrote that "the poem "Thursday" shows that he really is a Buddhist". 215 But then again, Ginsberg insisted on the natural Buddhist path Williams, a "saint of perception", 216 took in order to do the same practice as Buddhists' in his poetry:

Williams had arrived at the same place that everybody else was studying and got there early and on his own. 217 that it was because he did not intend to write poetry that was his best poetry ("things I didn't expect were important turned out to be the best poetry"221 ). But before arranging his prose into spontaneous poetry, it was necessary to write a spontaneous prose. In the method to do so, Allen Ginsberg quoted Williams three times: "measured pauses which are essentials of our speech", "divisions of the sounds we hear" and "time and how to note it down". 222 Allen Ginsberg, still about the rearrangement of his journal prose into poetry, mentioned Williams' influence and the spiritual poetry he found in doing so:

Here Williams told me poems journal were poetry, henceforth everything written has added selfconsciousness. 223 In fact, Allen Ginsberg suspected Williams to have rearranged his prose into poetry for the poem "To Elsie". Indeed, Ginsberg said to one of his students: "I bet you it was written in prose and he chopped it up". 224 First of all, we notice that the poem, and more particularly this extract, operates like a stream of consciousness, which represents the idea of the first line: "First thought, best thought". Allen

Ginsberg followed his inner poetic thoughts, writing them as they came. It is even more the case that according to the notes, this poem was "improvised from notes, transcribed from tape, lightly edited". 235 In fact, in "Mind Writing Slogans", "First thought, best thought" is the first advice, 236 the epigraph is Blake's quote "First Thought is Best in Art, Second in Other Matters" and there is a Shakespeare's quote, ending the circle of thoughts: "Every third thought shall be my grave". 237 But what is important is that Williams' guiding axiom "no ideas but in things" is written between two Buddhist references, making Williams' quote a part of a bigger Buddhist poetic rule. This expression is to be found in "Mind Writing Slogans" 238 too. In "Improvisation in Beijing", a curious verse also seems to be a reference to William Carlos Williams:

A parallel can be established with Williams' "Danse Russe" we encountered earlier. Indeed, a passage reads: Both of the poets described their loneliness and reaction to it. Williams said about this poem that, "the artist, generally speaking, feels lonely" and is "usually in rebellion against the world". 241

What is interesting is that the poet confirmed his choice to describe the present reality without artifice. Indeed, he told the interviewer that this poem "merely records a fact". 242 It is a way to crystallize this precise moment and, for Allen Ginsberg, to write what he found in Williams' poetry:

the "speech consciousness". 243 "It's a question of being conscious, as in WCW" 244 he would add in a letter about ordinary speech's rhythms. To some extent, this ordinary life also concerned the choice of subject for a poem, like "Turkey in the Straw" 245 which affected Ginsberg: "So Charles Olson and Williams were writing poems like that… like his wife sitting on a toilet". 246 It seems that what interested Allen Ginsberg when his active Buddhism and Williams' poetry are put side by side, is the acceptance of reality as it is. Williams' declared that "all poets have a tendency to dress up an ordinary person". 247 This characteristic seems to go along with what his editors called "the understanding and comprehension of a man who has seen more of life and death than the average person", 248 widening thus the prism through which reality was seen for Williams. According to Ginsberg, Williams was so good regarding his practice of poetry that he was able to use himself objectively as a subject for a poem. In a Naropa class, he declared about Williams' poem "Good

Night": 249 Then there's a point where, because he has become so objective, in that sense, that he is able to incorporate himself completely and use his self as the subject of the poem, without self-pity, even, almost, I think, in what we would call a tantric way. 250 It is very interesting to notice that Allen Ginsberg compared Williams' poetry with Tantra. Tantra, usually associated with sexuality in westerners' minds, is firstly a way to be united with the divine and a teaching based on the complementarity of opposites, like male and female. 251 Therefore, Allen

Ginsberg underlined the purity of Williams' inner perception of himself. That way, he implicitly described a deep and mystic mechanism that links perception and reality like two tangled opposites.

As a matter of fact, Allen Ginsberg also read Williams' "Good Night" "like a zazen reverie". 252 The word zazen refers to a sitting practice of meditation. Therefore, when in the poem Williams wandered in his thoughts, it is for Allen Ginsberg a way to observe objectively not only details from his past, but also his present mind recalling details. In others words, the poet is observing both past events and his present thoughts about those past events. This new meaning given to "Good Night" is once more a Buddhist vision of Williams' poetry. Furthermore, we have seen that Williams influenced Allen Ginsberg on his measures, rhythms and sounds. Regarding Williams' focus on sonorities and on a pure American language, Allen Ginsberg also built a bridge between Williams and Eastern practice, including Buddhism:

[…] he had also then to become a yogi of listening to people talk, a yogi of paying attention to talk, to hear the rhythms in the talk […] 253

A yogi is someone who mastered the physiological elements of his body, in order to unify the body and the mind. Concerning Williams on sounds, it appears that Allen Ginsberg was pointing out Williams' control of his ear. This ability led toward a new poetry in which subject and language as well as style and content are in perfect unison. 249 Williams, William Carlos.

  Moloch the incomprehensible prison! Moloch the crossbone soulless jailhouse and Congress of sorrows! Moloch whose buildings are judgment! Moloch the vast stone of war! Moloch the stunned governments! 136

I

  have had my dreamlike othersand it has come to nothing, so that I remain now carelessly with feet planted on the ground and loop up at the sky -feeling my clothes about me, the weight of my body in my shoes, the rim of my hat, air passing in and out at my noseand decide to dream no more. 202

  to be lonely, I am best so!" […] 240

  author of Paterson 111 and to his "relative measure to include his own breath's spoken cadence".112 This point is also pointed out in a Ginsberg's poetic essay: Shakespeare left his breath for us to hear his Cadence, so did Shelley and William CarlosWilliams and Kerouac. 113

York: New Directions, 1988, p. 308. Print.

the

  saw the best minds of my generation destroyed by madness, starving, hysterical, naked, [...] 134The form is different from Williams' poem in the Ginsberg's final version, but it is necessary to insist that it was originally written in triadic verses in his early drafts:

	I saw the best minds of my generation
	generation destroyed by madness
	starving, mystical, naked, [...] 135

  Desolation Angels wrote that "Kerouac compared Ginsberg to Dizzy Gillespie on trumpet because each comes on in waves of thought, not in phrases".146 Nonetheless, Secretary of the New England Association of Teachers of English".147 As Ginsberg also added, the former "mode of poetry lost track of music […] of American speech".148 This episode of "I'll kick yuh eye" is very important in Ginsberg's life. Indeed, it acted like a revelation. Many years later he composed a poem in which he confessed it is one of the reasons he wrote poetry:

	Furthermore, Williams' verses look and sounds like another of Ginsberg's poems, published in his
	journals of 1956:
	While I was alive
	I knew that others would come
	I write poetry because W.C. Williams living in Rutherford wrote New
	While I was alive Jerseyesque "I kick yuh eye", asking, how measure that in iam-
	I wrote as if I would die 139 bic pentameter? 149
	Besides the influence of Williams on "Howl" in terms of forms, it is interesting to focus on
	Williams' influences on speech, measures and rhythms too. The most influential account of
	Williams' influence is detailed several times by Allen Ginsberg, like for example in this 1968
	interview:
	Moral
	it looses me
	Moral
	it supports me Williams' ability to hear pure sounds and to turn them into poetry, containing thus real speech
	Moral rhythms, influenced Allen Ginsberg. This new method was unconventional, if not in contradiction,
	it has never ceased with what was extolled before in, as quoted by Ginsberg, "the metric system described in 1923 by
	to flow [...] 138
	139 Ginsberg, Allen. Journals Mid-fifties..., op. cit., p. 251.

I remember when visiting him in 1948 he said he had heard, on the street, a little fragment of speech: "I'll kick yuh eye". […] "How could that be fitted into the old iambic stress count […]" That's too subtle a gradation of rhythm to be measured by the relatively crude standard count of stress that was practiced.

140

This anecdote marked the beginning of both a quest toward a new American poetry and an appeal to hear "the actual speech around you" 141 that offered new rhythms. In fact, what Williams was doing was to focus on "breath stop" 142 like Allen Ginsberg said in the same interview. But of course, Ginsberg adapted this practice to his own poetry and went "forward from Williams", 143 in order to write a poetry that corresponded to his own "physical breath".

144

In fact, Ginsberg's poetry goes beyond a physical breath to reach a mental flow:

Tho poetry in Williams had depended a lot on little breath groups

[…]

and in Howl an extension into longer breaths

[…]

there is another possible approach to the measure of the line which is, not the way you would say it, a thought, but the way you would think it.

145

Sowhile Williams began a work on "breath stop" underlining the pure American speech, Ginsberg wrote on mental breath, extending therefore the physical sounds to inner reflections. John Tytell, quoting a passage of Kerouac's

140

Ginsberg, Allen, and David Carter. op. cit., p. 108. 141

Id.

142

Id.

143 Ginsberg, Allen, and Bill Morgan. The Letters..., op. cit., p. 208. 144

Id.

145

Id.

146

Tytell, John. op. cit., p. 218. the

  This shows how influential this poem was to Allen Ginsberg, especially regarding his work toward a mindful poetry. It seems that Ginsberg praised Williams' practice of living the reality, instead of covering it with plenty of words like his poem "Sky Words" criticized ("sky is covered with words / Day is covered with words..." 210 ). What is more is that Allen Ginsberg, when teaching about Williams at Naropa, added that he first read Williams' poem "with a background of sitting". 211 Still about Williams' "Thursday" and meditation practitioners, Allen Ginsberg declared:[…] It occurred to me that Williams, by himself, had arrived at the same place where we all were, in terms of his self-awareness, and awareness of his physiological functionings and the awareness between body and mind [...] 212He also came to an interesting conclusion which goes in the sense of a projection of a Buddhist cosmology into Williams' poetry, and more globally of poetry being an art of "sudden flash of recognition":213 That is to say not that he's a Buddhist, but that Buddhism should be so natural, or that meditation could finally come down to just some basic place in nature[…].214 This sentence goes in the sense of Williams not being aware of his meditating process we mentioned earlier. But contrary to what Ginsberg said in the extract above, Williams clearly appeared as a Buddhist in his eyes, especially with "Thursday". Indeed, in a 1976 essay on Williams,

	1980:
	One Thursday in 1919 William Carlos Williams stood in his
	shoes and remembered the breath coming in and out at his
	nose, [...] 209

  He added later that "everything is poetry[…] if you see it", 225 linking Williams' practice of pure imagism with Buddhism:He begins to see everything finally. And naturally it becomes poetry. Which is the point, again[…] on the iconography of Buddhism, where the upstairs guru is pointing out that if you look, and if you're attentive without resentment, every noise becomes punctuation in the big mantra and every little movement has a meaning of its own.226 It is then no curiosity when reading Allen Ginsberg about his spiritual teachers to find Williams among "Tibetan Lamas and Zen Masters". 227 In Ginsberg's mind, Williams was mindful, conscious of the world, "in touch with human feelings" 228 and his poetry would reveal his ordinary vision. sit because the Imagists breathed calmly in Rutherford and Manhattan232 This line refers to Williams because of the word "imagist" but also because Rutherford isWilliams' hometown. Furthermore, this verse conveys an important message with the verb "breathed" and with its Buddhist semantic charge: Williams embodies a Buddhist vision of poetry, connecting once again meditation and poetry. In the introduction of a class Allen Ginsberg taught at Naropa, he said about the context of the outbreak of modern poetry:It was really the beginning of an almost-Buddhist introspection (or intra-spection, if you want)[...] 233 This extract framed the class on Williams with Buddhist and contemplative characteristics.Williams' work on imagist poetry, close as we have seen to the immediate perception of thoughts as described in Buddhism, appears to be at the crossroad of Ginsberg's poetic aim and Ginsberg's Buddhism practice. This is the result of Ginsberg's subjective projection of Buddhist ideas into Williams' work. Indeed, though Williams' work can be linked with Buddhist meditation and aspiration, it does not express mysticism nor devotion, which play an important part in Buddhism.In Allen Ginsberg's "Improvisation in Beijing", a poem which summarized the reasons why he wrote poetry, it is clear that Allen Ginsberg introduced Williams' ideas into Buddhism, and not the contrary, reinforcing the fact that Ginsberg's made a very personal reading of Williams:

This is why Ginsberg said that "Williams' work as a poet is very similar to Zen Buddhist mindfulness practice". 229 Allen Ginsberg wrote in his "Mind Writing Slogans" Williams' expression "clamp the mind down on objects". 230 This is maybe why, just like William Blake and Walt Whitman, Williams is also an ignu in the eponymous poem ("Williams of Paterson a dying American ignu" 231 ). More interesting, Williams appears in a poem with a meaningful title, "Why I Meditate": I I write poetry "First thought, best thought" always.

I write poetry because no ideas are comprehensible except as manifested in minute particulars: "No ideas but in things." I write poetry because the Tibetan Lama guru says, "Things are symbols of themselves."

234

  Centre National De Ressources Textuelles Et Lexicales. "Tantra." CNRS, 2012. Web. 11 Aug. 2016. <http://www.cnrtl.fr/definition/tantra>. 252 Ginsberg, Allen. "Spiritual Poetics 11 (William Carlos Williams)." op. cit.

The Collected Poems of William Carlos Williams: Volume I..., op. cit., p. 85-86. 250 Ginsberg, Allen. "Spiritual Poetics 11 (William Carlos Williams)." op. cit. 251 253 Id.

Ginsberg, Allen. Howl: Original..., op. cit., p. 157.

Ginsberg, Allen, and David Carter. Spontaneous Mind: Selected Interviews, 1958-1996. New York: HarperCollins, 2001, p. 114.

Ginsberg, Allen, and Bill Morgan. op. cit., p. 144.

Ginsberg, Allen. Howl: Original..., op. cit., p. 162.

Miles, Barry. op. cit., p. 87.

Id.

Ginsberg, Allen, and David Carter. op. cit., p. 269.

Ginsberg, Allen. Collected..., op. cit., p. 305.

Id.

Ginsberg, Allen. Indian Journals: Notebooks Diary Blank Pages Writings March 1962[START_REF] Ginsberg | Indian Journals: Notebooks Diary Blank Pages Writings March[END_REF]. Harmondsworth: Penguin, 1990. p. 189-193.

Ginsberg, Allen, and Rachel Zucker. op. cit., p. 122.

Ginsberg, Allen. Collected..., op. cit., p. 305.

Ginsberg, Allen, and Rachel Zucker. op. cit., p. 182.

Ginsberg, Allen. Collected..., op. cit., p. 1161.

Ginsberg, Allen, and David Carter. op. cit., p. 422.

Ibid., p. 414

Miles, Barry. op. cit., p. 137.

Ginsberg, Allen. Howl: Original…, op. cit.

Ginsberg, Allen. Collected..., op. cit., p. 137.

Ginsberg, Allen. Howl: Original..., op. cit., p. 128.

Ginsberg, Allen. Collected..., op. cit., p. 138..

Ginsberg, Allen. Howl: Original..., op. cit., p. 11.

Ginsberg, Allen. Howl: Original..., op. cit., p. 13.

Ibid., p. 125.

Ginsberg, Allen, and Bill Morgan. Deliberate..., op. cit., p. 334.

Ginsberg, op. cit., p. 142.

Ginsberg, Allen. Howl: Original..., op. cit., p. 99.

Ginsberg, Allen, and Louis Ginsberg. op. cit., p. 25.

Blake, William, and Geoffrey Keynes. Blake Complete Writings; with Variant Readings. London: Oxford UP, 1972, p.708.

Williams, William Carlos. The Collected Poems of William Carlos Williams: Volume I..., op. cit., p. 217.

Ginsberg, Allen. Collected..., op. cit., p. 134.

Ginsberg, Allen. Howl: Original..., op. cit., p. 13.

Ginsberg, Allen. Collected..., op. cit., p. 139.

Williams, William Carlos. The Collected Poems of William Carlos Williams: Volume I..., op. cit.,

Ginsberg, Allen, and Bill Morgan. Deliberate..., op. cit., p. 216.

Id.

Ginsberg, Allen. Collected..., op. cit., p. 937.

Ginsberg, Allen, and David Carter. op. cit., p. 267.

Ginsberg, Allen, and Bill Morgan. The Letters..., op. cit., p. 235.

Ginsberg, Allen. Collected..., op. cit., p. 237.

Ginsberg, Allen, and Bill Morgan. The Letters..., op. cit., p. 412.

Ginsberg, Allen, and Rachel Zucker. op. cit., p. 182.

Ginsberg, Allen, and David Carter. op. cit., p. 402.

Ginsberg, Allen. Composed..., op. cit.,

Ginsberg, Allen, and David Carter. op. cit., p. 113.

Williams, William Carlos. The Collected Poems of William Carlos Williams: Volume I..., op. cit., p. 458.

Ginsberg, Allen, and David Carter. op. cit., p. 115.

Ginsberg, Allen, and Louis Ginsberg. op. cit., p. 359.

Williams, William Carlos. The Collected Poems of William Carlos Williams: Volume I..., op. cit., p. 224.

Ginsberg, Allen, and David Carter. op. cit., p. 271.

Ginsberg, Allen, and David Carter. op. cit., p. 271.

Ibid., p. 402.

Berzin, Alexander, Dr. "Refuge: A Safe and Meaningful Direction in Life." Studybuddhism.com. Study Buddhism, n.d. Web. 6 Aug. 2016. <http://studybuddhism.com/en/tibetan-buddhism/about-buddhism/buddha-s-basicmessage/refuge-a-safe-and-meaningful-direction-in-life>.

 197 Ginsberg, Allen, and David Carter. op. cit., p.

406.

 198 Id.199

Ibid., p. 408200 Williams, William Carlos. The Collected Poems of William Carlos Williams: Volume I..., op

. cit., p. 86-87.201 Ginsberg, Allen, and David Carter. op. cit., p. 409.

Williams, William Carlos. The Collected Poems of William Carlos Williams: Volume I..., op. cit., p. 157.

Vipassana meditation is based on the perception of the true nature of reality.

Ginsberg, Allen, and David Carter. op. cit., p. 385.

Ginsberg, Allen, and David Carter. op. cit., p. 406.

Ginsberg, Allen. Collected..., op. cit., p. 939.

Williams, William Carlos. The Collected Poems of William Carlos Williams: Volume I..., op. cit.,