Chapter 412: A Different Kind of Threesome

Friday, February 1 to Wednesday, May 7, 2008

In the 9th week of having 128 minds, something totally unexpected happened: we were mid-déjà vu and another one started, creating a three-way déjà vu. It took us to a linkage totaling 192 minds, and our proximity senses - all three of them - immediately jumped in range and level of detail. A check of the number of NP-fingertips a mind could create, their maximum size and forcefulness, and a few other quickly performed tests, confirmed that our abilities had increased to the 192-mind level. Our head didn't explode and there was no sign of any sudden worsening of my possible insanity, which all 192 or 193 of us were relieved about.

The reason the three-way déjà vu was so unexpected was that the mathematical possibility of this had occurred to all the Marks years ago. We'd discussed it during links, but none of us had ever heard of it happening. If it'd happened even once, word would definitely have spread because it's exactly the sort of thing that we find interesting. No word of it for years meant we had long since decided that it must be impossible.

To put some numbers on it, using just the 21 months one of the several subsets of my minds had spent as a five-merged Mark. During that time déjà vu's occurred an average of every 1,030 minutes and lasted 2.5 minutes. If a three-way déjà vu was possible and had the same probability as a two-way, then the chance of a second déjà vu starting while one is already going was simplistically 2.5/1,030. That assumes déjà vu's are uniformly likely within the 1,030 minutes which we know isn't the case as a second déjà vu follows the first by a number of hours that clusters around the expectation, like a normal distribution curve. Having a déjà vu in the first hour is about five times less likely than the average likelihood (and incidentally, about fifteen times less than the peak time's probability), so the chance of two simultaneous déjà vu's when we had thirty two minds would seem to be 2.5/1,030/5 = 1-in-2,060.

In those 21 months we had 21 (months) x 30 (days/month) x 24 (hours/day) x 60 (minutes/hour) / 1030 (minutes/déjà vu) = 880 déjà vu's. We slept through some of them, but you can see that something like one Mark in three should've had a three-way déjà vu, but none of us ever heard of anyone doing so. Across the W-Dimension, we tend to have déjà vu's at the same time, but it's only a tendency. While it would affect the above calculation significantly, it certainly wouldn't affect it enough so that a billion Marks never had a three-way. [[We were overestimating that tendency. Marks in similar dimensions tended to have déjà vu's at similar times, but as they were also the Marks that déjà vu'd together the most often, the impression we got was too strong. A lot of Marks had déjà vu's at other times, we just didn't hear about it nearly so often (statisticians call that sampling bias. If you want to know how much the average person weighs, don't do a survey outside a Weight Watchers meeting). That sadly meant that there were MANY Marks who did not déjà vu just before they died in their bathtub suicide.]]

Similar arithmetic could be done for the other periods since our first merge, but there's no need as it's obvious that had it been possible, we would've heard about it many times by now. The fact that we hadn't, meant we'd concluded that there was something operating that stopped three-way déjà vu's from being possible - so we were very surprised to be in one now.

[[As a metaphor for the force that brings dimensions into contact with each other, think of two magnets sliding down either side of a "U"-shaped ramp. The magnets have the same pole in the front so they'll repulse each other rather than collide. There was a natural mechanism that activated that repulsion once two dimensions were already linked, not repulsing themselves but repulsing any new links to prevent three-way déjà vu's. When my number of minds got high enough it overcame that 'repulsion', as would happen if one of the two magnets became massive enough but with the same strength magnetic field, forcing a physical collision at the bottom of the ramps.]]

The three of us - "A", "B" and "C" for the lack of better names - could all talk together. Initially we were just broadcasting our communication to everyone else, e.g., A to the rest of A as well as to B and C, but as soon as we were over the initial confusion we did tests of: A to just B, A to just C, B to just C, and in the reverse directions too. The six communication directions all worked fine, which strongly implied that we were in a three-way link, rather than two two-way links.

On the other hand, we had long been sure that déjà vu's happen between individual minds, with the other minds along for the ride. That's why the frequency of them increase the way it does, and we'd also experimented by getting a certain number individual minds to think aberrantly during a déjà vu, and the link failed in proportion to the fraction of minds that were in the test. If the links were to individual minds, then when C joined the existing link between A and B, C must've linked to either an A or a B mind (because A and B had both noticed C arriving at the exact same time, it wasn't believable that C had linked to each of them independently. We would have heard about many occasions of Cs linking to As and Bs many seconds apart had they been random, independent events). Let's say C linked to B. That means A is linked to B, and B to C, so A is not directly linked to C. But somehow, A, B and C could all communicate together. Either C had linked to both A and B, which seemed unlikely, or the communication was somehow bridged between A and C by B without B being aware of it, which also seemed unlikely.

[[Both options were wrong. We didn't know that copies of our minds are created in each other's 'skulls' (I'm using that colloquially, as minds aren't so physically constrained) and that the three-way communications were occurring in three different localities and locally only, so intra- rather than inter-dimensionally.]]

After a minute or so of our three-way link, one of my minds thought of something truly AMAZING. It had occurred to me because I would LOVE to be able to minimize the number of merges required for my Voyage since leaving each dimension is fucking horrible! We were thinking whether this three-way link offered any possible way of achieving a reduction in the number of deaths I'd go through. Assuming I'm A, then it's no good B and C dying now to merge into me as they would just add thirty two minds for each death, which is what I'm achieving anyway. The REALLY interesting question is: "What if A dies now?" I saw an AMAZING possibility for that: When I merge normally, I want my minds to cross the link, but I know from my very first merge that wishing my minds across isn't necessary. Simply dying during déjà vu accomplishes the transfer. Not that I was going to do it now - there'll always be another opportunity thanks to the magic of mathematical probabilities - but if I ("A") died now:

• Would a proportion of A's minds go to B and C, i.e., 50%/50%, 0%/100%, 100%/0%, or a random allocation such as 23%/77% (ignoring rounding errors!)?

• Would A just die, with his minds extinguishing?

• Would A's minds go to BOTH B and C? It seemed obvious that minds were pure information, so why couldn't they duplicate to go to both destinations?

We thought the middle ("Mind-death") result was the least likely. A is in a link, so the minds should go somewhere, fingers crossed. The only way mind-death seemed possible would be if there was an equal force pushing/pulling A's minds toward B and C, so A's minds got stuck in the middle. We could have B try hard to call A, while C is passive, in case that made a difference. We've NEVER heard of a merge attempt that didn't work, and the Marks from the destination dimensions would have reported that. Obviously a three-way déjà vu hadn't happened either, so not hearing of a failed merge wasn't proof of safety, but it was partially reassuring.

It seemed obvious that A's minds would split across B and C in some proportion, but that was only because it seemed sensible compared to the bizarre idea that A's minds might duplicate, effectively creating 128 NEW Marks! It was so bizarre we felt that surely it wouldn't happen, but using feelings was hardly a good decision-making process. Apart from its being bizarre, we didn't know of a reason why the last option wasn't possible. Admittedly we didn't understand this process hardly at all, but what we did know didn't make the last possibility impossible. We certainly couldn't see anything wrong with there being duplicate Marks because there already seemed to be billions of us, and there'd probably been at least a hundred times more than that when we started. The Universe doesn't seem to have anything against duplicates.

The REALLY freaky possibility - the one that had me so excited in this - is that if the third option is what happens, then B and C will both have 160 minds, and the NEXT time they déjà vu it might be with their only peer, especially considering how far they would be above the 32-minded alternative candidates. B could then merge into C to give C 320 minds! Admittedly 128 of them would be duplicates, but would that matter? The minds are damned near identical anyway. The benefit would be that I could get from 128 to 320 minds with only 2 deaths, rather than the 6 it'd normally take.

And it gets even freakier because I might be able to keep doing it! If the 320-minded Mark has another three-way déjà vu with two more 32-minded Marks, then he can kill himself to create two 352-minded Marks, who can then déjà vu with each other and merge to create a 704 mind version. So I could get from 128 to 704 minds in a total of 4 deaths rather than 18. The next two deaths would get me to 1,472 minds in 6 deaths rather than 42.

There were, to put it mildly, some major issues involved in this idea:

• The risk of the mind-death possibility was definitely a major issue! It was BAD! On the other hand, our body was going to die anyway, and it was worth the possible death of our minds to let all the other Marks know that it was essential to avoid dying in a three-way déjà vu. That was especially true because if a three-way link ever developed with them, chances were that throughout the Universe it would be happening with millions of triples at the same time, so there'd be a huge loss if they all tried to merge then.

• The chance that a proportion of A's minds might go to B and C didn't really matter in the grand scheme of things as nothing was lost. Unless the allocation of A's minds was very one-sided, B and C would probably déjà vu with each other next time as they'd be each other's best peer, whereupon they could merge and the end result would be boring. If the allocation was very uneven, then the largest Mark (say B) would continue his Voyage not caring whether he merged with C or some other Mark, as they'd have a similar number of minds.

• Assuming the exciting duplicate scenario happened (for this and the subsequent bullet points), then the first risk was IMMEDIATELY after A died. B and C would necessarily still be in a déjà vu with each other and their having duplicates of A's minds might kill them both, or something else bad. If nothing bad happened, then B could merge across to C immediately, but B's family would get no goodbye and that would be far too cruel.

• The next issue is that B and C might not déjà vu with each other again, but then B and C could roll a few dice each and spread what they'd/we'd rolled through the grapevine. It wouldn't take long for B and C to learn each other's rolls, and whoever had rolled highest - to be consistent with the Voyage starting with rolling 6s - would continue with the journey merging with random Marks +32 minds at a time.

• The next scary risk was when B and C next déjà vu'd together, assuming that happened. Their having the same minds might cause a major problem.

• Following immediately after the point above, if déjà vu'ing didn't cause an obvious problem, then they'd merge, which had to be even more likely to have problems because then the duplicate minds would be in the same brain. There was also the general risk of our head exploding or going insane because it suddenly contained too many minds. It was more dangerous this way because the increments were larger, but either brain explosions or insanity might happen anyway.

On the plus side:

• If it doesn't work, all the other Marks will learn not to try it, potentially saving many millions of lives.

• If it does work, it'll save a LOT of hurt families. Back when I started merging, I would never have guessed that even 16 minds could fit into a single brain, but here I was with 128 of them [[actually 192 right at this moment, but I didn't yet know that déjà vu did that]]. If the upper limit of the number of minds was a truly large number, in the thousands or more - which seems ridiculous, but so does 128 or even 16 - then getting there +32 minds at a time would probably make me insane from all the grief and anguish. There was a huge benefit in the "+32 Then Double-Up" system, if it worked.

• Also if it works, it creates more Mark-minds "out of thin air", increasing the number of us in the Universe. I wasn't sure what the benefit of that would be, but it sounded like an amazingly good thing, although I might be biased.

The Other Marks: <Creating duplicates of your minds and merging with them is a truly fascinating possibility, and it gets you upward WAY faster if there's still a long way to go, but only you can decide about the risks.>

One Of Us: <Yeah. I think I have to go for it. More minds gives us more power, and if there's a way to increase the total number of Mark-minds in the Universe, then I think I have to find out about it. It's not the objective we thought I was aiming for when I started this Voyage, and I normally wouldn't diverge from my core job, but it's a divergence that gets me upward faster. It's a shortcut that we learn something incredible from. The risk isn't the major factor, and if it fails, then the next one of you can work his way up thirty two minds at a time.>

One Of Them: <Agreed. Do you want us to spread the word that you're going to do it?>

One Of Us: <Not yet. Spread the word about the possibility, but let me think about it. I'm going to take my time - probably several weeks - before I try so there's no hurry to spread the word. I've got something weird happening in my head that could be a mental problem and I don't want to move forward until I've got a better idea how bad that's going to get... > I talked about the other things going on, starting with my "Mr. No One" stowaway. I'd call him "Mr. Nobody", except that #2 through to #128 are No Body already, having to use #1's.

Because the three-way had started quite a long way into the normal déjà vu, I hadn't finished talking when B (by which I mean the Mark that I'd linked to first) dropped out of the link, leaving just A (me) and C. C had definitely been the last to arrive, and his ability to continue to communicate with me implied he hadn't joined by linking just to B. He'd presumably been four times more likely to link to me because I had four times more minds to link to, but if enough three-way links continue to operate as successful two-way links after their Bs drop out, then we'll have learned something about the process.

One Of Us: <If three-way déjà vu's are possible, then four- or more-way déjà vu's might be possible too. As the number of minds we have rises, multi-way déjà vu's should become probable within a practical timeframe, and it'd mean trebling or quadrupling the number of our minds each time. That makes it even more important to find out whether it works or not.>

One Of Them: <Yeah. Although you're going to have a have a lot of minds to make that happen.>

One Of Us: <We get déjà vu's every 4.25 hours and they last about 4.25 minutes, so a 1-in-60 chance of another one arriving while the first is going. We know an extremely early déjà vu is about one-fifth as likely as average, so 1-in-300 assuming an average probability for the other end of the link. 300 x 4.25 hours between them is a three-way every 1,275 hours, just over 50 days or about 7.5 weeks. A four-way - presuming they're possible for us - would take 300 times longer for us to have, plus a bonus for either of my partners getting it, but I'm ignoring those as they don't add much. 300 x 7.5 weeks is 2,250 weeks, or nearly 50 years - too long. We should gain about a factor of three if we double-up because déjà vu's are twice as often and last 50% longer. The 50% applies to each of the partners, so it could be a factor of 6.75, so call it eight years between them. Two more double-ups would reduce the 50 years to 9 months, which is becoming a practical way of trebling the number of Mark minds there are. That's possible enough that it provides even more reason for us to find out whether duplication works.>

One Of Them: <I don't disagree with you. You've got big balls.>

One Of Us: <Probably much the same size as yours, unless your Julia asked you to change their size. I disagree that I'm being brave because I'm very much trying to avoid the pain of saying goodbye to so many families. Getting this over in only two or four more goodbyes would be a huge relief. We need to think about it and discuss it among ourself, but my thinking is that we wait for another three-way to occur before we decide what to do. If we haven't had one within twenty weeks, we'll carry on with the +32 process. But if another one arrives we'll probably go on the three-way after that. I don't want to give our families a leaving scenario unless we're sure it's going to happen as we describe.>

One Of Them: <Understood.>

The link ended without anything else significant being said.

I'd been in this dimension two months by now, and I'd started thinking about when I should resume my Voyage. I'd already learned pretty much all that I could from the experiments with my abilities, and I could probably learn more after additional merges, so I really should leave. I hadn't been serious about doing so, out of concern over the Mr. No One situation and because I was simply reluctant to restart hurting my families, but this new development gave me a welcome excuse to delay for much longer.

In subsequent déjà vu's, the Marks were very surprised that a three-way déjà vu had happened, and then even more surprised by my mind-duplicating shortcut idea. It excited and appealed to them, but they were very thankful that it wasn't their risk. That sounds selfish of them, but they'd be stupid to think in any other way.

I can't say it appealed to me, but going through a large number of goodbyes appealed even less. Plus, the idea was very mathematically interesting, and being able to create more Marks out of thin air might have enormous significance one day. Not that I like to think of it happening, but if ALL the Marks merged another couple of times to get to my current number of minds, then they'd presumably be able to three-way déjà vu, and they could duplicate themselves. They might even be able to three-way after only one merge because I hadn't spent long enough at that level to give that possibility a decent chance of happening. Once three-ways became possible for them, they'd never merge with their original minds as there'd be so many other Marks around to make that mathematically almost impossible, but the number of Marks in the Universe could be doubled with each subsequent merger, as the number of Mark bodies halved. It would be adding a great deal of power to us. I didn't know if we'd ever be forced to merge again, but it was good to know that if we were under enough threat to force it, then there was a way for us to gain more power from fewer merges than the normal process allowed. In the right circumstances, where a threat was patient but still great enough to force us to gain more power, our knowing to wait for three-ways would save a lot of Marks from dying, and save a lot of our families from grieving. In short, it was an experiment I should make.

In the 10th week of my time in this dimension, another interesting thing happened, fortunately with no scary aspect. I discovered a way to disconnect my proximity sphere from myself. It effectively became a "Proximity Blob" that I could send anywhere within my 590-foot range, although if I sent it to the edge, any part of it that was more than 590 feet from me didn't register anything.

Nor could I send it more than 590 feet away. Not in the way that if I sent NP-fingertips or the usual blobs that far away, they self-canceled; with the proximity blob, once it was at its extreme range, it refused to go any farther. If I walked in the opposite direction, it followed me to stay within range. Another difference is to do with the definition of "590 feet". I haven't bothered making an issue out of it before, but my ki-effects have a size, so am I measuring the 590 from me to their center, their far edge or their near edge? Back when they were small it didn't matter, but they can be so big now it can make a large difference. I lose control of NP-fingertips when their closest edge gets 590 feet away (so their farthest edge can be a few feet beyond 590). After I lose control, they carry on doing what they were doing, and then self-cancel after the Blinks Allowed period. Traditional blobs are different, self-canceling as soon as their center reaches 590 feet. A proximity blob can have its center go far enough beyond the 590-foot range that only about 15% of the blobs volume is still within range, but it wouldn't go any farther. Why these ki-effects all operated differently was a puzzle.