Array Without Double Quotes

I’m sure we can manage to tolerate each other’s company for one meal.” “I won’t say anything about farming. We can discuss other subjects. I have a vast and complex array of interests.” “Such as?” Mr. Ravenel considered that. “Never mind, I don’t have a vast array of interests. But I feel like the kind of man who does.” Amused despite herself, Phoebe smiled reluctantly. “Aside from my children, I have no interests.” “Thank God. I hate stimulating conversation. My mind isn’t deep enough to float a straw.” Phoebe did enjoy a man with a sense of humor. Perhaps this dinner wouldn’t be as dreadful as she’d thought. “You’ll be glad to hear, then, that I haven’t read a book in months.” “I haven’t gone to a classical music concert in years,” he said. “Too many moments of ‘clap here, not there.’ It makes me nervous.” “I’m afraid we can’t discuss art, either. I find symbolism exhausting.” “Then I assume you don’t like poetry.” “No . . . unless it rhymes.” “I happen to write poetry,” Ravenel said gravely. Heaven help me, Phoebe thought, the momentary fun vanishing. Years ago, when she’d first entered society, it had seemed as if every young man she met at a ball or dinner was an amateur poet. They had insisted on quoting their own poems, filled with bombast about starlight and dewdrops and lost love, in the hopes of impressing her with how sensitive they were. Apparently, the fad had not ended yet. “Do you?” she asked without enthusiasm, praying silently that he wouldn’t offer to recite any of it. “Yes. Shall I recite a line or two?” Repressing a sigh, Phoebe shaped her mouth into a polite curve. “By all means.” “It’s from an unfinished work.” Looking solemn, Mr. Ravenel began, “There once was a young man named Bruce . . . whose trousers were always too loose.” Phoebe willed herself not to encourage him by laughing. She heard a quiet cough of amusement behind her and deduced that one of the footmen had overheard. “Mr. Ravenel,” she asked, “have you forgotten this is a formal dinner?” His eyes glinted with mischief. “Help me with the next line.” “Absolutely not.” “I dare you.” Phoebe ignored him, meticulously spreading her napkin over her lap. “I double dare you,” he persisted. “Really, you are the most . . . oh, very well.” Phoebe took a sip of water while mulling over words. After setting down the glass, she said, “One day he bent over, while picking a clover.” Ravenel absently fingered the stem of an empty crystal goblet. After a moment, he said triumphantly, “. . . and a bee stung him on the caboose.” Phoebe almost choked on a laugh. “Could we at least pretend to be dignified?” she begged. “But it’s going to be such a long dinner.

This brings me to an objection to integrated information theory by the quantum physicist Scott Aaronson. His argument has given rise to an instructive online debate that accentuates the counterintuitive nature of some IIT's predictions. Aaronson estimates phi.max for networks called expander graphs, characterized by being both sparsely yet widely connected. Their integrated information will grow indefinitely as the number of elements in these reticulated lattices increases. This is true even of a regular grid of XOR logic gates. IIT predicts that such a structure will have high phi.max. This implies that two-dimensional arrays of logic gates, easy enough to build using silicon circuit technology, have intrinsic causal powers and will feel like something. This is baffling and defies commonsense intuition. Aaronson therefor concludes that any theory with such a bizarre conclusion must be wrong. Tononi counters with a three-pronged argument that doubles down and strengthens the theory's claim. Consider a blank featureless wall. From the extrinsic perspective, it is easily described as empty. Yet the intrinsic point of view of an observer perceiving the wall seethes with an immense number of relations. It has many, many locations and neighbourhood regions surrounding these. These are positioned relative to other points and regions - to the left or right, above or below. Some regions are nearby, while others are far away. There are triangular interactions, and so on. All such relations are immediately present: they do not have to be inferred. Collectively, they constitute an opulent experience, whether it is seen space, heard space, or felt space. All share s similar phenomenology. The extrinsic poverty of empty space hides vast intrinsic wealth. This abundance must be supported by a physical mechanism that determines this phenomenology through its intrinsic causal powers. Enter the grid, such a network of million integrate-or-fire or logic units arrayed on a 1,000 by 1,000 lattice, somewhat comparable to the output of an eye. Each grid elements specifies which of its neighbours were likely ON in the immediate past and which ones will be ON in the immediate future. Collectively, that's one million first-order distinctions. But this is just the beginning, as any two nearby elements sharing inputs and outputs can specify a second-order distinction if their joint cause-effect repertoire cannot be reduced to that of the individual elements. In essence, such a second-order distinction links the probability of past and future states of the element's neighbours. By contrast, no second-order distinction is specified by elements without shared inputs and outputs, since their joint cause-effect repertoire is reducible to that of the individual elements. Potentially, there are a million times a million second-order distinctions. Similarly, subsets of three elements, as long as they share input and output, will specify third-order distinctions linking more of their neighbours together. And on and on. This quickly balloons to staggering numbers of irreducibly higher-order distinctions. The maximally irreducible cause-effect structure associated with such a grid is not so much representing space (for to whom is space presented again, for that is the meaning of re-presentation?) as creating experienced space from an intrinsic perspective.