Tingling in the hand and fingers happens to every 10th person in the world.
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What to do? In this case, it is best to consult a doctor how to help yourself.


text:
\section*{Supplemental Material}

\section{Microscopic Polarization}
\label{sec:microscopic_polarization}

Any operator which transforms like a polar, T-even vector under the point group of the pyrochlore crystal should, on symmetry grounds, contribute to the polarization $\vec{P}$ (ie. couple to $\vec{E}$ linearly).
Ref.~\cite{Lantagne-Hurtubise2017} found all vector-like irreps of the diamond lattice point-group up to bilinear in nearest-neighbor spin operators; projecting these down into the spin ice manifold leads to quadratic coupling to $\vec{E}$. From the long-wavelength considerations, we expect a linear coupling to exist microscopically, but it will involve more than nearest neighbor spin operators and an exhaustive analysis would be exhausting. Rather, here we simply guess: the $\vec{b}$ corresponds to the flux of the lattice $\vec{a}$, so it should have something to do with oriented ring exchange coupled to a vector given by the right hand rule.

\begin{widetext}
We define the ring raising operator
	\begin{align}
	\Lambda_{ik}^{j, s} =
	S^+_{s + (-1)^s (\vec{t}_i/2)}
	S^-_{s + (-1)^s (\vec{t}_i - \vec{t}_j/2)}
	S^+_{s + (-1)^s (\vec{t}_i - \vec{t}_j+\vec{t}_k/2)}
	S^-_{s + (-1)^s (\vec{t}_i/2 - \vec{t}_j+\vec{t}_k) }
	S^+_{s + (-1)^s (- \vec{t}_j/2 + \vec{t}_k)}
	S^-_{s + (-1)^s (\vec{t}_k/2)}
\end{align}
\end{widetext}
which raises the circulation of the spins around the elementary cycle specified by  $(s,i\bar{j}k\bar{i}j\bar{k})$ for site $s\in A$ or $(s, \bar{i} j \bar{k} i \bar{j} k)$ for $s \in B$ with distinct $i,j,k \in \{1\cdots 4\}$ indexing the 4 $[111]$ directions in the lattice.
The hermitian conjugate of $\Lambda$ lowers the circulation, or equivalently, raises the circulation of the oppositely oriented cycle:
\begin{align}
	\left(\Lambda_{ik}^{j,s}\right)^\dagger = \Lambda_{ki}^{j,s}
\end{align}
Also, the following bookkeeping identities hold,
\begin{align}
	&\underbrace{\Lambda_{ik}^{j,s} = \Lambda_{kj}^{i,s+i-j} = \Lambda_{ji}^{k,s-j+k}}_{A\textrm{ site reference}}
	\nonumber \\ &= \underbrace{(\Lambda_{ji}^{k,s+i})^\dagger = (\Lambda_{ik}^{j,s+i-j+k})^\dagger   = (\Lambda_{kj}^{i,s+k})^\dagger}_{B\textrm{ site reference}}
\end{align}

Define the average lattice flux operator
\begin{align}
\label{eq:micro_b_polarization_SI}
	\vec{O} = i \sum_{s\in A} \sum_{\sigma \in S_4} \Lambda_{\sigma_1 \sigma_3}^{\sigma_2, s} \hat{t}_{\sigma_4} \, \mathrm{sign} (\vec{t}_{\sigma_4} \cdot (\vec{t}_{\sigma_1} \times \vec{t}_{\sigma_3}))
\end{align}
The sum on A sites automatically makes this operator invariant under lattice translations.
The sum on permutations $\sigma$ runs over all 24 of the oriented cycles running through each A site.
As every distinct cycle runs through 3 A sites, $\vec{O}$ triple counts the cycles, but this simply contributes a factor of 3 compared to the less formal definition in the main text.
The unit vectors $\hat{t}_i$ correspond to the 4 $[111]$ directions.

\begin{table}[t]
	\centering

	\begin{tabular}{l|cc}
	\hline

	\hline
	\textbf{Doublet} & \textbf{State} & \textbf{Number of Spins-1/2} \\
	\hline
	\textrm{Effective spin-1/2} & $\ket{\pm 1/2}$ & $n = 1$\\
	\textrm{Dipolar-octupolar}  & $\ket{\pm 3/2}$ & $n = 3$\\
	\textrm{Non-Kramers}	    & $\ket{\pm 1}$  &  $n = 2$\\
	\hline

	\hline
	\end{tabular}
	\caption{Types of crystal field doublets in pyrochlore spin ice.}
	\label{tab:spin_symmetry}
\end{table}

We next specify the behavior of the microscopic spin operators $\vec{S}_r$ under the point group and time reversal transformations.
Quantum spin ices are grouped according to the representation of the fundamental doublet `spin' \cite{Rau2019}, see Table~\ref{tab:spin_symmetry}.
We get a nice compact representation for each of the classes by simply putting $n = 2s$ `true' spin 1/2's per site with the following definitions:
\begin{align}
	S^z &= \frac{1}{n}\sum_{j=1}^n \sigma^z_j &
	S^{\pm} &= \prod_{j=1}^n \sigma^{\pm}_j
\end{align}
From these formulae, the transformation rules for the effective spin operators follow immediately from those of a fundamental spin $\vec{\sigma}$, which is a T-odd axial vector.
These choices normalize $S^z, S^\pm$ as Pauli matrices.

\paragraph{Spin-1/2---} If the spin operators behave like fundamental spin 1/2 objects, then $\vec{S}$ is a T-odd axial vector. That is:
\begin{align}
	T: \vec{S}_r &\to -\vec{S}_r \\
	R: \vec{S}_r &\to |R|R \vec{S}_{R^{-1}r}
\end{align}

Breaking this into local components, we find time reversal is straightforward
\begin{align}
	T: S^z_r &\to - S^z_r \\
		S^\pm_r&\to - S^{\mp}_r \\
		\Lambda_{ik}^{j,s} &\to \Lambda_{ki}^{j,s} = \left(\Lambda_{ik}^{j,s}\right)^\dagger
\end{align}

\begin{widetext}
Spatial operations require the spin fields to be re-expanded in the local basis at the new bond:
\begin{align}
	\vec{S}_r = S^z_r \hat{t}_r + S^+_r \vec{e}^-_r + S^-_r \vec{e}^+_r
\end{align}
Under point group transformations $R$ which preserve $s$ sites, the local $\hat{t}_r$ vector is preserved by $R$, even if it is improper:
\begin{align}
	\hat{t}_r = R \hat{t}_{R^{-1}r}\ .
\end{align}
The transverse planes are mapped into one another by $R$ as well, but the local choice of $\hat{x}$ and $\hat{y}$ may require an extra $O(2)$ rotation to be brought into alignment:
\begin{align}
	e^{\pm i \theta(R,r)} \vec{e}^{|R|\pm}_r =  R \vec{e}^{\pm}_{R^{-1}r}
\end{align}
Note that the O(2) rotation is improper if and only if $R$ is. The angle $\theta(R,r)$ only depends on the type $i$ of bond center $r$ and the point group transformation $R$.

Putting this together, we find that
\begin{align}
	R : \vec{S}_r &\to |R| R \vec{S}_{R^{-1}r} \\
	&= |R| R \left(S^z_{R^{-1}r}\hat{t}_{R^{-1}r} + S^+_{R^{-1}r} \vec{e}^-_{R^{-1}r} + S^-_{R^{-1}r} \vec{e}^+_{R^{-1}r} \right) \\
	&= |R| \left(S^z_{R^{-1}r} R \hat{t}_{R^{-1}r} + S^+_{R^{-1}r} R \vec{e}^-_{R^{-1}r} + S^-_{R^{-1}r} R \vec{e}^+_{R^{-1}r} \right) \\
	&= |R| \left(S^z_{R^{-1}r} \hat{t}_{r} + S^+_{R^{-1}r} e^{-i \theta(R,r)} \vec{e}^{|R|-}_{r} + S^-_{R^{-1}r} e^{+i \theta(R,r)}\vec{e}^{|R|+}_{r} \right)
\end{align}
which allows us to extract the transformation law for the component fields:
\begin{align}
	R : S^z_{r} &\to |R| S^z_{R^{-1}r} \\
      S^{\pm}_r &\to |R| e^{\mp i \theta(R,r)}S^{|R|\pm}_{R^{-1}r}
\end{align}
and for the ring exchange operators:
\begin{align}
	\Lambda_{ik}^{j,s} &\to |R|^6 e^{i \sum \theta}
	S^{|R|+}_{R^{-1}(s + \vec{t}_i/2)}
	S^{|R|-}_{R^{-1}(s + \vec{t}_i - \vec{t}_j/2)}
	S^{|R|+}_{R^{-1}(s + \vec{t}_i - \vec{t}_j+\vec{t}_k/2)}
	S^{|R|-}_{R^{-1}(s + \vec{t}_i/2 - \vec{t}_j+\vec{t}_k)}
	S^{|R|+}_{R^{-1}(s - \vec{t}_j/2 + \vec{t}_k)}
	S^{|R|-}_{R^{-1}(s + \vec{t}_k/2)} \nonumber\\
	&= \left\{ \begin{array}{ll}
	\Lambda_{R^{-1}i R^{-1}k}^{R^{-1}j, R^{-1}s} & |R| = +1 \\
	\Lambda_{R^{-1}k R^{-1}i}^{R^{-1}j, R^{-1}s} & |R| = -1
	\end{array} \right.
\end{align}
Here, $R^{-1}$ acts as permutation on the bond types $i$ because $R$ which preserves $s$ simply permutes the $\hat{t}_i$. More specifically, we define the permutation action of $R$ on the bond types by $R \vec{t}_i = \vec{t}_{R i}$.

Finally, consider inversion through a bond center $I$. This maps all $i$-type bonds to $i$-type bonds. Thus:
\begin{align}
	\hat{t}_r &= \hat{t}_{I^{-1} r} &
	\hat{e}^{\pm}_r &= \hat{e}^{\pm}_{I^{-1}r}
\end{align}
So we find the trivial action on the spin components
\begin{align}
	I : \vec{S}_r &\to |I| I \vec{S}_{I^{-1} r} = \vec{S}_{I^{-1} r} \\
		S^z_r &\to S^z_{I^{-1} r} \\
		S^\pm_r & \to S^{\pm}_{I^{-1} r}
\end{align}
On the other hand, the ring exchange orientation is flipped:
\begin{align}
	I: \Lambda_{ik}^{j,s} \to \Lambda_{ik}^{j, (I^{-1}s)} = \Lambda_{ki}^{j,I^{-1}s +(-1)^s(- i + j - k)}
\end{align}
That is, if $I$ is plaquette $p = (s, ijk)$ centered, then $\Lambda_p \to \Lambda_p^\dagger$.

Finally, we turn to the action of the symmetries on  $\vec{O}$. For proper $R$ preserving s:
\begin{align}
	R : \vec{O} &= i \sum_s \sum_\sigma \Lambda_{\sigma_1 \sigma_3}^{\sigma_2, s} \hat{t}_{\sigma_4} \, \mathrm{sign} (\vec{t}_{\sigma_4} \cdot (\vec{t}_{\sigma_1} \times \vec{t}_{\sigma_3})) \\
	&\to i \sum_s \sum_\sigma \left(\Lambda_{R^{-1} \sigma_1 R^{-1}\sigma_3}^{R^{-1}\sigma_2, R^{-1}s} \right) \hat{t}_{\sigma_4} \, \mathrm{sign} (\vec{t}_{\sigma_4} \cdot (\vec{t}_{\sigma_1} \times \vec{t}_{\sigma_3})) \\
	&= i \sum_s \sum_\sigma \Lambda_{\sigma_1 \sigma_3}^{\sigma_2, s} \hat{t}_{R \sigma_4} \, \mathrm{sign} (\vec{t}_{R \sigma_4} \cdot (\vec{t}_{R \sigma_1} \times \vec{t}_{R \sigma_3})) \\
	&= i \sum_s \sum_\sigma \Lambda_{\sigma_1 \sigma_3}^{\sigma_2, s} R \hat{t}_{\sigma_4} \, \mathrm{sign} (R \vec{t}_{\sigma_4} \cdot (R \vec{t}_{\sigma_1} \times R \vec{t}_{\sigma_3})) \\
	&= i \sum_s \sum_\sigma \Lambda_{\sigma_1 \sigma_3}^{\sigma_2, s} R \hat{t}_{\sigma_4} \, \mathrm{sign} (\vec{t}_{\sigma_4} \cdot (\vec{t}_{\sigma_1} \times \vec{t}_{\sigma_3})) = R \vec{O}
\end{align}
For improper $R$ preserving s,
\begin{align}
	R : \vec{O} &\to i \sum_s \sum_\sigma \left(\Lambda_{R^{-1} \sigma_3 R^{-1}\sigma_1}^{R^{-1}\sigma_2, R^{-1}s} \right) \hat{t}_{\sigma_4} \, \mathrm{sign} (\vec{t}_{\sigma_4} \cdot (\vec{t}_{\sigma_1} \times \vec{t}_{\sigma_3})) \\
	&= i \sum_s \sum_\sigma \Lambda_{\sigma_3 \sigma_1}^{\sigma_2, s} R \hat{t}_{\sigma_4} \, \mathrm{sign} (R \vec{t}_{\sigma_4} \cdot (R \vec{t}_{\sigma_1} \times R \vec{t}_{\sigma_3})) \\
	&= i \sum_s \sum_\sigma \Lambda_{\sigma_3 \sigma_1}^{\sigma_2, s} R \hat{t}_{\sigma_4} \, |R| \mathrm{sign} (\vec{t}_{\sigma_4} \cdot (\vec{t}_{\sigma_1} \times \vec{t}_{\sigma_3})) \\
	&= -i \sum_s \sum_\sigma \Lambda_{\sigma_3 \sigma_1}^{\sigma_2, s} R \hat{t}_{\sigma_4} \, |R| \mathrm{sign} (\vec{t}_{\sigma_4} \cdot (\vec{t}_{\sigma_3} \times \vec{t}_{\sigma_1}))
	= R \vec{O}
\end{align}
and for bond centered inversion $I$:
\begin{align}
	I : \vec{O} &\to i \sum_s \sum_\sigma \Lambda_{\sigma_3 \sigma_1}^{\sigma_2, (Is - \vec{t}_{\sigma_1} + \vec{t}_{\sigma_2} - \vec{t}_{\sigma_3})} \hat{t}_{\sigma_4} \, \mathrm{sign} (\vec{t}_{\sigma_4} \cdot (\vec{t}_{\sigma_1} \times \vec{t}_{\sigma_3})) \\
	&= i \sum_s \sum_\sigma \Lambda_{\sigma_3 \sigma_1}^{\sigma_2, s} \hat{t}_{\sigma_4} \, \mathrm{sign} (\vec{t}_{\sigma_4} \cdot (\vec{t}_{\sigma_1} \times \vec{t}_{\sigma_3})) \\
	&= - i \sum_s \sum_\sigma \Lambda_{\sigma_3 \sigma_1}^{\sigma_2, s} \hat{t}_{\sigma_4} \, \mathrm{sign} (\vec{t}_{\sigma_4} \cdot (\vec{t}_{\sigma_3} \times \vec{t}_{\sigma_1})) = I \vec{O}
\end{align}
and for time reversal $T$:
\begin{align}
	T : \vec{O} &\to -i \sum_s \sum_\sigma \Lambda_{\sigma_3 \sigma_1}^{\sigma_2, s} \hat{t}_{\sigma_4} \, \mathrm{sign} (\vec{t}_{\sigma_4} \cdot (\vec{t}_{\sigma_1} \times \vec{t}_{\sigma_3})) = \vec{O}
\end{align}
So, indeed, the $\vec{O}$ operator transforms like a T-even polar vector.

\end{widetext}

\paragraph{Other classes---}
For $n > 1$, the spin operators transform as:
\begin{align}
	T : S^z_r &\to - S^z_r \\
		S^\pm_r &\to (-1)^n S^{\mp}_r \\
	R : S^z_r &\to |R| S^z_{R^{-1}r} \\
		S^\pm_r &\to |R|^n e^{\mp i n \theta(R,r)} S^{|R|\pm}_{R^{-1}r} \\
	I : S^z_r &\to S^z_{I^{-1}r} \\
		S^\pm_r & \to S^\pm_{I^{-1}r}
\end{align}
It is straightforward to check that the additional $n$-dependent factors cancel out of the transformation rules for $\Lambda$ and, accordingly, $\vec{O}$.

\section{Units}

In SI units, the Lagrangian for the (native) electromagnetic field in matter can be written generally
\begin{align}
    \mathcal{L} = \frac{\epsilon_0}{2}(\vecE^2 - c^2 \vecB^2) - \phi \rho_f + \vecA\cdot \vec{J}_f + \vecP \cdot \vecE + \vecM \cdot \vecB
\end{align}
where $\vecE = - \vec{\nabla} \phi - \dot{\vecA}$ and $\vecB = \vec{\nabla}\times \vecA$.
This allows us to read off the magnetization $\vecM$ and polarization $\vecP$ by comparison with the Lagrangian of the coupled system in the main text.

The fine structure constant $\alpha = \frac{1}{4\pi \epsilon_0} \frac{e^2}{\hbar c}$ and $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$; thus, both $\epsilon_0$  and $\mu_0$ can be expressed in terms of fundamental constants $e, \hbar, c$ and $\alpha$.
Since $c$ and $\alpha$ are different in the native and emergent theories, we find it convenient to set $\hbar = e = e_e = 1$ and parametrize the theory by $c, c_e$ and $\alpha, \alpha_e$ explicitly as in Eq.~\eqref{eq:twomaxwell}.
The fields due to elementary emergent charges are then
\begin{align}
\label{eq:elementaryfields}
    \vec{e} &= \alpha_e c_e \frac{\hat{r}}{r^2} \\
    \vec{b} &= \frac{1}{2} \frac{\hat{r}}{r^2}
\end{align}
where we have taken the elementary $b$-monopole charge $q^m=2\pi$ due to Dirac quantization,
\begin{align}
    q^e q^m & = 2\pi \hbar n & n \in \mathbb{Z}
\end{align}

Noting that $\vec{P} = g_{bE} \vec{b}$ and that the bound native charge $\rho_b = - \vec{\nabla}\cdot\vecP$, we obtain the relationship $Q^e = - 2\pi g_{bE}$ for the charge bound on an elementary $b$-monopole using Eq.~\eqref{eq:elementaryfields}.

\section{Toy Model in Octahedral Spin Ice}

The crystal field environment of a hexagonal plaquette in pyrochlore spin ice is geometrically quite complicated.
Here, we provide a toy model in octahedral spin ice with cubic symmetry.
This permits a simple illustration of how the atomic dipole operator on a square plaquette rotates into the effective ring exchange operator $\vec{O}$ (see Eq.~\eqref{eq:micro_b_polarization}) by Schrieffer-Wolf rotation into the low energy manifold.

\begin{figure}[tb]
    \centering
    \includegraphics[width=0.8\columnwidth]{fig_toy_square_plaq.pdf}
    \caption{Representative square plaquette in toy model for octahedral spin ice. Each of the 4 atoms (transparent spheres) is located at the midpoint of an edge (red) of the plaquette. Each atom contains 4 orbitals arranged in a ring on the plane transverse to its edge, between which two spinless electrons hop. This leads to a ground state orbital doublet whose states correspond to orbital angular momentum aligned along or against the local axis.}
    \label{fig:fig_toy_square_plaq}
\end{figure}

In octahedral spin ice, the magnetic atoms sit on the midpoints of the bonds of a cubic lattice, see Fig.~\ref{fig:fig_toy_square_plaq}, and the ice rules take the form of 'three-in--three-out' configurations on each vertex of the cubic lattice.
In the extreme crystal field dominated limit, we model each `atom' by a hopping model on a set of four `atomic' orbitals arranged in a square ring transverse to the bond.
For example, the orbitals for an atom on an $\hat{x}$ bond are displaced from the midpoint of the bond by $l (\pm \hat{z} \pm \hat{y})/\sqrt{2}$ with some distance $l$ much smaller than the lattice length $1$.
The intra-atom crystal field Hamiltonian on atom $i$ is simply
\begin{align}
    H_{XF,i} = -t \sum_a c^{\dagger}_{i,a+1} c_{i,a} + \textrm{h.c.}
\end{align}
where $a$ runs over the four orbitals.
The single particle spectrum of $H_{XF}$ is $-t, 0, 0, t$, with the central doublet carrying angular momentum $\pm \pi/2$ (clockwise/counter-clockwise) around the ring.
By placing two spinless, non-interacting electrons on each atom, we obtain an easy-axis non-Kramers ground state doublet corresponding to whether the second electron is in the CW or CCW state -- that is, whether the current is clockwise or counter-clockwise.
The electrons cannot hop between atoms and they do not interact within the atom.

The ice rules emerge from magnetic (current-current) interactions between neighboring atoms
\begin{align}
    H_{ice} &= J \sum_{\langle i,j \rangle} \sigma^z_i \sigma^z_j
\end{align}
where $\sigma^z_i = \pm 1$ indicates whether the current on atom $i$ is flowing CW/CCW with respect to an appropriately oriented local bond.

The Coulomb interaction between two atoms $i$ and $j$ can be expressed as a quadratic form in the number operators on each atom.
\begin{align}
  H_{Coulomb} = \sum_{i,j,a,b} V^{ij}_{ab} n_{i,a} n_{j,b}
\end{align}
where $n_{i,a} = c^{\dagger}_{i,a}c_{i,a}$ and $a, b$ run over the four orbitals of each atom.
Since there are exactly two electrons on each atom, we have the linear constraints $\sum_a n_{i,a} = 2$ so we can express the quadratic form in terms of 3 linearly independent number operators.

For specificity, consider an atom $i$ lying on a $\hat{x}$ oriented bond.
Looking down the $\hat{x}$ axis, we index the orbitals
\begin{equation*}
    \tikz[scale=0.5]
        \draw[->] (0,-2.5) -- (0,2.5) node[right] {$y$};
        \draw[->] (-2.5,0) -- (2.5,0) node[above] {$z$};

        \coordinate (s0) at (1,1);
        \coordinate (s1) at (-1,1);
        \coordinate (s2) at (-1,-1);
        \coordinate (s3) at (1,-1);

        \filldraw (s0) circle (4pt) node[left] {$0$};
        \filldraw (s1) circle (4pt) node[right] {$1$};
        \filldraw (s2) circle (4pt) node[right] {$2$};
        \filldraw (s3) circle (4pt) node[left] {$3$};

        \draw (0,0) circle (1.8);
    }
\end{equation*}
The 3 linearly independent electric moment operators can then be taken as
\begin{align}
    d^z_i    &= d_0 (~~n_{i,0} + n_{i,1} - n_{i,2} - n_{i,3}) \nonumber\\
    d^y_i    &= d_0 (-n_{i,0} + n_{i,1} + n_{i,2} - n_{i,3}) \nonumber\\
    Q^{yz}_i &= Q_0 (~~n_{i,0} - n_{i,1} + n_{i,2} - n_{i,3})
\end{align}
Here, we have introduced dimensionful factors of $d_0$ and $Q_0$ which come from the geometry of the atom and dropped any 1-body terms as these have already been absorbed into the single-atom crystal field Hamiltonian $H_{XF}$.
These operators are adapted to the cubic symmetry of the system and have a particular simple action on the model atomic states: the dipole operators change the momentum of one electron by $\pm \pi/2$ while the quadrupole $Q^{yz}$ shifts it by $\pi$.

Now let us consider a representative square plaquette lying in the XY plane from $(0,0,0)$ to $(1,1,0)$ with four atoms at $(\pm 1/2, 0)$ and $(0,\pm1/2)$.
Cubic symmetry dictates that among the 9 possible nearest neighbor terms, only 4 are non-zero.
Terms of the type $d^z d^{x}$ and $Q^{xz} d^y$ are disallowed by the mirror reflection $z\to-z$.
This leaves the orbits of the terms $d^z_1 d^z_2$, $d^y_1 d^x_2$, $Q^{xz}_1 d^z_2$, $Q^{xz}_1 Q^{yz}_2$ under the symmetry of the lattice.

In the usual quantum spin ice hierarchy, $t \gg J \gg V$, we treat $V$ as a perturbation acting on the low energy ice manifold -- the ground states $P_0$ of $H_{XF} + H_{Ice}$.
In the Schrieffer-Wolf (SW) approach, the perturbative unitary $e^{S}$ with $S = S_1 + S_2 + \cdots$ can be used to rotate operators into the low energy manifold (we follow the notation of \cite{Bravyi2011a}).
The transverse atomic dipole moment operator of the $XY$ plaquette $p$ is
\begin{align}
\label{eq:toy_dz_eff_SW}
    d^z_{eff} &= P_0 e^{\hat{S}}(\sum_{i \in p} d^z_i)P_0
\end{align}
where $\hat{S}$ denotes the superoperator adjoint of $S$, $\hat{S}(X) = [S,X]$.
While it is straightforward to expand to Eq.~\eqref{eq:toy_dz_eff_SW} to low orders mechanically, the full expressions are not so enlightening.
Rather, let us consider a typical term in the expansion of Eq.~\eqref{eq:toy_dz_eff_SW}.
This is composed of a string of two-body operators coming from $H_{Coulomb}$, along with appropriate energy denominators of the intermediate states, and a single insertion of $d^z_i$.
In order to connect between ice states and not vanish when restricted to $P_0$, the momentum on each atom must shift by $\pi$ -- which is accomplished by an even number of dipole operators or an odd number of quadrupole operators.
This is impossible if the Coulomb potential only includes dipole-dipole or quadrupole-quadrupole terms.
However, so long as the dipole-quadrupole term, $Q^{xz}d^z$ is available, then terms of the form $P_0 \cdot Q^{zz}_4 Q^{zz}_3 \cdot Q^{zz}_2 d^y_1 \cdot d^z_1 P_0$ (neglecting denominators) do not vanish and we find the \emph{atomic transition dipole mechanism},
\begin{align}
\label{eq:toy_atomic_eff_d}
d^z_{eff} \sim d_0 \frac{V^2}{t J} \mathcal{O}_p
\end{align}
where the imaginary ring exchange operator
\begin{align}
    \mathcal{O}_p &= i (\sigma^+_0 \sigma^-_1 \sigma^-_2 \sigma^+_3 - \mathrm{h.c.})
\end{align}
is the cubic lattice analogue of Eq.~\eqref{eq:micro_b_polarization}.

\paragraph{Ionic Mechanism---}
The magnetic atoms in spin ice materials are typically ionized and surrounded by a matrix of compensating, non-magnetic ions. Since the restoring force for ionic displacements are typically smaller than the atomic energy scale $t$, motion of the ions can dominate the electric polarization.
In the toy model, we can understand this by adding an additional, non-magnetic ion at the center of the square plaquette.
Symmetry allows the transverse position $z$ of the ion to couple to $d^z$ and $Q^{xz}$ as follows,
\begin{align}
    H_{ion} &= \frac{p_z^2}{2M} + \frac{1}{2} M \Omega^2 z^2 \\
    &+ V_{d}\, z (d^z_0 + d^z_1 + d^z_2 + d^z_3)  \\
    &+ V_{Q}\, z (-Q^{yz}_0 + Q^{xz}_1 + Q^{yz}_2 - Q^{xz}_3)
\end{align}
where $M$ is the mass of the ion and $\Omega$ is of order the Debye frequency for the optical mode associated with ionic motion.
Rotating $H_{ion}$ into the ice manifold, it is clear that the $V_{d}$ term rotates into the form in Eq.~\eqref{eq:toy_atomic_eff_d}, and results in a coupling between the ionic polarization and $\vec{O}_p$,
\begin{align}
    d^z_{ion} \sim Z_{ion} \frac{V_{d} d_0}{M \Omega^2} \frac{V^2}{t J} \mathcal{O}_p
\end{align}
This may provide a quantitative enhancement of the effective polarization coupling.

The quadrupole coupling, $V_{Q}$, also rotates into the ice manifold
\begin{align}
    \sim V_{Q} z Q_0 \frac{V^2}{J^2} \mathcal{O}_p
\end{align}
which directly couples the center ion position to $\mathcal{O}_p$ without needing virtual excitation of the internal atomic level structure at (the typically large) energy scale $t$.
Although this coupling is naively larger, it appears with opposite signs on the 4 neighboring XY plaquettes and thus cancels in the long-wavelength limit.

\end{document}

redpajama_set_name: RedPajamaArXiv


Facebook wants you to "engage" with its service, so they have an algorithm that plucks your most favorited images out of your past stream and adds dancing whimsical cartoon characters and then rams the resulting animation into your eyeballs, because why not?
Patrick Gerard tweeted: "Facebook is pushing that 'share a memory' junk where they make custom videos out of your old photos to boost engagement and I just literally got shown a bunch of happy cartoon characters dancing on my mom's grave. 🤦♂"
Today, Alberta is having one of its bitterest, hardest-fought elections, with far-right/xenophobic elements on the upswing through the United Conservative Party, led by Jason Kenney, who has been awfully cavalier about the white nationalists in his party.


For many designers, the mere suggestion of putting wallpaper in the kitchen can raise eyebrows. It is a space whose aesthetic is typically relegated to a functional and clean look. However, happy additions to accent walls or backsplashes are on the rise recently through the strategic inclusion of wallpapers that don't distract but support the overall feel of the space.
From small applications such as the back of shelving to full wall covering, wallpaper is on the rise. It doesn't have to be a nightmare for cleaning, either, with the right tempered glass covers. For solid colored kitchens, you can paint the back of the glass. You can enjoy a beautiful kitchen wallpaper without fear of heat damage or grime ruining your chosen design.
Additionally, it must be said that the wallpaper route is much easier on the budget than most material costs. Whether you are a renter looking for options that won't break your lease or simply interested in a fresh look for your kitchen that won't break the bank, kitchen wallpaper may be ideal!
In this small and sensible kitchen making use of white cabinets, some mild color from the Jonesport Pink Cabin Stripe wallpaper adds loads of personality. The horizontal lines flow with the cabinet facing, forming a cohesive partnership. This is a great example of how a well thought selection can not only beautify a space, but increase the aesthetic value of the cabinetry.
A bold full-wall treatment can make a lasting impression against white cabinets and marble countertops / backsplash. A design that one might have found more likely in a bedroom instead adds an original and unique flair to the cooking space. It seems abuzz with activity, impressing upon you the natural purpose of the kitchen. The addition of marble backstops above the counters safeguards the wallpaper from spills or food.
While the thought of wallpaper borders may be inseparable from images of old 40s kitchens and antiquated design, a fresh imagining of their application has seen a resurgence of them across the United States. Inexpensive and easy to replace, vinyl strips like the above multicolor stripe from wallpops make it as easy as peel and stick to add an accent to your wall.
Kitchen wallpaper borders come in a huge variety of styles to match different decor or cabinets, so shop around and find the perfect complement to your unique tastes. Not the same application as the vinyl option, this stencil provides the same horizontal accent as a more permanent fixture. Along with the cream cabinets and festive dried flower arrangement, the autumn motif is in full effect.
Given the tight economy of space in some kitchens, it can be difficult to find an accent that doesn't visually crowd the space but still brings life to it. Wallpaper would seem like an unlikely option for your backsplash, given paper's propensity for burning (however manufacturers have created standards around this). But tempered glass strips can open up an amazing doorway to variety in your kitchen aesthetic that we think you'll find irresistible.
Bringing tranquil outdoor imagery into the kitchen amplifies a sense of the serene. For the patient and calm cook, this kitchen exemplifies a methodical approach to food preparation. Have you ever seen something so European in your life? We also love how the grayscale wood imagery creates a blend between the white cabinets and light brown countertop.


text:
'Diary of a Wimpy Kid' creator leads Oklahoma events to help rebuild Moore libraries
BY KEN RAYMOND kraymond@opubco.com
Published: Sun, September 22, 2013 12:00 AM
Stephan Pastis Susan Young - Provided
Jeff Kinney's travel plans had gone awry. He'd missed his connecting flight, and instead of winging away to his final destination, he was stuck inside Miami International Airport, facing the prospect of a dull wait.
When he looked up at a TV mounted on a wall, though, any trace of boredom disappeared.
It was May 20, and CNN was airing video of the tornado devouring parts of Moore.
"I was devastated by what was happening on screen," said Kinney, best-selling author/illustrator of the "Diary of a Wimpy Kid" series. "At the moment I saw the CNN reports, there were a huge number of people, especially children, unaccounted for. As a father, that really reached me. It was easy to picture myself in that situation, not knowing if my child was still alive."
Weeks passed, but the Moore tornado kept resurfacing in Kinney's mind. He'd never been to Oklahoma, but he couldn't forget what he'd seen on TV.
Children had died in the disaster — children close in age to his own kids, 8 and 10, children about the right age to be reading his books. He was struck by the need to do something to help, but he didn't know what. He contacted a few of his colleagues, and they shared his ambition.
If they worked together, maybe they could do something positive for the traumatized Moore community.
Thus was born Drawn Together, a two-day Oklahoma event featuring some of the biggest names in children's literature: Kinney, Stephan Pastis, Lincoln Peirce and Dav Pilkey.
Article: Author/illustrators share thoughts on Moore tornado
Pastis, best known for his "Pearls Before Swine" syndicated comic strip, is the author/illustrator of "Timmy Failure: Mistakes Were Made." Peirce produces the "Big Nate" books and syndicated comics, and Pilkey is the creator of the popular "Captain Underpants" book series.
The first Drawn Together session will be 7 to 9 p.m. Friday (doors open at 6 p.m.) at the Cox Business Center, 100 Civic Center, Tulsa.
The second will be 1 to 3 p.m. Saturday (doors open at noon) at the Lloyd Noble Center, 2900 S Jenkins Ave., Norman.
Tickets are $10 and can be bought at the door or in advance by going to www.showclix.com and searching for "Drawn Together."
Each author/illustrator will spend 15 to 20 minutes discussing or demonstrating his work. A question-and-answer session will follow each talk. Presentations are geared toward all ages, so parents and children should have fun.
Raffles will be held for an original work by each artist, and merchandise tables will feature books, T-shirts and posters.
All funds raised will go to rebuilding or restocking libraries damaged by the storm.
Becoming famous
Kinney, who lives with his family in Massachusetts, attended the University of Maryland and penned a comic strip for the campus newspaper.
After graduation, he tried but failed to become a syndicated cartoonist for newspapers, leading him to focus most of his attention elsewhere. Instead of sending his work to syndicators and continuing to receive "soul-destroying" rejections, he said, he began writing for himself, for years showing his work to no one.
Eventually he began releasing daily Wimpy Kid diary entries online, where they attracted readers who clamored for more. By 2006, he had about 1,300 manuscript pages and met with a publisher at a comics convention. Although Kinney had written for an adult audience, intending to remind grown-ups of what life was like when they were children, the publisher suggested turning his work into children's books.
The first "Diary of a Wimpy Kid" book was printed in 2007. When his eighth book in the series, "Diary of a Wimpy Kid: Hard Luck," is released Nov. 5, about 100 million copies of his books will be in print. Three of his books have been turned into movies.
"I've been on this kind of continuous ride," he said. "I've gotten to do the strangest things a person can imagine. I've met three presidents. I've traveled the world now and got to work on movies and meet actors and musicians. I feel like I'm on 'The Truman Show.' It'll be sad for me when it all ends. I'm trying to drink it all in while I still can."
When he's not writing books or touring, he works a 9-to-5 job as an online game developer. Doing so keeps him grounded, he said, and he enjoys the work.
Despite his success, Kinney is dismissive of his abilities, negatively comparing himself to his peers.
"I think I would say that I know my limitations and don't harbor illusions about my abilities," he said, "but I do think I make the most of the abilities I have."
Each illustration takes him about an hour to complete, he said. Each book contains about 350 illustrations drawn in his unique style.
"Cartooning is the art of distilling something to its essence," he said. "When I draw, I try to use as few lines as possible to communicate information. I tried to develop a style that looks like it could be by a middle-schooler and not just the scribblings of a child."
While he's in Oklahoma, he wants to show children that reaching their dreams, even if they dream of becoming cartoonists, is "an achievable goal," he said.
More than that, he said, "I hope to show people affected by the tornado that people all over the country were touched by this and care and hope to help out."
Dav Pilkey Karyn Carpenter - Provided
Lincoln Peirce - Provided
Jeff Kinney - Provided
Comments'Diary of a Wimpy Kid' creator leads Oklahoma events to help rebuild Moore libraries

redpajama_set_name: RedPajamaCommonCrawl


Simply to be safe you can fit a plastic sheet over the mattress, however you'll just have to try this for yourself. For some the plastic will make it difficult to rest because it can make noise whenever you roll over. If it keeps you from resting then you're defeating the function of getting a foam mattress pad. One final thought, why not get a pad for each bed in your house. It just might help your kids rest much better too, and I think most parents would concur it's a lot easier to rest when the kids are resting soundly.
With so numerous choices at your fingertips, it is worth your time to consider a brand-new bedspread for your space. Best of all, bedspreads have a tendency to last for numerous years and still look fresh and brand-new after several washings. If you are in the market for brand-new bedding, take some time today and look into a bedspread as a possible option.
Due to the fact that of the nature of bunk bed prices, more affordable bunk beds typically cut corners on vital details, like tough guard rails and safety ladders. Our assistance: examination the bunk bed before you purchase it.
More pricey (however not virtually as pricey as a brand-new mattress) is the memory foam pad. By now you've probably found out about how memory foam works. These pads will adapt your body shape and add added support where you require it. When the spending plan allows, we suggest going with a memory foam mattress, however for now, the pad will do. As a side note, you need to likewise check out memory foam pillows to go with your brand-new pad.
Having bedroom sets that are inadequately made in a bedroom will only make it look unattractive. How can anybody be expected to relax and charge in a bedroom that is substandard looking with a bedroom set that appears careless? Bedroom sets that are well-constructed can make the space a real haven which a lot of weary, active individuals require.
Weave of the material figures out the sheets level of softness, crispness, breathability, and longevity. Percale weave produces a sturdy and long lasting bed sheet. Percale sheets are breathable and have a crisp feel that will soften with repeated washings.
The overall health and well-being of individuals depends to a big level on the quality of sleep. If you are not able to obtain, great evening's sleep, it can detrimentally influence your health. It may be a number of reasons for inadequate sleep, an awkward bed mattress is one of the leading elements. If you're not in a position to have to get a proper evening's sleep and you may deal with the possibility of altering your bed mattress. Memory foam bed mattress is preferred for the high level of comfort and appropriate spine placement, which is essential to ensure appropriate sleep and health. Instead of purchasing a new memory foam bed mattress, you can have the exact same advantages by purchasing a memory foam bed mattress and put it over your original bed mattress to finish. However your original bed mattress must be firm enough to offer the essential support than memory foam mattress pads are very soft.
The gartered sheets which were first utilized by individuals have actually gone with a number of changes with the years. Nowadays, you can purchase various designs, sizes and shades of fitted queen sheets and you can even place an order for these items with the World Wide Web.
Most of the silk pillowcases that are readily available in the market today offer exceptional quality materials making it a best selection for those who are prepared to invest extra dollars for an elegant pillowcase. Other pillowcases in the market today are somewhat coarse as well as if it claims to be made from one hundred percent silk, it does not have the luxurious quality of premium and genuine silk pillow cases. In addition to that, the soft qualities of this sort of silk fibers ought to not also be mistaken for weakness since this can be as resilient as any various other sort of silk fibers established in this industry and sometimes, this is much more powerful than various other sort of fibers in the market. There is no contesting that exceptional quality silk pillow cases are your best selection and the greatest quality of silk material the market today can offer.


The romantic words of the Marquise de Lafayette are as relevant today as during the time of the American Revolution. O! If you knew how much I sigh to see you on a Mobius strip symbol of endless love . . . will convey to your beloved the state of your heart.
A message of love from an age of gentility, repeated ad infinitum. But how? Begin reading, and you will return to where you began, as if by magic!
Sterling silver; approximately 1 in. in diameter on an 18 in. chain. Weight: approx. 4-5gm. This necklace is made with the geometric form known as a Mobius strip, named for the German mathematician August Ferdinand Mobius who discovered it. A plane without end is a fitting symbol of infinity representing eternal life and love.
Posy jewelry is lovingly hand-crafted in the U.S. via the lost-wax casting method. Includes history card and organza jewelry bag.


text:
> THE FANCLUB / INTERVIEW
Interview with Stephanie Anderson
(# 276 in the fanclub)
Stephanie and Ludwig from T(I)NC.
Tell me something about yourself!
My name is Stephanie, I am 18 and I live in Southern California in the US. I'm an artist, a student, and have a deep interest in radical politics. Most of my political
views is shown in the pieces of art that I do.
How did you find this site?
I did a search a while back on some Refused sites. I think that within one of those sites, I saw a link to this one.
When did you discover Refused?
I started listening to Refused about a year ago, because I had been a fan of the T(I)NC before, and wanted to see what Refused was all about.
What was your reaction when you first heard them?
They were awesome, unlike most punk bands I had heard before. I think what I found at first (and still do) to be most incredible about Refused to this day is their
energy, and the views they conveyed through the music. Dennis is a great lyricist.
Which was the first Refused record you bought?
"The Shape of Punk to Come" oh, yes!
Which is your favourite Refused record?
Just one!?! I have 2 that are the best in my opinion. "Shape of Punk .." is "the best" in that the band put a lot into making that album, and it really gets the listener
thinking ... about what's going on in the world around them and so on. "The Ep Compilation" is "the best" in that it really shows the band's versitility, you hear
differen't songs being played at different speeds .. none of them sound really the same, plus there's a track sang in Svenska. Good stuff!
Which is your favourite Refused song?
There are too many to list ... I do like "Summerholidays Vs. Punk Routine" a lot .. the lyric, "Rather be forgotten, then remembered for giving in!" yes, yes very good.
Have Refused or their politics inspired you in any way?
Not so much Refused, but The (International) Noise Conspiracy has ... a lot. I was into them first, and began finding an interest in politics, such as Socialism,
Situationism, and some Anarchism. I think that when I heard Refused, they kind of helped me look into it even more, thus creating a stronger interest in the topic.
Have you seen them perform live?
Pssssh, no way! Refused broke up when I was 13, and I had no idea of who they were until I was 17 ... I do have this video, however, of 2 live performances from
them. Man, are they intense live! One of the shows was done after Refused "broke up" in 98 .. it was the last show on the tour, and Dave Sandström was using
Frodus drums. You couldn't hear Dennis sing at all because they were so loud. Man O man.
Have you met anyone in the band?
I have only met members from the T(I)NC. And one of them was Dennis. I met him several times in that one occasion, it was when they did a show here back in
December.
It was pretty funny, I was talking to this guy before the show who had been a long time Refused fan, and asked me who the man standing in the distance with all
these people around him was. I responded "the one in the green jacket?" and he replied "yes"' and I told him, "That's Dennis". He responded very quickly was and was in
disbelief "No way!" he said. "Way!" I told him. He was in shock when he met Dennis, I think Dennis might have thought this guy was nuts or something. When I got
to talking to Dennis, we discussed this program I am in at school that is all about ending descrimination and predjudice, and celebrating diversity. We went on to talk
about our heritage, as we are both Scandinavian (only I'm Norwegian .. =D) It was an interesting conversation, mainly because it was just us talking about normal
everyday things, quite cool.
What do you think about the Refused related projects?
Let's see .... The T(I)NC is fucking rad! Lost Patrol is AMAZING .... and TEXT... is ... well .... interesting... if you like that sort of thing.
Any favourite?
The T(I)NC Most definately!
How do you think Refused would sound today if they were still around?
Still the same (musically) I'd assume. Perhaps lyrically, they'd have even MORE of a political edge, since that's what Dennis really wanted to aim for toward the end
of Refused.
Interview by Webmaster.
Published on March 31, 2002.


Why not go on vacation to the Principality of Monaco millionaires? And although most eligible bachelor of this elite corner of the planet – Prince Albert – ceased to be Charlene Wittstock thanks, there are still a lot of millionaires who can find lonely ladies. It's time to hurry, because beach season, and with it the traditional holiday in Monaco, completed in September. The fact that the traveler should know that during the rest of Monaco wants to find a millionaire on northernhotels.co.uk. Of course, you can find a rich husband and during HOLIDAY IN THE PHILIPPINES, where too many millionaires, while exotic VACATION IN MOROCCO , or even ECOLOGICAL REST IN VIETNAM , but it was all Monaco associated with luxury – here are the best casinos and fantastic resorts. Even in normal traffic are not ordinary cars, and BUSINESS CARDS all millionaires – Limousine, Rolls-Royces and Cadillacs, which move the fans of gambling and "Formula 1″. Monaco – a paradise for millionaires.
Feel most comfortable in this tiny principality with knowledge of the French language. Although tourist sign language will not get lost in Monaco, which can cross on foot in a few hours. But the basic language skills will not hurt, especially those on holiday in Monaco is sent to find a millionaire.
But if the goal is not only TO MARRY A MILLIONAIRE , but also excursions to visit, it is worth to visit Le Rocher – to see the old city quarter where the princely palace Grimaldi.
This part of the city – its formal and business heart. It should also look at the cathedral, which buried the legendary Grace Kelly (Monaco idolize her today), the Oceanographic Museum with an underground aquarium, Wax Museum … At Monaco Palace Square can enjoy the change of the guard of honor.
If plans shopping, you need to go to the district of La Condamine. Here are the main shopping areas, and in them – boutique brands. But enthusiasm for shopping do not forget about the exotic cactus park "Jardin Exotique" and the Museum of Prehistoric Anthropology.
New Monaco can be seen in the area of Fontvieille. Interestingly, that once there was a sea, but persistent monaktsy conquered land. The Principality is surrounded by water, so here appreciate every piece of land and carefully treat it clean. The main attractions of the area – Museum of Antique Cars of Prince Rainier III, with more than 100 exhibits, the largest stadium in the principality named Prince Louis II, philately and numismatics Museum, the Maritime Museum with a collection of copies of famous ships, zoological garden and landscape park.
Despite the tiny size of the principality, resorts where tourists will be happy, yet a lot. This Larvotto (of almost 4 km), Les Porter, Le Revuar, Monaco-Ville, Moneghetti, Port de Cap's daily life, Saint-Michel and Saint-Roman.
Due to its climate Monaco gained fame and the best European thalassotherapy centers in Europe. There are many thermal and mud baths, where customers are offered programs, including massage, hand massage, underwater shower and mud.
Gambling heart of Monaco – a Monte Carlo. Here at the light as butterflies fly gamblers. Here is the leading gambling house in Europe – Monte Carlo Casino. But if gambling is not your thing, welcome to the National Park dolls, and Japanese Garden. Try your luck at the roulette table in Monaco permitted to those who have reached 21 years. But that's not all restrictions. Doors swing open casinos welcome if guests meet the dress code. For men – this jacket and tie for the ladies – an evening outfit.
Fans of different gambling choose to STAY close to them in the spirit of Monaco casino. For example, in San Le Casino you'll find most fans of roulette and blackjack. And at Cafe du Paris – not the main part of the game and the title. Here come the famous dukes, princes, and other representatives of blue blood.
Despite the long history of the casino in Monaco, here still believe that beginners luck. The audience always complacently refers to the lucky ones who with glowing with excitement eyes tear big jackpot.
Racing "Formula 1″ this year already in the past. And the following are expected in May. At this time on VACATION in Monaco attracts thousands of fans speed driving on the car. Tickets for the race are very expensive – from a few thousand euros. But even such a tidy sum does not deter those wishing to watch the action.
Some particularly prudent fans "Formula 1″ advance rent a room or even an apartment on the races as race suit, including, and in the city.
But for the sake of objectivity say that endure the race for the lead on the car can only fan. After all the noise from the powerful cars worth deafening, and the May heat is exhausting.
Tourism in Monaco – a fairy tale for many. But if you're lucky to be in this tiny principality, use vacation at 100%. Go tell that to SAVE ON HOLIDAY is unlikely, but the returns will be relevant!
And when all the planned entertainment come to an end and before the flight will remain a matter of hours, not be amiss to give a farewell to REST ON THE SEA and make a last run to the shops. After leaving Monaco without branded sweets would be unforgivable. We suggest you pay attention to the candied fruit and chocolate. Well, if you bring home will be able to grab a millionaire, the rest, you might say, was a success!


Gentle Giants Draft Horse Rescue facilitates the rescue of draft and draft cross horses from slaughter, abuse, and neglect. We've rescued over 600 horses who have been adopted into permanent, loving homes. We house over 100 horses at our Maryland facility, and offer lifetime sanctuary for those horses who are less likely to be adopted.


The meeting with the Salamanders and Ultramarines has amounted to little but wasted operational time and a foul taste in my mouth. However, the presence of the Deathwatch, and the fact that a fellow brother ranks among them, is encouraging. No Xenos shall stand against us, and the habitual over-cautiousness of the other chapters will not hinder us any further. My honor guard and myself are en route to the city-ship Esmerelda, where we will pluck this infestation root and stem, by whatever means necessary.
By the tribes of Sacris, our will be done.
Binary Stars follows the tales of the Deathwatch. Seconded from the most elite martial units of the Imperium, the Deathwatch are the chamber militant of the Ordo Xenos, the Inquisitorial branch granted nearly unlimited power to fight overt and covert alien threats to mankind. Dropped into the middle of a decades-long multiple-front stalemate, the soldiers of the Deathwatch face threats that could break the dwindling strength of the Achilus Crusade and seek opportunities to finally break out in kind.
James – Zaphiel. A Dark Angel Consecrator, split in devotion between the Sixteen Laws of the Cult Mechanicus, the retrieval and protection of artifacts to protect humanity in both body and culture, and the teachings of the fallen Chapter Master, Lion El'Jonson. A nigh-invincible man-machine, he serves the Golden Throne with both lore and firepower, forming the bulwark at the foundation of the fire-team's assaults.
Matt – Michael. Ultramarine Apothecary. A veteran of the First Tyrannic War and a follower of the holy Codex Astartes penned by Ultramarine founder Roboute Guilliman. Led in devotion to the protection of the Imperium from existential threats that its populace need not know and its other forces unfit to fight, it is his duty to keep his brothers fighting until his last breath.
Max – Hixus. A recalcitrant Librarian of the Carcharadons. While their vanishing traces and echoing legacies lead many to believe they were a myth the unearthly void hunters of the Carcharadons are proven to exist by the Hixus's cryo survival amongst the space hulk of his patrol's ship. Tall (even for a space marine), quiet, and uncomfortably calculating he continues to show the brutality and cunning of his chapters whims, fighting for the Ordos Xenos in place of the direction his shattered life has lost. Now in this perplexing anachronistic world he still finds himself driven with his mastery of the warp and penchant for silently disposing of those not worthy of life.
Danielle – Tyche. A decorated and devoted Sister of Battle haunted by her latest experience in the warp. Her obsessive hatred of demons made her unfocused in battle, prompting her Abbess to choose her as the first Adepta Sororitas to accompany a Deathwatch Kill-Team, the only place her fury would be guaranteed a target.
Axe – Ramsay Mac Cuin. Veteran of twenty years of tank battles in Achilus Crusade and Tactical Marine of the mysterious Storm Wardens chapter. Gregarious and proud, he considers each engagement to be a step on the path to perfect understanding of war. While willing to defer to specialists, his broad knowledge base and knack for leadership make him a perfect fit for Kill-Team Commander, or so he believes.
This entry was posted in Deathwatch, Warhammer 40k and tagged binary stars, deathwatch, kevin, sci-fi, warhammer 40k. Bookmark the permalink. Follow any comments here with the RSS feed for this post. Leave a trackback: Trackback URL.


This is one of my favorite side dishes. It is a great way to consume cinnamon, vegetables, fruit, and seeds together. I also love its home-warming aroma. Enjoy!
Preheat the conventional oven to 425°F.
Line two baking sheets with parchment paper or foil.
Peel the squash, cut in half lengthwise, and scoop out the seeds with a metal spoon and discard. (You can save the seeds to bake later).
Peel the potatoes and cut in half lengthwise.
In a small bowl, mix the syrup, oil, and Ceylon cinnamon with a spoon or whisk.
In a large bowl, combine potatoes, squash, raisins, and nuts.
Pour the liquid cinnamon mixture over the squash and potatoes in the large bowl. Mix, with hands, until squash and potatoes chunks are thoroughly coated.
Spread the mixture across both baking sheets making sure that they lie in one layer.


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I asked myself this when my wife was pregnant with our second child, Justice. I even Googled this very question. I don't remember what the answers were, but I knew they weren't for me. A divorce was going to cost me money, a divorce was going to cost me time, and a divorce was going to cost me my family.
When my wife was pregnant with our first child, Journey, pregnancy was a new experience for both of us. It was such an exciting time. I was all in and completely connected with the entire process, from the second my wife's said "I'm pregnant" all the way through the birth.
I once heard someone say the devil does everything he can to get you in the bedroom before you're married and everything he can to keep you out of the bedroom once you are married. I also heard someone say the biggest intimacy killer in a marriage is responsibility. The more responsibility you have, the less time you have to focus on being intimate. Many couples with young families fall prey to this intimacy killer without even realizing that their relationship is slipping away. We didn't want to fall prey to that.
Before our struggle became too great, we started seeing a marriage counselor. This turned out to be very good for our relationship. So good, in fact, that we decided to have a second child. But as the second pregnancy progressed, I was a little less engaged than I was the first time around.
By this point, my wife and I had been married for nearly 10 years. I knew she had become a person, who, if she really wanted something, would tell me. I trusted she would let me know if she had a need so I could connect with her. However, I had disengaged to the point that I didn't notice some emotions she was feeling during the second pregnancy.
I thought that I was all in. I made sure things were good with our first child, so much so, that I began to neglect what my wife was experiencing and feeling during her second pregnancy. It got so bad that at one point we sat down at the table and asked ourselves, "Do we want to be married?" That was a very difficult question to ask.
What are your biggest barriers to your relationship with God?
What are your biggest barriers to your relationship with your spouse?
What are the most serious temptations you're facing right now?
What are your greatest points of vulnerability?
Do I truly want what is best for my spouse?
Do I want my spouse to feel loved by me?
Does my spouse believe that I have his/her best interest in mind?
Does my spouse see me looking out for myself first, or him/her first?
This routine kept us on track for where we wanted to go as a couple and in our walk of faith.
The obvious thing was actually getting divorced. We were both talking about it and thinking about it. The conversation was intense. If we were willing to pay the cost and go all the way to the very end, we needed to know that we had thought everything out. So, we asked ourselves the "what if" question.
The next week we came to the table, my wife had a list of things that she knew she would be responsible for if we got a divorce. The answers she provided surprised me because there were things that I thought she felt, but I didn't think she would ever say. Then, I shared what I thought I would be responsible for. It drew us closer. So close, in fact, that we realized divorce was not worth it. We recognized we were just in a tough spot. This is part of being married. I feel, from my personal experience, that marriage is one of the things that you just don't do by accident. You do it by choice. You do it intentionally.
Each day I wake up and I choose to be married. There are going to be certain things in life that cause me to know that I'm choosing to be married, not just the "getting by" type of married, but striving to have a flourishing growing marriage. I don't want a marriage where my daughters are miserable watching their parents together. I want them to see two broken people coming together daily for the better good of what they believe that they can have and offer one another.
How much does a divorce cost? Too much for me to ever want to find out because I am not willing to make the sacrifice. These are the types of conversations that should happen in marriages when children are involved. They need to be asked, they need to be discovered and deciphered because, if not, it's too easy to get blindsided by not knowing what your spouse is thinking or feeling.
Marriage is a constant routine of re-evaluating, tweaking and re-engaging. Sometimes hard questions in marriage have to be asked, and when they're answered, the goal is to see the answers from my spouse's perspective. In essence drawing us closer to becoming one.
How much would a divorce cost you?
Jonathan "J.O." Oliver is a personal development coach, motivational speaker, author and a stay-at-home dad. He is happily married to Dr. Saran Oliver and together they have two adorable daughters, Journey and Justice. Being diagnosed with the gift of dyslexia and ADHD has allowed him to see what is possible rather than feel limited by his condition. He has authored two books, Joy In The Journey: 1st Year Chronicles From A Stay At Home Dad, and Impersonations. His next book, To The Little Boy In Me: Learning with Dyslexia & ADHD will be released in spring 2019.
Awesome insight. Love your attitude and thanks for sharing.


I arrived at Chongqing International Airport around noon on September 30, 2016 after spending the previous two days in Yangshuo. A waiting bus took me from the the airport on the 40-minute drive through traffic into the city to the Yangtze River where the river cruise ship Victoria 5 was docked below the Qiansimen Bridge. That evening I would depart Chongqing and spend the next few days, until midday on October 3, cruising down the Yangtze.
Official check in wasn't until 6:00 pm, but they let me aboard and into my room anyway. I dropped my bags off and then headed back ashore for lunch at a small restaurant a few blocks from the boat. I spent the afternoon exploring the city, which was remarkably difficult to navigate as the city center is situated on a relatively narrow strip of hilly land between two rivers.
The overall feel of Chongqing was drastically different than all the other megacities I've visited in China. Chongqing definitely isn't much of a tourist destination, with most foreigners visiting at either the start or finish of their journey on the Yangtze. The terrain also resulted in fairly unique transportation options in the city. The metro system consists of the world's largest operational monorail network, and two cable car systems stretch across the rivers.
I eventually made my way to one of the cable cars, which was an attraction for many of the Chinese as well. After about 15 minutes waiting in line, I boarded the cable car for the journey across the Yangtze River. On the other side I disembarked, took in the views of the city, and later boarded the cable car for the return trip. On the return walk to the boat, I stopped at a supermarket for extra snacks and drinks for the next few days.
As 9:00 pm approached, I went up to the ship's upper deck to view the lights of Chongqing as we began the trip downstream. I awoke the following morning with the Victoria 5 docked next to several other cruise ships. I didn't disembark the boat until later in the afternoon at the day's second stop, Shibaozhen. Shibaozhen is a hill with a temple and pavilion constructed on it. Originally constructed around 1819 along the Yangtze River, a concrete wall was constructed around it to protect it from the rising waters of the river that resulted from the construction of the Three Gorge Dam. I walked around the hill, up the pavilion, through the temple, and then back down the hill before returning to the ship.
Meals on the the cruise ship were decent and mostly traditional Chinese food (only about 15 of the 150-200 passengers were not Chinese). Breakfast and lunch were buffet-style, whereas dinner was table service. On October 2, I again awoke with the ship docked. This time we were at a small town just upstream of the entrance to the Qutang Gorge, the first of the Three Gorges. Qutang Gorge is also the shortest in length of the Three Gorges, but the mountains still towered above the river.
About an hour and a half after passing through Qutang Gorge, we passed the city of Wushan and entered the Wu Gorge. I thought the Wu Gorge was the most scenic of the Three Gorges, and as we were nearing the end of the gorge, the ship stopped for the second time in the day. This time we boarded smaller boats that took us on the short trip up Goddess Stream, a small, narrow side gorge. As with all the excursions, a guide told us all about the area during our ~1.5-hour journey.
Back on the cruise ship, I sat on the the upper deck as the boat traversed the rest of the gorge and the sun set before dinner. Around 11:30 pm the ship arrived at the locks at the Three Gorges Dam. I again watched from the upper deck as we entered the locks, two other cruise ships packed into the same lock, and we were lowered. I only stayed around for the first lock as traversing the entire set of locks takes 3.5 hours, although I was routinely awakened by the screeching sound of the ships rubbing against each other and the side of the locks.
The morning of October 3 the boat was docked downstream of the Three Gorges Dam for our last excursion. This excursion was to the dam itself, where we were able to view the locks and dam from a small hill between the two. The excursion ended at the northern upstream end of the dam. We were not permitted to go anywhere on the dam itself for security reasons, and poor air quality made getting a good view of the dam from the downstream side during the drive to/from the ship difficult.
Back aboard the cruise ship, we passed through the last of the Three Gorges, the Xiling Gorge, which is the longest of the three, but still very scenic. Before noon the boat docked at the end of our journey in the city of Yichang. After disembarking, I had the afternoon to explore this unremarkable city of 1+ million people, but since it was very hot and I had my bags with me, I ended up spending most of the afternoon at a restaurant in a shopping mall.
That evening I boarded an overnight sleeper train to my next stop, Xi'an. On this train I was placed in a cabin with six beds, all occupied by other westerners. The ride to Xi'an was a bit rougher than the next overnight train I would take, but I only woke up a couple of times during the night.


text:
Is there a difference between incompleteness and unknowable? [closed]
Want to improve this question? Update the question so it's on-topic for Theoretical Computer Science Stack Exchange.
Godel proved that there are statements that are true but not provable. Unproven conjectures such "Twin Primes" might fall into such a class, as I understand. If so, does it mean that we will never know if it's true or false? If true would it only be in the sense that some infinitely large and infinitely fast computer determined so by brute force? Or might it be that the conjecture (or another conjecture) could be neither true nor false and instead forever indeterminate?
computability
Jim Lewis
Jim LewisJim Lewis
$\begingroup$ I hate people downvoting reasonable queries without comment. What a tragedy has this site come to? $\endgroup$ – T.... Sep 21 '18 at 12:22
$\begingroup$ Well, I didn't downvote the question (I even answered it), but to be quite honest, the question has very little to do with theoretical computer science and is not research-level. It belongs to math.stackexchange.com. $\endgroup$ – Andrej Bauer Sep 21 '18 at 12:51
$\begingroup$ @AndrejBauer I agree that the question is not research-level, and belongs elsewhere. So why not vote to close? This seems to me to be a problem these days that questions below the level of this site are rarely closed and referred to a more appropriate place. Instead they are just downvoted into oblivion. While the downvotes are justified in many cases, overall this is not a very productive outcome for anybody. $\endgroup$ – Emil Jeřábek supports Monica Sep 21 '18 at 13:34
$\begingroup$ That's true, downvotes are not for signalling that the subject is unfit. Perhaps we should have the ability to migrate questions a bit more aggresively. $\endgroup$ – Andrej Bauer Sep 21 '18 at 14:23
$\begingroup$ Hi Jim Lewis, I suppose that it is a little problematic to say that "the conjecture (or another conjecture) could be neither true nor false". The TWIN PRIMES conjecture is a logical statement, and can be either true or false by the definition of a logical statement, not neither true nor false... The ability to tell weather it is true or false is another question, and we may never know the answer or be able to prove either way. $\endgroup$ – Avi Tal Sep 21 '18 at 17:28
Yes, there is a difference.
Incompleteness is a property of a formal system logic. Given a formal system $L$, we say that it is incomplete if there is a sentence $S$ such that $L$ does not prove $S$ and $L$ does not prove $\lnot S$.
Knowing is an activity of an agent, such as a human, or a robot which holds beliefs about its environment. To say that an agent knows a statement $S$ means that the agent correctly believes $S$ is the case.
So the first thing to make clear is that incompleteness and knowing are two very different sorts of things. It makes no sense to say that a formal system of logic "knows" that $S$ holds. And knowledge may be obtained by many different means, some of which are not related to logic. (For instance, I know that it is sunny outside at the moment through direct observation.)
There is a relation though: if an agent uses a sound formal system $F$ to prove a sentence $S$, then it will know $S$. This is what mathematicians do: they prove things so that they can correctly believe them. In that sense, your question may be understood as follows:
Given the incompleteness of formal systems, are there some mathematical facts which we will never know? What if we give ourselves infinite time to exhaustively search through all proofs?
The answer is this: for a fixed formal system $F$, such as first-order logic with Zermelo-Fraenkel set theory (which is proclaimed by many to be the "official" formal system of mathematics), there is always a sentence $S$ such that $F$ neither disproves nor proves $S$. Even if we had infinite time so that we could check all proofs of $F$, we still would not be able to prove $S$, nor would we be able to disprove $S$ using $F$. There just isn't a proof, and it doesn't matter how much time we have. Consequently, we cannot acquire knowledge of $S$ by using the formal system $F$. This does not mean that $S$ is uknowlable. It just means that $F$ is not helping us determine whether $S$ is true, but there might be another formal system $F'$ which does.
Mathematicians are not forced to use a single formal system $F$ all the time. Mathematical activity and knowing by mathematicians is not the same as a fixed formal system. For instance, mathematicians might agree to add another axiom to set theory, and thus some previously undecidable sentences will become decidable (and therefore knowable). In fact, such changes do occur in the history of mathematics, although it is difficult to track them back in time because mathematicians did not know what a formal system of logic was before the work of the modern logicians (Peano, Frege, Russell, and others).
How, why, and whether mathematicians should change the underlying rules of mathematics is a question for a different day, and a different forum.
Supplemental: Let me address the question in the comments about the Twin Primes. I am going to take the formal system of Peano arithmetic $PA$, but any other formal system would do. Recall that:
$PA$ is consistent if it does not prove a contradiction.
$PA$ is sound if, for any sentence $\phi$, if $PA$ proves $\phi$ then $\phi$ is actually true.
Here we take truth with respect to the intended model, i.e., our mathematical reality (I am not going to get into a discussion of what that might be, the OP is presuming one.) A sound formal system is consistent, but a consistent formal system need not be sound.
Another point of importance is this: truth and provability are different! Do not confuse "we cannot prove something" with "it is neither true nor false". By definition truth is always determined, i.e., a statement must have a truth value, but it need not have a proof.
Let $TP$ be the statement of the Twin Primes conjecture. Here are the possibilities, assuming Peano arithmetic is sound:
If Twin Primes conjecture is true, then there is a sound formal system which proves it, namely Peano arithmetic extended with the axiom stating $TP$.
If Twin Primes conjecture is false, then there is a sound formal system which proves it, namely Peano arithmetic extended with the axiom stating $\lnot TP$.
We can also look at the other side:
If Peano arithmetic proves $TP$ then the Twin Primes conjecture is true.
If Peano arithmetic proves $\lnot TP$ then the Twin Primes conjecture is false.
If Peano arithmetic does not prove $TP$ and does not prove $\lnot TP$, then we may extend it at will with either $TP$ or $\lnot TP$. We will obtain a consistent formal system in either case, but it might be unsound.
Andrej BauerAndrej Bauer
$\begingroup$ Is it possible that for a given statement (e.g. Twin Primes conjecture) there is no consistent formal math system that can prove the statement? If so is there really still a sense to continue to say that the statement is true or false? Is it possible that the Twin Primes conjecture, for example, could be neither true nor false? $\endgroup$ – Jim Lewis Sep 21 '18 at 22:32
$\begingroup$ Please see the definition of "statement": math.ucsd.edu/~benchow/Week1notes.pdf $\endgroup$ – Avi Tal Sep 22 '18 at 0:18
$\begingroup$ @AviTal: that definition of statement is really bad and I would advise you not to take it too seriously. It's an outdated and simplified notion which historically comes from the early attempts to distinguish syntax from semantics. It's a mix of both. $\endgroup$ – Andrej Bauer Sep 22 '18 at 7:29
$\begingroup$ @JimLewis: I addressed your question in the comments. $\endgroup$ – Andrej Bauer Sep 22 '18 at 7:48
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