The familiar sign that marked the turnoff from the main highway leading toward
Albuquerque, some thirty or so miles farther north, read:
ABSOLUTELY NO ADMITTANCE
SHOW PASSES - 1½ MILES AHEAD
Accompanied by the falling note of a barely audible electric whine,
the Ford Cougar decelerated smoothly across the right-hand traffic lane and
entered the exit slipway. Without consciously registering the bleeped warning
from the driver's panel, Dr. Bradley Clifford felt the vehicle begin responding
to his touch as it slipped from computer control to manual drive. The slipway
led into a shallow bend that took him round behind a low sandy rise, dotted
with clumps of dried scrub and dusty desert thorn, and out of sight of the main
The road ahead, rolling lazily into the hood of the Cougar, lay draped around
the side of a barren, rock-strewn hill like a lizard sunbathing on a stone.
In the shimmering haze beyond and to the right of the hill, the rugged red-brown
bastions that flanked the valley of the Rio Grande stood row behind row in their
ageless, immutable ranks, fading into layers of pale grays and blues that blended
eventually with the sky on the distant horizon.
The road reached a high point about halfway up the shoulder of the hill, and
from there wound down to commence its long, shallow descent into the barren
valley beyond, at the far end of which was situated the sprawling complex of
the Advanced Communications Research Establishment. At this time of the morning
the sun shone from the far side of the Establishment, transforming the jumble
of buildings, antenna towers, and radio dishes into stark silhouettes crouching
menacingly in front of the cliffs that marked the head of the valley. From a
distance, the sight always reminded Clifford of a collection of gigantic mutant
insects guarding the entrance to some dark and cavernous lair. The shapes seemed
to symbolize the ultimate mutation of science—the harnessing of knowledge to
unleash ever more potent forces of destruction upon a tormented world.
About a mile farther on and halfway down to the valley floor, he came to the
checkpoint where the road passed through the outer perimeter fence of ACRE.
A black Army sergeant in shirtsleeves but armed and wearing a steel helmet waled
forward from the barrier as Clifford slowed to a halt beside a low column. Nodding
his acknowledgment to the guard's perfunctory "Morning," Clifford extracted
his card from a pass folder, inserted it into a slot in the box at the top of
the column, handed the folder to the guard, and pressed his thumb against the
reader plate. Clearance was flashed to another guard seated inside the guardhouse.
The Cougar moved through, and the barrier dropped into place behind.
Fifteen minutes later, Clifford arrived at his office on the third floor of
the Applied Studies Department of the Mathematics & Computer Services Building.
On average, he spent probably not more than two days a week at ACRE, preferring
to work remotely from home. On this occasion he hadn't been in for eight days,
but he found no especially pressing messages, since all the urgent calls had
been routed to his home number and dealt with from there. So, no unexpected
panics to worry about before his eleven-o'clock meeting.
No sooner had he thought it, when the chime sounded to announce an incoming
call. He sighed and tapped a button to accept. "Clifford."
The screen showed the features of a thin, pale-faced man with thinning hair
and a hawkish nose. He looked mean. Clifford groaned inwardly as he recognized
the expression of righteous and pained indignation. It was Wilbur Thompson,
Deputy to the Deputy Financial Controller of Mathcomps and self -appointed guardian
of protocol and all things subject to proper procedures.
"You might have told me!" The voice, shrill with outrage, grated on Clifford's
ears. "There was absolutely no reason for you to keep quiet about it. I would
have thought that the least somebody with my responsibilities could expect would
be some kind of cooperation from you people. This kind of attitude doesn't help
anybody at all."
"Told you what?"
"You know what. You requisitioned a whole list of category B equipment despite
the fact that your section is way over budget on capital procurement for the
quarter, and without an SP6 clearance. When I questioned it, you let me go ahead
and cancel without telling me you'd gotten a priority clearance from Edwards.
Now the whole thing's a mess, and 've got everybody screaming down my throat.
"You didn't query it," Clifford corrected. "You just told me I couldn't do
"But . . . You let me cancel."
"You said you had no alternative. I took your word for it."
"You knew damn well there'd be an exception approval on file." Thompson's
eyes were bulging. "Why didn't you mention the fact or give me an access reference
to it? How was I supposed to know that the project director had personally given
it a priority 1 status? What are you trying to do, make me look like some kind
of an idiot?"
"You manage that okay without me."
"You listen to me, you smartassed young bastard! Do you think this job isn't
tough enough already without you playing dummy? There was no reason why I should
have checked for an exception approval against that requisition. Now I'm being
bawled out because the whole project's bottlenecked. What in hell made you think
I'd want to check it out?"
"It's your job," Clifford said dryly, and cut off the screen.
He selected some folders lying on his desk and sauntered out into the corridor.
After collecting a coffee from the vending area, he proceeded to one of the
graphics rooms, which he had reserved for the next two hours. Since the meeting
demanded his presence at ACRE that day, he thought he might as well make the
most of the opportunity presented to him.
An hour later, Clifford was still sitting at the console in the darkened room,
frowning with concentration as he studied the array of multidimensional tensor
equations glowing at him from the opposite wall in effect one huge display screen
and pondered the subtle implications contained in the patterns of symbols. At
length he turned his head slightly to direct his words at a grille set into
the console and spoke without taking his eyes off the display. "Save current
screen, name Delta Two. Retain modules two and three; erase remainder. Rotate
symmetric unit phi- zero-seven. Quantize derivative I-vector using isospin matrix
function. Accept I-coefficients from keyboard two; output on screen in normalized
He watched as the machine's interpretation of the commands appeared on one
of the console screens, nodded, then tapped in a series of numerals. "Continue."
The lower part of the display went blank for a moment, and then began filling
with new patterns of symbols. Clifford watched intently, his mind totally absorbed
with trying to penetrate the hidden laws within which Nature had fashioned its
strange interplays of space, time, energy, and matter.
In the early 1990s, a German theoretical physicist by the name of Cart Maesanger
had formulated the long-awaited mathematical theory of Unified Fields, combining
into one interrelated set of equations the phenomena of the "strong" and "weak"
nuclear forces, the electromagnetic force, and gravity. According to this theory,
all these familiar fields could be expressed as projections into Einsteinian
spacetime of a complex wave function propagating through a higher-order, six
dimensional continuum. Being German, Maesanger had chosen to call this continuum
eine sechsrechtwinkelkoordinatenraumkomplex. The rest of the world preferred
simply sk-space, which later became shortened to just k-space.
Maesanger's universe, therefore, was inhabited by k-waves—compound oscillations
made up of components that could vibrate about any of the six axes defining
the system. Each of these dimensional components was termed a "resonance mode,"
and the properties of a given k-wave function were determined by the particular
combination of resonances that came together to produce it.
The four low-order modes corresponded to the dimensions of relativistic spacetime,
the corresponding k-functions being perceived at the observational level simply
as extension: they defined the structure of the empty universe. Space and time
were seen not merely as providing a passive stage upon which the various particles
and forces could act out their roles, but as objective, quantifiable realities
in their own right. No longer could space be thought of as simply what was left
after everything tangible had been removed.
Addition of the higher-order modes implied components of vibration occurring
at right angles to all the coordinates of normal spacetime. Any effects that
followed from these hogher modes were incapable, therefore, of occupying space
in the universe accessible to man's senses or instruments. They could impinge
upon the observable universe only as dimensionless points, capable of interacting
wit each other in ways that depended on the particular k-functions involved;
in other words, they appeared as the elementary particles.
The popular notion of a particle as a smooth, tiny ball of "something" was
finally put to rest. "Solidness" was recognized at being an illusion of the
macroscopic world, even the measured radius of the proton being reduced to no
more than a manifestation of the spatial probability distribution of a point
When high- and low- order resonances occurred together, they resulted in a
class of entities that exhibited a reluctance to alter their state of rest or
steady motion in normal space, thus giving rise to the quantity called "mass."
A 5-D resonance produced a small amount of mass and could interact via the electromagnetic
and weaker forces. A full 6-D resonance produced a large amount of mass and
added the ability to interact via the strong nuclear force as well.
The final possibility was for high-order modes to exist by themselves without
any component of vibration in normal spacetime at all. This yielded point-centers
of interaction that offered no resistance to motion and therefore always moved
at the maximum speed observable in normal spacetime, that of light. These were
the massless particles: the familiar photon and neutrinos, and the hypothetical
In one sweeping, all-embracing scheme, Maesanger's equations gave a common
explanation for the bewildering morass of facts that had been cataloged throughout
the 1950s through 1980s. They explained, for example, why it is that a particle
that interacts strongly always interacts in all possible weaker ways as well,
although the converse was not true: clearly, the 6-D resonance responsible for
the strong nuclear force had to include all possible lower modes as subsets
of itself. This picture also explained why heavy particles always interact strongly.
Theory predicted that a 5-D resonance would produce particles of small mass,
unable to participate in strong interactions; the existence of the electron
and muon proved it. Further considerations suggested that any heavy particle
ought to be capable of assuming three discrete states of electric charge, each
of which should be accompanied by just a small change in mass; sure enough,
the proton and neutron provided prime examples.
If an interaction occurred between two resonances whose respective components
on the time axis were moving in opposite directions—and there was nothing in
the theory to say this couldn't happen—, the two temporal waves would cancel
each other to produce a new entity that had no duration in time. To the human
observer they would cease to exist, producing the effect of particle-antiparticle
As a young graduate at CIT in the late 1990s, Bradley Clifford had shared
the excitement reverberating around the scientific world after publication of
Maesanger's first paper. K-theory became his passion and uncovered his dormant
talents. By the time he entered his postdoctoral years, he had already contributed
significantly to further development of several aspects of the theory. Driven
by the restless, boundless energy of youth, he thrust beyond the widening frontier
of human knowledge, and always the need to know what lay beyond the next hill
drew him onward. Those were his idyllic days, when there were not enough hours
in the day, days in a year, years in a lifetime to accomplish all the things
he knew he had to do.
But gradually, the realities of the lesser world of lesser men closed in.
The global political and economic situation deteriorated, and fields of pure
academic research became subjected to more stringent controls and restraints.
Funds that had once flowed freely dried to a trickle; vital equipment was denied;
the pick of available talent was lured away as as military requirements assumed
priority. Eventually, under specially drafted legislation, even the freedom
of the nation's leading scientists to work where and how they chose became a
luxury that could no longer be allowed.
And so he had come to ACRE, virtually as a conscript . . . to find more effective
methods of controlling satellite-borne antimissile lasers.
But though they commandeered his body and mind, they could never commandeer
his spirit. The computers and facilities at ACRE surpassed anything he had dreamed
of at CIT. He could still let his mind fly free, to soar into the realm of Carl
Maesanger's mysterious k-space.
It seemed to him that only minutes had passed when the reminder began flashing
in the center of the wall screen, warning him that the meeting was due to commence
in five minutes.