She just shook her head. “I will not think that way, and shall not understand those who do. Should two mites on the ear of an elephant bite each other to death, when the elephant is plunging off a cliff’s brink? You asked of me what I wanted killed. Are you willing to enter the lists?”

“Fight a duel? My dad would have approved. He thought womenfolk should talk that way. But you—you’re not serious.”

“I am.”

“You got armies. And a ship. You’re a princess.”

“I am a woman, and a young woman, and armies cannot grapple this foe of mine. My enemy is not a thing of flesh and blood. The mystery of that Monument is my dragon. It will devour me if I am not saved.”

“The Monument?”

“Can you read it?”

It was the moment he had been waiting for his whole life.

Menelaus was astonished at how evenly and calmly the words rolled off his tongue, “Ma’am, I can read that damn Monument for you, if anyone on Earth can.”

2. The Logic Behind Logic

The corridor was lit, but was not exactly bright. Candles, good old-fashioned pre-Edison candles, stood on small tables every ten paces or so, between antique suits of gold-chased armor, or glass cases containing china curios or silver cups. Behind each candle was a dark drape, evidently meant to preserve the wallpaper from smoke stains. The buttery-gold light breathed and lived, and made the hallway into an elfin place, alive with shadows.

Without a further word, she reached over and tapped one of the mirrors facing the corridor. It was smartglass, just as back in Blackie’s chalet, and an image of the Xi Segment of the Monument came up in the view.

The right window showed differential equations from the Divarication Theory; the left showed the symbol-groups of the Xi-wave function-group being organized into a matrix. This left window was connected by little red threads to show which symbol in the matrix represented which Monument sign. More than one information view of the process was displayed: one was a branching tree, one was a rippling set of Venn diagrams, like a rainy pond, one was a polar axis view, one was a Cartesian diagram, one was a basic-grammar theory spiderweb.

When the matrix was entirely filled in, the information began to sequence itself. One pattern after another was superimposed on the various trees and ponds and spiderwebs, and where there were partial matches, the letters to the right lit up with colors, matching a color-coded version of the Monument symbols.

“I know that sequence,” said Montrose. “I designed it. That is what I had the Zurich computer use to go through the alien math, to make the codes to establish the nerve-channels in my brain.”

“But what does the Xi Segment express?”

“I don’t know. I just copied it.”

“Compare the table results. Everything the Monument says, it says in repeating patterns. Logic in the Opening Statements underpins mathematics according to the Russell-Whitehead meta-language, which is in the Gamma Segment. Mathematics in the Alpha Segment underpins geometry and physics, the sections labeled Alpha 357 to Beta 120. Game-theory in Eta underpins economics in Theta. So then, what underpins the basic statements of logic? You see? Compare this here to those untranslated expressions in the first two bands of the Monument pole. They come before the scientific statements, the periodic table, or the Maxwell equations. Assume these are metaphysical expressions, needed to explain and justify the basic physics here, symbols written in a pattern we humans cannot grasp, because the physical roots of the laws of physics are unknown to us.”

“I don’t follow you.”

“We have yet to deduce a logical system proving the physical constants of the universe must be those of our cosmos, and none other. Obviously these are matters physics cannot address, since empiricism can only examine the universe we have before us. So, the physics of before physics: I would call it meta-physics, but the word is taken. Let us call it Axiomatics, the justification of fundamental physical constants.”

“So they know the basic rules for why the universe is the way it is and not some other way. So what?”

“So I suggest the symmetry is maintained for the Mu-Nu Group over here. I suggest to you that these groups of expressions are, as the Monument Builders are great lovers of symmetry, the meta-logical expression: a symbolic code for the expression that would justify the basic rules of logic. The basic rules for why the mind is as it is and not some other way.”

“That makes no sense. You cannot use logic to justify logic. Either you assume the rule work, or you’re an ass. Um, pardon my…”

“The meta-logic rules, I am saying, do not use logic to justify the axioms of logic logically—as you correctly point out, that would be a paradox. But what is the underpinning for logic in the ultimate sense?”

“It works.”

She smiled graciously. “Many philosophers believe this indicates an intimate connection between the laws of physics, the laws of mathematics, and the way the human mind works. Odd, is it not? In an infinite universe, why would we just so happen to evolve brains that could comprehend the laws that just so happen to underpin the physical universe?”

“Not so odd. I’ll tell you why. Natural selection and the damn fool common sense God gave a goose. Lookit here: Animals who thought is was the same as is not might think a predator what is about to eat them up, is not about to dine so fine, and then the natural difference between is and is not would be clear as either-or: namely either you vamoose out from those sharp teeth, or you’ll be an is not in no time.”

“Nicely spoken, but you are familiar with Divarication theory. You are one of its primary authors, are you not? Put any information value you wish into the expression for whatever gene controls the organism’s logic. Somewhere in the little bits of matter that make us up, is something written in our DNA—think of it as a symphony written in a chemical code of four notes—somewhere is the arpeggio that programs us to believe A is A. Estimate the volume needed to carry that abstraction forward between all the generations of organisms possessing neural systems since the pre-Cambrian. Look at how the figure falls out.”

He ran his finger on the mirror surface, and drew out a few calculations. “It’s impossible,” he said at last. “If there was a gene for logic, it would have mutated by now, and cropped up. There would be other creatures with other rules for other types of logic—which is something I can’t imagine, anyhow. I mean, even a mama bird counting her eggs don’t make twice two equal to five.”

“To me, this suggests a simpler and more universal structure to thought,” Rania said. “The laws of optics form a limiting set to the divarication for the principles of how to evolve an eye. Likewise, other laws must form a limit to how logic, language, and thought can evolve. The basic rules of the universe make it so that no organism can evolved into a rational creature for whom A equals not-A.”

“What are you saying?”

She pointed at the mirror: “That! The rules of meta-logic, my champion, is what you have in your brain. A set of neural logic gates which allow you to see meta-logical patterns, and recognize those patterns where they appear. It is your lance to slay my dragon. Because those patterns appear in the Monument: it is written in nothing but patterns.”

“Lady, I still don’t understand, and that is something I am not used to saying.”

“Remember the oldest problem in Sign Theory: How do you communicate with a species so alien that nothing in your psychology or culture is the same? How do you refer to things with no shared references? And I am suggesting we are looking at the handiwork of some race that solved that problem. The mere fact that the Monument exists proves that a universal language is possible, which means that the relation of field theory to physics to molecular chemistry to DNA to brain to brain structures to thought to logic to symbol cannot be arbitrary—despite that our Earthly theories hold them to be.”