text:
\section{Introduction}
General Relativity (GR) has a really solid kinematical
morphology, based on the covariant formulation of the
spacetime geometry. Nonetheless, its dynamical features
are more questionable, in view of extensions of the
Einstein-Hilbert Lagrangian versus more general scalar functions \cite{Bergmann:1968ve,Lovelock:1971yv,Whitt:1984pd,Jackiw:2003pm,Schmidt:2006jt}.
Among the available choices, when we consider the
generalization of the Einstein gravity to larger
frameworks, the so-called $f(R)$ models \cite{Cognola:2007zu,Sotiriou:2008rp,Nojiri:2010wj,Berry:2011pb,Capozziello:2019cav} stand for
their simplicity and viability. Especially, such an extended approach turns out to be very suitable in specific applications, by virtue of its equivalence with Brans-Dicke theories \cite{Bergmann:1968ve,Wagoner:1970vr,Capone:2009xk,ST,Ruf:2017xon}.
\\ \indent The recent detection of gravitational waves from
compact objects coalescence \cite{TheLIGOScientific:2016src,Abbott:2017tlp,Abbott:2018utx} suggests that in the near future it
will be possible to test GR via the
morphology of the observed gravitational wave template and
spectra \cite{Maggiore1,Maggiore2,Chatziioannou:2012rf,Maselli:2016ekw,Zhang:2017sym,Blaut:2019fxb,Katsuragawa:2019uto}. Then, it becomes very relevant to be able to predict the modifications induced by extended theory of gravity on the morphology and detectability of spacetime ripples. In this respect, a crucial role is surely played by $f(R)$ models and many efforts have been pursued in past and recent years to suitably characterize the specific track left by this modified theory of gravity.
\\ \indent  The analysis of linear modes featuring $f(R)$ theories, even on a flat space-time background, suffers from a certain extent of ambiguity concerning the exact number of degrees of freedom carried by the gravitational wave during its propagation. In particular, if in \cite{Capozziello:2008rq} it was claimed the existence of three independent propagation modes, consisting in ordinary tensorial degrees of freedom along with an additional massive scalar mode, other analyses introduced a further massless scalar field, eventually establishing four degrees of freedom \cite{Rizwana:2016qdq}, in contrast with the scalar tensor representation of the theory. A primary contribution of clarification on this literature debate, was provided by the Hamiltonian approach in \cite{Liang:2017ahj}, where the existence of only three independent modes was clearly inferred from the constraint algebra analysis.
\\ \indent Here, we give a definitive word on this debate, by using fully gauge-invariant quantities to treat gravitational waves and looking the problem both in the scalar-tensor formulation of $f(R)$, as well as in the forth order modified equation approach, obtaining the same firm result: the number degrees of freedom is, as expected by its scalar-tensor formulation, equal to three, i.e. the two standard tensorial modes and an additional scalar one. In this regard, we show also that this extra degree is detectable as a superposition of a longitudinal and breathing stresses. The key point of the obtained results is that these two components, in principle corresponding to distinct pure modes, are actually never separable in the wave dynamics. Eventually, we investigate the nature of the emerging polarizations, in order to get information of the effective morphology that a modified wave could manifest in the interferometers of present and further generations.
\\ \indent The paper is organized as follows: in Sec.~\ref{Sec2} we study the fourth order equation stemming from metric $f(R)$ theory in terms of gauge invariant variables, outlining the emergence of an additional degree of freedom with respect to GR; in Sec.~\ref{Sec3} we repeat the analysis in the scalar-tensor representation. Eventually in Sec.~\ref{Sec4} conclusions are drawn.

\section{Metric $f(R)$ theories of gravity}\label{Sec2}
The action for a generic $f(R)$ model is given by\footnote{In the following we set $c=1$ and $\kappa=8 \pi G$.}
\begin{equation}
S=\dfrac{1}{2\kappa}\int d^4 x \sqrt{-g} \, f(R) + S_M(g_{\mu\nu},\chi_M),
\label{action f(R)}
\end{equation}
where $f(R)$ is a function of the Ricci scalar $R$ and $S_M$ the action for the matter fields collectively denoted by $\chi_M$, which we assume to be only minimally coupled to the metric. According the metric approach (or second order formulation), we consider the Ricci scalar as a function of the metric variable only, \textit{i.e.}
\begin{equation}
R=g^{\mu\nu}R_{\mu\nu}(g),
\label{eq2}
\end{equation}
with the Ricci tensor obtained by the following contraction of the Riemann tensor
\begin{equation}
R_{\mu\nu}=R\indices{^{\rho}_{\mu\rho\nu}}=\partial_{\rho}\Gamma\indices{^\rho_{\mu\nu}}-\partial_{\nu}\Gamma\indices{^\rho_{\mu\rho}}+\Gamma\indices{^\rho_{\tau\rho}}\Gamma\indices{^\tau_{\mu\nu}}-\Gamma\indices{^\rho_{\tau\nu}}\Gamma\indices{^\tau_{\mu\rho}},
\end{equation}
where the connection components are the usual Christoffel symbols (Levi-Civita connection).
Varying \eqref{action f(R)} with respect to $g_{\mu\nu}$ yields the field equations:
\begin{equation}
    f'(R) R_{\mu\nu}-\dfrac{1}{2}f(R) g_{\mu\nu}-\nabla_{\mu}\nabla_{\nu}f'(R)+g_{\mu\nu}\Box f'(R)= \kappa T_{\mu\nu},
    \label{equation f(R) general}
\end{equation}
where a prime indicates differentiation with respect to the argument and $T_{\mu\nu}$ is the stress energy tensor defined as
\begin{equation}
T_{\mu\nu}=\dfrac{-2}{\sqrt{-g}}\dfrac{\delta S_M}{\delta g^{\mu\nu}}.
\label{eq4}
\end{equation}
We note that the class of solutions offered by this reformulation is clearly wider than that one viable in GR, as one can easily infer by the inspection of the trace of \eqref{equation f(R) general} (the so-called structural equation), \textit{i.e.}
\begin{equation}
f'(R)R-2f(R)+3\Box f'(R)=\kappa T,\label{f(R)metric_trace}
\end{equation}
that even in the vacuum case ($T=0$) does not compel any more the Ricci scalar to identically vanish, as it occurs in the standard formulation in the absence of cosmological constant.
\\ \indent In the following, we will restrict our attention to metric perturbations around the Minkowski background, i.e.
\begin{equation}
g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu},
\label{pert metr}
\end{equation}
keeping in mind that, in extended theories of gravity, the Minkowski space-time can no longer be considered as the unique "ground state'' of General Relativity (a privileged globally flat state in the quantum dynamics of the gravitational field). Actually, by the inspection of \eqref{f(R)metric_trace}, it is clear that we could deal with equivalently possible "ground states'', as far as we determine forms of the Ricci scalar that are solutions of the vacuum trace equation.
In such cases we could have a non-vanishing background Ricci scalar $R^{(0)}$ and therefore we would be considering gravitational waves propagating on a curved space-time. Although this situation is surely of physical interest, we restrict our analysis to ordinary propagation on Minkowski geometry. Indeed, there exist no experimental evidences that the detection of gravitational waves by present interferometers is affected by an appreciable value of background curvature, except for local turbulent effect, like the Newtonian noise \cite{Fiorucci:2018had}. Our only aim is to clarify the nature of the wave polarization, in view of their possible detection, and to give a contribution to the debate concerning the number of degrees of freedom featuring the considered extended theories. In fact, this information should be not affected by the curvature of the background metric, but it must be an intrinsic information of the gravitational dynamics.
\\ In \eqref{pert metr} we retain $|h_{\mu\nu}|\ll 1$ valid in some reference frame, $\eta_{\mu\nu}=diag(-1,1,1,1)$ and the inverse metric given by
\begin{equation}
g^{\mu\nu}=\eta^{\mu\nu}-h^{\mu\nu},
\label{pert metr inv}
\end{equation}
in order to $g^{\mu\rho}g_{\rho\nu}=\delta^\mu_\nu+\mathcal{O}(h^2)$ be preserved.
At the first order in $h_{\mu\nu}$ the Riemann and the Ricci tensor read as, respectively:
\begin{align}
R^{(1)}_{\rho\sigma\mu\nu}&=\frac{1}{2}\leri{\partial_{\sigma}\partial_{\mu}h_{\rho\nu}+\partial_{\rho}\partial_{\nu}h_{\sigma\mu}-\partial_{\sigma}\partial_{\nu}h_{\rho\mu}-\partial_{\rho}\partial_{\mu}h_{\sigma\nu}}\label{Riemann_lin}\\
R^{(1)}_{\mu\nu}&=\frac{1}{2}\leri{\partial_{\mu}\partial_{\rho}h\indices{^{\rho}_{\nu}}+\partial_{\nu}\partial_{\rho}h\indices{^{\rho}_{\mu}}-\partial_{\mu}\partial_{\nu}h-\Box h_{\mu\nu}}\label{Ricci_ten_lin},
\end{align}
where the trace $h$ is defined as $h\equiv \eta^{\mu\nu}h_{\mu\nu}$ and $\Box\equiv \partial^\mu\partial_\mu$. Lastly, by virtue of \eqref{Ricci_ten_lin}, the Ricci scalar turns out to be
\begin{equation}
R^{(1)}=\eta^{\mu\nu}R^{(1)}_{\mu\nu}=\partial_{\mu}\partial_{\nu}h^{\mu\nu}-\Box h,
\label{Ricci_sc_lin}
\end{equation}
 which is, in general, not vanishing.
Concerning the functional form of $f(\cdot)$, we can imagine to perform a Taylor expansion around the background value $R^{(0)}$, which taken into account \eqref{pert metr} is constrained to be zero. We point out that with respect the analysis pursued in \cite{Olmo:2005hc}, we are considering a spacetime globally flat at the lowest order, neglecting the issues of a non vanishing background curvature on cosmic scale. Accordingly, the function $f(R)$ can be put into the form
\begin{equation}
    f(R)\simeq R+\alpha R^2 + \mathcal{O}(R^3),
    \label{taylorfR}
\end{equation}
that inserted in \eqref{equation f(R) general} carries out
\begin{equation}
    R^{(1)}_{\mu\nu}-\dfrac{1}{2}\eta_{\mu\nu}R^{(1)}-2\alpha\leri{ \partial_\mu \partial_\nu - \eta_{\mu\nu} \Box }R^{(1)}=\kappa T_{\mu\nu}.
    \label{equation f(R) lin}
\end{equation}
Similarly to \eqref{f(R)metric_trace}, by tracing \eqref{equation f(R) lin} we can get a differential equation for the $R^{(1)}$, that is
\begin{equation}
    \left( \Box -m^2\right) R^{(1)}=m^2\kappa T,
    \label{KG R}
\end{equation}
which represents a massive Klein Gordon equation, where $m^{-2}\equiv 6\alpha>0$ holds for $\alpha>0$. Finally, by means of \eqref{KG R} the gravitational field equation can be recast as
\begin{equation}    R^{(1)}_{\mu\nu}-\dfrac{1}{6m^2}\leri{m^2\eta_{\mu\nu}+2\partial_\mu \partial_\nu }R^{(1)}=\kappa\left( T_{\mu\nu}-\dfrac{1}{3}\eta_{\mu\nu}T\right).  \label{equation f(R) lin 2}
\end{equation}
\\ Following \cite{Weinberg:2008zzc,Flanagan:2005yc}, we introduce for the metric perturbation $h_{\mu\nu}$ the generic decomposition of a rank two symmetric tensor, i.e.
\begin{equation}
\begin{split}
h_{00}&=2\phi ,\\
h_{0i}&=\beta_i+\partial_i \gamma ,\\
h_{ij}&=h^{TT}_{ij} + \dfrac{1}{3}H\delta_{ij}+\partial_{(i}\epsilon_{j)}+\left(\partial_i\partial_j-\dfrac{1}{3}\delta_{ij}\bigtriangleup\right)\lambda,
\end{split}
\label{eq13}
\end{equation}
where $\delta_{ij}$ is the Kronecker delta, $\bigtriangleup\equiv\partial_i\partial^i$ the Laplacian operator and symmetrization is defined as $A_{(ij)}\equiv \frac{1}{2}(A_{ij}+A_{ji})$.
\\  The irreducible parts introduced in \eqref{eq13} are accompanied by the conditions:
\begin{equation}
\begin{split}
\partial^i \beta_i&=0 \\
\partial^i h^{TT}_{ij}&=0 \\
\eta^{ij}h^{TT}_{ij}&=0\\
\partial^i \epsilon_i &=0,
\end{split}
\label{metric dec}
\end{equation}
which, as stressed in \cite{Flanagan:2005yc} (or more generally in \cite{Weinberg:2008zzc} for a curved background), are required in order to preserve the uniqueness and the consistency of the splitting \eqref{eq13}. Then, it can be demonstrated that under a generic gauge transformation the following combinations of fields, together with $h_{ij}^{TT}$, turn out to be invariant
\begin{equation}
\begin{split}
\Phi &= -\phi + \dot{\gamma}-\dfrac{1}{2}\ddot{\lambda} \\
\Theta &= \dfrac{1}{3} \left ( H-\bigtriangleup \lambda\right)\\
\Xi_i &= \beta_i-\dfrac{1}{2}\dot{\epsilon}_i,
\end{split}
\label{eq15}
\end{equation}
with a dot denoting time derivative. The trace component of the metric perturbation $h_{\mu\nu}$ is now encoded in the gauge invariant scalar fields $\Phi$ and $\Theta$ and, with respect to the usual trace-reverse approach, we are not assuming a priori any condition on $h$. In fact, if in General Relativity the latter
is ultimately non dynamical and can be conveniently made vanishing by a gauge fixing, in $f(R)$ formulations that does not hold anymore and trace contributions cannot be neglected. Indeed, it is easy to show that the first order Ricci scalar can be rewritten as
\begin{equation}
    R^{(1)}=3\ddot{\Theta}-2\bigtriangleup(\Theta+\Phi),
\end{equation}
and by virtue of \eqref{KG R} the trace elements $\Theta$ and $\Phi$ are inherently related to an evolving quantity, and cannot be set to zero. Eventually, the two standard tensorial degrees of freedom for $h_{\mu\nu}$ are instead enclosed in the symmetric transverse and traceless part $h_{ij}^{TT}$, whereas $\Xi_i$ is a divergence free vector (see \eqref{metric dec}), endowed with two independent components. As a result, the decomposition of $h_{\mu\nu}$ in the set of fields $\{\Theta,\Phi,h_{ij}^{TT},\Xi_i\}$ depletes entirely all six of the independent degrees featuring a rank two symmetric tensor for diffeomorphism invariant theory.
\\ Now, in order to unambiguously identify the propagating degrees of freedom, we express the components of $R^{(1)}_{\mu\nu}$ in terms of the set of variables \eqref{eq15}:
\begin{subequations}
  \begin{align}
        R^{(1)}_{00}&=\bigtriangleup\Phi-\dfrac{3}{2}\ddot{\Theta} \\
        R^{(1)}_{0i}&=-\dfrac{1}{2}\bigtriangleup \Xi_i-\partial_i \dot{\Theta} \\
        R^{(1)}_{ij}&= -\partial_{(i}\dot{\Xi}_{j)}-\partial_i\partial_j \left (\Phi+\dfrac{1}{2}\Theta\right)-\dfrac{1}{2}\Box\left(\delta_{ij}\Theta+h_{ij}^{TT}\right).
        \end{align}
\end{subequations}
In turn, a completely analogous decomposition can be performed on the stress energy tensor, namely
\begin{equation}
\begin{split}
T_{00}&=\rho,\\
T_{0i}&=S_i+\partial_i S ,\\
T_{ij}&=\sigma_{ij}+P\delta_{ij}+\partial_{(i}\sigma_{j)} + \left( \partial_i\partial_j-\dfrac{1}{3}\delta_{ij}\bigtriangleup\right)\sigma,
\end{split}
\label{eq16}
\end{equation}
with the relative set of constraints
\begin{equation}
\begin{split}
\partial_i S^i& =0 \\
\partial^i\sigma_{ij}&=0\\
\eta^{ij}\sigma_{ij}&=0\\
\partial_i \sigma^i&=0.
\end{split}
\label{eq17}
\end{equation}
Due to the fact that the stress energy tensor must satisfy the conservation law, that in linearized theory reads as $\partial_\mu T^{\mu\nu}=0$, the irreducible parts just introduced are not independent. Indeed, the following relations must hold
\begin{equation}
\begin{split}
\bigtriangleup S &=\dot{\rho}, \\
\bigtriangleup \sigma &= -\dfrac{3}{2}P+\dfrac{3}{2}\dot{S}, \\
\bigtriangleup \sigma_i&=2 \dot{S}_i.
\end{split}
\label{eq18}
\end{equation}

In terms of the set of variables \eqref{eq15} the field equations \eqref{equation f(R) lin 2} are equivalent to the set of differential equations:
\begin{subequations}
\label{sist}\begin{align}
\bigtriangleup \Phi-\dfrac{3}{2}\ddot{\Theta}+\dfrac{1}{6}R^{(1)}-\dfrac{1}{3m^2} \ddot{R}^{(1)}&=\kappa\left( P+\dfrac{2}{3} \rho \right)\\
 \dot{\Theta}+\dfrac{1}{3m^2}\dot{R}^{(1)} &=-\kappa S \\
 \bigtriangleup \Xi_i &=-2\kappa S_i \\
 \Box h^{TT}_{ij}&=-2\kappa\sigma_{ij}\\
 \dot{\Xi}_i&=-\kappa\sigma_i\\
\Phi+\dfrac{1}{2}\Theta+\dfrac{1}{3m^2} R^{(1)}&=-\kappa\sigma \\
\Box \Theta +\dfrac{1}{3}R^{(1)}&=\dfrac{2}{3}\kappa\left(\bigtriangleup\sigma -\rho \right).
\end{align}
\end{subequations}
Then, by implementing \eqref{KG R} and \eqref{eq18} and operating the substitution $\left(\Phi,\Theta\right)\to \left(\Phi_R,\Theta_R\right)$ with
\begin{equation}
   \Phi_R=\Phi+\dfrac{1}{6m^2}R^{(1)}  \qquad \qquad \Theta_R=\Theta + \dfrac{1}{3m^2} R^{(1)},
   \label{new deg stat f(R)}
\end{equation}
which still provides gauge invariant combinations, we get a much simpler form for system \eqref{sist}:

\begin{subequations}
\begin{align}
\bigtriangleup \Phi_R&=\dfrac{\kappa}{2}\left( 3P+ \rho-3\dot{S} \right)\label{phiR}\\
 \bigtriangleup\Theta_R &=-\kappa \rho\label{thetaR} \\
 \bigtriangleup \Xi_i &=-2\kappa S_i \label{xiR}\\
\label{httR} \Box h^{TT}_{ij}&=-2\kappa\sigma_{ij}.
\end{align}
\end{subequations}
By the inspection of the system \eqref{phiR}-\eqref{httR} we see that the two tensorial modes $h_{ij}^{TT}$ are the only propagating degrees of freedom, in conjunction with $R^{(1)}$. The two modified scalars $\Phi_R$ and $\Theta_R$ together with the vector $\Xi_i$ are instead solutions of Laplace equation and they cannot exhibit radiative behaviour. Therefore, we claim that metric $f(R)$ theories are naturally equipped with three independent propagating degrees, in agreement with the results of \cite{Liang:2017ahj}.
\\Now, since we are interested in analyzing the effects due to \eqref{KG R} and \eqref{httR} on a sphere of test masses, it may be instructive to consider the geodesic deviation equation in the comoving frame, having set $T_{\mu\nu}=0$. In this case, the only relevant Riemann components are given, in terms of gauge invariant quantities, by
\begin{equation}
    R_{i0j0}=-\dfrac{1}{2}\ddot{h}_{ij}^{TT}+\partial_{(i}\dot{\Xi}_{j)}+\partial_i\partial_j\Phi-\dfrac{1}{2}\delta_{ij}\ddot{\Theta}.
    \label{geod f(R)}
\end{equation}
Even if it seems that the only proper dynamical effects be induced by the ordinary $h_{ij}^{TT}$ gauge invariant part, we stress the fact that now the truly static degrees are not $\Theta$ and $\Phi$. In fact, by virtue of \eqref{new deg stat f(R)} they actually depend on the propagating degree $R^{(1)}$ and, solving these relations for the new static components $\Theta_R$ and $\Phi_R$, expression \eqref{geod f(R)} can be recast as
\begin{multline}
    R_{i0j0}=\overbrace{\partial_{(i}\dot{\Xi}_{j)}+\partial_i\partial_j\Phi_R-\dfrac{1}{2}\delta_{ij}\ddot{\Theta}_R}^{\text{Static part}}+ \\
   +\underbrace{\alpha \leri{\delta_{ij}\partial_t^2-\partial_i\partial_j }R^{(1)} -\dfrac{1}{2}\ddot{h}_{ij}^{TT}}_{\text{Radiative part}}.
\end{multline}
Now, if we consider a gravitational wave travelling along the $z$ axes, the contributes of the solely $R^{(1)}$ mode to the geodesic deviation equation are given by
\begin{equation}
\begin{split}
&\frac{\partial^2 \delta_x}{\partial t^2}\simeq\frac{R^{(1)}}{6}\leri{1+\frac{k_z^2}{m^2}}\;x_0\\
&\frac{\partial^2 \delta_y}{\partial t^2}\simeq\frac{R^{(1)}}{6}\leri{1+\frac{k_z^2}{m^2}}\;y_0\\
&\frac{\partial^2 \delta_z}{\partial t^2}\simeq\frac{R^{(1)}}{6}\;z_0
\end{split}
\label{geodesic R}
\end{equation}
where we set the vector denoting the separation between two nearby geodesics as
\begin{equation}
    \vec{x}=(x_0+\delta_x,y_0+\delta_y,z_0+\delta_z),
    \label{vec}
\end{equation}
with $x_0$ and $\delta_x$ indicating the rest position and the displacement of order $\mathcal{O}(h)$ induced by the wave, respectively\footnote{Analogously for $y,z$.}. Lastly, the wave vector for $R^{(1)}$ is fixed in $k^\mu=(\sqrt{k_z^2+m^2},0,0,k_z)$.
\\ We remark that the phenomenology associated to the $R^{(1)}$ mode is actually the result of a superposition of two distinct kind of polarizations. In particular, from \eqref{geodesic R} is easy to identify in $R^{(1)}$ excitations a breathing mode acting on the transverse plane $xy$ and a longitudinal mode along the $z$ direction, which is moreover independent on the mass parameter $m$. In this regard, it is useful to define the polarization matrices\footnote{We point out that such a decomposition is strictly applicable only in the case of waves following null geodesics, i.e. in the presence of massless modes. Therefore, despite the application of this method is not formally allowed in this case, we suggest it could still give a precious physical insight about the emerging new phenomenology.} $\mathbb{E}_b$ and $\mathbb{E}_l$ (see \cite{Isi:2015cva} for a comparison):
\begin{equation}
\mathbb{E}_b\equiv
\begin{pmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 0
\end{pmatrix}\qquad\mathbb{E}_l\equiv
\begin{pmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 1
\end{pmatrix},
\end{equation}
which allows us to recast \eqref{geodesic R} as
\begin{equation}
  \partial_t^2\delta\vec{x}=\leri{P_1\,\mathbb{E}_b+P_2\,\mathbb{E}_l}\vec{x}_0
  \label{geod matr1}
\end{equation}
with $P_1\equiv \frac{R^{(1)}}{6}\leri{1+\frac{k_z^2}{m^2}}$, $P_2\equiv \frac{R^{(1)}}{6}$ and $\vec{\delta}_x$, $\vec{x}_0$ representing the rest and the $\mathcal{O}(h)$ component of \eqref{vec}, respectively.
However, we can introduce a new set of polarization matrices $\{\mathbb{E}_t,\,\mathbb{E}_d\}$, related to the irreducible representations for a spin 2 particle described by a symmetric tensor of rank 2, namely
\begin{equation}
\mathbb{E}_t\equiv \frac{1}{3}
\begin{pmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{pmatrix},\quad
\mathbb{E}_d\equiv \frac{2}{3}
\begin{pmatrix}
1/2 & 0 & 0 \\
0 & 1/2 & 0 \\
0 & 0 & -1
\end{pmatrix},
\end{equation}
where $\mathbb{E}_t$ is the trace part concerning the state $|0,0\rangle$ and $\mathbb{E}_d$ the traceless component pertaining the state $|2,0\rangle$.
\\ Then, expressing the set $\{\mathbb{E}_b,\,\mathbb{E}_l\}$ in terms of $\{\mathbb{E}_t,\,\mathbb{E}_d\}$
the geodesic deviation \eqref{geod matr1} can be rearranged as
\begin{equation}
  \partial_t^2\delta\vec{x}=\frac{1}{3}\leri{(2P_1+P_2)\,\mathbb{E}_t+(P_1-P_2)\,\mathbb{E}_d}\vec{x}_0.
    \label{geod matr2}
\end{equation}
Therefore, we see from \eqref{geod matr2} that the additional degree of freedom $R^{(1)}$ is actually capable to excite two distinguished scalar parts of the available modes for the $h_{\mu\nu}$ tensor, and this is ultimately due to the fact that trace free condition cannot be achieved in $f(R)$ gravity in Minkowski background as well. Such an outcome is also consistent with the fact that, even in the absence of ordinary matter, $f(R)$ theories are equipped with an effective stress energy tensor related to the additional degree of freedom, as it can be appreciated in the scalar-tensor reformulation (see Sec.~\ref{Sec3}). In this respect, we note that it is in agreement with ordinary General Relativity results, where the trace of $h_{\mu\nu}$ cannot be set vanishing within matter sources.

\section{Scalar-tensor representation for $f(R)$ models}\label{Sec3}
Scalar-tensor representations of $f(R)$ theories represent a useful tool for investigating the enlarged dynamical content of these models. In particular, such a reformulation enables us to single out the additional degree of freedom contained in the functional form $f(\cdot)$, by means of a scalar field non minimally coupled to gravity and self-interacting. Hence, let us rearrange \eqref{action f(R)} as
\begin{equation}
S=\frac{1}{2\kappa}\int d^4x \sqrt{-g}\leri{f(\Upsilon)+f'(\Upsilon)(R-\Upsilon)}+S_M,\label{f(R)metric_xi}
\end{equation}
where $\Upsilon$ is an auxiliary field whose variation carries out the dynamical condition $\Upsilon=R$, provided $f''(R)\neq 0$. Then, introducing the scalar field $\xi\equiv f'(R)$, action \eqref{f(R)metric_xi} can be recast in the scalar-tensor form\footnote{Especially, expression \eqref{f(R)metric_xi} can be considered as a Brans-Dicke model of parameter $\omega=0$.}
\begin{equation}
S=\frac{1}{2\kappa}\int d^4x \sqrt{-g}\leri{\xi R - V(\xi)}+S_M,\label{f(R)metric_phi}
\end{equation}
the potential term $V(\xi)$ being defined by
\begin{equation}
V(\xi)\equiv \Upsilon(\xi)\xi-f(\Upsilon(\xi)).
\end{equation}
Variation of \eqref{f(R)metric_phi} with respect to the metric and the field $\xi$ gives us, respectively:
\begin{equation}
    G_{\mu\nu}-\frac{1}{\xi}\leri{\nabla_\mu\nabla_\nu-g_{\mu\nu}\Box}\xi+\frac{1}{2\xi}g_{\mu\nu}V(\xi)=\frac{\kappa}{\xi}T_{\mu\nu}
    \label{STmetric_eqg}
\end{equation}
and
\begin{equation}
    R=V'(\xi),
    \label{STmetric_eqphi}
\end{equation}
where $G_{\mu\nu}=R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R$. Eventually, by close analogy with \eqref{f(R)metric_trace}, taking the trace of \eqref{STmetric_eqg} and using \eqref{STmetric_eqphi}, it is easy to get a dynamical equation for the scalar field $\xi$, that is
\begin{equation}
3\Box\xi+2V(\xi)-\xi V'(\xi)=\kappa T\label{STmetric_trace}.
\end{equation}
Now, since we are interested in the linearized limit of the theory (see \eqref{pert metr}), it is reasonable to assume also for the field $\xi$ the perturbative expansion
\begin{equation}
    \xi=\xi_0+\delta\xi,
    \label{pert xi}
\end{equation}
where $\delta\xi=\mathcal{O}(h)$. Thus, by virtue of \eqref{pert xi}, we can expand the potential $V(\xi)$ around $\xi_0$ as well, \textit{i.e.}
\begin{equation}
    V(\xi)\simeq V(\xi_0)+V'(\xi_0)\delta\xi+\frac{1}{2}V''(\xi_0)\delta\xi^2.
    \label{pert V}
\end{equation}
However, when  we required Minkowski background be a solution, i.e. $R^{(0)}=0$, from \eqref{STmetric_eqphi} it follows the constraint $V'(\xi_0)=0$, and consistency at the lowest order for \eqref{STmetric_trace} leads to the additional condition $V(\xi_0)=0$. That also guarantees that in \eqref{STmetric_eqg} cosmological constant contributions do not appear, in which case we should instead deal with de Sitter-like backgrounds. Of course, the requirement of having a stable minimum in $\xi_0$ for the potential $V(\xi)$ cannot be always attainable \cite{Clifton:2006ug,Nojiri:2017ygt}, but in the following we shall disregard these cases.
\\Now, analogously to \eqref{KG R} we can rearrange \eqref{STmetric_trace} in the following way
\begin{equation}
    \leri{\Box-M^2}\delta\xi=\frac{\kappa}{3} T,
    \label{KG xi}
\end{equation}
where we define $M^2=\frac{\xi_0 V''(\xi_0)}{3}$ and we require $V''(\xi_0)>0$ in order to avoid instabilities of the solution.

We write \eqref{STmetric_eqg} at first order in $h_{\mu\nu}$ and $\delta\xi$, obtaining
\begin{equation}
    R^{(1)}_{\mu\nu}-\dfrac{1}{2}\eta_{\mu\nu}R^{(1)}-\leri{\partial_\mu\partial_\nu - \eta_{\mu\nu}\Box}\zeta=\kappa ' T_{\mu\nu} ,
\end{equation}
where we have introduced $\kappa'\equiv \kappa / \xi_0$ and $\zeta\equiv \delta\xi/\xi_0$.
Accordingly with the previous section, we obtain a set of ten differential equations that must be solved together with equation \eqref{KG xi}. Therefore, we remove the redundancies by virtue of \eqref{eq18} and we define the new couple of scalars $\leri{\Phi_\zeta,\Theta_\zeta}$ in the following way
\begin{equation}
    \Phi_\zeta=\Phi+\dfrac{1}{2}\zeta \qquad  \qquad \Theta_\zeta=\Theta+\zeta.
\end{equation}
Lastly, we manage to reduce the number of independent equations to six:
\begin{subequations}
	\begin{align}
	\bigtriangleup \Phi_\zeta&=-\dfrac{1}{2}\kappa' \left(3\dot{S}-3P-\rho\right)\\
	\bigtriangleup \Theta_\zeta &=-\kappa' \rho \\
	\bigtriangleup \Xi_i &=-2\kappa'S_i \\
	\Box h^{TT}_{ij}&=-2\kappa'\sigma_{ij}.
	\end{align}
\end{subequations}
As in the metric case it is easy to recognize that only the tensorial degrees $h_{ij}^{TT}$ and the massive scalar $\zeta$ are solutions of wave-like equations, whilst the transverse vector $\Xi_i$ and the couple of scalars $\leri{\Phi_\zeta,\Theta_\zeta}$ are static.
Given the fact that the two transformations $\leri{\Phi,\Theta} \to \leri{\Phi_R,\Theta_R}$ and $\leri{\Phi,\Theta} \to \leri{\Phi_\zeta,\Theta_\zeta}$ are identical if one makes the identification $2\alpha R^{(1)}\leftrightarrow\zeta$, it follows that the phenomenology associated with the presence of the massive scalar $\zeta$ is the same described in the previous section. Especially, the amplitudes of the polarizations are rescaled by the $\xi_0$ factor and the coincidence of the results is reached if $\xi_0\to 1$, corresponding to \eqref{taylorfR}, where the coefficient of the linear term is set to unity.

\section{Concluding Remarks}\label{Sec4}
We investigated the nature of the oscillating linear modes that the gravitational field outlines in metric $f(R)$ models. In particular, our analysis relies on a gauge-invariant formulation of the gravitational wave propagation, obtained from a linear expansion of the dynamics near the Minkowski spacetime.
\\ \indent The necessity for such an approach finds its justification
in the debate present in literature, concerning the number of degrees of freedom that the theory possesses in the considered formulation. In this regard, the advantage of a gauge-invariant study consists in the possibility to unambiguously identify the actual propagation modes, in order to evaluate their
effects on test particles arrays via the geodesic deviation.
\\ \indent We clarified out of any doubts that only three independent dynamical degrees are present in the linear theory, consistently with the degrees of freedom of the full non-linear theory.  Our findings are also compatible with \cite{Suvorov:2019qow}, where perturbations around a Kerr metric are studied.\\
\indent We elucidated that the source of the debate regarding the exact number of modes is originated by a very subtle feature of the obtained gauge invariant formulation. Indeed, even though we deal with a single scalar degree
in addition to the metric field of the standard Einstein-Hilbert action, such a  degree appears in the geodetic deviation equation like the superposition of two different and well known polarizations, i.e. a breathing and a longitudinal mode.
However, we remarked that these two polarizations can be never physically separated and they always act on particle arrays like a single one, bringing features of its basic constituent at the same level.
\\ \indent  We stress that a characteristic feature of General Relativity is the traceless nature of vacuum gravitational waves. Especially, in Minkowski space-time this property is an exact output of the dynamics, while on a curved background it is valid up to higher order terms \cite{Maggiore1,Misner:1974qy,Straumann:2013spu}. In $f(R)$ theories of gravity, instead, the traceless character of vacuum gravitational waves is intrinsically lost both in Minkowski and curved backgrounds. Indeed, our analysis clearly elucidates the dynamical and non-vanishing nature of the trace and this feature is expected to be preserved on any background, since the gauge invariant variables method can be applied straightforwardly to the general case (see \cite{Weinberg:2008zzc}). The reason for such a different morphology of modified gravitational waves consists of the scalar-tensor nature of the $f(R)$ model, in which the non-minimally coupled scalar field plays the role of matter source. With this regard, we suggest that the excitation of the trace part of the metric tensor could be due to the presence of an effective stress energy tensor, related to the additional scalar degree. Exactly as in General Relativity the passage from flat to curved space-time does not alter the number of degrees of freedom associated to the wave, at least at the considered order of approximation, analogously we expect that the two tensorial and the scalar modes of the present Minkowski model unaltered survive in the same curved space-time extension. This firm conjecture is also validated by the Hamiltonian analysis performed in \cite{Liang:2017ahj}, verifying the first class nature of the emerging Hamiltonian constraints.
\\  \indent It has been demonstrated in \cite{Kijowski:2016qbc,Afonso:2018hyj} that a class of extended theories of gravity, which $f(R)$ models belong, is equivalent to standard General Relativity possibly coupled to scalar fields, which may not coincide with the scalar field we deal with in the Jordan frame. This interpretation is certainly viable, and without entering the details of a possible quarrel about the geometrical or matter representation of this more general framework, we observe that the present analysis about the number of physical degrees of freedom remains significant in both these scenarios, even if the associated phenomenology could be altered by the peculiar representation adopted. \\ \indent In conclusion, since the morphology of the theory is now under control and the actual features of the gravitational polarizations are well-traced, it is possible to better characterize the phenomenological implications and the detectability of such extended gravitational ripples.

redpajama_set_name: RedPajamaArXiv


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The linguistics program at MIT evolved in a highly unusual manner for an academic discipline with ancient beginnings. Essentially, the linguistics section was formed not so much to teach a body of knowledge as to contribute to it. From the beginning, research has been primary at MIT. In fact, the linguistics group was originally a research group, associated with the Research Laboratory of Electronics (RLE), with certain of its members also teaching language courses within the Department of Modern Languages. This dual affiliation still exists, with RLE providing the group with various administrative services, a portion of its funding, and physical facilities, but with the majority of the staff holding faculty appointments in what is now the Department of Foreign Literatures and Linguistics.
In an easily traceable chronology, the origins of the framework within which linguistics was to grow at MIT lie in the development of radar. Even before World War Two, there was increasing interest at the Institute in the new fields of communications and electromagnetic theory, with a concomitant increase in collaboration between physicists and electrical engineers. After the Radiation Laboratory was organized in 1940 to participate in the development of an airborne radar, scientists from still other fields joined the related projects. The impressive output of their combined efforts, both applied and theoretical, encouraged those involved to seek to extend the collaboration into peacetime. Thus, when in 1946 the Radiation Laboratory ceased to exist, a new Research Laboratory of Electronics was formed to absorb its programs. In order to resolve problems of funding and of title to incalculably valuable projects and resources which had been financed by the government, the support of basic research at RLE and other such facilities was given to agencies of the Armed Services. The terms of this sponsorship were such as to allow continuation of the open research climate that had proved so fruitful.
RLE was a new kind of laboratory. It existed independently of any department at MIT and still does, although laboratory workers are often affiliated with one of the teaching departments as well. The original staff consisted of physicists and electrical engineers, but quite quickly mathematicians, biologists, psychologists, and chemists, as well as linguists and others, were attracted by the communality of interests and the research climate that encouraged it.
From the start, much of the investigatory effort at RLE was devoted to communications problems of various sorts: in 1946, when the laboratory was formed, one of the four major research groups was labeled "Communications and Related Subjects." It was probably Norbert Wiener who was most personally responsible for the development of the communication sciences at MIT. His cybernetics, along with Claude Shannon's mathematical theory of communication, stimulated interested scientists from various fields to probe further and further into the implications of information theory and communications engineering.
In addition to and separate from the RLE communication sciences group there was at MIT an Acoustics Laboratory where work was being carried out on speech and phonetics. Out of this laboratory came the still very active Speech Analysis Group in RLE headed by Kenneth N. Stevens.
An early impetus for the formation of the linguistics group at MIT came from a number of speech communication conferences organized originally by William N. Locke, then Chairman of the Department of Modern Languages. The first meeting on speech analysis, chaired by Locke, was held on 2 December 1949. Marking the opening of formal discussion between linguists and engineers as well as others, the conference was attended by forty scientists, including Roman Jakobson of Harvard, commonly regarded as one of the first linguists to sense the potential of the new scientific developments, Gunnar Fant of the Royal Institute of Technology of Stockholm, who spent some time at MIT and was to coauthor the pioneering Preliminaries to Speech Analysis, and John Lotz of Columbia, who soon afterward gave a series of lectures at MIT on the problems of linguistics.
As far as the incipient approach to linguistics was concerned, it was clear that interest at this point was directed toward a machine-type analysis of language.
At the Research Laboratory of Electronics, William Locke was directing a small group doing research on the acoustics of speech. The facilities and equipment were made available to interested scholars outside of MIT, one of whom was Morris Halle, then studying at Harvard. Born in Latvia, Halle specialized in Slavic languages in his Harvard Ph.D. studies but, as an associate of Roman Jakobson's, had the deep concern for general properties of language that had characterized traditional linguistics and much of Jakobson's work. In 1951 Halle officially joined the faculty of the Department of Modern Languages, where he taught Russian and German, and the staff of RLE, where he participated in phonetic research. It can be said that Morris Halle's official arrival marked the actual beginning of the linguistics group at MIT, not only because he was its first member but also because it is generally acknowledged that he has been its chief architect and builder as well.
The character of the speech investigations carried out by Halle and others at RLE in the early fifties was distinctive in its linguistic orientation. Research emphasis was placed on the relationship between the behavior of the human vocal tract and its acoustical output, and the resulting studies provided much information on how the anatomical makeup of man's vocal tract is utilized in producing the acoustical signal of speech. Examples of acoustical investigation of the period include measurements of the acoustical spectra of consonants, studies of the sounds of Russian, and an attempt to realize a complete automatic recognition scheme for English speech (Hughes (1960)). Speech perception also came under examination, leading to such results as evidence of the influence of context on the perception of stop consonants (Schatz (1954)).
This report proposes some questions to be discussed by specialists working on various aspects of speech communication. These questions concern the ultimate discrete components of language, their specific structure, their inventory in the languages of the world, their identification on the acoustical and perceptual levels and their articulatory prerequisites.
Preliminaries was thus an attempt to categorize the phonetic capabilities of the human vocal apparatus by positing a framework underlying the sound structure of all natural languages. Speech sounds are approached as complexes of properties, regarded for a variety of reasons as binary categorial markers. Termed "distinctive features," these properties are the elements made use of by all languages in the formation of their sound systems.
This conception of sound structure represented an elaboration of ideas of Jakobson's dating back as far as the 1920's, a development made possible by the refined equipment newly available to phoneticians. At the same time, in its approach to phonology Preliminaries represented a departure from contemporary linguistic studies.
There was still another area of study which turned out to be a source of stimulation and manpower for the nascent linguistics group, namely, machine translation. Also carried out at RLE as part of the general program of investigation into communication problems but separate from speech research, work on the translation of languages by computer during the 1950's attracted worldwide attention. The tie-up with linguistics was a direct one: in order to program a machine to translate one language into another, it is necessary to have a thorough grasp of the structure of both languages.
The first conference on machine translation was held at MIT in June 1952. At RLE Y. Bar-Hillel, for one, worked in this area. Also interested was William Locke, who later coedited a book on Machine Translation of Languages (Locke and Booth (1955)). Then, in 1953, Victor Yngve, a physicist who had concerned himself with the idea of translating languages by machine as early as 1949, arrived at MIT. He became director of the Mechanical Translation Research Project at RLE and, with Locke, edited the journal Machine Translation.
L71, L72. SOCIAL LINGUISTICS. Seminar to examine the social functions of language, the interrelations of language and culture; types of languages, primitive and modern; advantages and disadvantages of various systems of writing; the implications of illiteracy; international communication; language planning.
L73, L74. APPLIED SEMANTICS. Seminar to stimulate meaning-consciousness through the discussion of questions such as: What happens when we make or interpret a statement? Why do words get confused with things? What causes semantic blockages? How can they be removed? What are the verbal means of mobilizing emotions? How is language used by the politicians, the salesmen, etc.? What are the most commonly practiced tricks in verbal argument? When is clarity not enough?
In 1952, courses L71, 72 became L75, LANGUAGE AND SOCIETY. The course descriptions remained the same in both cases until 1955.
In their first two years the linguistics courses attracted about twenty students in all. But by 1952 the combined enrollment rose to about forty and remained there until 1961, by which time the offerings had been expanded somewhat.
14.77. PSYCHOLOGY OF COMMUNICATION. Survey of phonetic, acoustic, perceptual, statistical, developmental, behavioral, and social studies of the psychology of language and communication. Particular emphasis is placed upon the effects of verbal habits upon perception, learning, and thinking.
6.696. HEARING, SPEECH AND LANGUAGE. Discussion of properties of signals in audio communication systems in the light of characteristics of listeners and speakers. Auditory thresholds, masking, perception of complex acoustic stimuli. Production of natural and synthetic speech. Physical methods of speech analysis. Effects of filtering and clipping. Linguistic units of analysis. Statistical properties of speech signals. Intelligibility criteria for audio communication systems. Integration of experimental data on hearing and speech with recent developments in linguistics and information theory.
The direct descendants of these courses continue to be given by the corresponding departments at MIT today.
To summarize, by 1955 the situation at MIT is as follows. Morris Halle, William Locke, and Victor Yngve are on the faculty of the Modern Language Department and, at the same time, on the staff of RLE, where, as part of the group investigating various aspects of communication, they and others are working on speech analysis (Halle) and machine translation (Yngve). The general tone of the research is to bring to bear upon the study of language the results of the wartime advances in fields such as information theory, communications engineering, and acoustics, while at the same time making available to interested specialists in other areas the results of language study. This was directly reflected in the coursework that came out of RLE research, namely, Halle and Rosenblith's HEARING, SPEECH, AND LANGUAGE, and Miller's PSYCHOLOGY OF COMMUNICATION. Also being offered were two undergraduate courses in linguistics, taught by Bodmer. Finally, the most significant published work of the pre-1955 years was Preliminaries to Speech Analysis (Jakobson, Fant, and Halle (1952)), which was to critically affect the nature of phonological investigation for a great many linguists.
Until 1955 the focus of linguistic study at MIT was on the sound structure of language, that is, phonology and morphology, with special emphasis on applied aspects in the form of speech analysis and machine translation. With the arrival of Noam Chomsky that year, however, more and more attention was to be devoted to syntax and to general linguistic theory.
one cannot describe a linguistic system in any meaningful way without some conception of what is the nature of such a system, and what are the properties and purposes of a grammatical description. For this reason it is important to develop a precisely formulated and conceptually complete construction of linguistic theory, based on the clearest possible elementary notions… (Chomsky (1955, pp. 1-3)).
That is, he posited a theory of transformations which was conceived as part of a theory of grammar, "part of an attempt to construct a formalized general theory of linguistic structure and to explore the foundations of such a theory" (Chomsky (1957, p. 5)).
It could probably be agreed that in the two decades since Chomsky's first publications, his work has stimulated a re-evaluation and ultimately a restatement of the fundamental problem of linguistics. First to feel the impact, quite naturally, was MIT. There the focus of attention began to shift away from the use of linguistic knowledge and methods in the solution of engineering problems. Instead, linguistic theory became the prime concern, and the complexities of syntax attracted more attention as their susceptibility to study appeared to increase.
The evolving theory began to be presented in a number of published works and at various professional meetings, and although there was no formal linguistics program until 1961, interested scholars began to come to MIT. The machine translation project, especially, aided by a Carnegie grant, was able to support the work of a considerable number of linguists during this period, including, among many others, not only Chomsky but Applegate, Matthews, Klima, Lees, Lukoff, and Viertel.
In 1956 Joseph Applegate, who like Chomsky had a Ph.D. in linguistics from the University of Pennsylvania, joined RLE and the Modern Languages Department where he was to relate ongoing work to the study of Berber languages. That same year G. Hubert Matthews, a Ph.D. from the University of Pennsylvania, arrived at RLE and in 1961 became part of the Modern Language faculty as well. With a background in mathematics, German literature, linguistics, and anthropology, he was to become particularly interested in formal languages and in studying American Indian languages in the light of new theoretical devices. Edward Klima, a Ph.D. candidate in linguistics at Harvard, joined the Modern Languages Department in 1957 and the following year became associated with the machine translation group as well. His interests were to center around comparative and historical linguistics, English, and later the study of language acquisition.
In 1959 Jerry Fodor became an instructor in the Department of Humanities. After then spending some time in 1960, along with Jerrold Katz, as a research assistant on the Transformation and Discourse Analysis Project at the University of Pennsylvania, he joined the staff of RLE in 1961. Since that time he has done much work in the philosophy of language, in language perception and acquisition, and with Katz, who also came to RLE in 1961, in the development of a semantic theory. In 1960 Roman Jakobson was officially appointed an Institute Professor in the Department of Modern Languages while still retaining his affiliation with Harvard. It should be pointed out, however, that Jakobson had not only been a Visiting Professor in 1957 but had, from the beginning of Morris Halle's affiliation with MIT, been deeply interested in the direction of research there. Thus he maintained a close and continuous association with the MIT group long before his official appointment.
The published studies that came out of MIT during the late fifties represented the beginnings of what some have called a new "paradigm" of work in linguistics. Chomsky's Syntactic Structures in 1957 was preceded not only by the formidable unpublished work on which it was based, i.e., Chomsky (1955), but also by Chomsky, Halle, and Lukoff's "On Accent and Juncture in English" (1956), where it was shown that intricate stress patterns could be predicted from syntactic structure, and by Chomsky's "Three Models for the Description of Language" (1956). In 1959 "On Certain Formal Properties of Grammars" appeared, and that same year (1959) saw the publication of what struck many as an explosive review by Chomsky of Skinner's 1957 work, Verbal Behavior.
Although a good portion of these studies, by virtue of their mathematical approach, seemed inaccessible to many linguists, the theories they represented could not long go unnoticed in a small field where ordinarily everyone read everything and knew everyone. Of great help was the more reachable review of Syntactic Structures in Language (1957) written by Robert Lees, a member of the machine translation project and later a student of Chomsky and Halle's. Then in 1958 the third of a series of conferences held in Texas on the subject of Problems of Linguistic Analysis in English provided an opportunity for Chomsky to personally present, explicate, and defend his work. Out of this conference came the well-known article on "A Transformational Approach to Syntax" (1962). In 1958 five representatives of MIT presented papers at the annual meeting of the Linguistic Society of America – Applegate, Halle, Lees, Matthews, and Lenneberg (a psychologist doing work related to the MIT approach to language). The following year, 1959, Halle's Sound Pattern of Russian was published. And in 1960 Halle, Jakobson, and Chomsky were on the program committee of a symposium held in New York on the Structure of Language and its Mathematical Aspects. Chomsky's "On the Notion 'Rule of Grammar'" (1961) was presented at this meeting, as was Halle's paper "On the Role of Simplicity in Linguistic Descriptions" (1961).
By 1960, then, the "MIT school," as it had come to be known, had undoubtedly emerged as a force to be reckoned with in linguistics, though whether for better or worse was still very much an open question for a good many workers in the field.
An understanding of the early history of MIT linguistics involves explicit recognition of the fact that it was not developed in an intellectual or academic void. By itself it could be interpreted as a synthesis of the seventeenth- and eighteenth-century interest in universal and philosophical grammar and the scientific advances of a new age. However, between the classical period and the late fifties linguistics had taken on a different form, and it was the existing science that the new theories and theorists had to react to. The profoundly different approach that transformationalists espoused was offered to a well-established field, one that had attained a highly refined stage in many areas. In some respects the new approach was seen as growing out of the accomplishments of structural linguistics, particularly with regard to the emphasis on precision of formulation. But in still other, deeper ways it was regarded as a reaction against what were judged to be serious shortcomings in the linguistic science of the fifties. Inevitably, then, a substantial part of the work of this period dealt not only with the revised theoretical and methodological principles themselves, but also with what were interpreted, on the basis of these principles, as weaknesses in modern structuralism. As a result a portion of the writing and speaking took on a certain polemic tone that was to have some effect on work in the field for several years.
Returning now to the increasing exposure MIT ideas were receiving by the end of the fifties, we may note the accompanying increase in interest in them, particularly on the part of scholars attracted to the math/engineering and language/linguistics combination. By 1959 two Ph.D. theses were being completed under the auspices of the Electrical Engineering Department by students working with Chomsky and Halle: one dealt with speech analysis (Hughes (1960)) and the other was Lees's well-known syntactic work, published the following year (1960) as The Grammar of English Nominalizations. The years 1959 and 1960 saw, in addition, two undergraduate linguistics theses and a Master's thesis in speech analysis, again carried out under the supervision of Chomsky and/or Halle. Also studying with them on one basis or another were a linguistics student from Columbia, a speech student from Boston University, and a Slavic specialist from Harvard. Still another group of students pursuing academic degrees at different levels and with different specialties were associated with the machine translation project. They included linguists, logicians, mathematicians, and engineers, and they were affiliated with, for example, Harvard, UCLA, Columbia, the University of Texas, Brown, and MIT.
During the years under examination, the actual course offerings in linguistics were somewhat extended. Such expansion was limited, however, by the absence of a degree-granting program, as well as by the research-centered orientation of a still new subject area that was just developing teachable subject matter.
L78. LINGUISTIC STRUCTURE. Problems and methods of the descriptive study of language. Study of form in language: definition and determination of linguistic elements; techniques of analysis; mathematical models for linguistic behavior (communication theory, logical syntax); construction of an objective and abstract theory of formal linguistic structure; systematic application of this theory to the description of English structure. Study of meaning in language: relation of linguistic form and meaning; various approaches to a theory of meaning; contemporary philosophies of language and the influence of symbolic logic; extensional and intensional structure. Comparison of the logic of natural languages with that of special purpose language systems (mathematics, science).
L76. PROBLEMS OF PHONOLOGY. Aims and principles of a scientific description of the structure of a spoken language. The mechanism and the acoustics of speech. The phonemic system of a language. The pair test. Distinctive features as a descriptive framework. The phoneme. The interrelation between phonology and other linguistic levels. Some problems of historical phonology. Practical exercises in preparing a phonemic analysis of a language with the help of a native informant.
L75. LANGUAGE AND SOCIETY. Introduction to the scientific study of human language. Outline of syntactic theory; brief survey of English syntax. Elementary data on production and physical nature of speech. The phoneme and distinctive features. Phonemic systems. Morphology: review of some morphological devices. Languages of the world, their historical relationships and structural classification. Speech and writing. Language, culture, and cognition.
L71. SPECIAL PROBLEMS IN LANGUAGE AND LITERATURE.
L72. SPECIAL PROBLEMS IN LANGUAGE AND LITERATURE. Advanced work in literature or linguistics for unusually well-prepared students. Offered by members of staff in their special fields.
L79. LANGUAGE, SYMBOLIC PROCESSES, AND COMPUTERS. Symbols, their storage and manipulation: formal systems of symbols, natural languages, computer programming languages, codes, notation; systems of mathematics, logic, physics, etc.; relation of symbols and symbol systems to the physical means of representation and manipulation; relation of symbols and symbol systems to the subject matter represented and its systematization; symbolic processes, induction, deduction, reasoning; translation and translatability.
To summarize, by 1960 the MIT "school" of linguistics had gained a considerable reputation. Interest on the part of graduate students at the Institute and elsewhere was growing, and a few new courses were set up to teach the new subject matter. Involved in MIT research projects were from eight to twelve graduate students from other universities, and additional requests for graduate study in linguistics were being received at a growing rate.
Not surprisingly, then, a proposal for a graduate program in linguistics at MIT was prepared by a committee consisting of Roger Brown (a social psychologist with an interest in the psychology of language), Noam Chomsky, Morris Halle, Roman Jakobson, William Locke, Walter Rosenblith, Jerome Wiesner (now President of MIT and at that time Director of RLE and a leader in the development of communication sciences), and Victor Yngve. The completed proposal was submitted by the Department of Modern Languages on 1 July 1960. The recommendation made was that a graduate program in linguistics be introduced at the Institute in the fall of 1961, under the Department of Modern Languages, leading to the degree of Doctor of Philosophy in Linguistics. A preference was expressed for at first accepting only candidates who had already proven their competence in one of the two main areas with which the group was concerned, language-linguistics or mathematics-logic-computers.
Our plan is to emphasize the areas in which we have strength and in which training is badly needed by young linguists all over the world. It is not the intent of the Department to staff what might be called a "classical" linguistics department. Thus, we do not expect to have subjects in many of the conventional areas such as the history of particular languages and their development or methods of field work. Students would be expected to master these on their own, or to take subjects in other institutions, such as summer institutes of linguistics.
("Graduate Work in Linguistics at the Institute: A Proposal from the Department of Modern Languages" (1960)).
The program was visualized as beginning modestly, with a gradual increase over the first three years to about fifteen students. It was hoped that needed fellowships would come in large part from the National Science Foundation, which had been supporting the research programs in linguistics, and from the National Institutes of Health.
According to Institute rules and regulations, the authorization of a department to grant a new graduate degree had to come from the MIT Corporation, on the basis of a favorable recommendation from the President on administrative aspects of the proposed program and a recommendation from the MIT Faculty on its academic aspects. The Faculty based its recommendation on the report of the Committee on Graduate School Policy. And this Committee, in turn, generally based its recommendation on the report of a small ad hoc committee set up expressly for the purpose of examining and appraising the academic resources within and available to the department seeking to offer the degree.
Also present at the meeting as invited guests were Harold Hazen, Dean of the MIT Graduate School, John Burchard, Dean of Humanities, William Locke, Roman Jakobson, Noam Chomsky, Morris Halle, and Victor Yngve.
That the Faculty recommend to the Corporation that it authorize the Department of Modern Languages to recommend the award of the Degree of Doctor of Philosophy in the field of Linguistics.
The MIT Corporation approved the motion in December 1960.
In September 1961 the first officially registered graduate students in linguistics entered MIT. The program they became part of had, it is apparent, a distinctive development. Indeed, it is because the years before its official inception were so critical to the ultimate form and shape of the program that they have been examined so closely here.
The linguistics program developed as a natural outgrowth of the research activities of the MIT linguists, and an attempt is still made to maintain a close tie between teaching and research. Graduate students have always been expected to play an active role in research, that is, to work on real problems, from an early point. The academic program, therefore, was organized so as to encourage students to participate in the ongoing research of the group. This fact should be borne in mind as the different facets of the MIT program are surveyed, for without it the picture is fragmentary. The course descriptions found in the MIT catalog, for example, are only partially revealing. They do not show that the advanced courses particularly, but to some extent the introductory courses as well, take up whatever relevant study the instructor is engaged in at the moment, and that the subject matter of most of the published work to come out of MIT appeared first in one class or another and was shaped by the resulting discussion and criticism. As one of the effects of this classroom approach, there was and still is an unusual amount of "sitting in" on courses by both faculty and students.
A related factor was the absence, during the early years of the program, of an extensive body of immediately relevant literature. Available to the students of the early sixties at MIT were the classical studies and an impressive array of work out of the structuralist school, but very little that dealt directly with transformational generative grammar. The field was simply too new.
Halle and Chomsky deliberately sought to avoid traditionally run courses in which large numbers of students were lectured to on the known works in the field. There was a time, however, when such courses would not have been possible anyway, for there were too few works – known or unknown. Gradually, of course, this changed, but for many years the motto at MIT still remained "If it can be read, it needn't be taught." To a certain extent this holds today.
Beginning students, especially those with a traditional academic background, often found the lack of something concrete to study disconcerting. The advice was simply to hang around a lot and let all the talk seep in; eventually it would start to come together. Sometimes this did not happen; more often it did.
Although no particular background is required of program applicants, eligible students in mathematics or science have generally been preferred over those in humanities or social science, all other things being equal. Students who are uncomfortable with scientific constructs and methods may be uncomfortable at MIT, and it is generally more difficult for them to develop a working familiarity with the theory. This is not to say that there is no place for non-science majors at MIT. On the contrary, many are accepted and many do extremely well. Indeed, of the MIT alumni presently on the linguistics faculty, not one had a background in science.
At the beginning the special nature of the MIT program entailed a certain problem for its survival, namely, the finding of qualified staff. A heavy responsibility was thus laid on Halle and Chomsky, and then Klima, in the first few years for the group had to train its own personnel. Klima and Matthews, as we have noted, spent several years at MIT before the program officially began. Paul Postal, with a Ph.D. from the Yale Department of Anthropology, was a research associate for two years before joining the linguistics faculty in 1963. And both Jerrold Katz and Jerry Fodor also put in their RLE years before becoming Assistant Professors on the humanities staff in 1963. Later, Kenneth Hale in 1966 was an exception. But the current faculty includes, in addition to Halle, Chomsky, and Hale, four graduates of the MIT program – Paul Kiparsky, who entered MIT in 1962, and John Ross, James Harris, and David Perlmutter, who became graduate students in 1964.
A further characteristic of study at MIT has been the availability of the faculty for discussion and guidance. It is expected that students will begin serious independent research in the second year of the program, and it is also expected that they will work closely with one or another of the staff as their research progresses. Indeed, it is hoped that they will feel free to discuss any point with any of the instructors at any time: this is necessary if the hang-around-and-let-it-seep-in approach is to work. As the field has grown and pressures on staff members have increased, this approach has been somewhat modified and the easy and open faculty availability of the early days has undergone a certain constriction; nevertheless, there is a constant attempt to preserve as much of it as possible.
It was always understood that to maintain the research emphasis, the informal classroom approach, and the give and take necessary to both, it was imperative to restrict the size of the group. Seven students were accepted the first year, ten the next, ten the year after, and so it went. Since the program is designed to be completed in four years, the entire enrollment of full-time students rarely exceeded thirty-five or so. This number was augmented by post-Doctoral scholars in the program, numbering five or six a year. Today, despite the ascendancy of the MIT school and the expansion of graduate linguistic study in general, limiting the size of the group is still considered necessary to maintain the quality and flavor of the program. Thus, although applicants now total about eighty each year, the number of admissions remains at ten or eleven.
The current program has undergone changes since the early sixties, but by and large they have been changes of degree rather than substance. For example, a substantial literature now exists, and so does a widespread interest in linguistics, even on the undergraduate level. Thus students often arrive at MIT knowing more about transformational generative grammar than advanced theorists knew not so many years ago. At the same time, the enthusiasm that accompanies genuine discovery has passed into the questioning and criticism that arise when a theory has gained wide acceptance and is being pushed to its limits. As a result, although students are better prepared in some ways to deal with what they find at MIT, they are still not offered a Body of Truth to learn.
There are now some classes, more things to read, more people to talk to. But there is probably also more pressure and, as a result of alternative ways of grappling with the theory, more dissension. There are more introductory courses and they are a good deal more introductory than they ever were, but the opportunities for casual faculty-student contact have narrowed. On balance, it could probably be said that certain focuses have shifted and certain extremes have been blunted, but the particular flavor of the MIT linguistics program appears in general to persist.
No survey of this program would be complete without mention of the special role Morris Halle has played in its development. Others have given significantly of their time and their efforts, as well as their brainpower. But it is generally agreed that Halle, intellectually, spiritually, and practically, has been the strongest single force in building the group and in guiding and guarding its growth.
In order to be accepted as a full-time student in the linguistics program, it is necessary to satisfy Institute requirements for admission to the Graduate School and to have done well in previous academic work. However, beyond competence (i.e., three years of formal study) in two languages in addition to English, there are no explicit prerequisites in terms of courses or fields of specialty. Rather, applicants should demonstrate evidence of their ability to effectively engage in serious study of complex subject matter. This may take the form of academic work of very high quality, original research, challenging work experience, in-depth mastery of a language or language group, and so on.
A full-time student is expected to take the equivalent of four subjects for credit each semester.
The degree candidate must also complete a program of studies in a minor field, the choice of which is made by the student, subject to the approval of the department. The minor program ordinarily involves three one-semester graduate subjects, selected so as to form a meaningful whole. Likely fields for the completion of minor studies include electrical engineering, mathematics, philosophy, psychology, anthropology, literary theory, and advanced work in some group of languages. Work done before entering MIT is sometimes accepted as satisfying all or part of the minor requirement. Students may also take advantage of the cross-registration agreement with Harvard to complete their minor.
In the middle of the second year of full-time study, students normally take a general examination given by the linguistics section. Originally this was a written examination testing the following areas – general linguistics (problems of grammatical and phonemic structure), linguistic theories and methods, practical linguistic analysis, the relation between linguistics and adjacent fields, and questions on the student's special field. Later the last two topics were changed to historical linguistics and the structure of English. Still later (1970), the examination was replaced by the required preparation of two original in-depth studies, one syntactic and the other phonological. A board of three faculty members then administers an oral examination on the papers submitted by the student and related topics. Passage or failure is determined by the linguistics faculty, and revision of one or both of the papers and/or re-examination may be requested.
Finally, there is the research leading to a dissertation project, the completion of the dissertation, and the passing of an oral thesis defense.
From time to time, at the discretion of the department, special students are admitted who wish to study in the program without being degree candidates. Also admitted are post-Doctoral fellows who demonstrate a serious interest in the study of linguistics as undertaken at MIT. Such appointments are normally made for a period of one year.
Although the original proposal by the linguistics group called for the admission of from three to five students each year at first, the program actually started with seven regular students, one of whom later left, and three special or part-time students. The regular students included a psychologist, a chemist, a philosopher, an electrical engineer, and several mathematicians. All are at present actively involved at various institutions.
The linguistics section of the newly formalized Department of Modern Languages and Linguistics (MIT course of study number 23) began with a staff of six: Jakobson, Halle, Chomsky, Klima, Matthews, and Yngve (who by then was officially affiliated with the Department of Electrical Engineering but maintained his contact with the linguistics group). Furthermore, a significant shift was taking place: both interest and funding were now settling on the linguistics program itself, and researchers who were becoming increasingly concerned with linguistics in its theoretical aspects no longer had to operate through machine translation or other projects. It now became possible for the linguistics group directly to support the work of interested scholars such as S. Jay Keyser, Carlotta Smith, and a good many others.
23.71. SPECIAL PROBLEMS IN LANGUAGE AND LITERATURE.
23.72. SPECIAL PROBLEMS IN LANGUAGE AND LITERATURE. Advanced work in literature or linguistics for unusually well-prepared students. Offered by members of staff in their special fields.
It should be noted that the official beginning of the graduate linguistics program marked the official end of undergraduate linguistics courses at MIT for almost a decade. Although qualified undergraduates could and did enroll in several of the courses, there was not to be another specifically designed undergraduate introductory course until 1970.
Reviewing the first-year courses, it is immediately evident that the linguistics offerings had been expanded but not altered in any radical way. The aim and the scope of the teaching program remained entirely consistent with those of the research program. The mathematical-computer and machine translation aspects of the field were covered, as was the other applied form, speech analysis; but there was a greater number of courses relating to theoretical aspects. English was the only language covered in any comprehensive way, and it was treated in fairly great depth and breadth. In short, as the original proposal had stated, there was no attempt to duplicate linguistics programs elsewhere.
It might be noted that although this was undoubtedly deliberate, it might not have been possible without the presence of Harvard some blocks away, together with a long-standing exchange program that permitted full-time graduate students from one university to take as much as half their work at the other.
The linguistics group remained subsumed under the retitled Department of Modern Languages and Linguistics, which in 1969 was renamed the Department of Foreign Literatures and Linguistics. Its ties to the Research Laboratory of Electronics were also maintained, and in 1961 there were a number of related projects being carried out there.
Ten new graduate students were admitted in the fall of 1962, the second year of the program's existence, bringing to sixteen the total enrolled for a degree. This time there were linguists in the group as well as mathematicians, a computer specialist, a biologist, and a philosopher-psychologist. One failed to complete the program and a second went into medicine after finishing; the rest remain active in the field.
23.783 TYPOLOGY OF GRAMMARS. Study of the grammars of languages belonging to divergent families with a view to reaching a sharper characterization of universal features of grammatical structure, with the majority of examples to be drawn from non-Indo-European languages.
23.771. MATHEMATICAL BACKGROUNDS FOR COMMUNICATION SCIENCES. Fundamentals of discrete mathematics for non-mathematicians. Introduction to various topics in set theory, probability and information theory, logic, foundations, theory of automata and computability.
23.702. SEMINAR IN LINGUISTICS. Special problems in linguistics. Permission of instructor required.
23.701. CRUCIAL PROBLEMS IN LINGUISTICS. Sound and meaning: a study of the various types of relationships between phonetic and semantic aspects of language.
The year 1963 again saw the admission of ten new students, with what was becoming the typical diversity of backgrounds. Accordingly there were further additions to the staff and to the roster of courses. Matthews, formerly a research associate, became an Associate Professor, and Paul Postal, who had been associated with RLE, became an Assistant Professor in the department. Moreover, Jerrold Katz and Jerry Fodor, who had also been at RLE, joined the staff of the Humanities Department.
It is clear that at the close of the academic year 1963-1964, with twenty-six students, six of whom had completed three years and were deeply into their dissertations, with a growing number of special students and post-doctoral scholars, with a staff of six, plus three members of other departments, offering a roster of more than twenty courses, and with RLE research activities continuing, MIT had a full-scale linguistics program in operation.
For each language we attempt to construct abstractly a device (called technically a generative grammar of this language), which specifies the structural information about sentences that is available in principle to the speakers of the language. … A generative grammar provides an explicit account of one primary aspect of the state of the perceiving organism… Thus language provides a unique opportunity for precise formulation and fruitful empirical study of some of the central questions of perceptual psychology.
…our training and research programs have a strongly interdisciplinary flavor, and consequently most of the faculty have close contacts with members of other departments and are frequently involved in joint research projects with members of other departments at MIT and Harvard. Most of our students have similar interests, or acquire them during their graduate training, and we attempt to encourage their participation in such work…as fully as possible.
The syntactic component of a grammar generates an infinite set of structures which support phonological and semantic interpretation. … Our work in syntax divides naturally into two subparts, theoretical and applied. In theoretical syntax we are concerned to formulate the general properties of this recursive system…in as explicit and narrow a fashion as possible, on the basis of the data concerning syntactic structures of given languages which is provided by the work in applied syntax.
A consistent interpretation of the orientation and depth judgments in optical illusions, as well as a description of human performance in the psychophysics of space, can be made by constructing an abstract (generative) theory for the geometry of the visual perceptual world. A visual impression is "recognized" when the postulates adopted by the observer generate a precept well-formed according to the rules of the theory.
Linguistics applicants in 1964 totaled over forty; eleven were selected to become part of the program. Permanent-staff expansion came to a temporary halt that year. Aside from the addition of two Visiting Professors – Jerzy Kuryłowicz (for whom this marked a return) and Peter Colaclides – the only change was the replacement of William Locke as Chairman of the Department of Modern Languages and Linguistics by William F. Bottiglia, who taught French and Italian literature in the department. Chomsky was on leave, working at the Center for Cognitive Studies at Harvard, and Postal took over the teaching of STRUCTURE OF ENGLISH I, LINGUISTIC STRUCTURE, and SURVEY I.
23.701. CRUCIAL PROBLEMS IN LINGUISTICS. The history and present state of phonemic analysis. Phonemes and distinctive features. Phonetic typology and universals.
With all the research that was being carried on, a respectable literature was being built up. The most significant 1964 additions were Postal's Constituent Structure, Fodor and Katz's collection of the major relevant articles up to that time, and Katz and Postal's An Integrated Theory of Linguistic Descriptions, wherein a significant modification of the theory of linguistic descriptions was proposed.
Furthermore, an increasing number of languages were being studied within the framework of the developing theory. In addition to English, Russian, and German, which were continually being subjected to analysis in MIT classes, there was Paul Postal's work on Mohawk, Matthews' studies of Siouan languages (e.g., (1964)), and student investigations of Slavic (Lightner), French (Schane), Japanese (McCawley), and Spanish (Foley and then Harris).
21.722T. PHILOSOPHY OF LANGUAGE. Study of recent philosophical movements concerned with the treatment of traditional philosophical problems from a linguistic movement; in particular, logical positivism and ordinary language philosophy. Consideration of the treatment of philosophical problems within the framework of linguistic theory. Some acquaintance with Chomsky's theory of generative grammar desirable.
This was the year of the dissertation: eleven theses were accepted in 1965, representing the work of students of the first two classes to enter and dealing with various topics in phonology, syntax, and theory. Published in 1965 was Chomsky's major study of syntactic theory, Aspects of the Theory of Syntax.
With the staff additions in these years, the linguistics faculty reached its present composition except for David Perlmutter, who did not join the staff until 1970. John R. Ross, who had come to MIT as a linguistics student in 1964 and who has since made major contributions to the development of syntactic theory, was appointed Assistant Professor, as was James W. Harris, whose area of concentration is Romance phonology with particular emphasis on Spanish and who had also begun as a student in the program in 1964. The group lost the services of Edward S. Klima, who had played a significant role in the program since its formative years, but gained Kenneth Hale, a specialist in the study of non-Indo-European languages.
Note that Halle and Ross together were now teaching an introductory set of courses.
23.701. CRUCIAL PROBLEMS IN LINGUISTICS. The Moscow school – Fortunatov, Trubetzkoy, further stages – and its place in world linguistics.
23.732. STRUCTURE OF ENGLISH II: ADVANCED SYNTAX. Selected topics in the syntax of English.
23.756. INDO-EUROPEAN. Selected topics in the grammar of Indo-European.
9.59 PSYCHOLOGY OF LANGUAGE AND COMMUNICATION. Study of psychology of language processes in light of recent advances in structural linguistics; extensive critique of learning-theoretic accounts of verbal behavior; examination of problems of language acquisition and speech perception. Methodological implications of psycholinguistic experiments and theory will be stressed.
9.591. SEMINAR IN PSYCHOLOGY OF LANGUAGE AND COMMUNICATION. Reading, discussion, and criticism of selected topics. One or more of the following themes will be emphasized in a particular semester: theories of language, speech perception, communication in sub-human species, aphasia, language acquisition, language and thought, interaction between grammatical structure and verbal performance.
Undoubtedly the most important study of these years was the long-awaited Sound Pattern of English (1968) by Chomsky and Halle, still the standard work in generative phonological theory and its application. Earlier, on other topics, Chomsky's Cartesian Linguistics (1966) and Katz's Philosophy of Language (1966) had appeared.
23.741. TOPICS IN THE GRAMMAR OF A NON-INDO-EUROPEAN LANGUAGE.
Note that LINGUISTICS AND LITERARY STUDY and HISTORY OF THE ENGLISH LANGUAGE are offered jointly with the Humanities Department; SEMANTICS and ADVANCED SEMANTICS are offered jointly with the Philosophy Department; and LABORATORY ON THE PHYSIOLOGY, ACOUSTICS AND PERCEPTION OF SPEECH and SPEECH COMMUNICATION are offered jointly with the Department of Electrical Engineering.
9.592. SEMINAR IN PSYCHOLOGY OF LANGUAGE AND COMMUNICATION II. Advanced topics in psycholinguistics.
The specificity and detail of linguistic description is related to a theoretical apparatus of considerable complexity and power. … [V]ery severe limitations [are imposed] on how particular facts are to be characterized in a linguistic description. They allow us to deduce consequences beyond the facts that led to formulation of the rules in the first place, and to confirm or disconfirm the principles by testing these empirical consequences. Existence of such a theoretical apparatus is one of the distinctive features of a developed science, and linguistics shows signs of progress in this direction.
These principles that limit the possible hypothetical rules and systems of rules cannot be learned; rather, they serve as the preconditions for learning. It is reasonable to suppose that they form part of the innate capacity of every normal child. It is these principles that constitute the theoretical apparatus of linguistics mentioned above. And since these principles are part of the natural endowment of all men, an understanding of the principles must be part of our understanding of man's mental makeup.
…The theory of grammar is concerned with the overall structure of grammars, the question of evaluating grammars and determining their empirical adequacy. It attempts thus to delineate the innate knowledge that allows children to master languages.
An early hypothesis…held that the "semantic component" of the grammar assigns to each deep structure a semantic interpretation that represents the logical form of sentences… More recent work has explored the possible contribution of other aspects of syntactic structure to semantic interpretation, in particular, in connection with anaphora, scope of logical elements, focus and presupposition, and related matters. Some linguists have proposed that there is no separate semantic component in language, but that the transformational rules themselves directly relate semantic interpretations to surface structure, with no intermediate level of deep structure. A crucial issue is the structure of the lexicon and the rules that insert lexical items into derivations. Topics in this general area are now the subject of lively discussion and intensive research. Within our program, many points of view are represented.
…The central problems of phonology are to characterize the rules that constitute this [input-output] system and to define the manner in which the rules may function. …The study of the primitives of phonology directly involves questions that are on the borderline between linguistics and acoustics, motor physiology, psychology of perception, and neuroanatomy. Work here is conducted in active collaboration with Professor K. N. Stevens of the Electrical Engineering faculty and other members of the research group.
Work in psycholinguistics proceeds within the Department of Psychology, under joint auspices of the Department of Psychology and the Research Laboratory of Electronics. This work has been primarily directed toward the construction and evaluation of psychological models of syntax recognition and of speech development. Work in the first area has included a variety of studies of the interaction between syntactic formalisms and the sentence recognition heuristics employed by speaker/hearers in recovering the structure of messages in their language. Work in the second area has been concerned with establishing the ontogenetic sequence of syntactic development and, recently, with the development of experimental techniques for assessing the operation of constancies in phonetic perception by 3- to 5-month-old infants.
Fraser, Bruce, An Examination of the Verb-Particle Construction in English.
Gruber, Jeffrey, Studies in Lexical Relations.
Hall, Barbara, Subject and Object in Modern English.
Kiparsky, R. Paul V., Phonological Change.
Kuroda, Sige-Yuki, Generative Grammatical Studies in the Japanese Language.
Langendoen, Terence, Modern British Linguistics.
Lightner, Theodore, Segmental Phonology of Modern Standard Russian.
McCawley, James, Accentual System of Standard Japanese.
Petrick, Stanley, A Recognition Procedure for Transformational Grammars.
Rosenbaum, Peter, Grammar of English Predicate Complement Constructions.
Schane, Sanford, Phonological and Morphological Structure of French.
Zwicky, Arnold, Topics in Sanskrit Phonology.
Lieberman, Philip, Intonation, Perception, and Language.
Chapin, Paul, On the Syntax of Word-Derivation in English.
Harris, James W., Spanish Phonology.
Bedell, George, Kokugaku Grammatical Theory.
Dougherty, Ray C., A Transformational Grammar of Coordinate Conjoined Structures.
Naro, Anthony, The History of Portuguese Passives and Impersonals.
Perlmutter, David M., Deep and Surface Constraints in Syntax.
Anderson, Stephen, West Scandinavian Vowel Systems and the Ordering of Phonological Rules.
Jackendoff, Ray S., Some Rules of Semantic Interpretation for English.
Kayne, Richard S., The Transformational Cycle in French Syntax.
Stanley, Richard, The phonology of the Navaho Verb.
Woo, Nancy, Prosody and Phonology.
Akmajian, Adrian, Aspects of the Grammar of Focus in English.
Brame, Michael, Arabic Phonology: Implications for Phonological Theory and Historical Semitic.
Dell, François, Les Règles Phonologiques Tardives et La Morphologie Derivationelle du Français (Topics in French Phonology and Derivational Morphology).
Emonds, Joseph, Root and Structure-Preserving Transformations.
Fodor, Janet Dean, Linguistic Description of Opaque Contexts.
Geis, Michael, Adverbial Subordinate Clauses in English.
Kimball, John, Categories of Meaning.
Caplan, David, Probe Tests and Sentence Perception.
Culicover, Peter, Syntactic and Semantic Investigations.
Fischer, Susan D., The Acquisition of Verb-Particle and Dative Constructions.
Helke, Michael, The Grammar of English Reflexives.
Nakau, Minoru, Sentential Complementation in Japanese.
Williams, George, Networks of Anaphora: An Essay in the Syntax of Pronominalization.
Bresnan, Joan W., Theory of Complementation in English Syntax.
De Rijk, Rudolphus, Studies in Basque Syntax: Relative Clauses.
Howard, Irwin, A Directional Theory of Rule Application in Phonology.
Jenkins, Lyle, Modality in English Syntax.
Lasnik, Howard B., Analyses of Negation in English.
Pope, Emily A. Norwood, Questions and Answers in English.
Selkirk, Elisabeth O., The Phrase Phonology of English and French.
Wasow, Thomas A., Anaphoric Relations in English.
Bowers, John S., Grammatical Relations.
Erteschik, Naomi, On the Nature of Island Constraints.
Higgins, F.R., The Pseudo-Cleft Construction in English.
Kornfeld, The Perception of Syntactic Boundaries.
Leben, William R., Supra-Segmental Phonology.
Maling, Joan M., The Theory of Classical Arabic Metrics.
Permesly, Sylvia Schwartz, Some Aspects of Presupposition in Generative Grammar.
Vergnaud, Jean-Roger, Syntax of French Relative Clauses.
 It might be added that the "glamour" of the work and workers at RLE is in inverse proportion to the glamour of the physical environment. Surrounded by the gleaming products of the sixties' building boom, as well as by a parking garage and a railroad track, sits squat old Building 20, a "temporary" wooden barracks building dating back to World War Two. It is here, in the alphabetically non-ordered wings of the building (wing A is followed by E, D, and C, with wing B perpendicular to all), that radar was developed and the MIT linguistics group still has its offices.
 The Proceedings of the conference were published in the Journal of the Acoustic Society of America (1950).
 It is worth noting that one of the mathematicians was female – Barbara Hall (Partee). The classes entering in 1963 and 1964 as well each included a woman, and since then a fair proportion of each class has been female.
 As it turns out, the flow of linguistics students from Harvard to MIT has consistently been heavier than that in the opposite direction. Harvard has more students, of course. But there is also the fact that for some time the content of the courses at MIT was simply not available elsewhere.
 All the quotations that follow in this section are from an Application for Graduate Training Grant under the Public Health Service Act dated 29 May 1964.
 Paula Menyuk, now with the Boston University School of Education, was then associated with Stevens' speech research group at RLE.
 Murray Eden, a physical chemist associated with the Department of Electrical Engineering, was also involved in RLE communications research.
 See the Appendix, especially for 1965.
 These courses were offered jointly with Electrical Engineering.
 Staal's course on Pānini is not included here since it was taught only one semester while Staal was visiting MIT.
 Not included is G. H. Matthews, who left the staff in 1973 after an affiliation dating back to 1956.
 Omitted from this list are courses taught only once since 1968 and courses not actually offered for several years prior to 1973.
1944 The Loom of Language, ed. by L. Hogben (New York: Norton).
1953 "Systems of Syntactic Analysis," Journal of Symbolic Logic.
1956 "Three Models for the Description of Language," I.R.E. Transactions on Information Theory, IT-2; reprinted in Readings in Mathematical Psychology, II, ed. by R. D. Luce, R. Bush, and E. Galanter (1965) (New York: Wiley).
1957 Syntactic Structures (The Hague: Mouton).
1959a "On Certain Formal Properties of Grammars," Information and Control 2; reprinted in Readings in Mathematical Psychology, II, ed. by D. Luce, R. Bush, and E. Galanter (1965) (New York: Wiley).
1959b Review of Verbal Behavior by Skinner, Language 35; reprinted in Fodor and Katz (1964).
1961 "On the Notion 'Rule of Grammar'," Proceedings of the Twelfth Symposium in Applied Mathematics, ed. by R. Jakobson (Providence, R.I.: American Mathematical Society); reprinted in Fodor and Katz (1964).
1962 "A Transformational Approach to Syntax," Proceedings of the Third Texas Conference on Problems of Linguistic Analysis in English, 1958, ed. by A. A. Hill (Austin: The University of Texas); reprinted in Fodor and Katz (1964).
1964 Current Issues in Linguistic Theory (The Hague: Mouton); reprinted, in a slightly earlier version, in Fodor and Katz (1964); originally presented, in a somewhat different version, as a paper in the session "The Logical Basis of Linguistic Theory" and appears under this title in Proceedings of the Ninth International Congress of Linguists, ed. by H. Lunt (1964) (The Hague: Mouton).
1965 Aspects of the Theory of Syntax (Cambridge, Mass.: MIT Press).
1966 Cartesian Linguistics (Cambridge, Mass.: MIT Press).
1968 The Sound Pattern of English (New York: Harper & Row).
1956 "On Accent and Juncture in English," For Roman Jakobson, ed. by M. Halle, H. Lunt, and H. MacLean (The Hague: Mouton).
Fodor, J. A. and J. J. Katz, eds.
1964 The Structure of Language: Readings in the Philosophy of Language (Englewood Cliffs, N.J.: Prentice-Hall).
1954 "The Role of Context in the Perception of Stops," Language 30.
1957 Verbal Behavior (New York: Appleton-Century-Crofts).
1959 The Sound Pattern of Russian (The Hague: Mouton).
1961 "On the Role of Simplicity in Linguistic Description," Proceedings of the Twelfth Symposium in Applied Mathematics, ed. by R. Jakobson (Providence, R.I.: American Mathematical Society).
1960 On the Recognition of Speech by Machine, MIT Ph.D. dissertation.
1952 Preliminaries to Speech Analysis (Cambridge, Mass.: MIT Press).
1966 The Philosophy of Language (New York: Harper & Row).
1964 An Integrated Theory of Linguistic Descriptions (Cambridge, Mass.: MIT Press).
1960 The Grammar of English Nominalizations [Indiana University Research Center in Anthropology, Folklore, and Linguistics, 12] (Bloomington: Indiana University Press).
1955 Machine Translation of Languages (Cambridge, Mass.: MIT Press; New York: Wiley).
1964 Hidatsa Syntax (The Hague: Mouton).
1964 Constituent Structure: A Study of Contemporary Models of Syntactic Description [Indiana University Research Center in Anthropology, Folklore, and Linguistics, 30] (Bloomington: Indiana University Press).


text:
Two infrastructure projects along Jakarta-Cikampek toll road postponed
Jakarta / Wed, November 21, 2018 / 02:50 pm
Traffic moves at a snail's pace on the Cikampek-Jakarta toll road as workers are busy building the elevated toll road in Bekasi, West Java, on Aug. 8. (Antara/Risky Andrianto)
The central government will postpone two out of three infrastructure projects passing along the Jakarta-Cikampek toll road, namely the Jakarta-Bandung high-speed railway and the light rail transit (LRT) projects, owing to traffic congestion caused by the construction.
Construction of the Jakarta-Cikampek II elevated toll road, meanwhile, is still ongoing with a targeted completion date of June 2019, during the Idul Fitri holiday.
Transportation Minister Budi Karya Sumadi said on Tuesday that the decision was made to alleviate severe traffic congestion at several points along the 73-kilometer toll road, which is operated by PT Jasa Marga, such as the 11 km and 17 km points.
"For example, I've asked the KCIC [PT Kereta Cepat Indonesia-China] not to carry out [the Jakarta-Bandung high-speed railway] construction here [on the toll road] for the time being, but [do other parts] somewhere else. While for the LRT, I've asked to postpone their work at the 14 km point for several months," he said as quoted by kompas.com.
Jasa Marga president director Desi Arryani suggested that road users not enter the toll road at night as the toll operator was speeding up the Jakarta-Cikampek II elevated project.
"From 10 p.m. to 6 a.m. please don't use the toll road because that's when construction is happening," she said. (vla)
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redpajama_set_name: RedPajamaCommonCrawl


I had just moved my things into my home and had to go off island to help my 82-year-old mother move from her home where she had lived for 51 years. All of my belongings were still in boxes. You didn't have a key so you ripped open the screen and took the glass out and crawled in through the window.
I am guessing that you wanted to help me unpack, so you ripped open the boxes and threw my belongings on the floor. That wasn't quite the place I was planning to put them.
Anyway, you then decided to go through the things that were in the boxes and now on the floor. I am guessing that you thought you should get paid for helping me unpack so you decided to take two full face snorkels, a waffle maker, an electric pot to heat water, good kitchen knives, a woven basket from Africa as well as what was in the basket, and more.
Let me share with you about a couple of items you took.
The waffle maker has made hundreds of waffles for students, teachers, parents, and church members as well as others. The electric hot water pot has made hundreds and hundreds of cups of hot water for hot tea and hot chocolate for teachers, students, parents, and church members.
You may have taken these things but you didn't take the fond memories of sitting around sharing stories and talking and laughing and sometimes crying together.
The basket from Africa may not mean much to you so I will share where I got it. A student brought that basket from Africa to give me for helping her learn English because she wanted to show her appreciation for guiding her with her lessons.
I am guessing that you didn't feel that was enough pay so you decided to decorate my new home with pig poop. You decided it couldn't stay out in the fields or be used for fertilizer, you decided to decorate my blank walls with the pig poop.
Now, after returning from the mainland, I find where I am having to pick up after you and clean up after you and you still have taken items that don't belong to you that have memories attached.
I hope you will enjoy making and sharing waffles with family and friends and share a cup of hot tea or hot chocolate with children and adults alike. I hope you will enjoy the snorkel masks as much as I have.
Oh, by the way, be careful with the electric pot, it is getting old and sometimes it doesn't want to automatically turn off. Be careful because the water gets very hot.