text:
Children, Especially, Are At Risk From ElectroSmog
August 18, 2018 / Dr. Gerald H. Smith / No Comments
All children from Embryo to adulthood need protection from non-ionizing radiation or avoidance and avoidance is impossible. A child's tissues are growing and more susceptible. Adults will have a shorter duration of their lifetime in the electrosmog we live in, but need protection as well. Noise fields provide this protection. (See: MRET-Ohm EMF Protection Shield)
Scientific Evidence of Why the MRET Polymer Works To Eliminate EMR Damage. [ Download PDF]
Exp Oncol. 2011 Jun;33(2):62-70.
Long-term exposure to microwave radiation provokes cancer growth: evidences from radars and mobile communication systems.
Author information: Yakymenko Il, Sidorik E, Kyrylenko S, Chekhun V.
In this review we discuss alarming epidemiological and experimental data on possible carcinogenic effects of long term exposure to low intensity microwave (MW) radiation. Recently, a number of reports revealed that under certain conditions the irradiation by low intensity MW can substantially induce cancer progression in humans and in animal models. The carcinogenic effect of MW irradiation is typically manifested after long term (up to 10 years and more) exposure. Nevertheless, even a year of operation of a powerful base transmitting station for mobile communication reportedly resulted in a dramatic increase of cancer incidence among population living nearby. In addition, model studies in rodents unveiled a significant increase in carcinogenesis after 17-24 months of MW exposure both in tumor-prone and intact animals. To that, such metabolic changes, as overproduction of reactive oxygen species, 8-hydroxi-2-deoxyguanosine formation, or ornithine decarboxylase activation under exposure to low intensity MW confirm a stress impact of this factor on living cells. We also address the issue of standards for assessment of biological effects of irradiation. It is now becoming increasingly evident that assessment of biological effects of non-ionizing radiation based on physical (thermal) approach used in recommendations of current regulatory bodies, including the International Commission on Non-Ionizing Radiation Protection (ICNIRP) Guidelines, requires urgent reevaluation. We conclude that recent data strongly point to the need for re-elaboration of the current safety limits for non-ionizing radiation using recently obtained knowledge. We also emphasize that the everyday exposure of both occupational and general public to MW radiation should be regulated based on a precautionary principles which imply maximum restriction of excessive exposure.
Decreased Survival for Childhood Leukemia in Proximity to Television Towers
Bruce Hocking & Ian Gordon
Pages 560-564 | Published online: 07 Aug 2010
Previously, an increased risk of childhood leukemia was identified among children who resided in an inner ring (radius ~4 km) of 3 municipalities surrounding television towers, compared with children who resided in an outer ring (radius ~4-12 km) of 6 municipalities surrounding, but farther away from, the towers, which are situated in North Sydney, Australia. In the current study, the authors examined the survival experience of these children for all childhood leukemias, and for acute lymphatic leukemia (International Statistical Classification of Diseases and Related Health Problems, 9th revision [ICD-9] rubric 204.0) in particular. Of 123 cases of acute lymphatic leukemia, 29 cases (16 of whom died) were in the inner ring of municipalities nearest the towers, and 94 cases (34 of whom died) occurred in the outer, more-distant ring. There was a significant difference in survival rates between the 2 groups (log-rank test, p = 0.03; Wilcoxon, p = 0.05). The 5-yr survival in the inner ring of municipalities was 55%, and in the outer ring was 71% (i.e., subjects in the inner ring were 23% less likely to survive than those in the outer ring); at 10 yr, survival in the inner and outer rings was 33% and 62%, respectively. Following adjustment, the mortality rate ratio that the authors used to compare the inner ring with the outer ring was 2.1 (95% confidence interval = 1.1, 4.0). There was an association between residential proximity to the television towers and decreased survival among cases of childhood leukemia in North Sydney, Australia.
Video: Who Needs MRET?
Dr. Smith Explains.
MRET-Ohm EMF Protection Shield
Dr. Gerald H. Smith is certified by the World Organization for Natural Medicine to practice natural medicine globally. He is also a certified dental practitioner. His broad base of post-graduate training in dentistry and natural medicine enabled him to integrate many health care specialties.
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My father's history of making sourdough pancakes for us.
Used to make sourdough pancakes.
Take sourdough starter out of the refrigerator.
Use 1 cup of starter for Recipe or throw away.
Stir and return to the refrigerator.
Put the 2 cups of milk in a glass jar or crock and cover with cheesecloth.
Leave in a warm place at room temperature for about 24 hours, or until it sours.
Stir in the flour and blend well.
Let stand again at warm temperature until bubbly and sour. It will take from 2 to 5 days. The starter should have a good, yeasty, sour smell.
Replenish the starter after each use by stirring in equal amounts of milk and flour. Then store covered in the refrigerator.


text:
Analytical notes are relatively short papers that explain interesting and stand-alone findings of analytical work by Treasury staff. They include technical material but this is presented in technical appendices at the end of the notes, so that readers can focus on the insights from the analysis and how they help the Treasury do its job.
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redpajama_set_name: RedPajamaCommonCrawl


We develop high-speed circuit technologies and design methods that enable novel architectures. Our circuit technologies include asynchronous circuits, low-power circuits, and communication links. Our design methods include intellectual tools and computer-aided design tools to help with circuit design, implementation, and testing.
The VLSI Research group dates back to the beginning of Sun Labs. In 1990, Sun Microsystems formed Sun Labs by acquiring the consulting firm of Sutherland, Sproull, and Associates. That year, Ivan Sutherland and Bob Sproull founded the Asynchronous Circuits Research Group in Sun Labs to continue their work in understanding and applying asynchronous circuits to system design. Ivan and Bob, now retired from Sun/Oracle, became Sun Fellows and Vice Presidents. Later, the group changed its name to the "VLSI Research Group" and broadened its research scope.
As a research lab, we prototype solutions to future problems that we predict will confront Oracle engineered systems. Our efforts are most active in high-performance and low-energy VLSI technologies and design methods, and our technology demonstrations involve fabricated silicon test chips, software code, and design and test methodologies. To date we've attacked problems in low-energy communications, both on-chip and between chips; highly scalable computer systems designs; memory and compute-in-memory packaging and system architectures; design optimization; and CAD tools.
We collaborate broadly with university partners and U.S. Government agencies, and many group members are active in international technology communities, such as technological conference committees, journal editorial boards, and international technology prize juries.
The VLSI group is also the development center for the open-source Electric VLSI Design System (manual and users).
Jo Ebergen, David Rager, Dmitry Nadezhin, Austin Lee, Cuong Kim Chau, Ben Selfridge, Formal Methods in CAD 2016, to be presented on 6 Oct.
Dmitry Nadezhin, PSSV 2016, a workshop in Russia.
Circuits without clocks: What makes them tick?
Circuits without a clock: what makes them tick?
How big should a printed circuit board be?


As per news, Samsung Galaxy S6 and the soon to be released Galaxy Note Edge will have much smaller displays than the previous series, which likewise affirms prior reports of an Edge with screens on both sides. Now that definitely is something. Referring to individuals with direct information of Samsung's arrangements, the new Smartphone's are probably going to have a much smaller display,approximately around 5.1 inches.
During a period when contenders are running the race with bigger screens, this is an inversion of sorts for Samsung, which was one of the main thrusts behind mobiles with big screens. Samsung's Galaxy Note from 2011,well defined the "phablet" class with its 5.3-inch screen and the current Samsung Galaxy Note Edge utilizes a 5.6-inch display alongside a little bended screen along the right side.
Beside that goody, a lot of data jives with prior gossipy titbits about Samsung reveals information about Samsung utilizing its own particular chips rather than others, however for the Galaxy Note Edge with a second side screen, with metal protection and for the handsets which Samsung is at present utilizing for its Alpha handset line. The organization is soon to reveal information about the release dates for the new phones, probably. As per sources it is believed that they have a press meeting booked in March, where it is relied upon to launch the new Galaxy S6 and Note Edge telephones which will run Google Android programming. When it comes to pricing, one can also get the best deal by using cashback sites which provide free discount coupon codes and cashback.
We likewise hear odds and ends about the fabrication and configuration of the gadget. Clearly it is going to gush a metal casing, which is everything except justifiable perceiving how metal phones are in style these days and will most likely have a projecting cam, like the one on Galaxy Note.
A metal body would be a movement from Samsung's ordinary plastic, however it's not clear whether the new gadgets would be all-metal or a mixture of metal and plastic. However leaked pictures recommend an all-metal edge. This would likewise be in accordance with the recently declared Galaxy A7 Smartphone, which additionally has a metal casing.
Moreover, Samsung will supposedly divulge another smart watch with a round showcase like the Moto 360. It's not clear what the product gimmicks of the watch will be yet it will probably be controlled by Samsung's Tizenplatform like the Gear S i.
Both the handsets and the smart watch are required to be revealed at the up and coming Mobile World Congress in March. Both handsets and the smart watch are relied upon to be uncovered at the forthcoming Mobile World Congress in March, however the prices and the ratio of availability is not clear.
Well you should also consider the fact that all the information above is derived directly out of the talk factory and ought to be brought with a dash of pepper, yet for the time being this is what to expect from Samsungs next big launch that is long overdue. With the competitive edge around the market and Micromax giving firm competition to them in India, they are likely to create a buzz around the world, but only time will tell their fate in India.


text:
Eve Online Review Space-based MMORPG
By zakaluka, April 10, 2009 in Computer Gaming
zakaluka 0
Eve Online is an MMORPG (Massively Multi-player Online Role Playing Game) made by CCP out of Iceland. Their main (only?) game to date is Eve Online. There are a couple of things that distinguish Eve from other MMORPGs:
(1) You pay a monthly fee to play the game. However, all updates to the game are free. So far, 11 major expansions to the game have been released to subscribers at no cost.
(2) Training skills takes time, not use. Players' attributed (Perception, Intelligence, Willpower, Memory, Charisma) decrease training time for skills, but do not contribute to combat in any way.
(3) Combat is based on your learned level of relevant skills. Because there are hundreds of skills available that would take decades to train up completely, each character is different based on the interests of the actual person behind them.
(4) Combat is not based on twitch action, but on overall tactical analysis. That is to say, the physics engine in the game makes it so that changes in direction, targets, weapons take a not-insignificant time to execute, so the details have to be thought of beforehand.
(5) The economy is almost completely player driven. If you are scammed in-game by another player and they did it without exploiting the game code, you are out of luck. It is a much harsher world, but a lot of more mature in some ways.
(6) No area (except the inside of a station) is completely safe from attack. The penalties are more severe in high security areas, but any player can attack any other player at any time for any reason.
(7) Eve runs on a single-shard server, i.e. all players in the game are playing in the same universe. This means that there is much more scope for players affecting each others' actions and goals.
(8) Eve's client is free to download. A boxed version is available and comes with additional game time and some other items, but is definitely not required.
(9) Even if you hate PvP (a core aspect of Eve), you can go into fields like mining, manufacturing, scientific research, exploration, mission running, trading, ratting, ninja salvaging, and many others. Each of these jobs can earn you money to sustain yourself. In addition, each of these jobs is important to the corporations and alliances that exist throughout Eve. Also, focusing on more than one field is completely possible and probably a good idea. -- thanks to onscreen
Basically, humans found a wormhole when expanding out from Earth. Thousands of people left to find a better life and expand into new colonies. This continued for quite a while, until, one day, the wormhole suddenly collapsed. Now, the people on the other side of the wormhole have to survive with no contact to Earth. The time period is set 21,000 years in the future.
The various factions (Caldari, Gallente, Amarr, Minmatar) are fighting to hold their own territory. However, thanks to the fact that most of the universe is player-driver, player corporations / alliances can and do hold vast tracts of space to rival that held by the 4 major empires.
Eve Online's graphics are extremely creative, yet the game has low system requirements. The game's latest release made it so that a minimum of Shader Model 2 is required to play. However, the textures and models are very detailed and beautifully crafted. The backgrounds truly lend a sense of awe to how large the universe really is compared to an individual pilot.
Eve's sound is quite well done. The music, when coordinated correctly, adds much to the excitement of entering battle or escaping from an engagement.
The game's story line is very deep. There is constant conflict going on in the universe, both driven by CCP and players. CCP also regularly releases short stories that describe various aspects of life in the Eve universe.
Players are able to craft their characters to be good at everything from combat to mining to manufacturing and research. There is a place for all these professions in Eve.
The game is mostly controlled by the mouse with a certain number of keyboard shortcuts that make life simpler when performing repetitive tasks.
Eve Online is a fantastic game that allows people to participate in a non-standard RPG without the grind. Additionally, players can buy game time with the in-game currency (ISK). This means that a successful pilot can play the game for free indefinitely, as long as they keep making money.
There is a 15-day demo available from the Eve website for anyone who wants to try the game. Since character creation and introduction to the Eve universe has been recently revamped, it is a great time to new players to try it out or old players to return to the game.
Edited April 13, 2009 by zakaluka (see edit history)
Here are some images to show people what Eve is like:
A stargate activating, allowing you to jump between solar systems:
My Rifter (a frigate class ship, very nice):
Flying to a stargate (that streak in the middle is me):
Warping through a solar system at 6 AU/s, very nice indeed:
rpgsearcherz 5
Trap Double Mocha Member
Interests:Working on my Rift fansite
Thanks for the review! I almost got Eve Online at one point until I found out it was space based...I'm more into the fantasy type where you play an actual character and go kill monsters/other players and stuff.I may end up checking this out for a little though due to the review talking about a trial...Didn't know there was one, .So thanks again!
Thanks for the review! I almost got Eve Online at one point until I found out it was space based...I'm more into the fantasy type where you play an actual character and go kill monsters/other players and stuff.
I may end up checking this out for a little though due to the review talking about a trial...Didn't know there was one, .
So thanks again!
I'm glad you liked the review. It's a little light on the details, so I'll try to make additional posts about it. Just like you, I am much more into fantasy type games (started with Final Fantasy and Phantasy Star on the original NES / Sega). I've played WoW and still play Guild Wars. However, the biggest reason I moved to Eve Online was that I couldn't stand the grind required to increase level and improve skill. After reaching level 40-45 in WoW, I just got bored running to the same areas and killing the same monsters over and over.
In contrast, there was a battle involving a few hundred ships in Eve recently. All happened in one region of space between a couple of large player alliances. I believe over a hundred large ships were killed. Very spectacular.
If you do use the trial, do post your character (not account!) name here. I'll try to help you out if I can. Best of luck.
Awesome. If I do, it will be a short while before I get the chance.
As for the grinding aspect of games...I really prefer it. My favorite game so far is Lineage II, and it's because it is hardcore anti-carebear. In case you haven't played it, it takes around a year of no-lifing to hit maximum level on one class, and you can have up to 4. On top of that, if you die in PvP, PvE, Sieges, or any other way, you lose experience(at max level one death = around 4 days of nolifing to regain the experience).
I can't stand games where people can lose over and over without worrying because there is no true loss. In L2 if you die you are using up your time. It causes there to be a lot more competition and people are much more efficient in playing.
Regardless, can't pass up the chance to try out another game for free, .
Sounds great. I've heard of Lineage 2 but never played it. I'll definitely have to check that out in the future.
I think my biggest problem with grinding was time, since I was working a 60+ hour a week job when I started Eve. Nowadays, I have a little more available, but I'm just addicted now .
If you don't like care-bearing, you will really love Eve. The kill anywhere rule is fantastic. If a player is running missions, you can loot the NPC wrecks behind them, tempting them to engage you. Plus, when you kill players, their ship will drop loot based on inventory and current equipped modules (can be worth a LOT). In addition, the player will end up in a pod (no-defense capsule that can exist in space). At that point, you can destroy the pod, destroying any implants they have currently equipped (some implants go for 100's of millions of ISK, so you can imagine they might be a little pissed). Look forward to seeing you there in the future!
onscreen 0
Location:Earth, somewhere in the middle
14 Days from CCP and 21 days from Steam client on the trial.
I used to play EvE Online and pilot one of the baddest Gallente Battlecruiser. The fun part is that i am a tugboat in most warfare, salvaging all the wrecks for income. EvE isnt just about PVP. Its about trust and alliance. Its up to your playstyle in this sandbox MMO, you can be cunning or truthful.
Unique part is the character development. Your playstyle is the foundation to the development and the priority of skill development too.
If you don't like care-bearing, you will really love Eve.
I strongly disagree on this. Carebear or non alike will still enjoy EVE Online. If you hate combat and all the pvp, you can be a trader specialize in manufacturing, mining and so on and your only true enemy is the pirates. If you like combating but dislike in being part of the pvp, ratting mission running can be a good source for enjoying EVE Online. Generally its up to you on how you see things running in EVE, you are the judge to yourself when it come to these.
Edited April 13, 2009 by onscreen (see edit history)
This part has changed a lot too (for example, you can't adjust attributes during character creation anymore. And I completely agree about the trust / alliance part.
I had meant to say, "if you don't like care-bears, ....". This is because, more than any other MMO I've played, you can go after care-bears in Eve anywhere, anytime. I know, because I am a carebear to a large degree and have felt the pain of losing my only mission running ship to pirates (luckily, I got into a PvP ship with some corp members and was able to hunt down and kill the pirate).
I've added the other jobs to the review, thanks.
Ousk 0
Location:Iasi, Romania
played the game for two years, but my character is just waiting there now for some much needed improvements. I got bored by the pvp part of the game and that is the only part where the game succeeds. Also with the last addons they just expanded the pvp part of the game, soo if u'r not a pvp fan this game may not be for u cause just shooting npc dots or clicking on an asteroid may not cut it for you. I'm waiting impatiently for now for some space mmos that are in closed beta. As for eve i'll just wait for them to expand the game in other directions than just pvp.
HoRuS 0
Location:Netherlands
Excelent review OP.I play EVE Online now for 5 years and still loving the game!I do have to say, this is a game in wich the longer you play, the more fun it gets. Flying Titans and Supercarriers (very very big ships) is usually for players who play at least 2-3 years and imo not the ships every player would like to fly, due to their time and costs.Instead you start with frigate class, cruiser class and up. Improved frigates and cruisers, battlecruisers and so on, wich are way more fun to fly in pvp. The owners (CCP) also made it easier now for newer player to jump in with gifts that shorten train times, moneymaking etc etc.Awesome game
I've never played EVE but people still talk about it a lot in modern games. Many claim it has the best PvP ever. And my understanding is you don't have to pay monthly since people can "trade" game time for items/gold?
Indeed it is possible to trade for game time for ingame money (ISK) or items, CCP has a nifty systems since 2 years called PLEX, wich allows a player to buy a PLEX (gametime) for ingame marketprices. Thing is it's not very easy make 400 Million ISK when you first start playing, but after several months, depending on the player, you could afford it.And it's indeed the best PvP I've ever played in an mmo


text:
\section{Introduction\label{s:intro}}

Gravitational scattering at extreme energies ($s\gg M_P^2$) and possibly small
impact parameters ($b\gtrsim R\equiv 2G\sqrt{s}$) was devised, from the
beginning~\cite{tHooft:1987rb,Muzinich:1987in,ACV87,GrMe87,ACV88,VeVe91,ACV90,ACV93},
as a probe of quantum gravity in a regime close to classical collapse.  More
recently, transplanckian scattering has been revived at both
classical~\cite{GrVe14} and quantum
level~\cite{Dvali:2014ila,CCV15,Addazi:2016ksu} with the purpose of describing
the radiation associated to extreme energies and of gaining in this way a better
understanding of the possibly collapsing system.

By analyzing string-gravity in the parameter region
$b\gg R\gg l_P\equiv\sqrt{G\hbar}$, ACV proposed a semiclassical
approach~\cite{ACV93} to gravitational scattering, based on an effective
action~\cite{Li91,VeVe91} which allows to compute the eikonal function
$\delta({\boldsymbol{b}},s)$ as an all-order expansion in the parameter $R^2/b^2$. In the
axisymmetric reduced-action model they~\cite{ACV07} obtained
\begin{equation}\label{deltabs}
  \delta({\boldsymbol{b}},s) = \ag \left[\log\frac{L}{R}+\Delta({\boldsymbol{b}})\right] \;,\qquad
\Delta({\boldsymbol{b}}) \equiv -\atanh(t_b)+\frac12 - \frac1{2t_b} \;,
\end{equation}
where $t_b(b/R)$ is determined by the criticality equation
\begin{equation}\label{criticality}
  t_b(1-t_b^2) = \frac{R^2}{b^2}
\end{equation}
and $L$ is an IR cutoff, factorized in the elastic $S$-matrix expression
\begin{equation}\label{Sel}
  S_\el({\boldsymbol{b}},s) = \esp{2\ui\delta}
  = \esp{2\ui\ag\log\frac{L}{R}}\esp{2\ui\ag\Delta({\boldsymbol{b}})} \;.
\end{equation}
We notice that the leading contribution $\ag\log(R/b)$ is corrected in
$\Delta({\boldsymbol{b}})$ by higher order terms, providing the ACV resummation, and that the
criticality equation~\eqref{criticality} identifies a branch-cut singularity of
the series at $b^2=b_c^2\equiv(3\sqrt{3}/2)R^2$, below which the eikonal
function acquires a (positive) imaginary part. As a consequence, starting from a
small impact parameter $b<b_c(R)$, the elastic channel acquires the suppression
factor
\begin{equation}\label{suppression}
  |S_\el({\boldsymbol{b}},s)|^2 \simeq
  \begin{cases}
    \displaystyle\exp\left[-\frac{4\sqrt{2}}{3}\ag
      \left(1-\frac{b^2}{b_c^2}\right)^{3/2}\right]
    & \qquad(b_c-b\ll R) \\[6mm]
    \displaystyle\exp\left[-2\ag\left(\pi-\frac{3\sqrt{3}}{2}
        \left(\frac{b}{R}\right)^{2/3} \right)\right] &\qquad(b\ll R)
  \end{cases}
\end{equation}
which has the interpretation of tunneling probability~\cite{CC08} through a
repulsive Coulomb-type barrier in metric space, which is classically
forbidden. Eqs.~\eqref{deltabs}-\eqref{suppression} summarize the main
properties of the elastic ACV $S$-matrix~\eqref{Sel} for $b>b_c\sim R$ and
$b<b_c$, respectively.

More recently, the semiclassical (eikonal) framework has been revived in various
approaches at both classical~\cite{GrVe14} and quantum
level~\cite{CCV15,CCCV15,CC16} in order to describe the graviton radiation
associated to scattering. Since the typical graviton energy
$\omega\sim 1/R \sim M_P^2/E \ll M_P$ is soft in the transplanckian regime
$(\ag\sim s/M_P^2\gg 1$), the radiation amplitude is well described by the
Weinberg current~\cite{We65} in the fragmentation region of phase space.
Furthermore, it has been noticed in~\cite{CCV15,CCCV15} that actually a unified
formulation of the amplitude applies to the central (Regge) region as well,
leading to the so-called ``soft-based representation'' of graviton emission.
Finally, the latter can be extended~\cite{CC16} to the ACV resummed formulation
of the eikonal mentioned before, in the ``reduced-action'' model.

Properties of the radiation sample generated in such a way in transplanckian
scattering have already been described in~\cite{CC16} by applying the soft-based
representation for both small and finite scattering angles ($b\geq b_c$). The
results emphasize the role of the gravitational radius $R$: by combining the
relatively small emitted energy ($\omega/E \ll 1$) with the large-number
$n\sim\ag=ER$ of single-hits in eikonal scattering, the variable $\omega R$ emerges
and identifies the main features of the energy emission distribution. The
outcome is an operator $S$-matrix combining the resummed-eikonal and radiation
in a (unitary) coherent state
\begin{align}
  \hat{S}&=\esp{2\ui\delta} \exp\left\{\int\frac{\dif^3 q}{\hbar^3\sqrt{2\omega}}\;
    2\ui\left[\sum_\lambda \ampRid_\lambda({\boldsymbol{b}},\vq) a^\dagger_\lambda(\vq)
      +\text{h.c.}\right] \right\}\label{Shat} \\
  \frac{\ampRid_\lambda({\boldsymbol{b}};\omega,{\boldsymbol{q}})}{\esp{\ui\lambda\phi_{\boldsymbol{\theta}}}} &=
  \sqrt{\ag}\frac{R}{\pi}\int\frac{\dif^2{\boldsymbol{x}}}{2\pi|{\boldsymbol{x}}|^2\esp{\ui\lambda\phi_{\boldsymbol{x}}}}
  \frac{\esp{\ui{\boldsymbol{q}}\cdot{\boldsymbol{x}}}}{2\ui\omega R}\left\{\esp{2\ui\omega R\left[
        \Delta({\boldsymbol{b}}-{\boldsymbol{x}})-\Delta({\boldsymbol{b}})\right]}-\esp{2\ui\omega R\frac{E}{\omega}\left[
        \Delta({\boldsymbol{b}}-\frac{\hom}{E}{\boldsymbol{x}})-\Delta({\boldsymbol{b}})\right]} \right\} \label{ampRis}
\end{align}
with $\Delta$ given in eq.~\eqref{deltabs}, while $q$ and $\lambda$ denote
  graviton momentum and helicity, respectively.

We should remark, as a premise to the following investigation, that the unitary
form of eq.~\eqref{Shat} --- which is part of the proposal
in~\cite{CCV15,CCCV15,CC16} --- was based on appropriate and factorized
virtual corrections [eq.~\eqref{P0}], which are argued for in secs.~\ref{s:usbr}
and \ref{s:mge}, but are not really derived from some underlying quantum gravity
theory. For that reason we prefer to talk of ``unitarization procedure'' rather
than ``unitarity proof'' in passing from the tree-level amplitude $\ampRid$ to
the final unitary coherent state~\eqref{Shat}, with its factorized emission
structure.

Furthermore, we have shown~\cite{CC16} that such (approximate)
independent-particle picture can be extended to the approach-to-collapse regime
$b\to b_c^+$ of enhanced radiation by incorporating energy-conservation
constraints in the unitarization procedure. The latter cause the emergence of a
novel, exponential frequency damping whose coefficient $\tb R$ defines what we
call a ``quasi-temperature'' $T\equiv\hbar/(\tb R)$ which is naturally related
to the Hawking temperature~\cite{Hawking:1974sw,Hawking:2015qqa}. The main
difference, though --- and the motivation for its unconventional name --- is
that $\tb$ is supposed to keep quantum coherence, and is not due to a
statistical averaging.  Rather, the lack of sizeable correlations in such result
is due to the soft-graviton dynamics we started with, which led to the unified
form of the $b\to b_c^+$ emission amplitudes.

A basic question then arises: what about the collapse regime of $b<b_c$, in
which the energy $2E$ appears to be ``trapped'' because elastic unitarity is
exponentially violated by the suppression factors~\eqref{suppression} without
apparent contributions in the most naive radiation
models~\cite{CC08,CC09,CCF11,CC14}? In other words, is unsuppressed radiation
predictable for $b<b_c$ in our present soft-based representation? That is
precisely the question that we address in this paper. We shall argue that during
eikonal scattering, the soft-radiation process has indeed the ability to reduce
the amount of ``trapped'' energy crossing the barrier, and thus to gradually
eliminate (sec.~\ref{s:mge}) the suppression factor~\eqref{suppression}. As a
consequence (secs.~\ref{s:urqt},~\ref{s:icc}), our
coherent radiation sample can efficiently contribute to the unitarity sum, and
still may have a ``normal'' quasi-temperature of order $1/R$. For that reason,
it is a good candidate for the generalized unitarization procedure that we shall
describe, as discussed in sec.~\ref{s:d}.

\section{Unified soft-based representation of single-emission amplitude\label{s:usbr}}

We start, in the ACV framework, from the (irreducible) resummed eikonal
$\ag\Delta({\boldsymbol{b}})$ in eq.~\eqref{deltabs}, whose Fourier transform defines a
``potential'' $\tilde\Delta({\boldsymbol{Q}})$ in transverse space. In the soft limit and in
the fragmentation region, the emission amplitude is then given by the
external-line insertion formula, which factorizes in ${\boldsymbol{Q}}$-space as follows
($\hbar=1$):
\begin{equation}\label{Msoft}
  \tfa^\mathrm{soft}_\lambda({\boldsymbol{b}},E,{\boldsymbol{q}},\omega) = \sqrt{\ag}\frac{R}{\pi}\int
  \frac{\dif^2{\boldsymbol{Q}}}{2\pi}\;\tilde\Delta({\boldsymbol{Q}})\esp{\ui{\boldsymbol{Q}}\cdot{\boldsymbol{b}}}
  \left[\frac{E}{\hom}\left(
      \esp{-\ui\lambda(\phi_{{\boldsymbol{q}}-\frac{\hom}{E}{\boldsymbol{Q}}} -\phi_{\boldsymbol{q}})}-1\right)\right]
  \;,
\end{equation}
where ${\boldsymbol{q}}$ is the transverse momentum of the emitted graviton, $\phi_{\boldsymbol{q}}$ is
its azimuth in the transverse plane, $\lambda = \pm2$ its helicity, and the
factor in square brackets comes from the explicit computation of the Weinberg
current on helicity states~\cite{CCV15}.

It was shown in~\cite{CCCV15} that a similar formula is able to describe graviton
emissions in the central region --- where the Lipatov current~\cite{Li91} should
be used in the Regge limit --- by just performing a simple subtraction of the
same expression at scale $E\to\hom$. The unified amplitude thus reads
\begin{align}
  \tfa_\lambda({\boldsymbol{b}},E,{\boldsymbol{q}}) &= \sqrt{\ag}\frac{R}{\pi}\esp{\ui\lambda\phi_{\boldsymbol{q}}}
  \int\frac{\dif^2{\boldsymbol{x}}}{2\pi|{\boldsymbol{x}}|^2\esp{\ui\lambda\phi_{\boldsymbol{x}}}}\;
  \esp{\ui{\boldsymbol{q}}\cdot{\boldsymbol{x}}} \nonumber \\
  &\quad\times \left[
    \frac{E}{\hom}\Big(\Delta\big({\boldsymbol{b}}-\textstyle{\frac{\hom}{E}}{\boldsymbol{x}}\big)-\Delta({\boldsymbol{b}})\Big) -
    \Big(\Delta({\boldsymbol{b}}-{\boldsymbol{x}})-\Delta({\boldsymbol{b}})\Big)\right] \;, \label{uniamp}
\end{align}
where we have exchanged the ${\boldsymbol{Q}}$ integration with an ${\boldsymbol{x}}$ integration that
provides a convenient representation of phase-transfers (e.g.\ for $\lambda=-2$):
\begin{equation}\label{zRep}
  \esp{2\ui \phi_{{\boldsymbol{\theta}}}} - \esp{2\ui \phi_{{\boldsymbol{\theta}}'}}
  = -2 \int \frac{\dif^2{\boldsymbol{x}}}{{2\pi x^*}^2} \left( \esp{\ui A {\boldsymbol{x}} \cdot {\boldsymbol{\theta}}}
    - \esp{\ui A {\boldsymbol{x}} \cdot {\boldsymbol{\theta}}'} \right) \;, \qquad(A\in \R^*) \;.
\end{equation}

We notice that eq.~\eqref{uniamp} is directly expressed in terms of the eikonal
function $\delta({\boldsymbol{b}}) \cong \ag\Delta({\boldsymbol{b}})$ of eq.~\eqref{deltabs}, which occurs
in the modulating function
\begin{align}\label{PhiR}
  \Phi(\omega,{\boldsymbol{x}}) &\equiv \frac{E}{\hom}\left[\Delta({\boldsymbol{b}}-\textstyle{\frac{\hom}{E}}{\boldsymbol{x}})-\Delta({\boldsymbol{b}})
    \right] -\left[\Delta({\boldsymbol{b}}-{\boldsymbol{x}})-\Delta({\boldsymbol{b}})\right]
    \equiv \Phi_A({\boldsymbol{x}}) - \Phi_B({\boldsymbol{x}}) \;,
\end{align}
where the first (second) term is in correspondence with external (internal)
insertions. Thus, the single-exchange amplitude~\eqref{uniamp} measures the
Fourier transform of the ``soft-field''
\begin{equation}\label{hsoft}
  h_s^{(\lambda)}(\omega,{\boldsymbol{x}}) =
  -\frac{\Phi(\omega,{\boldsymbol{x}})}{\pi^2|{\boldsymbol{x}}|^2\esp{\ui\lambda\phi_{\boldsymbol{x}}}} \;,
\end{equation}
which plays an important role in the expression of the ACV metric
also~\cite{CCCV15}.

\begin{figure}[ht]
  \centering
  \includegraphics[width=0.66\linewidth]{eikEmission.eps}
  \caption{\it Graviton emission from the eikonal ladder. The $n$-rung diagram
    with the emission from the $j$-th exchange is denoted by $\tfa^{[n,j]}$ in
    the text.}
  \label{f:eikEmission}
\end{figure}

The full graviton radiation amplitude is now obtained by superimposing the
single-exchange amplitudes~\eqref{uniamp} over all the $n$ rungs of the eikonal
diagrams (fig.~\ref{f:eikEmission}). The contribution of the $j$-th rung can be
written as
\begin{align}
  \tfa^{[n,j]}_{\lambda}({\boldsymbol{b}},E,{\boldsymbol{q}}) &= \esp{\ui\lambda\phi_{\boldsymbol{\theta}}}
  \sqrt{\alpha_G}\frac{R}{2} \frac{(2\ui\ag)^{n-1}}{n!} \times \nonumber \\
  &\quad\int\dif^2{\boldsymbol{x}} \;\esp{\ui{\boldsymbol{q}}\cdot{\boldsymbol{x}}}
  \left[\Delta({\boldsymbol{b}}-\frac{\hom}{E} {\boldsymbol{x}})\right]^{j-1} h_s^{(\lambda)}(\omega,{\boldsymbol{x}})
  \left[(E-\omega)\Delta({\boldsymbol{b}})+\omega\Delta({\boldsymbol{b}}-{\boldsymbol{x}})\right]^{n-j} \;, \label{Mnj}
\end{align}
where we notice two important effects. Firstly, the $j$-th incidence angle is
rotated with respect to the $z$-axis, by translating the ${\boldsymbol{\theta}}$-dependence by
the quantity ${\boldsymbol{\Theta}}_j=({\boldsymbol{Q}}_1+\cdots+{\boldsymbol{Q}}_{j-1})/E$. That produces in turn, after
Fourier transform, the shift $-(\omega/E){\boldsymbol{x}}$ in the impact parameter of the
elastic amplitudes before emission.

Secondly, after emission we have the rescattering effects: the energetic
particle acquires the recoil energy $E-\omega$, and the emitted graviton at
position ${\boldsymbol{x}}$ rescatters with energy $\omega$ and relative impact parameter
${\boldsymbol{b}}-{\boldsymbol{x}}$.

Finally, the summation over $j$ of the contributions~\eqref{Mnj} is performed by
the formula
\begin{equation}\label{sum1}
  \sum_{n=1}^\infty \frac1{n!}\sum_{j=1}^n A^{j-1} B^{n-j}
  =\sum_{n=0}^\infty \frac1{n!}\frac{A^n- B^n}{A-B}
  = \frac{\esp{A}-\esp{B}}{A-B} \;,
\end{equation}
where
\begin{equation}\label{phiAB}
  A \equiv 2\ui\ag\left[\Delta({\boldsymbol{b}})+\frac{\hom}{E}\Phi_A({\boldsymbol{x}})\right] \;, \qquad
  B \equiv 2\ui\ag\left[\Delta({\boldsymbol{b}})+\frac{\hom}{E}\Phi_B({\boldsymbol{x}})\right]
\end{equation}
are given in terms of the $\Phi_{A,B}$ of eq.~\eqref{PhiR}. We thus realize that
the factor $\Phi({\boldsymbol{x}})=\Phi_A-\Phi_B$ in the soft field $h_s^{(\lambda)}$ cancels
out with the $A-B$ denominator of the summation~\eqref{sum1}. That cancellation
is conceptually surprising. Somehow, the identity
\begin{equation}\label{softRegge}
  \tfa_\match =
  \left.\mathrm{soft}\right|_E -\left.\mathrm{soft}\right|_{\hom}
  \simeq \left.\mathrm{Regge}\right|_E
\end{equation}
--- that was interpreted as a decomposition of external plus internal insertions in
the soft language --- acquires now the interpretation of ``incidence-changing''
plus ``rescattering'' terms in the Regge language.

The final result can thus be written as
\begin{align}
  \tfa_{\lambda}({\boldsymbol{b}},E,{\boldsymbol{q}}) &= \esp{2\ui\ag\Delta({\boldsymbol{b}})}
   \ampRid_{\lambda}({\boldsymbol{b}},\omega,{\boldsymbol{q}}) \nonumber \\
  \ampRid_{\lambda}({\boldsymbol{b}},\omega,{\boldsymbol{q}})
  &= \sqrt{\alpha_G}\frac{R}{\pi}\esp{\ui\lambda\phi_{\boldsymbol{q}}} \int
  \frac{\dif^2{\boldsymbol{x}}}{2\pi|{\boldsymbol{x}}|^2\esp{\ui\lambda\phi_{\boldsymbol{x}}}} \;
  \esp{\ui {\boldsymbol{q}}\cdot{\boldsymbol{x}}} \esp{2\ui\omega R\Phi_A({\boldsymbol{x}})}
  \frac{\esp{-2\ui\omega R \Phi({\boldsymbol{x}})}-1}{2\ui\omega R} \;.\label{ampRid2}
\end{align}

\section{Multi-graviton emission and unsuppressed radiation in the collapse
  regime\label{s:mge}}

As we have just seen, the CC~\cite{CC16} method for incorporating the resummed
eikonal $\ag\Delta({\boldsymbol{b}})$ of eq.~\eqref{deltabs} in the radiation process is best
illustrated (fig.~\ref{f:amplitude2to3}) by the one-graviton emission amplitude
\begin{equation}
  \tfa_{2\to3} = \int\frac{\dif^2{\boldsymbol{x}}}{(2\pi)^2} \; \frac{\sqrt{\ag}}{x^{*2}}
  \frac{\esp{\ui {\boldsymbol{q}}\cdot{\boldsymbol{x}}}}{\ui\omega} \left[ \esp{2\ui(E-\omega)R\Delta({\boldsymbol{b}})
      +2\ui\omega R\Delta({\boldsymbol{b}}-{\boldsymbol{x}})} - \esp{2\ui\ag\Delta({\boldsymbol{b}}-\frac{\hom}{E}{\boldsymbol{x}})}
  \right] \label{M23}
\end{equation}
which contains {\it(i)} the rescattering term with its typical $(E-\omega)$ recoil
energy (which is here listed as first term) and {\it(ii)} the incidence-changing
term with its $\omega$-dependent shift (second term). From eq.~\eqref{M23}, by
dividing out the $2\to2$ $S$-matrix $\exp[2\ui\ag\Delta({\boldsymbol{b}})]$, we obtain the
single-emission probability amplitude
\begin{align}
  \ampRid_\lambda({\boldsymbol{b}},\omega,{\boldsymbol{q}}) \simeq \int\frac{\dif^2{\boldsymbol{x}}}{(2\pi)^2} \;
  \frac{\sqrt{\ag}}{|x|^2\esp{\ui\lambda\phi_{\boldsymbol{x}}}}
  \frac{\esp{\ui {\boldsymbol{q}}\cdot{\boldsymbol{x}}}}{\ui\omega}
  &\Big\{ \esp{-2\ui\omega R \left[\Delta({\boldsymbol{b}})-\Delta({\boldsymbol{b}}-{\boldsymbol{x}})\right]} -1
       \nonumber\\
      & +1 - \esp{2\ui\ag\left[\Delta({\boldsymbol{b}}-\frac{\hom}{E}{\boldsymbol{x}})-\Delta({\boldsymbol{b}})\right]}
        \Big\} \label{ampRid} \;,
\end{align}
where in curly brackets we have singled out the rescattering and
incidence-changing terms.

\begin{figure}[ht]
  \centering
  \includegraphics[width=0.65\linewidth]{amplitude2to3.eps}
  \caption{\it Radiation diagram of the soft-based representation: (a) External
    line insertion shifts the impact parameter ${\boldsymbol{b}}-\frac{\hom}{E}{\boldsymbol{x}}$ and rotates the
    incidence angle. (b) Internal line insertion scatters at recoil energy
    $E-\omega$ and rescatters at position ${\boldsymbol{b}}-{\boldsymbol{x}}$ and energy $\omega$.}
  \label{f:amplitude2to3}
\end{figure}

Multiple emission is then treated by arguing~\cite{CCCV15} that, in the soft
region $\omega_i \ll E$, real emission factorization holds in the form
\begin{equation}\label{factorization}
  \tfa_{2\to2+N} \simeq \esp{2\ui\ag\Delta({\boldsymbol{b}})} \prod_{i=1}^N
  \ampRid_{\lambda_i}({\boldsymbol{b}},\omega_i,{\boldsymbol{q}}_i) \times
  \left[1+\ord{\frac{\omega_j^2}{E^2}}\right] \;.
\end{equation}
In the case $b>b_c$, $\Delta({\boldsymbol{b}})$ is real and the
factorization~\eqref{factorization} can be extended to virtual corrections by
addition of a factor $\sqrt{\Pr_0}$ --- the no-emission amplitude ---, where
\begin{equation}\label{P0}
  \Pr_0 = \exp\left\{-2\int\frac{\dif^3 q}{\omega}\;\sum_\lambda
    |\ampRid_\lambda|^2\right\}
\end{equation}
is the no-emission probability. Eq.~\eqref{factorization}, with the correction
factor~\eqref{P0} is then equivalent to using the unitary $S$-matrix
parametrization
\begin{align}
  S &= \esp{2\ui\delta}\exp\left\{\int\frac{\dif^3 q}{\sqrt{2\omega}}\;
    2\ui \sum_\lambda \left[ \ampRid_\lambda a^\dagger_\lambda(q)
      + \ampRid_\lambda^* a_\lambda(q) \right] \right\} \label{Smatrix} \\
  \omega \po(\omega) &= 2\sum_\lambda \int\dif^2{\boldsymbol{q}}\; |\ampRid_\lambda|^2 \label{oPo}
\end{align}
corresponding to the ``linear'' coherent-state operator~\eqref{Shat} and to
its emission density.

In~\cite{CC16} we noticed that the independent-particle picture just outlined is
not fully consistent when scattering angle and coupling enter the collapse
region and radiation should be corrected for energy-conservation effects. The
latter can be taken into account by introducing, besides $\sqrt{\Pr_0}$, an
amplitude renormalization factor $1/\sqrt{\Nor(E)}$, where $\Nor(E)$ is
dependent on the available energy $E$ and is determined by unitarity, by
including the kinematical constraints event by event. The outcome is then the
occurrence of the quasi-temperature factor $\esp{-\omega/T}$ in inclusive
distributions~\cite{CC16}, which allows the correspondence of our coherent
radiation sample with a Hawking radiation.

The case $b<b_c$  is deeply different, however. In fact, in such case
$\Delta({\boldsymbol{b}})$ acquires an imaginary part which is of size $\ui\pi/2$ in the
$b\ll R$ limit of deep collapse and has the interpretation of tunneling through
a barrier~\cite{CC08}. As a consequence, the elastic amplitude in the
Ansatz~\eqref{factorization} is exponentially suppressed like
$\esp{-\pi\ag}=\esp{-\pi ER}$ (for $E=\sqrt{s}/2$), and thus the combined use of
eq.~\eqref{factorization} and \eqref{P0} cannot possibly correspond to a unitary
parametrization of type~\eqref{Smatrix}. How to reach unitarity then?

Our purpose here is to single out those emission processes which, on the basis
of~\eqref{M23} and \eqref{ampRid} are not suppressed and can possibly lead
to unitarity recovery. We start noticing that, even at small impact parameters
$b\ll R$, the emission amplitude~\eqref{ampRid} stays unsuppressed
in~\eqref{factorization} if the graviton is emitted at sufficiently large
$|{\boldsymbol{x}}|$, outside the trapped region, so that the corresponding eikonal is
real-valued. For the rescattering terms (with $\Delta({\boldsymbol{b}}-{\boldsymbol{x}})$) such "exit''
occurs already at $|{\boldsymbol{x}}|>R\gg b$, while for the incidence-changing terms (with
$\Delta({\boldsymbol{b}}-\frac{\hom}{E}{\boldsymbol{x}})$) we have to require that $|{\boldsymbol{x}}|>(E/\omega)R$ be much
larger, in which case the ${\boldsymbol{x}}$-integration is suppressed by a phase space
factor $\omega^2/E^2$ in the interesting soft region $\omega R\ll\ag$.

Therefore, for $b\ll R$, the rescattering terms appear to provide the best
visible radiation window and will be investigated firstly at multi-graviton
level in the following. Indeed, according to sec.~2 of~\cite{CC16}, the
multi-graviton factorization~\eqref{factorization} appears to hold exactly in
the rescattering case --- if incidence-changing terms are turned off --- because
the $\omega_j R$-dependence is simply additive. Furthermore, the probability
amplitude $\ampRid$ of the rescattering term in~\eqref{ampRid} is increasing
like $\exp(\pi\omega R)$
\footnote{Here we treat in detail, for definiteness, the $b\ll R$ case, but our
  arguments about suppression and compensation are valid for general $b<b_c$ by
  just replacing $\pi$ by $2\Im\Delta(b)$.}
within the kinematical bounds and thus yields a strong
radiation enhancement. The physical reason of such increase is just energy
conservation, because the recoil energy $(E-\omega)$ signals the corresponding
suppression decrease.

As a consequence, by collecting all exponential terms, the independent
particles' distribution would read, approximately,
\begin{equation}\label{dPN}
  \dif\Pr(\{\omega_j,N_j\}) = \Pr_0(E) \Theta(E-\sum_j\omega_j N_j) \prod_{j}
  \frac{\left[\po(\omega_j)\Delta\omega_j\right]^{N_j}}{N_j!} \;,
\end{equation}
where
\begin{equation}\label{P0E}
  \Pr_0(E) = \esp{-2\pi ER} \;, \qquad
  \po(\omega_j) \equiv \esp{2\pi\omega_j R} \pp(\omega_j)
\end{equation}
and $\pp(\omega)\sim \ag/(\pi\omega^3 R^2)\times[1-\ord{\esp{-2\pi\omega R}}]$ is
obtained from the ${\boldsymbol{x}}$-integration of the leading rescattering term with
important subleading corrections for $\omega R\lesssim 1$. In more detail,
referring to one jet, we have from eq.~\eqref{ampRid} --- by use of the Parseval
identity --- the estimate of the rescattering density for
$|{\boldsymbol{x}}|\gtrsim\ord{R}\gg|{\boldsymbol{b}}|$
\footnote{Integrating over ${\boldsymbol{q}}$ phase space in eq.~\eqref{oPo} limits
  $|{\boldsymbol{q}}|=\omega\sin\theta<\omega=\ord{1/R}$ and thus introduces a natural cutoff
  $|{\boldsymbol{x}}|>R$ in eq.~\eqref{omPom} for the validity of the Parseval identity at
  small $x$-values.}
\begin{align}
  \omega\po(\omega) &= \int\sum_\lambda|\ampRid_\lambda|^2 2\omega^2\dif\Omega
  = \ag\int\frac{\dif^2{\boldsymbol{x}}\;4(2\pi)^2}{(2\pi|{\boldsymbol{x}}|)^4\omega^2}
  \left| \esp{\omega R[\pi+2\ui\Delta(-{\boldsymbol{x}})]}-1 \right|^2 \nonumber \\
  &\simeq \frac{\ag}{\pi\omega^2 R^2}\esp{2\pi\omega R}
  \left[(1-\esp{-\pi\omega R})^2+4\bk{\sin^2\omega R\Delta({\boldsymbol{x}})}\esp{-\pi\omega R}
  \right] \nonumber \\
  &\equiv \omega\pp(\omega)\esp{2\pi\omega R} \;, \label{omPom}
\end{align}
where $\bk{\cdots}$ denotes ${\boldsymbol{x}}$-integration (averaging).  We thus realize by
eq.~\eqref{dPN} that the suppression factor $\Pr_0(E)$ is compensated by the
rescattering enhancement factors $\esp{2\pi\omega_j R}$ in $\po(\omega_j)$ provided
$\sum_j \omega_j N_j = E$, that is close to the energy conservation boundary in
which the whole energy $E$ is radiated off. That compensation may occur for a
few hard gravitons as well as a bunch of soft ones with $\omega_j R=\ord{1}$, thus
allowing in principle a unitary behaviour with a normal quasi-temperature of
order $1/R$.

\section{Unitarity restoration and quasi-temperature:\\
  the rescattering terms\label{s:urqt}}

In order to better understand how suppression is avoided and unitarity is
possibly restored in the rescattering case, note that the
expressions~\eqref{dPN} and \eqref{omPom} allow the use of the energy-conserving
unitarization method based on the $\Nor(E)$ rescaling~\cite{CC16,GriVe_pc,AGK72}
in the $b<b_c$ case also.  In fact we can replace the independent-particle
distribution~\eqref{dPN} by
\begin{equation}\label{dPNt}
  \dif\tilde{\Pr}(\{\omega_j,N_j\}) = \frac{\Pr_0(E)}{\Nor(E)}
  \int_{c-\ui\infty}^{c+\ui\infty} \frac{\dif\lambda}{2\pi\ui\lambda}\;
  \esp{\lambda(E-\sum_j \omega_j N_j)}
  \prod_{j} \frac{\left[\po(\omega_j)\Delta\omega_j\right]^{N_j}}{N_j!} \;,
\end{equation}
where $\Pr_0/\Nor$ plays a role similar to the $b>b_c$ case, but
$\Pr_0=\esp{-2\pi ER}$ is the ACV-resummed suppression result.

The unitarity requirement $\sum_{\{N_j\}}\dif\tilde{\Pr}(\{\omega_j,N_j\})=1$ (with
the kinematical constraint $\sum_j \omega_j N_j \leq E$) determines $\Nor(E)$ as
\begin{align}
  \Nor(E) &\equiv \Pr_0(E) \left[ 1+\sum_{N=1}^\infty\frac1{N!} \int
  \left( \prod_{j=1}^N\dif\omega_j P(\omega_j) \right)
  \Theta(E-{\textstyle\sum_{j=1}^N\omega_j}) \right] \nonumber\\
  &= \int_{2\pi R-\ui\infty}^{2\pi R+\ui\infty}
  \frac{\dif\lambda}{2\pi\ui\lambda}\; \Pr_0(E) \esp{\lambda E +\int_0^\infty
    \dif\omega\;\esp{-\lambda\omega} \po(\omega)} \;, \label{NE}
\end{align}
where we have set $\Re\lambda\geq c = 2\pi R$ to let the exponent integrand to
formally converge. By the translation $\lambda = (2\pi+\tau)R$ we then obtain
\begin{equation}\label{NEtau}
  \Nor(E) = \int_{-\ui\infty}^{+\ui\infty}\frac{\dif\tau}{2\pi\ui(\tau+2\pi)}\;
  \esp{\tau RE+\int_0^\infty\dif\omega\;\esp{-\tau\omega R}\pp(\omega)} \;,
\end{equation}
where $\Pr_0$ has been replaced by 1 and $\po(\omega)$ by $\pp(\omega)$ of
eq.~\eqref{omPom}.%
\footnote{
  In writing~\eqref{NE} (\eqref{NEtau}) we have to exchange the order of
  $\lambda$ ($\tau$)-integrations with $\omega$-integrations. That is simply
  achieved by the truncation of $\po(\omega)$ at the kinematical boundary:
  $\po(\omega)\to\po(\omega)\Theta(\sqrt{s}/2-\omega)$. That truncation is understood in
  the following, and is a consequence of the kinematical constraints also for
  $E\leq\sqrt{s}/2$.}
Therefore, all suppression and enhancement factors are now
eliminated and the determination of the energy-conserving $\dif\tilde{\Pr}$'s
can proceed as for $b>b_c$. Firstly, the distribution~\eqref{dPNt} in the
$\tau$-representation is
\begin{equation}\label{dPNtau}
  \dif\tilde\Pr = \frac1{\Nor(E)}\int_{\epsilon-\ui\infty}^{\epsilon+\ui\infty}
  \frac{\dif\tau}{2\pi\ui(\tau+2\pi)} \esp{\tau R (E-\sum_j \omega_j N_j)}
  \prod_j \frac{[\pp(\omega_j)\Delta\omega_j]^{N_j}}{N_j !} \;,
\end{equation}
where $\Nor(E)$ in~\eqref{NEtau} can be estimated by a saddle point method.
Actually, in the simple example $\pp(\omega)= \ag R \hat\pp = \text{const}$, we
find directly $\Nor(E)\sim\exp[2\sqrt{\ag E R \hat\pp}]$ showing that
$\Nor(E)\gg1$ despite the $\Pr_0(E)$ factor in~\eqref{NE}. That suggests the
direct interpretation of $\Nor(E)$ as a sort of entropy of the ``trapped
energy'' fragmentation process.

Secondly, the general saddle point equation reads
\begin{align}
  \ag &= \frac1{\tb+2\pi} + \ag F(\tb) \label{sadpoi} \\
  F(\tb) &\equiv \int_0^\infty \dif\omega\;\frac{\omega}{E}\esp{-\tau\omega R} \pp(\omega)
  \nonumber \\
  &= \int_0^\infty\dif(\omega R)\;\frac{\ag}{\pi(\omega R)^2}
  \left[(1-\esp{-\pi\omega R})^2+4\bk{\sin^2\omega R\Delta({\boldsymbol{x}})}\esp{-\pi\omega R}
  \right] \esp{-\tb\omega R} \;, \nonumber
\end{align}
which for $\ag\gg 1$ leads to approximately $F(\tb)=1$, that is to
$\sum_j \omega_j N_j = E$, or radiation of the total ``trapped'' energy.
Furthermore, we can calculate from eq.~\eqref{dPNt} the single-graviton
inclusive distribution $\dif N/\dif\omega$, which involves fixing $\omega_j=\omega$ for
some $j$, and integrating over the remaining ones at $E-\omega$ fixed.  It is
straightforward to see that this provides --- apart from small fluctuation
corrections $\ord{1/\ag}$ ---
\begin{equation}\label{dNdom}
  \frac{\dif N}{\dif\omega} = \pp(\omega)\frac{\Nor(E-\omega)}{\Nor(E)}
  \simeq \pp(\omega) \esp{-\tb R\, \omega} \;,
\end{equation}
which is consistent with the average emitted energy in~\eqref{sadpoi} and,
together with eqs.~\eqref{NEtau}-\eqref{sadpoi}, appears to solve the $b\ll R$
model with a meaningful unitarization.

The exponential damping at large $\omega R$, which affects all the inclusive
distributions as in eq.~\eqref{dNdom}, allows us to interpret $(\tb R)^{-1}$ as
the quasi-temperature of graviton radiation, and provides an effective cutoff in
frequency, superimposed to the density $\pp(\omega)$, typical of our soft-based
representation. The overall picture of the ``trapped-energy'' fragmenting into
soft gravitons according to the distribution~\eqref{dPNtau} looks generically
compatible with ideas discussed in refs.~\cite{Dvali:2014ila} and
\cite{Addazi:2016ksu}, although applied --- in our case --- to the precise ACV
framework at fixed impact parameter $b$ and with $s$-channel iteration.  Arguments
for a cutoff are given also in the approach of ref.~\cite{Addazi:2016ksu} to the
transplanckian scattering without impact parameter identification of
ref.~\cite{Dvali:2014ila}.

\begin{figure}[ht]
  \centering
  \includegraphics[width=0.4\linewidth,angle=-90]{collapseTemperature.eps}

  \caption{\it Dependence of the saddle-point value $\tb$ (solid-blue, left
    axis) and of the rescattering quasi-temperature $T\equiv 1/(\tb R)$
    (dashed-red, right axis) in units of $T_H\equiv 1/(4\pi R)$ on the cutoff
    parameter $|{\boldsymbol{x}}|_\cut$ introduced in the approximate determination of the
    saddle-point eq.~\eqref{sadpoi}. Including incidence-changing effects at
    first order (see sec.~\ref{s:icc}) the saddle-point values increase
    (solid-light-blue) and correspondingly the quasi-temperature decreases
    (dashed-orange).}
  \label{f:taubarVSxcut}
\end{figure}

The precise determination of the inverse quasi-temperature $\tb$ for
rescattering requires a small-${\boldsymbol{x}}$ cutoff parameter $|{\boldsymbol{x}}|_\cut = \ord{R}$
which takes contributions from $\Im\Delta({\boldsymbol{x}}) > 0$ if $|{\boldsymbol{x}}|_\cut^2 < b_c^2 =
(3\sqrt{3}/2) R^2$, region where the ${\boldsymbol{x}}$-dependence starts being suppressed
in~\eqref{sadpoi}. We then find the numerical results of
fig.~\ref{f:taubarVSxcut}, showing that $\tb \simeq 3$ is a reasonable estimate
(solid-blue curve), to be compared with $\tb=1.2$ from $b\to b_c^+$~\cite{CC16}.
We should notice, however, that $\tb$ is rather sensitive to the value of
$|{\boldsymbol{x}}|_\cut$ around and below $b_c$. That means that the inclusion of
incidence-changing contributions to radiation may possibly be needed to provide
a more stable temperature estimate and a firmer conclusion on the unitary
behaviour on the basis of eqs.~\eqref{NEtau} and \eqref{sadpoi}.

We should add finally that, starting from eq.~\eqref{M23}, we can also compute
the probability distribution for the residual energy of the ``trapped''
gravitons $E'=E-\sum_j \omega_j N_j$. By introducing the $\delta$-function
constraint, we get the formula
\begin{align}
  \frac{\dif\Pr}{\dif E'} &= \frac{\Pr_0(E)}{\Nor(E)} \sum_{\{N_j\}}
  \delta(E-E'-\sum_j \omega_j N_j) \prod_j \frac{[\po(\omega_j)\Delta\omega_j]^{N_j}}{N_j!}
  \nonumber \\
  &= \frac{\Theta(E')}{\Nor(E)}\esp{-2\pi R E'} \int_{-\ui\infty}^{+\ui\infty}
  \frac{\dif\tau' R}{2\pi\ui}\; \esp{\tau'(E-E')R +\int_0^\infty \dif\omega\;
    \pp(\omega)\esp{-\omega R\tau'}} \;, \label{dPdEp}
\end{align}
which can be estimated by a saddle point method also.

We note that the unitarity condition
$\int_0^\infty \dif E'\;\dif\Pr/\dif E'=1$ fixes again $\Nor(E)$ as in
eq.~\eqref{NEtau} by reproducing the translation $\tau'\to\tau'+2\pi$ in the
denominator. Indeed, the $E'$ distribution is mostly dependent on the tunneling
exponent $2\pi R$, which appeared in $\Pr_0(E)$. At $E'$ fixed the saddle point
$\tb'$ is determined by
\begin{equation}\label{tbp}
  F(\tb') = 1-\frac{E'}{E} \quad \left( \simeq 1 - \frac1{\ag(\tb+2\pi)} \right)
\end{equation}
and the average $\bk{E'}\simeq 1/(2\pi R+\tb R)$ makes $\tb'$ roughly consistent
with $\tb$ in eq.~\eqref{sadpoi}, with a maximal residual ``bound'' energy of
order $1/(2\pi R)$. It seems therefore that both the ``bulk'' temperature
$1/(\tb R)$ and the residual-energy temperature $1/(2\pi R)$ (reminiscent of the
Schwarzschild black-hole limit~\cite{ACV07}) play a role in this model. We
stress the point, however that, because of~\eqref{dPdEp}, they are consistent
with each other, due to their different definition.

\section{Incidence-changing contributions\label{s:icc}}

We have so far considered the rescattering terms in~\eqref{M23} and
\eqref{ampRid}, because they offer the first ``exit'' window at
$|{\boldsymbol{x}}|\gtrsim R$. Now we want to estimate the incidence-changing window at
varying values of $\frac{\hom}{E}|{\boldsymbol{x}}|$, in which the parameter $\omega/E$ affects directly
the ${\boldsymbol{x}}$-dependence.

The single-emission density of eq.~\eqref{omPom} becomes, approximately,
\begin{equation}\label{omPapp}
  \omega\po(\omega) \simeq \frac{\ag}{\pi\omega^2\bk{{\boldsymbol{x}}^2}} \left|
    \esp{\omega R[\pi+2\ui\Delta(-{\boldsymbol{x}})]} -
    \esp{\ag[\pi+2\ui\Delta(-\frac{\hom}{E}{\boldsymbol{x}})]} \right|^2 \;,
\end{equation}
while the no-emission probability is $\Pr_0=\esp{-2\pi\ag}$ as usual for
$b\ll R$. We note that in the incidence-changing term the enhancement occurs at
coupling $\ag > \omega R$, but there is further suppression, due to the $\omega/E$
dependence in the eikonal expansions at small $\omega|{\boldsymbol{x}}|$ values
($\frac{b}{R} \ll \frac{\omega|{\boldsymbol{x}}|}{ER} \ll 1$) \cite{ACV07}
\begin{align}
  2\Delta\big(-\frac{\omega}{E}{\boldsymbol{x}}\big) &\simeq \ui\pi - 3 \esp{\ui\pi/3}
  \left(\frac{\omega|{\boldsymbol{x}}|}{ER}\right)^{2/3} +
  \ord{\frac{b^2}{R^2}}^{2/3} \;, \label{delomex} \\
  \esp{\ag\big[\pi+2\ui\Delta\big(-\frac{\hom}{E}{\boldsymbol{x}}\big)\big]} &\simeq
    \esp{a\ag\left(\frac{\omega R}{\ag}\right)^{2/3}} \;, \qquad
    \Big(a = \frac{3\sqrt{3}}{2}~\text{for}~\bk{{\boldsymbol{x}}^2} = R^2\Big) \;.
    \label{defa}
\end{align}

We thus realize, by~\eqref{omPapp} and~\eqref{defa}, that we should consider two
regions for incidence-changing terms. In the region $|{\boldsymbol{x}}|\geq \frac{\hom}{E} R$ the
trapping suppression is indeed canceled out, but the outcome is reduced by the
phase-space factor $(\omega/E)^2$, yielding small ($\sim 1/\ag$) contributions in the
hard-graviton corner. On the other hand, in the region $|{\boldsymbol{x}}|\gtrsim R$ we are
interested in, there is a small-$\omega R$ configuration
$(\omega R/\ag)^{1/3} < a/\pi < 1$ in which the enhancement~\eqref{defa} --- though
insufficient by itself to overcome the damping --- is anyway larger than the
single-density rescattering contribution, and therefore should be taken into
account. To this purpose, we can provide from~\eqref{defa} a crude estimate of
the Laplace transform
\begin{equation}
  \tilde{\po}_\ic(\lambda) \equiv \int_0^\ag \dif\omega\;
  \po_\ic(\omega)\esp{-\omega\lambda} \simeq
  \begin{cases}
    \esp{\frac23 a\ag\left(\frac{4a}{3\lambda}\right)^2} &\qquad
    \left(\frac{4a}{3\lambda} < 1\right)\\
    \esp{(2a-\lambda)\ag} & \qquad \left(\frac{4a}{3\lambda} \geq 1\right)
  \end{cases}
  \;, \label{ptilde}
\end{equation}
where the last expression is provided by a saddle-point at
$\bar\omega R=\ag\left(\frac{4a}{3\lambda}\right)^3$, if below $\bar\omega R=\ag$, and
by the end-point $\omega R=\ag$ otherwise. We note that
\begin{equation}\label{ppic}
  -\frac{\tilde\po'_\ic(\lambda)}{\tilde\po_\ic(\lambda)} =
  \begin{cases}
    \ag\left(\frac{4a}{3\lambda}\right)^3 = \bar\omega R & \qquad
    \left(\frac{4a}{3\lambda} < 1\right) \\
    \ag & \qquad \left(\frac{4a}{3\lambda} \geq 1\right)
  \end{cases} \;.
\end{equation}

Our task, however, should be to provide a reliable estimate of the
incidence-changing terms at the many-graviton level required by
eq.~\eqref{dPNtau}, and that raises a variety of questions, involving both
matter of concept (factorization is justified for rescattering terms only) and
technical approximations for $b\ll R$.  Therefore, further analysis is needed
and treating incidence-changing contributions in detail in addition to
rescattering ones is outside the scope of the present paper.

We only point out that the rescattering estimate of $\Nor(E)$ in the
$\tau$-representation~\eqref{NEtau} can be improved by including
incidence-changing-effects at the level of single power of $\po_\ic(\omega)$. In
that case the exponent in the integrand of~\eqref{NEtau} is corrected by adding
a $\log\tilde\pp_\ic(2\pi+\tau)$ from~\eqref{ptilde} and the saddle point
equation~\eqref{sadpoi} becomes
\begin{equation}\label{icsp}
  \ag = \frac1{\tb+2\pi} + \ag \left[ F(\tb) + \left(\frac{4a}{3(\tb+2\pi)}
      \right)^3 \right] \;,
\end{equation}
where the logarithmic derivative is taken from~\eqref{ppic}. The meaning
of~\eqref{icsp} is that a fraction of the overall energy is now radiated by
$\po_\ic$ also. The addition of such incidence-changing effect on the
saddle-point and temperature values is shown in fig.~\ref{f:taubarVSxcut}. There
is a moderate increase in $\tb$ (solid-light-blue curve) and a corresponding
decrease in temperature (dashed-orange curve).

\section{Discussion\label{s:d}}

Here we have investigated the collapse regime of gravitational scattering at
extreme energies ($E\gg M_p$) and small impact parameters ($b<b_c\sim R$), and
we have pointed out that --- in the present approach --- graviton radiation is
not necessarily suppressed, and actually multi-graviton amplitudes suggest how a
unitary $S$-matrix may still be found.

Our framework is semiclassical scattering~\cite{ACV93} in the
ACV-resummed~\cite{ACV07} eikonal formulation and in the soft-based
representation~\cite{CC16} of graviton radiation. Our suggestion is based on two
main points. Firstly, starting from jet energy $E=\sqrt{s}/2$ at impact
parameter $b\ll R\equiv 4GE$ elastic scattering to free-particle states is
exponentially suppressed by $|S_\el(b)|\simeq \esp{-\pi ER}$ because of
$\Im\Delta(b) \simeq \pi/2$ [eq.~\eqref{suppression}]. But rescattering
contributions of an emitted graviton at position ${\boldsymbol{x}}$ is regulated by
$\Delta({\boldsymbol{b}}-{\boldsymbol{x}})$ [eq.~\eqref{M23}] and is thus unsuppressed if
$|{\boldsymbol{x}}|^2>b_c^2\equiv(3\sqrt{3}/2)R^2\gg b^2$. That large-distance radiation is
in turn associated to the recoil energy $E-\omega$ of the energetic particle, so
that the suppression amplitude is reduced --- and the emission one is enhanced
--- by the factor $\esp{\pi\omega R}$, within the kinematical bounds. The same
conclusion is reached for general $b<b_c$ by replacing $\pi$ by
$2\Im\Delta(b)$.

Secondly, that suppression-enhancement correspondence goes through to
multi-graviton states provided the related soft-graviton ($\omega_j\ll E$)
amplitudes are factorized, as argued for in~\cite{CC16} on the basis of eikonal
factorization, at least for rescattering amplitudes. In such a case, the overall
suppression factor in multi-graviton emission becomes
\begin{equation}\label{mulgrasup}
  \exp\Big[-\pi\big(E-\sum_{j=1}^N\omega_j\big)R\Big]
  \Theta\big(E-\sum_{j=1}^N\omega_j\big)
\end{equation}
and is therefore $\ord{1}$ (meaning no suppression) if $E=\sum_j\omega_j$ or, in
other words, if the whole energy is radiated off. That may happen for a few hard
gravitons, but also for a bunch of soft ones, thus allowing in principle
unsuppressed emission amplitudes with a normal quasi-temperature of order $1/R$.

Therefore, if we take multi-graviton factorization for granted, the above
argument hints at the probability distribution~\eqref{dPNtau}, which is
unitarized by the normalization factor $\Nor(E)$ in~\eqref{NEtau} and is
characterized by the saddle point $\tb$ in~\eqref{sadpoi}, the inclusive
distribution~\eqref{dNdom} and thus the quasi-temperature $1/(\tb R)$.

That looks as the right path to follow in general, but unfortunately we do not
quite understand how to combine the incidence-changing contributions with the
rescattering ones at the multi-graviton level required by~\eqref{mulgrasup},
because of their uncertain factorization properties. That is not surprising,
because the incidence-changing terms (which regulate the rotation of the
incidence axis) are basically dependent on the overall coupling $\ag$ of the
energetic particles, while their $\omega_j R$-dependence is tied up with the
${\boldsymbol{x}}$-dependence and is normally non-factorizable.

For those reasons, in sec.~\ref{s:urqt} we concentrate on the rescattering terms
(for which multi-graviton factorization is justified) by introducing a cutoff
$|{\boldsymbol{x}}|_\cut=\ord{R}$, to regulate small-${\boldsymbol{x}}$ contributions. We thus find that
the unitarization method suggested by~\eqref{mulgrasup} actually works, with
some cutoff dependence of $\tb$ with $\tb\simeq 3$ for $|{\boldsymbol{x}}|_\cut = R$. We feel
that a better understanding of incidence-changing contributions could be able to
close the gaps and reduce the cutoff dependence, as suggested by the provisional
estimate of fig.~\ref{f:taubarVSxcut}. Such analysis is deferred to further
investigations.

A perhaps more fundamental question to be discussed is what our results in
sec.~\ref{s:urqt} actually mean for the gravitational scattering and, possibly,
for black-hole physics. We have already noticed that there are two ways the
``trapped energy'' $\sqrt{s}=2E$ can be observed: either in full, without
accompanying soft-gravitons, by the amplitude $\sim\esp{-\pi\ag}$ (corresponding
to the residual energy temperature $1/(2\pi R)$) which is exponentially
suppressed, or instead by a sort of collective fragmentation into
soft-gravitons, described by the distribution~\eqref{dPNtau} and the
quasi-temperature $1/(\tb R)$. Shall we say that the latter is the most probable
issue and that, therefore, the unitary distribution~\eqref{dPNtau} represents
the quantum black-hole spectrum?

If that is really the case, then the solution of the unitarity problem and,
perhaps, of the information paradox would rely only on our ability to keep track
of the phases and to describe the quantum states. That brings us back to the
previous question of whether or not we are able to disentangle the full
multi-graviton amplitudes, and that, finally, seems to be matter of technique
and not matter of principle.

To conclude, we are aware of the fact that our framework is not a consistent
quantum gravity theory and is thus providing a limited description of
gravitational processes. Nevertheless, our discussion suggests that some
difficulties previously found with unitarity and the information paradox may be
solved by our proposal in a simpler way than previously thought.

\section{Acknowledgments}

It is a pleasure to thank Gabriele Veneziano for a number of interesting
conversations on the topics presented in this paper. We also wish to thank the
{\em Galileo Galilei Institute for Theoretical Physics} for hospitality while
part of this work was being done.

\bibliographystyle{h-physrev5}

redpajama_set_name: RedPajamaArXiv


text:
Worries about Chesterton
This is a 'book review' I wrote in 2011 for the now-defunct 'Faith in the Home'. Chesterton's influence in the Church continues and I thought it would be good to put this out there somewhere.
'Orthodoxy' by G.K. Chesterton (first published 1908; Baronius Press edition, 2006) pp181
Review by Joseph Shaw
It's not often I review a book which has been published for more than a century, but at this time of rising Chestertonian revivalism, with Chesterton studies, Chesterton institutes, and reprints and references constantly appearing, it is as well to take stock of what is going on on planet 'GCK'. Contrary to my own expectations, I am not very enthusiastic about what I see. Rather than trying to give a balanced assessment of GKC's overall work, which would be a monumental task, let me list some of my misgivings, based on this one work.
As GKC himself notes, this is not a conventional work of apologetics (p160), although it is frequently described as one. Rather, it is an account of his own philosophy, by way of the considerations giving rise to it. Along the way various prejudices and arguments against Christianity are addressed, but the only positive reasons given for belief are either personal or social: that Christianity fits neatly into his own Romantic imagination, or that widespread belief in it is better for society, particularly in promoting the interests of the downtrodden. These are not, of course, reasons for believing that Christianity is actually true; they are simply reasons for wishing it were true (or being glad that it is). The view that one ought to believe what it would be useful to believe is Pragmatism, and that of course is totally opposed to the objective view of truth at the heart of Orthodox Christianity. Does GKC realise that there is a problem here? There is no indication that he does. So this is the start of my worries about GKC.
My second major problem is GKC's enthusiasm for democracy. He is a great supporter of democracy, because he believes in the wisdom of the 'ordinary' man. He tells us, however, 'there is one thing I have never from my youth been able to understand. I have never been able to understand where people got the idea that democracy was in some way opposed to tradition.' (p47) As I read the passages in the book on this topic I began to realise that GKC is being perfectly honest: one of the biggest, most influential, and most dangerous currents of thought for the previous two centuries is something he just fails to understand.
My dear GKC, if you were alive I could easily enlighten you. As to 'where' the idea comes from the locus classicus is J-J Rousseau, and it works like this. Whereas most Europeans up to the 17th Century were governed day to day by laws and institutions which represented the continuation of immemorial traditions, such as marriage and property, laws forbidding theft and incest, and processes of conflict resolution, Rousseau called these 'chains', and thought that we could all be 'free' if we followed the dictates of pure reason. Since all men have a rational faculty, this could be done by a system in which everyone could vote for startling new laws and institutions, and throw off the shackles of the old. These votes would of course be unanimous, because pure reason would always come to the same conclusions, and we could all bask in the knowledge that each law was in accordance with our personal will, and not, like the old traditions, imposed from without. The only exception would be if some people's reason was impeded by selfishness; they would need the guidance of the more enlightened citizens.
This is simply a secular political version of the Protestant rejection of tradition in religion. Luther said that each man could get the truth directly from God, via the pages of Scripture. Everyone, consulting Scripture, would naturally agree, since Scripture is an infallible presentation of Divine Revelation, unless they were impeded by moral turpitude; given the danger of turpitude getting in the way, people needed to be led by a cadre of properly drilled Lutheran ministers. The great thing was that either way they would get the truth direct, or nearly direct, from source, and all those complicated traditions, which come between the Christian and the source of all religious truth, could be thrown away.
Is it really possible that GKC didn't understand this argument? His failure to understand it would explain not only his remarks about democracy, but the strange soft spot he harboured for the French Revolution, which was directly inspired by Rousseau's ideas. There may be some connection with the tribal allegiance he had towards the Whig party. Be that as it may, while democratic institutions are not necessarily Rousseauist, GKC's failure to understand the origin and drift of the democratic ideology as Rousseau had formed it unfits him as a commentator on a wide range of topics. What you don't understand you cannot, effectively, oppose.
My third major problem is this. A major part of GKC's Romantic imagination, which attracted him to Christianity, was his 'wonder' at created things. This is often brought up in treatments of GCK's thought, and Orthodoxy has extended discussions of it. GKC repeatedly says, against scientific rationalism, that things could easily have been different, and that really it is quite miraculous that even quite ordinary things around us exist as they do. He applies this general view both to physics, saying that it is astonishing that the sun should rise each morning, and only does so thanks to God, and also to morality, saying that the basic principles of human action could so easily have been completely different (in a chapter appropriately title 'The Ethics of Elfland').
It tells us a lot about the state of Catholic education in the 20th Century that this attitude of GKC has apparently never troubled his Catholic supporters—either of his own day or of ours. GKC's view here is based, whether he realises it or not, on the twin Protestant principles (usually regarded as rather extreme, on the scale of Protestantism) of Occasionalism (the heat from the fire may be the occasion for the bread toasting, but really it is God making it toast), and Divine Command Ethics (the obligation not to kill doesn't follow from the objective moral importance of human life, but merely from the fact that God has chosen to forbid killing). These views were established in conscious opposition to the thought of St Thomas Aquinas. Aquinas, and the Aristotelian tradition which he incorporated into Catholic thought, holds that while God can certainly intervene miraculously into the physical world, and can certainly create new obligations for us by issuing commands, there is nevertheless such a thing as a 'law of nature', in physics and morality alike. This gives us, in the natural world, the important distinction between the natural and the miraculous, and in morality between Natural Law and Divine Law. Both distinctions seem to have disappeared in GKC.
I have given three examples of GKC being apparently influenced by anti-Christian or specifically anti-Catholic currents of thought, apparently without his knowledge or comprehension. He does not necessarily endorse these ideas; if they were laid out clearly, it is probable that he would reject them. The problem is that he doesn't see them, and their influence on the general thought of the 20th Century, clearly. His work embeds them, and in that way promotes and perpetuates them. In this way he is similar to many popular writers of course, and this is partly why popular writers have to be treated with caution, and tend not to have long-term influence.
My conclusion is that the great enthusiasm for Chesterton to be found among Catholics today is troubling. He obviously has his virtues, otherwise he would not be as popular as he is; he has lots of good things to say, and says them in a highly engaging way. I am myself a great fan of his poetry and the Fr Brown books; he often seems to get to the heart of the matter. But at the end of the day GKC is not a profound thinker, and worse than that he does not have reliably Catholic instincts.
'Orthodoxy' was, in fact, written long before he became a Catholic, but it is constantly reiterated that despite this is it is Catholic in spirit. No, it is not: its spirit can be identified as combining Romanticism, Evangelical Protestantism, and political Liberalism. The Romanticism brings the reverence for tradition. The Evangelical Protestantism brings the awe-struck attitude towards God and Creation. The political Liberalism brings a concern for the poor. In these respects these things have affinities in Catholicism, but that doesn't make them Catholic, even in combination. On the contrary, they make GKC vulnerable to some of the most dangerous trends in modern thought: Romanticism encourages Pragmatism, an attitude of wishful thinking which even Evangelical Protestants usually reject. Evangelical Protestantism brings in Occasionalism and Divine Command Ethics, an attitude of anti-rationalism which even Political Liberals usually reject. And Political Liberalism brings in a democratic ideology which undermines the very respect for Tradition fostered by Romanticism. GKC has not purified his respect for tradition of wishful thinking, he has not purified his wonder and gratitude for creation of anti-rationalism, and he has not purified his concern for the poor of the democratic ideology. Catholics, by contrast, must do these things.
Posted by Joseph Shaw at 9:12 pm
Colin Kerr said...
Hi Joseph,
A friend put me on to this post of yours because I am using Orthodoxy in a class I am teaching, basically Great Books in the Catholic Intellectual Tradition from the 17th century to today.
Everything you said here is a worthwhile concern, but I must disagree with you, or at least disagree that these are serious flaws in Chesterton, because of two things:
1) this is a work of apologetics, not as much as it is a commentary on the Creed, even though he does acknowledge that the Creed is his starting point.
2) as apologetics, it is directed against certain tendencies in his own culture that he thinks are deleterious and that he wants to dissuade people from.
You and I both know that he was an astute observer of the philosophical tendencies of his time. He was directing his exposition (his sales pitch, his reconsideration) of the Faith against materialists, against scientism, most of all. In this light we can say that he was making the case that it is okay, and even healthy and good, to acknowledge that there are important dimensions of life outside of the merely empirical. I don't take him to be trying to accomplish much more than that.
What you say about democracy, etc., is all true in the literal sense, but I think you have to acknowledge the basic point he is trying to make: that God directly, and indirectly through the world, has given us a law to which we can become privy, that we don't have to superimpose a theoretical and unnatural doctrine (probably Marxism, which sought to dispense with the family, and everything else good in nature) upon human culture in order to save it from itself.
In the end, he is not trying to close all the loopholes of Christianity, but to make a basic case for its reconsideration, which is what he realized he had to do.
Thanks for making me think about these things.
As it is I am quite happy that I chose Orthodoxy for my rather uninitiated students. It is a great bridging point between extreme secularism and Orthodoxy.
Joseph Shaw said...
Well I'm glad I've give you something to think about. If there is anything to my criticisms, Chesterton's bridge doesn't lead to the Faith, but to something else.
David McPike said...
Colin,
Your comment makes me think of MacIntyre's account of emotivism in After Virtue. According to MacIntyre, the theory of emotivism was a reaction to the (plainly false) non-natural moral intuitionism of G.E. Moore; but the emotivists, because of their historical ignorance, thought that their reaction to "moral utterance at [Moore's] Cambridge" actually constituted a reaction to "moral utterance as such." So in a way, emotivism was an understandable response to the "great silliness" of G.E. Moore and his followers. But if the emotivists can be applauded for seeing the falseness of Moore's theory, it remains that their own alternative theory was just as (or even more) obviously false. It failed to get to the real root of Moore's error. Moore's false theory called for a response, but the emotivist response was a dead-end, another false, unenlightening theory, rather than a bridge to truth (orthodoxy, Christian faith, or whatever). So the question is whether some of GKC's responses to certain problems are genuine bridges to better understanding or rather dead-ends, failures to understand the roots of certain typical modern errors.
With the hope that we are not trying Joseph's patience, let me add that since the matter seems now to be one of "proof is in the pudding," I have little hesitance to say that, since this work of Chesterton's was singularly influential in bringing people to Christ a century ago, including none other than the most influential C.S. Lewis, Chesterton's methodology seems to be vindicated thereby. Now, since people have grown dumber since his time, it may have now outlived its usefulness... but that is another argument.
That's a truly terrible argument.
C.S. Lewis acknowledged the positive influence heterodox writers like the Universalist, George McDonald, had on him when he was an atheist; that doesn't mean they weren't heterodox. Thomas Merton was drawn towards the Faith by James Joyce's depiction of Catholic culture. Arnold Lunn's materialism was shaken by the Idealism of Prof Huxley ('Darwin's Bulldog').
It all depends on where you are starting from.
Daniel Vartan said...
Just so you know, I think your explanation of Rousseau's idea of democracy misses the mark. Its hard for your argument to seem legitimate when your explanation of other thinkers arguments use subtle means of persuasion to make them look bad. If you want, read that paragraph again and see if you can find what i'm talking about.
Carl Kuss said...
Democracy expresses the truth that political authority is rooted in the people. This is what Chesterton means when he says that tradition is the democracy of the dead, that by paying attention to tradition we are respecting man's sovereignty, we are counting the vote of our forebears.
Integralists believe that there is some contradiction between this sovereignty of man and the sovereignty of God.
They believe that if political authority is rooted in God it cannot at the same time be rooted in man.
But this integralist belief reflects a shallow anthropology, rather than the Christian anthropology whose witnesses are thinkers such as Aquinas, Chesterton, and St. John Paul II.
Chesterton's philosophy as enunciated in Orthodoxy is a profound defense of the rationality of the faith. Still the faith is a gift, and not something I can give to you through my reasonings. The evidence is Revelation, whose witness is the prophets and the apostles. Chesterton is not one of those shallow apologists who attempts to prove the faith by merely rational means.
One could compare Orthodoxy to that other great work of apologetics Newman's Grammar of Assent. I as speaking particularly of the powerful part at the end where he speaks of the witness of the martyrs, to which his philosophical analysis of assent is preamble. This is indeed powerful and full of the power of the Word of God.
But Chesterton is also sublime and supernatural when he says "I have often fancied it was his mirth." This is also powerful and sublime.
Chesterton doesn't tell us that God's commandments could be turned inside out: Thou shalt kill, thou shalt commit adultery, thou shalt have strange God's before me.
He does tell us that God's commandments are a fruit of his Will. So what does that mean then? It means that God's commandments are at root acts of love which guide and give a spiritual impulse to his people. They oblige, but they oblige from within.
Similarly when Chesterton tells us that it is something marvelous that the sun rises each morning, he is not denying the laws of nature, but he is telling us that there is something marvelous in the fact that there are laws of nature.
In this he his being a good Thomist. He is not an Occasionalist.
Swinburne on sexual morality


text:
Le Wissgrut est un sommet du sud du massif des Vosges culminant à  d'altitude. Son sommet est caractérisé par une grande chaume.

Toponymie
Le Wissgrut se nomme ainsi depuis 1597. Ce nom provient de l'expression allemande , qui se traduit par . Les habitants du versant alsacien le nomment de préférence  ou , en témoignent les nombreux panneaux aux orthographes contradictoires posés par le Club vosgien de Masevaux, balisant les différents chemins d'accès au sommet.

Géographie

Situation
Le Wissgrut est situé à la limite entre le Haut-Rhin et le Territoire de Belfort. Il sert de tripoint aux communes de Lepuix, Riervescemont et Sewen. Il est proche du ballon d'Alsace.

Topographie
Le Wissgrut culmine à  d'altitude. Il est entouré de deux sommets secondaires : le Plain de la Gentiane (), au nord-ouest et le Tremontkopf (), au sud.

Hydrographie

Plusieurs ruisseaux issus du massif alimentent la Savoureuse sur le versant ouest et la Doller sur le versant est, qui coulent tous deux au pied du Wissgrut. Une source est captée près de la ferme.

Géologie
Le massif est constitué de granites dits . Des moraines et des verrous sont présents dans les environs

Flore

La faible pression pastorale exercée sur la chaume du Wissgrut est source d'une importante diversité florale. Elle est particulièrement recouverte de fleurs de gentiane jaune, de fenouil sauvage, de thym serpolet, de pensées sauvages. La présence de genévrier y est également relevée.

Histoire
L'agriculture s'est développée dès le  au sommet de la montagne et deux fermes y sont construites. La première, portant le nom de ferme des Plaines, est située à une centaine de mètres en contrebas de la seconde en direction de Giromagny ; elle disparaît au . La chaume est jalonnée de bornes séparant les versants nord et sud qui matérialisent la frontière franco-allemande de 1870 à la suite de l'annexion de l'Alsace par l'Allemagne.

Dans les années 1940, la ferme sommitale qui existe encore aujourd'hui, est exploitée par Xavier Berna, dit . Celui-ci, enrôlé de force dans l'armée allemande pendant la Seconde Guerre mondiale, fait le vœu d'ériger une statue de la Vierge Marie au point le plus haut du site s'il en revenait vivant. Cette statue est érigée en 1946.

Après la mort accidentelle de son propriétaire en 1970, la ferme du Wissgrut n'est plus occupée et tombe rapidement en ruines. Elle subit de gros dommage en 1999 lors du passage de la tempête Lothar puis est frappée par la foudre en 2011.

Elle est entièrement rasée en 2013 et la construction à l'identique d'un nouveau bâtiment commence dans la foulée. La ferme est achevée depuis 2015 ; une auberge est ouverte en 2016 et tenue par la famille Morcely. À l'occasion de ces travaux, le chemin d'accès depuis la Gentiane a été refait à neuf et élargi ; ces travaux ont permis la connexion au réseau d'eau et d'électricité de la ferme.

Activités
Une chaume s'est formée au sommet sous l'activité du pastoralisme. Elle reçoit chaque année un important troupeau de vaches de race salers qui y est monté en estive, donnant lieu à une fête animée par l'association Transhumance et Traditions de Giromagny dès le milieu printemps, au moment de la montée et une autre, au retour, à l'automne.

La randonnée pédestre est pratiquée en raison du panorama à 360° sur le massif des Vosges, la trouée de Belfort, la plaine d'Alsace et par temps clair, les Alpes suisses. Ce panorama est permis par l'étendue et l'altitude de la chaume.

Notes et références

Voir aussi

Article connexe
 Massif des Vosges

Lien externe
 Ferme-auberge du Wissgrut - Les Plaines

Sommet du massif des Vosges
Sommet dans le Haut-Rhin
Sommet dans le Territoire de Belfort

redpajama_set_name: RedPajamaWikipedia


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We're Obsessed: The Samsung Airdresser Might Just Be the Coolest Luxury Appliance in the World
Timothy Beck Werth
Have you heard of the Samsung Aidresser yet? It only recently came across our radar here at SPY. Technically, this appliance was first released back in 2020 with limited availability, but we first heard about it during a virtual event with Samsung earlier this Fall. Ever since then, we've been low-key obsessed with this luxury Samsung appliance, which is unlike anything we've seen before.
Why haven't we written about it before? Well, it's definitely a luxury appliance, and it's not something the average guy is going to add to his closet.
But with Christmas right around the corner, we figure someone out there is looking for a big gift for the impossible-to-shop-for man in their life. What do you buy the impeccably well-dressed gentleman who prefers to pick out his own clothes, accessories and top-shelf whiskey? We recommend the Samsung Airdresser, which would be a godsend for any fashionista or clotheshorse in your life.
Okay, so what is it? The Samsung Airdresser is an at-home dry cleaning cabinet.
You simply load it up with your dry-clean-only suits, dress shirts and accessories, close the door, and the Airdresser goes to work sanitizing, deodorizing, de-wrinkling, and otherwise cleaning your garments. And, of course, this smart appliance is also Wi-Fi connected. For anyone with a walk-in closet, it's the ultimate luxury flex.
Think about it this way: you could actually save money if you're already dropping hundreds of dollars at the local dry cleaners every few months.
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The Samsung Airdresser: How It Works
While it might sound like a complicated piece of machinery (and it is), it's actually pretty easy to use and install.
Per Samsung, "Simply plug your AirDresser into a standard 120V outlet and you're all set. No separate water line or professional installation necessary — the refillable water reservoir and filtered water are all you need."
Meanwhile, the "built-in deodorizing filter eliminates 99% of common odors in fabrics like house pet smells, smoke, perspiration, unpleasant food, and other musty odors."
So the next time you need to spruce up a suit ahead of a big fundraiser or wedding, the Airdresser has you covered.
You can even buy the Airdresser with a mirror finish, which means it will function as a full-length standing mirror.
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If there's a catch, it's the cost. The regular Airdresser will set you back $1,350, although it is available via Amazon. The Airdresser With Mirror Finish and Airdresser Grand, which has a larger capacity, are closer to $1,500 and $1,700 respectively, though they're currently on sale via Samsung.
Like we said, it's not the kind of purchase you really need, but it's exactly the kind of appliance you know you want. If you can afford it, that also makes it the perfect Christmas gift.
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