Graham’s Number
I’ve never quite been able to let go of the idea that the Crucible might be a lie. It re-visited me tonight, and the result? About 2400 words of “alternate ending”-adjacent speculations, below the cut...
‘So we’re all agreed,’ Alice said. ‘The Crucible is a lie.’
Alice Shepard was sat at the Normandy’s comms-and-conference table, currently in conference mode. She was leaning forward, elbows were wrested on the tabletop in front of her, fingers interlocked and steepling together. She looked around at the other people sat at the table.
‘It’s what I’d do,’ Javik said, ‘if I were them. Spread a fiction, a myth. Make people waste their time chasing a mirage.’ He paused. ‘And it failed in my cycle, like every cycle before. With a record like that, why should we hope for different now?’
Overhead, the Normandy’s ventilation fans hissed away. Somewhere in one of the bulkheads, a pipe groaned as a pressure-bubble worked its way through. Alice took a deep breath. The air was a little cool, rather dry and carried a faint-but-noticeable astringent smell. The cleaning fluids, again, she supposed.
‘The evidence does sound convincing,’ Hackett’s hologram said. He was being routed through from the QEC room to here; the image occasionally fritzed with static and his voice crackled every now and then, but the broadcast quality was good enough for their purposes.
Liara looked frustrated. ‘I don’t like this,’ she said. ‘But, yes. It feels too convenient. A recoverable data-drive, just right there on Mars, where anyone could find it? Intact and incorrupt after fifty thousand years without maintenance? No damage. No meteor impacts, no radiation-induced bit-rot. On Mars – a planet with nearly no atmosphere, and no magnetosphere! The more I think about it, the less I believe it.’
Tali said, ‘Bits of the prothean network did survive into our time.’
Liara grimaced. ‘Yes, but remember the state Vigil was in when we found him? Crumbling, barely holding together. This was nothing like that. At the time I thought we’d lucked out – but now? This was the opposite of luck. Clean, easy-to-interpret data – no other prothean records are like that!’ She glanced at Javik. ‘No offence intended.’
‘None taken, Liara Asari,’ he said, all his eyes blinking. Overhead a lighting panel flickered for a moment.
‘So someone planted it,’ Alice said. ‘I wonder when?’
This time, EDI spoke. ‘The data module was found in a destruction layer, whose dating was consistent with the prothean extinction,’ she said. ‘Superficially, the linkage seems obvious. The surrounding Martian regolith showed no signs of subsequent artificial interference. Hence why we all initially believed the record was authentic.’
‘But we don’t, now,’ Alice said. ‘Think that, I mean.’
‘No,’ EDI said. ‘I believe the Admiral may have more to say on this. But I find it strange that after six months of intensive study, no-one understands the Crucible plans any more now than at the start.’
Hackett’s hologram nodded. A wave of static fuzzed across his face and his visage briefly broke apart before knitting together again. Apparently, they’d just used up a bad batch of qubits, or something.
He said, ‘We’ve got the best minds in the galaxy looking at it. Every angle, every nook and cranny. It’s elaborate, sophisticated, and nonsensical. A vast collection of individual systems, but no clarity on what any of them do. Some of them might – maybe – point toward breakthrough physics. Others just look like nonsense. I was in a meeting with the Scientific Steering Board this morning. That’s what they said, too. They’re starting to think the Crucible doesn’t do anything – except maybe waste our resources and our funds.’
Alice sighed. ‘Interesting they’ve reached the same view we have.’
That was why she’d called this meeting. Liara and EDI had come to her privately a few days before. The pair of them had quietly been studying the Crucible plans, even after the chaos on the Citadel. They’d both become increasingly-concerned by what they were seeing, but that concern hadn’t become concrete until recently.
Liara said, ‘We have a third analysis. It corroborates the others.’
‘Go on,’ Hackett said.
With a polite nod to Tali, Liara said, ‘Now that things are … quieter … over on Rannoch, we put in a request. To the geth.’
‘The geth?’ Hackett actually looked surprised.
Tali shrugged. ‘We’re all friends now, strange as that is.’
Liara said, ‘They were genuinely-interested. We gave them a copy of the plans to analyse. I understand they used their network to model them, at high resolution. Thousands of iterations, probabilistic simulations. Every sort of initial condition and every sort of boundary-parameter. They told me they considered over thirty-nine million possible scenarios.’
‘And what did they find?’ Hackett asked.
‘They didn’t find a single one where the Crucible acted against the Reapers,’ Liara said. ‘Not one. Zero.’
Above them, a ventilation fan rattled, momentarily loose in its housing.
Tali said, ‘They did find forty-eight thousand scenarios where it did something to us, though.’
‘Well, fuck,’ Alice said.
Tali added, ‘Granted, these are simulations, and they do have assumptions underlying them. Some of those assumptions could be wrong. But still.’
‘This is true,’ EDI said. ‘But three different groups of people – us, the geth, the Steering Board – have all reached essentially the same conclusion. And by differing methods. While hard to quantify precisely, this raises the chance that the conclusion is correct.’
‘So,’ Hackett said, ‘the Mars data was planted, then. When?’
‘Hard to know exactly,’ Liara said. ‘I went over the methodology at the dig, and it all looked solid. But Reaper tech is a long way in advance of ours. It’s quite possible they could have faked up a sensible-looking archaeological site. And, well, we know they’re into deception. I know it’s not the same, not really, but just look at what they do with indoctrination. They like playing mind-games with us. And I think that’s what they’ve done here.’
‘Commander,’ Hackett said, ‘what do you think of this?’
Alice rubbed her brows and leaned back. The chair creaked under her. She said, ‘Ideally I would have liked to have the salarians look at it. Their scientific establishment could have given us a decent ruling. But of course they’re not talking to us right now, thanks to the dalatress. Remind me to strangle Linron, the next time I see her.’
‘I’ll put it in your calendar, Commander,’ EDI said. ‘You have a free slot on Tuesday afternoon. Eleven minutes. That should be adequate for one political murder. Would that be adequate?’
Just for a moment, everyone stared at her.
‘That was a joke,’ EDI said.
Alice said, ‘Given what we know, I don’t think we can justify wasting any more time on the Crucible. If we’re lucky – lucky! – then it’s just useless. If we’re not lucky, it could be something that actually hurts us. Hell, for all we know, the thing could be some sort of giant indoctrination booster. Perhaps when you crank up the handle, it brain-fries the entire galaxy. Or something nightmarish like that.’
The mood at the table visibly shifted. Javik look angry. Tali seemed to wilt, though it was hard to tell past the mask. Liara looked tired and depressed. Overhead, the lighting panel flickered again, and another pipe groaned somewhere in a bulkhead.
‘Goddess,’ the asari said. ‘It’s true, then. Our one hope is gone. We’ve lost.’
‘So what do we do now?’ Hackett asked. ‘Keep wasting soldiers in futile ground actions? Try and find a really deep hole and hide down it? Load up a few ships and point them out of the galactic disk, like the Andromeda Initiative?’
Tali said, ‘Taking a chance on an extragalactic leap with today’s technology … no, that would be suicide. Our people, the Migrant Fleet – we’re probably the best astrogators in the galaxy. And we have - had! - as close as you can get to an actual ship-based, closed-loop economy. And we even we never considered that.’
Alice said, ‘There has to be something. I’m not minded to just sit here and wait for death!’
It was EDI who spoke. ‘Commander, there may be another possibility.’
Shepard lifted an eyebrow. ‘Go on?’
EDI said, ‘Commander, remember Vigil’s data-file, from Ilos? We still have a copy of it. Alliance Command pulled from your old omnitool while you were being debriefed, after the Battle of the Citadel. And it raises some ideas.’
‘Such as?’
‘It gives us concrete data on Reaper encoding and networking protocols,’ EDI said. ‘These were what the prothean scientists used, when they hacked the Citadel. Combined with recent research on shackled and unshackled Ais, and what the geth have shown us about large distributed networks … I think I can see the outlines of something we can do to the Reapers.’
‘You’re suggesting we hack them?’ Alice said.
EDI nodded. ‘I believe “hack” is the colloquial term, yes. The Reapers’ internal network is well-protected, but it does have to have some interaction with the outside universe. It’s not absolutely-isolated. Like we do, they transmit their packets through the mass relays. The proposal is straightforward – we intercept some of those and substitute them for our own. I believe we have what we need to access the Reaper network, and force an update.’
‘An update?’ Hackett said. ‘You mean turn them off?’
EDI shook her head. ‘Nothing so unsubtle, Admiral. The Reapers will have protocols to prevent bogus shutdowns. No, I propose something different. Essentially, a denial of service attack. On God.’
Alice blinked. ‘What?’ Outside the meeting room, a crewman walked past, their feet scuffing loudly on the flooring.
‘Explain,’ Hackett said, his eyes narrowing.
EDI said, ‘Have any of you ever heard of Graham’s Number?’
Alice was baffled. ‘No I don’t – wait, no, that sounds familiar. From somewhere. Something on the extranet, maybe?’
EDI said, ‘It’s a semi-regular theme on popular science broadcasts. It often turns up as a supposed “largest number ever”, which incidentally it isn’t. What it is, is an integer of extremely large value. Large enough that it cannot be represented inside this universe.’ She paused. ‘Though the last digit is seven.’
‘Can’t be represented in the universe – that makes no sense,’ Alice said.
EDI shook her head. The lights overheard gleamed over the metal-and-composite surface of her robot body. She said, ‘Not at all. The smallest physically-meaningful region of space is a Plank volume. Graham’s Number has more digits than there are Plank volumes in the observable universe. If even every one of them was a single bit, you still couldn’t fit it inside the universe. While the number exists and has a conventional value, no system of finite representation can present it in its entirety.’
‘How do we know it ends in seven, then?’ Javik said. ‘This sounds like nonsense.’
EDI said, ‘While the number cannot be – as it were – written down, it is possible to present the mathematical operations that would be used to compute its value. Insofar as it can be described, it is through those operations that we describe it. It was by this method, for example, that its last digit was determined.’
Hackett said, ‘Yes, all very interesting, but what has this got to do with the Reapers?’
Alice was frowning. She took a deep, slow breath, smelling the artificially-cycled air of the Normandy as she did. It still smelt a little of cleaning agents – no surprises there. She said, ‘I have a feeling I know where this is going. But lay it out for the organics, if you would, EDI.’
EDI nodded. ‘Thank you, Commander. Actually, I got the idea from Jeff.’
Tali sounded surprised. ‘I didn’t know he was into mathematics!’
‘He’s not,’ EDI said. ‘But during the Collector attack, after we took the IFF, he said something. While I was guiding him to remove my AI shackles. He said something about plugging in the overlord, and computing the value of pi. It – I suppose you would say, it stuck in my mind? And I’ve been considering it ever since.’
Alice said, ‘You mean to suggest … forcing the Reapers to waste computational resources? On a task that’s effectively infinite?’
EDI nodded. ‘Yes Commander. I use the example of Graham’s number – there are others could serve too. The point is, while the Reapers are powerful, they are physical things, existing in the physical universe. They are advanced but ultimately, they are bound by the laws of physics. The capacities of the Reaper network are large, but not infinite. It is conceivable that those capacities could be exhausted. Like, for instance, being forced to calculate and store every digit of a number that cannot be represented inside our universe.’
‘Shit,’ Alice said, as the full chain of inference clicked into place. ‘You’re proposing that we force them into a blue-screen, basically.’
EDI nodded. ‘In practise the Reapers likely have hardware and software safeguards, to prevent this sort of exploit. While pi – Jeff’s example – has an infinite extension of digits, they likely have some hard-coded upper-limit approximation to use instead. It’s hard to see a real-world need to know pi more accurately then thirty or forty decimal places.’
Alice blinked. She’d never needed pi to anything more than seven digits, even back in engineering school.
EDI was continuing, ‘So in practise attacking them with a normal irrational number is probably futile. But, this is why I raised Graham’s Number. We know that it has a finite – if very large – value. In pure principle its value could be computed. As such it is possible something like this might thus bypass the Reapers’ built-in safeguards.’
Hackett was nodding. ‘So we force an upload of this code – a sort of firmware update from Hell – and it quickly saturates the Reapers’ entire systems.’
‘Forcing them into shutdown,’ Alice said. ‘As they’ll quickly have no spare resources left for anything, from running engines, firing guns or setting course solutions. Or, I suppose, controlling Husks.’
‘And while they’re down, we pick them off,’ Javik said. A hungry light was glinting in his eyes. ‘Perhaps I may start to like you, EDI AI, after all.’
Alice said, ‘Essentially, our problem was that we were viewing the war through the wrong lens. We were all still imagining it, somehow, as a conventional war of attrition. Hence how we were initially deceived by the Crucible plans. A super-weapon would be the only way to win that sort of war. Except it never was, was it?’
‘The whole time, it was really a problem in applied information theory,’ EDI said.
Tali sighed. ‘Kee’lah. You do have to be an AI to come to a conclusion like that, don’t you?’
Hackett was looking thoughtful. ‘EDI,’ he said, ‘with the Commander’s approval, can you send us everything you have on this?’
EDI looked briefly at Alice, who nodded. EDI said, ‘Of course, Admiral. I’ve begun the upload right now.’
Hackett said, ‘We have some of the best minds in the galaxy here, on this boondoggle of a project. If they can’t do something useful with this, no-one can. No promises, but just perhaps this is the miracle we’ve been looking for…’