THE ANTHROPIC LANDSCAPE OF STRING THEORY
Leonard Susskind
I. A Fish Story
Once upon a time, on a planet completely covered by water, there lived a
race of big-brained fish. These fish could only survive at a certain depth
and none had ever seen either the surface above or the bottom below. But
their big brains made them very smart and also very curious. In time their
questions about the nature of water and other things became very
sophisticated. The most brilliant among them were called fyshicists. The
fyshicists were wonderfully clever and in a few generations they understood
a great deal about natural phenomena including fluid dynamics, chemistry,
atomic physics and even the nuclei of atoms.
Eventually some of the fyshicists began to question why the laws of nature
are what they are. Their sophisticated technology allowed them to study
water in all its forms, especially ice, steam and, of course, the liquid
state. But with all their efforts there was one thing that stumped them.
With all the possible values from zero to infinity, how could they account
for the fact that background temperature, T, was fine tuned to be in the
very narrow range that allowed H_2 O to exist in its liquid form? They
tried many things including symmetries of various kinds, dynamical
relaxation mechanisms, and many other ideas. But nothing could explain it.
Now closely allied with the fyshicists, another group, the cod-mologists
were also studying their watery world. The cod-mologists were less
interested in the ordinary depths, where the big-brained fish lived, than
they were in discovering if there was an upper boundary to their
water-world. The cod-mologists were well aware that much of the
water--world was not habitable, the pressure being wrong for their big
brains. Journeying by fin to the upper reaches was by no means possible.
Their big brains would explode if exposed to the very low water pressure in
these regions. So instead, they speculated.
It happened that there was one school of thought among the cod-mologists
that held a very radical (some said ridiculous) idea about the fine tuning
of T. And they had a name for the idea -- the Ickthropic Principle. The
I.P. maintained that the reason that the temperature was in the liquid
water range was because only in this case could fish exist to observe it!
Garbage! said the fyshisits , that is not science. It's religion. It's just
giving up. And besides, if we agree with you everyone will laugh at us and
take away our funding.
Now not all of the cod-mologists meant the same thing by the Ickthropic
Principle. In fact it was hard to find any two who agreed. One thought that
it meant that the Head Angel Fish had made the world just for the purpose
of accomodating big-brained fish. Another thought that the quantum wave
function of the waterverse was a superposition of all values of T and only
by observing it did some ancestral fish ``collapse the wave function."
A small number of cod-mologists led by Andrei-The-Very-Big-Brained, and
Alexander-Who-Swims-Deep held a very extraordinary idea. They believed
that a stupendously big space existed beyond the upper water-boundary. In
this very big space there might be many other bodies similar in some ways
to the their water-world but different in other ways. Some worlds would be
unimaginably hot. So hot that the hydrogen nuclei might even fuse to form
helium and then perhaps grow even hotter. Other worlds would be so cold
that frozen methane would exist. Only a tiny fraction of the bodies would
be at temperatures conducive to the formation of fish. Then it would be no
mystery why T was fined tuned. As every angler knows, most places are
fishless but here and there conditions are just right. And that's where the
fish are.
But the fyshisits sighed, Oh Lord, there they go again with their fishy
ideas. Just ignore them.
II. The Cosmological Constant
Steven Weinberg, in his very wise book, ``Dreams of a Final Theory" says:
``Thus, if such a cosmological constant is confirmed by observation, it
will be reasonable to infer that our own existence plays an important role
in explaining why the universe is the way it is." Weinberg, whom Ernst
Mayr called an ``uncompromising reductionist", a tireless enemy of
creationism and a champion of the view that the laws of nature can all be
traced to a small number of basic interactions between elementary
particles, was saying the unthinkable, possibly the most shocking
admission that a modern scientist could make: Man's place in the scheme of
things may indeed be at the center. The laws of nature, at least in part,
may be tailored to our own existence.
In fact Weinberg goes on to say: ``For what it is worth, I hope that this
is not the case. As a theoretical physicist, I would like to see us able to
make precise predictions, not vague statements that certain constants have
to be in a range that is more or less favorable to life. I hope that string
theory really will provide a basis for a final theory and that this theory
will turn out to have enough predictive power to be able to prescribe
values for all the constants of nature, including the cosmological
constant. We shall see."
Weinberg was expressing the hope of almost all physicists, that the laws of
nature, are somehow impersonal and unique; that only one set of elementary
particles, masses, constants of nature and rules of interaction will
eventually survive the rigorous tests of mathematical and conceptual
consistency that theoretical physicists, of the future, will demand of
their final theory. He is expressing the longings for abstract Pythagorean
simplicity, consistency and beauty that is the physicists creed; a kind
of Myth of Uniqueness. But why then does he appeal to ``our own existence"
playing ``an important role in explaining why the universe is the way it
is"? Why the appeal to the Anthropic Principle? In part, the answer is
that Weinberg is not just a physicist; he is also a cosmologist.
By contrast with physicists who, as a rule, focus on the simplest examples
of nature's handiwork, cosmologists, with the help of astronomers look out
and see a big messy world. From all that they have learned during the last
century, there seems to be one overriding pattern. The world is very big
and contains many stars and planets. In its early history it was lumpy
enough to have formed galaxies but not so lumpy that all matter collapsed
into black holes. It is expanding but not so fast that everything flew
apart before galaxies, stars and planets could form. The laws of nuclear
physics are just right for carbon nuclei to have formed in the interior of
hot stars, later to be recycled into new stars and solar systems. And the
laws of atomic physics allow for the formation of the most unlikely helical
tinkertoy molecules. In other words the pattern that seems to trump all
other considerations is that the natural laws are conveniently fine--tuned
just to insure our own existence.
Physicists hate this idea. Especially string theorists.
What is this remarkable cosmological constant and why is it forcing
physicists to rethink their entire paradigm? The cosmological constant has
several facets. First of all it represents an energy content of the vacuum,
i.e. empty space. That may sound like an oxymoron, empty space having
energy, but in modern physics the vacuum is a complicated object in which
violent quantum fluctuations are continually taking place. Electrons,
positrons, photons and all the other elementary particles are constantly
being created and annihilated so quickly that to our slow ponderous
detectors they are usually invisible. But they are there and they give rise
to an energy density in what we ordinarily think of as empty space. The
terms vacuum energy density and cosmological constant mean the same thing
and are used interchangeably.
Why does such vacuum energy make any difference? If it is always there in
the background why don't we reset the zero of energy and just ignore it?
The answer lies in the theory of gravitation.
According to Newton, the measure of an objects gravitational potency is its
mass. Physicists describe this by saying that mass is the source of the
gravitational field in much the same way that electric charge is the source
of the electric field. Thus, the gravitational field surrounding the sun
is about a million times the field of the earth because the sun is a
million times more massive. But according to Einstein, mass and energy are
really the same thing. Every object has an energy content given by the most
famous of all formuls, E=mc^2. Therefore we can equally well consider the
gravitational field to be a response to the presence of
energy. This means that the hypothetical energy of empty space would
produce a gravitational field, i.e. it would cause particles to accelerate
even in the absence of other objects. It's effect would resemble a
universal repulsion that increases with distance.
The best way to visualize gravitational field caused by a hypothetical
cosmological constant is in terms of the expansion of space, the expansion
that cosmologists call the Hubble expansion of the universe. The universe
is certainly expanding. But without a cosmological constant, the expansion
would slow down with time. It might even stop expanding and start
collapsing. But a (positive ) cosmological constant would have the effect
of accelerating the expansion causing the distant galaxies to forever
recede away from one another at a faster and faster rate. The cosmological
constant is a kind of pressure that expands space in a way that resembles
the inflation of a balloon, the stars and galaxies being thought of as
marks on the surface of the balloon. Accelerated expansion due to vacuum
energy is often referred to as inflation of space.
The most striking thing about the cosmological constant is that it is
either zero or extremely small. If it were at all sizable it would have a
serious effect on the motion of astronomical objects. For example it would
work against ordinary Newtonian attraction between the sun and earth. If
it were sufficiently big it would overcome the attraction and cause the
earth to accelerate away from the sun. Because the effect of the
cosmological constant increase with distance, it can be important
cosmologically even if the cosmological constant is very small. For this
reason the most sensitive determinations of the vacuum energy involve
cosmological distance scales. Until recently the best that could be said is
that the cosmological constant is smaller than about 10^{-8} Joules per
cubic meter.
To appreciate just how small such a cosmological constant would be, we
need a benchmark; a theoretical expectation for how big it could be. Modern
elementary particle physics gives us such a benchmark. As I mentioned,
quantum field theory visualizes the vacuum as a complicated state of
``virtual" particles and anti--particles constantly being created and
annihilated. Each kind of particle contributes to the vacuum energy with
some particles footnote{Particles come it two types; fermions and bosons.
Electrons, neutrinos and quarks are fermions while photons gluons and some
others are bosons. Bosons contribute positively to the vacuum energy while
fermions contribute with a negative sign. } giving positive contributions
to the vacuum energy and others giving negative contributions.
How big is the contribution from the virtual photons? The answer depends on
the precise assumptions but a typical calculation would give an answer
10^{112} Joules per cubic meter; one hundred and twenty orders of
magnitude (10^{120}) too large! As many of my colleagues have remarked,
this is by far the all time worst discrepancy between theory and
experiment.
However, there is the possibility that different contributions have
different sign and cancel when they are all added up. But the cancellation
must be staggeringly precise. It is as if we had several ordinary
decimals, none of which are particularly small but when we add them up the
result cancels to 120 decimal places! This seems like an absurd accident
and we have no idea why it should happen.
Concerning this incredible failure, theorists have played a little
psychological game with themselves. It goes something like this:
If the cosmological constant is that fine--tuned, it probably means that
there is some as yet unknown principle that requires the vacuum energy to
be exactly zero. Since string theory is our favorite theory, it must be
some marvelous mathematical property of string theory that insures the
cancellation.
But there are two flies in this ointment. First, no one has ever found
anything in string theory (or any other theory for that matter) that
suggests that the cosmological constant vanishes, at least for a
realistic version of the theory. And second, astronomical observations in
the last few years have turned up a very big surprise. The cosmological
constant is not zero! It seems that the expansion of the universe is
accelerating albeit with a very small cosmological constant . As absurd as
it seems, the vacuum energy exactly cancels for the first 119 decimal
places but then in the 120 place BINGO, a bit of vacuum energy. How
can such a situation possible be explained? And what does the partially
understood String Theory really have to say?
III. The Anthropic Principle
In 1961 the great cosmologist, Robert Dicke, raised an interesting
question. Given the infinite range of the real numbers, how do we explain
the numerical fact that the universe is about ten billion year old? Why not
some very different number? Dicke gave what at first sounds like
a ridiculous answer which goes as follows:
In order for anyone to be around to ask this question intelligent life
must exist. This implies that the universe has to be old enough for planets
to have formed and intelligent life to evolve. According to standard
astronomical and evolutionary theories, that would take about 10 billion
years. On the other hand if the universe is very much older, the stars will
all have burned out and could not support life. Therefore there is a finite
window of time for us to be here to ask the question.
This kind of reasoning came to be known as the Anthropic Principle; this or
that is true because if it weren't true there would be nobody to ask the
question. Since Dicke's observations cosmologists have speculated about
other applications of the Anthropic principle. The general idea is to find
some numerical parameter in the laws of atomic physics, nuclear physics,...
which, if slightly different, would not have permitted the existence of
life as we know it. There are surprisingly many such coincidences. Then, if
there is no other ``natural" explanation for its value, it becomes a
candidate for an anthropic explanation. This idea is of course anathema to
physicists, who see the existence of themselves as an accidental property
of a universe determined by mathematical principles, to be discovered by
disinterested analysis.
It was Steven Weinberg, wearing his cosmological hat, but deeply aware of
the consequences for physics, who raised the question: Is the improbable
fine tuning of the cosmological constant a consequence of the Anthropic
principle? For the answer to be yes, he would have to show that a value of
the cosmological constant much bigger than the tiny empirical bound would
have prevented the formation of life! And indeed Weinberg found this to be
so. If the cosmological constant were a ten or a hundred times bigger than
the bound, the resulting accelerated expansion would have overcome the
natural tendency of gravity to clump matter into gravitationally bound
structures. All matter would have flown apart before it ever had a chance
to condense into galaxies, stars and habitable planets.
This argument could be interpreted as a prediction: If the cosmological
constant is so small for anthropic reasons alone, then there would be no
reason for it to be very much smaller than required by that principle. This
suggests that there ought to be a non--vanishing cosmological constant at
a level that could soon be measured. If the cosmological constant was very
much smaller then required by the anthropic principle, then the explanation
must lie elsewhere.
Weinberg's use of the Anthropic principle superficially sounds similar to
Dicke's but it is really far more speculative. Dicke was talking about the
current age of the universe. The age of the universe is not a constant of
nature. Assuming the universe lives forever, the age will eventually
attain every numerical value. The only question is how long does it take
for life to form and how long can it last? These are questions that a
combination of biology, chemistry, physics and astronomy can answer.
By contrast the cosmological constant is supposed to be a constant of
nature having a unique value. The question is; what agency chose that
value once and for all and for what reason? But suppose for a minute that
the situation is similar to the one faced by the big--brained fish.
Suppose that as Andrei Linde, Alexander Vilenkin and many other
cosmologists believe, the universe is vastly larger than the region that
has been astronomically explored. footnote{Astronomical observations are
limited to regions which are close enough to us that light has had time to
reach us.} Might it be that the cosmological constant is not really a
constant but varies throughout the unimaginably larger space. And might
it also be that the number of possible values that it takes on is so
large that practically every value occurs somewhere. If this were the case
then the use of the Anthropic principle would be just as trivially correct
as it was for Dicke. Life would form only in those environmentally
friendly regions where the cosmological constant permitted itfootnote{
Perhaps I should refer to this idea not simply as the Anthropic Principle
but rather the Environmental--Anthropic Principle in order to distinguish
it from other meanings of the term Anthropic Principle. But to spare you
the constant repetition of this awkward construction I will simply say that
from now on this is what I will mean by the A.P.}.
As I said, physicists, especially string theorists, are appalled by this
idea. Believers in the Myth of Uniqueness, they would all have predicted
that the cosmological constant is exactly zero although they didn't really
know why. The Myth of Uniqueness is very pervasive, especially among
string theorists.
It was in this intellectual environment that the most
recent observational discoveries were made. I won't go into the details
but suffice it to say that several different kinds of data now support the
existence of a cosmological constant at just about the level to be
expected by Weinberg's argument. This is not small stuff. It has the
potential to overturn hundreds of years of thinking about the laws and
constants of nature. Things, maybe all things, that we thought were ``hard
wired" into the equations may only be properties of our local environment,
just like the temperature of of the sea.
My own view is that there is no alternative to some form of anthropic
explanation of the almost, but not quite, vanishing cosmological constant
. footnote{To give my own horn a little toot, I will mention that I first
wrote the Story of the big--brained fish about ten years ago as a
contribution to Martinus Veltman's 60th birthday festschrift.} On the other
hand I also count myself among the ranks of the string theorists, having
been associated with the theory since 1969 when Y.Nambu and I (and in a
slightly different form, H.B. Nielsen) first proposed it. For obvious
reasons, the discovery of a cosmological constant in the range suggested
by Weinberg, makes me more than a little uncomfortable. But about a year
and a half ago I became rather skeptical that string theorists had the
right idea about their own theory. Perhaps I should say, the right
expectations for their theory. Was Weinberg justified in his hope that ``
string theory really will provide a basis for a final theory and that this
theory will turn out to have enough predictive power to be able to
prescribe values for all the constants of nature, including the
cosmological constant" or was his ``We shall see" expressing a more
suitable skepticism? The answer, I am now convinced, is that the pursuit
of the Unique was a quixotic quest. In fact I would go as far as to say
that the whole point of string theory may be the huge diversity of
environments that it can lead to. It, among all theories, is uniquely well
suited to an environmental/anthropic theory of the constants of nature.
In my view there two things are required of a theory in order that we can
justly say that some or all of its constants are anthropically determined.
The first is that the mathematical equations of the theory should have an
enormous number of solutions each describing a different environment with
different values of the constants. Physicists refer to these solutions as
vacua. To a theoretical physicist a vacuum means more than just empty
space. It is also a description of all the things that can be added to
empty space; in other words all the particles and fields that can exist in
otherwise empty space as well as the cosmological constant (and other
constants). An anthropic theory must have a huge number of vacuum
solutions; so many that we can be reasonably sure of finding at least one
with the desired fine tuned properties.
But it is not enough that the theory should have many solutions. The
big--brained fish might realize that the equations of chemistry and
physics permit a wide variety of different kinds of planets but still
not realize that these possibilities all occur somewhere out in space.
To make a convincing case Andrei-The-Very-Big-Brained, and
Alexander-Who-Swims-Deep would also need a theory of the formation of the
universe which would explain why space is filled with such diversity.
Accordingly, the cosmic evolution of the universe should lead in a natural
way to an extraordinarily large universe filled with every possible
environment.
IV. What Does String Theory Really Say?
One of the earliest discoveries about string theory was that the dimension
of space--time is not arbitrary. Most mathematical theories make sense in
space--times of any dimension. Neither Newton's nor Einstein's theory of
gravity dictate three dimensions of space. Nor does Maxwell's theory of
electromagnetism (By the way, the existence of life probably does require 3
spatial dimensions). But string theory is far more demanding. Depending on
one's viewpoint it either requires nine or ten dimensions of space and one
of time. On the face of it this would immediately preclude the theory both
on anthropic and observational grounds. But string theorists have a good
trick up their sleeves. Nothing says the extra six or seven dimensions
have to big enough for our large selves to move around in the way we move
in ordinary space. These dimensions may be far smaller than even the minute
sizes of the particles that we ordinarily consider to be elementary. They
may be rolled up into tiny spaces such as a microscopic six dimensional
torus or more complicated geometric six dimensional shapes called Calabi
Yau spaces. This process is called compactification. There are millions of
distinct Calabi Yau spaces to choose from. But in this business a million
possibilities is not a large number.
Choosing a Calabi Yau space is only part of the story. String theory has a
large number of different kinds of ``moving parts". The shape and size of
the compact space are described by a set of variables called moduli. A
typical Calabi Yau space must be supplemented with a couple of hundred
moduli to completely specify it. Furthermore there are objects called
Branes that can wrap around the compact dimensions. There are other objects
called fluxes that can also be stuck in. All in all a generic
compactification requires several hundred variables to fix it. These
variables are not constants. They may vary either with time or with
location in ordinary space.
Because the compact dimensions are so small, one might think that the
particulars of the compactification don't have any effect on large scale
physics. But this is not correct. They completely determine the microscopic
laws. Thus one choice might lead to a world with no electrons but six types
of quarks and a cosmological constant so big that the earth itself would
fly apart if indeed it ever formed. Another choice might have quarks and
electrons but no photon. Varying the parameters of compactification changes
the type of particles, the nature of forces and constants of nature. To
plot out the possibilities we could draw a set of axes, one for each of the
several hundred variables. This of course could not be done on a sheet of
paper. It would take a space of several hundred dimensions to embed all
those axes footnote{This space should in no way be confused with ordinary
space.}.
One of the many things that vary as we move around in this space of
possibilities is vacuum energy. But not every value of the parameters is a
legitimate solution of string theory. The real solutions or vacua are the
local minima of this horrendously complicated energy function. And of great
importance, the cosmological constant is different for each of these
vacua. In fact it is nothing but the value of the energy at the minimum.
Think of the energy function as defining a landscape on the space of the
parameters. The energy is like the altitude. The landscape is of course in
a space of several hundred dimensions but nonetheless it has
mountain peaks (maxima), valleys (minima) ridges and even flat plains. Due
to the large number of dimensions, the landscape is wildly diverse. One can
make a rough estimate of the number of minima that such a function will be
likely to have and the answer is astonishingly big. A typical function of
500 variables may have as many as 10^{500} distinct minima. Each of these
is an environment with its own cosmological constant as well as other
properties. The evidence points, not to a unique vacuum but to an
unimaginably large number. With that many vacua it would be very surprising
if there was not one with a cosmological constant in the range indicated by
Weinberg's anthropic argument.
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ The mathematical
evidence for this humongous landscape of string theory is mounting. The
techniques for exploring it are being developed by string theorists and all
signs point toward diversity of exactly the kind required for an anthropic
theory. Although this is not what string theorists originally envisioned,
the reader should make no mistake; The mathematical tools of string theory
and all the discoveries of the last few decades are not only fascinating
in themselves but are essential to exploring the landscape. Turning the
Anthropic principle into hard science can only be done if and when the
landscape is quantitatively understood. For now our best hope lies in the
mathematics of string theory.
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
V. Populating the Landscape
But will the equations of cosmology and string theory lead to a universe
that populates all, or at least enough, of the landscape to be sure that
somewhere there is a region of space that has the desired fine features?
Although these equations are incompletely formulated the answer is likely
to be yes. The starting point for cosmology is a small universe with an
exceedingly large energy density; a small ``seed" at some point of ``high
altitude" footnote{By high altitude I mean a large energy density} in the
landscape. The large energy density caused the seed to rapidly expand, thus
diluting the energy. Alternatively, the universe, while growing, rolled
down the landscape toward regions of lower altitude.
What we find at these lower altitudes is a landscape full of valleys and
hills where it is overwhelmingly likely to get stuck in some valley where
the vacuum energy is at a local minimum. But the likelihood of arriving in
a valley which is hospitable to life is neglibible. The overwhelming
majority of the valleys have a vacuum energy far outside Weinberg's window
of opportunity for life to form.
But that's not the end. First of all as we learned many years ago from the
work of Alan Guth and others, a universe with a positive vacuum energy will
begin to inflate at an exponential rate, doubling its size in a very small
time. It will soon be many orders of magnitude bigger than when it began.
By this time the original details of the seed have long been forgotten.
That is one of the effects of accelerated expansion; it tends to dilute
away all traces of the starting point.
But this is still not all. It is a feature of string theory that there will
always be regions of the landscape with smaller vacuum energy. Every
physicist knows that this indicates an instability. The nature of this
instability was worked out years ago by Sidney Coleman and ....De Lucia.
What typically happens is that small bubbles slowly form in the inflating
vacuum. These bubbles are regions in which the cosmological constant is
smaller than in the ambient inflating background. If the bubbles are too
small they will shrink and disappear. But every so often a larger bubble
will nucleate and then start to grow. Because the seed has grown so large
there is enough volume for a huge number of bubbles. These bubbles are
regions where the universe has made a transition to a neighboring region of
the landscape. But although the vacuum energy is smaller inside the bubble
it is not likely to be zero. Thus the space inside these bubbles inflates.
The bubbles themselves soon become prodigiously large and the process
continues with new bubbles forming inside the old, effectively populating
the entire landscape with every possible kind of vacuum. Although this
phantasmagoric image seems like something out of the mind of a madman, it
is hard to see how it could be wrong. Given the diverse string theoretic
landscape of possibilities, and the well known the rules for quantum
nucleation of bubbles in an inflating space it is inevitable that an
indefinitely large number of bubble-universes will form. Some small
fraction will be within the anthropic window. And it is in one of these
regions that we find ourselves.
To say that all of this rigorously follows from the precise mathematics
of string theory is not justified at the present time. We don't know with
certainty what the landscape is really like and how many valleys at each
altitude are there. We also don't have the technology to rigorously study
the evolution as the population of bubbles spreads out over the landscape.
But the individual elements all seem increasingly plausible and I think we
will know, in not too long a time, if string theory really does have the
properties that I am suggesting. If it does then I think it will not be
long until string theorists readjust their sights and begin to see the
non--uniqueness and diversity as the best and most convincing argument for
their theory.
Direct observational confirmation of the vastness and diversity of the
landscape is probably not possible. The space between bubbles is typically
expanding so rapidly that no signals can reach one of them from any other.
Physicists would say they are out of causal contact. They are outside each
other's cosmic horizons. But our own region, has passed through several
valleys in the landscape before standard cosmology had its start. In
principle those earlier epochs left an observable imprint on the relic
microwave radiation from the big bang. The problem is that the enormous
inflation of the universe dilutes most of these imprints to the point where
they can not be observed. However if we are very very lucky, the last
episode of inflation which began our current big--bang cosmology might not
have lasted long enough to obliterate all evidence of a transition from
some neighboring valley. In the words of Weinberg, ``We shall see."
If this view of nature is correct then there is cold comfort for those who
look to the anthropic principle for a deeper meaning to their own
existence. As Darwin's, principle of survival of the fittest, eliminated
the need for the hand of god to guide evolution, so too does the
environmental intepretation of the anthropic principle eliminate the
necessity for a guardian angel to fine tune the laws of nature. But the one
thing that we can be sure of is that the last word on these matter is yet
to be said.